Olariu, C. - Quantitative Sedimentology Laboratories

Transcription

QUANTITATIVE STUDY OF DELTA FRONT DEPOSITS
APPROVED BY SUPERVISORY COMMITTEE:
___________________________________________
Janok P. Bhattacharya, Chair
___________________________________________
John F. Ferguson
___________________________________________
Matthew I. Leybourne
____________________________________________
Tom H. Brikowski
Copyright 2005
Cornel Olariu
All Rights Reserved
To my family
by
CORNEL OLARIU, M.S.
DISSERTATION
Presented to the Faculty of
The University of Texas at Dallas
in Partial Fulfillment
of the Requirements
for the Degree of
DOCTOR OF PHILOSOPHY IN GEOSCIENCES
THE UNIVERSITY OF TEXAS AT DALLAS
December, 2005
ACKNOWLEDGEMENTS
I would like to give special thanks to my advisor Professor Janok P. Bhattacharya
for his support throughout my graduate studies. I am grateful to my committee members
Professor John F. Ferguson, Professor Matthew I. Leybourne and Professor Tom H.
Brikowski for their guidance during the project and careful and thoughtful reviews. They
helped me in the field to collect data and guided me with patience and passion,
encouraging me to achieve the goal that I have proposed. I would also like to thank to
Professors Robert J. Stern, George A. McMechan, Carlos L.V. Aiken, and Mohamed
Abdel-Salam to whom I shared my thoughts about the project and from them I received
constructive feedbacks.
I am grateful to Boyan K. Vakarelov, Adam Franklin, Li Sun and Iulia Olariu for
assisting me in different stages of my field work on Lake Texoma. John W. and Ruth
Smith help me to collect field data on Lake Texoma and I am grateful for their time. I
also wish to express my sincere gratitude to my professors and colleagues of the
Geoscience Department and the Center for Lithospheric Studies for their help and
friendship.
The British Petroleum and Chevron-Texaco companies supported the research
leading to this dissertation. Financial was also supplied through a ACS-PRF grant #
35855-AC8. Financial support was also received by me as graduate research grant from
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the American Association of Petroleum Geologists-SW and International Association of
Sedimentologists.
July, 2005
vi
Publication No. ___________________
Cornel Olariu, Ph.D.
The University of Texas at Dallas, 2005
Supervising Professor:
Janok P. Bhattacharya
ABSTRACT
This project represents a combination of modern, ancient and numerical modeling studies
to understand some of the processes that are associated with delta front sedimentation and
discuss the delta front heterogeneities of the resulting deposits. This study is the first that
describes delta terminal distributary channels in ancient deposits and quantifies them in
terms of dimensions and occurrence within the delta system. Sedimentary facies
associations and facies architecture of terminal distributary channels of fluvial-dominated
deltas indicate that delta front deposits are more complex than were previously described,
with channelized deposits and upstream accretion surfaces. Delta fronts of fluvialdominated deltas formed in shallow-water basins have multiple-scale, coeval terminal
distributary channels with mouth bars that coalesce into a relative thin sandy apron.
This is the first study that describes a natural system that has a continuous, river-derived
hyperpycnal flow. The Red River/ Lake Texoma system is a peculiar modern
environment where the river water is saltier than the lake water. This study demonstrates
vii
that the combination between the saltier river water during low discharge and high
suspended sediment concentration during high discharge creates permanent hyperpyncal
(negatively buoyant or sinking) plumes. To demonstrate the type of the river plumes, a
new remote sensing methodology is described in addition to historical and field data
collection. Because the river effluent forms a hyperpycnal plume, delta progradation into
Lake Texoma is controlled by basin (lake) topography. A multi-temporal aerial and
satellite geomorphological observation of Red River Delta progradation indicate that (1)
delta plain morphology changes with discharge and (2) some parts of the lake are
bypassed by the delta, as it follows the steepest gradient, in this case the old river talweg.
The magnitude of plume deflection, which is a function of river discharge and lateral lake
slopes, was tested using a simple numerical exercise.
To evaluate the variability and the uniqueness of delta deposits formed as a function of
initial parameters that control sedimentation, a stratigraphic inversion model has been
built. Because the sedimentary processes are non-linear, an inversion method using
genetic algorithms has been used. Genetic algorithms represent a novel tool for
stratigraphic studies and in this project have been applied for the first time to a 3-D
stratigraphic numerical model. The inversion procedure can estimate a most probable
model (not necessarily the correct model) as well as assess the parameter accuracy and
the range of non-uniqueness (which should cover the correct model).
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TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION .......................................................................................1
1.1
Motivation and Objectives...........................................................................1
1.2
Deltas ...........................................................................................................2
1.3
Delta Front ...................................................................................................4
1.4
Publication Status.........................................................................................6
CHAPTER 2 TERMINAL DISTRIBUTARY CHANNELS AND DELTA FRONT
ARCHITECTURE OF FLUVIAL-DOMINATED DELTA SYSTEMS ............................7
2.1
Abstract ........................................................................................................7
2.2
Introduction..................................................................................................8
2.3
Scales of Channels .....................................................................................11
2.4
2.5
2.3.1
Fluvial “Trunk” Channel................................................................12
2.3.2
Distributary Channels ....................................................................13
2.3.3
Terminal Distributary Channels.....................................................14
Terminal Distributary Channel Examples .................................................14
2.4.1
Modern Deltas................................................................................15
2.4.2
Ancient Deltas................................................................................24
Summary of Terminal Distributary Channel Examples.............................32
2.5.1
Terminal Distributary Channel Dimensions ..................................32
2.5.2 Terminal Distributary Channel Orientation Relative to the “Trunk”
Channel ......................................................................................................32
2.6
2.5.3
Terminal Distributary Channel Formation and Evolution .............33
2.5.4
Terminal Distributary Channel Sedimentary Facies......................36
Discussion ..................................................................................................37
2.6.1
River-Dominated Delta Facies Architecture..................................37
2.6.2 Implications of Multiple Terminal Distributary Channels Presence
on Delta Front Deposits .............................................................................40
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2.6.3
2.7
Implications for Interpretation of Ancient Deposits ......................44
Conclusions................................................................................................49
CHAPTER 3 REMOTE SENSING OF HYPERPYCNAL PLUMES: RED RIVERLAKE TEXOMA SYSTEM, TEXAS AND OKLAHOMA, USA ...................................52
3.1
Abstract ......................................................................................................52
3.2
Introduction................................................................................................53
3.3
Remote Sensing Applied to Differentiate Turbid River Plumes Geometries56
3.4
Regional setting .........................................................................................58
3.5
Methods......................................................................................................60
3.6
Results........................................................................................................63
3.7
Discussion ..................................................................................................72
3.8
Summary ....................................................................................................75
CHAPTER 4 INTERPLAY BETWEEN RIVER DISCHARGE AND LAKE BOTTOM
TOPOGRAPHY IN A HYPERPYCNAL LACUSTRINE DELTA, RED RIVER, LAKE
TEXOMA, TEXAS/ OKLAHOMA, USA. .......................................................................77
4.1
Abstract ......................................................................................................77
4.2
Introduction................................................................................................78
4.3
General Settings .........................................................................................80
4.4
Methodology and Data Used .....................................................................81
4.5
4.6
4.4.1
Aerial Photos and Satellite Images ................................................82
4.4.2
Historical Measurements ...............................................................83
4.4.3
Field Data Collection .....................................................................85
4.4.4
Numerical Model ...........................................................................86
Results........................................................................................................88
4.5.1
River Plume - Hyperpycnal Flow ..................................................88
4.5.2
Red River Delta Progradation........................................................89
4.5.3
Numerical Model Experiments on Hyperpycnal Plume Deflection104
Discussion ................................................................................................107
4.6.1
Conditions for Delta Deflection...................................................107
4.6.2
Hyperpycnal Deltas......................................................................108
4.6.3
Basin Topography Influence on Delta Progradation ...................109
4.6.4
Discharge Variability and Delta Progradation.............................110
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4.7
Conclusions..............................................................................................112
CHAPTER 5 STRATIGRAPHIC INVERSION USING A GENETIC ALGORITHM:
LESSONS ABOUT NON-UNIQUENESS .....................................................................114
5.1
Abstract ....................................................................................................114
5.2
Introduction..............................................................................................115
5.3
Forward and Inverse Modeling................................................................117
5.4
5.3.1
Forward Modeling .......................................................................117
5.3.2
Inverse Modeling .........................................................................118
Inversion of a Numerical Delta Model ....................................................122
5.4.1
A Numerical Delta Model............................................................122
5.4.2
Genetic Algorithms......................................................................127
5.4.3
Observed Data and Objective Function .......................................130
5.4.4
Genetic Algorithm Performance ..................................................132
5.5
Inverse Modeling Results ........................................................................133
5.6
Dependence on the Well Locations .........................................................137
5.7
Discussion and Conclusions ....................................................................139
CHAPTER 6 CONCLUSIONS......................................................................................141
6.1
Concluding Remarks................................................................................141
6.2
Summary ..................................................................................................142
6.3
Future Work Related to the Results of this Project..................................144
6.3.1
Delta Distributary Channel Networks..........................................144
6.3.2
Hyperpycnal Red River Plume into Lake Texoma ......................147
6.3.3
Topography Influence on Delta Progradation..............................148
6.3.4
Delta Front Sedimentation Rates and Depocenter Migration ......152
Bibliography ....................................................................................................................155
Vita
xi
LIST OF TABLES
Number
Page
Table 2.1. Characteristic facies for terminal distributary channels and mouth bars in
ancient deposits......................................................................................................36
Table 4.1. Red River Delta characteristics on successive aerial and satellite images .......84
Table 4.2. Description of delta progradation stages relative to the old river talweg. ........96
Table 5.1. Parameters used for synthetic model. .............................................................125
Table 5.2. Grainsize characteristics of the modeled sediment.........................................126
Table 5.3. Possible range values of the initial parameters. ..............................................128
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LIST OF FIGURES
Number
Page
Figure 1.1. Examples of river-dominated, tide-dominated and wave-dominated modern
deltas ........................................................................................................................3
Figure 1.2. Formation of delta topsets, foresets and bottom sets.........................................5
Figure 2.1. Pennsylvanian Booch delta................................................................................8
Figure 2.2. Modern delta examples with multiple terminal distributary channels ............10
Figure 2.3. Sketch with formation of distributary systems. ...............................................12
Figure 2.4. Modern Atchafalaya Delta. .............................................................................16
Figure 2.5. Cross section through eastern Atchafalaya Delta............................................17
Figure 2.6. Modern Wax Lake Delta .................................................................................19
Figure 2.7. Modern Volga Delta.. ......................................................................................21
Figure 2.8. Distributary channels variations in Lena Delta. ..............................................23
Figure 2.9. Strike oriented photomosaic of the Cretaceous Panther Tongue sandstone....25
Figure 2.10. Dip-oriented photomosaic of the Cretaceous Panther Tongue sandstone .....27
Figure 2.11. Outcrop example of terminal distributary channels in the Pennsylvanian
Placid Shale Formation, Texas. .............................................................................29
Figure 2.12. Orientation of terminal distributary channels in modern deltas ....................33
Figure 2.13. Conceptional formation and evolution of a terminal distributary channel mouth bar system ...................................................................................................34
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Figure 2.14. Comparison between digitate versus lobate river dominated deltas. ............39
Figure 2.15. The shape of sand bodies for the main energy factors encountered in delta
systems and expected number of terminal distributary channels...........................42
Figure 2.16. Fluvial – trunk system in Dunvegan River, and example of a tributarydistributary system, Volga basin............................................................................47
Figure 3.1. Possible types of plumes formed by river effluent into a basin. .....................53
Figure 3.2. Theoretical patterns of remote sensing images for different types of river
plumes. ...................................................................................................................58
Figure 3.3. Study area location, Red River Delta. .............................................................59
Figure 3.4. Methodology to establish different type of water on remote sensing images. 62
Figure 3.5. Time series of ASTER satellite images of Red River plume ..........................64
Figure 3.6. Lake bathymetry in front of the Red River Delta............................................65
Figure 3.7. Digital number (DN) variation along a dip-oriented profile. ..........................66
Figure 3.8. Total dissolved solids (TDS) and suspended sediment concentration (SSC). 68
Figure 3.9. Physical measurements in Lake Texoma in front of the Red River.. ..............71
Figure 3.10. Relative penetration of remote sensing bands into turbid river water and lake
clear water. .............................................................................................................73
Figure 3.11. Suspended sediment grainsize distribution at different discharges. ..............75
Figure 4.1. Study area location. .........................................................................................80
Figure 4.2. Data type used in this study and the time intervals when were colected ........82
Figure 4.3. Deflection of a hyperpycnal plume flowing on an inclined (lateral) plane.. ...87
Figure 4.4. Physical measurements, total dissolved solids (TDS) and suspended sediment
concentration (SSC) of the Red River water..........................................................90
xiv
Figure 4.5. Delta progradation and morphology changes on successive satellite and aerial
photos.....................................................................................................................92
Figure 4.6. A- Lake Texoma initial bathymetry ................................................................95
Figure 4.7. Summary variation of Red River delta progradation direction. ......................96
Figure 4.8. Lake Texoma bathymetry in front of the Red River Delta..............................98
Figure 4.9. Red River Delta progradation into Lake Texoma for 1944- 2004 period. ....102
Figure 4.10. Result of plume deflection numerical model...............................................105
Figure 4.11. Delta progradation with discharge under topography influence.. ...............106
Figure 5.1. Chart indicting the relationships of forward and inverse modeling. .............117
Figure 5.2. Variation of forward model parameters and resulted output.........................124
Figure 5.3. Observed and modeled clinoforms................................................................126
Figure 5.4. Flow chart of steady state reproduction genetic algorithm ..........................129
Figure 5.5. (A) Location of control data (observation wells) on the synthetic model. (B)
Evolution of bed elevation at well location. ........................................................131
Figure 5.6. Genetic algorithm performance.....................................................................132
Figure 5.7. Results of inversion using 4 wells (control points) into the basin.................134
Figure 5.8. Resolution matrix for all models (74220) resulted from inversion ...............135
Figure 5.9. Crossplot parameters pairs.. ..........................................................................136
Figure 5.10. Distribution of different arrays of 9 wells into the basin and the resolution
matrix for the best models....................................................................................138
Figure 6.1. Example of a delta distributive system with typical morphometric
characteristics.......................................................................................................145
Figure 6.2. Number of distributary channels of shallow water fluvial-dominated delta .146
xv
Figure 6.3. Actual morphology of Danube Delta with location of wells.........................148
Figure 6.4. Figure 6.4 Topography of predeltaic sediments in Danube Delta area .........149
Figure 6.5. Reinterpretation of dip oriented crosssections based on well data from Liteanu
and Pricajean (1963). ...........................................................................................151
Figure 6.6. Isopach maps in front of Pass a Loutre distributary of Mississippi delta......153
xvi
CHAPTER 1
INTRODUCTION
1.1
Motivation and Objectives
Modern geological studies require more quantitative approaches to have a better
understanding of processes over different spatial and temporal scales. In sedimentology,
description has been traditionally used and is still used to report new findings.
Descriptive reports are useful but difficult to repeat and understand by nonsedimentologists (geophysicists and engineers) that are the main beneficiary of
sedimentology reports. One problem results from perpetual changes in the way that
sedimentary deposits are described (i.e. new facies models). Because of this I tried to use
as much as possible a quantitative (dimensional) approach when describing sedimentary
deposits and processes of delta fronts.
This study refers to processes (hyperpycnal flows, influence of basin topography) and
features (terminal distributary channels, mouth bars) only from a specific part of a delta
(delta front). This introduction will present some generalities about deltas and delta
fronts. The specifics about delta fronts are discussed and exemplified in the following
chapters. The objective of the project is to improve the knowledge of delta fronts through
a more quantitative description of processes and resulting delta front deposits. Delta
fronts have been chosen to be studied because these represent the most dynamic setting of
1
2
a delta. Most of the processes that act on the delta front will be reflected in the delta front
sedimentary architecture that subsequently affects the overall delta architecture.
1.2
Deltas
Deltas have been named after the fourth letter of the Greek alphabet by Herodotus
through analogy with the shape of the area defined by the Nile distributaries. A river delta
is defined as an area that is built by river sediments within a basin and has been
recognized to have different shapes (Galloway, 1975). The sedimentological definition
states that a delta represents progradational sedimentary deposits that are formed partially
subaerial and partially subaqueously by a river that discharged into a standing body of
water (Barrell, 1912, Bhattacharya and Walker, 1992). Deltas can be marine or lacustrine
according to the basin type.
Studies of modern deltas are important for multiple reasons. The first reason is that deltas
represent the cradle of human civilizations. Major deltas, such as the GangesBrahmaputra, Indus, Shaat-el-arab, Chianjing, Nile and Danube represent areas of the
early flourish of human civilizations. Archeological studies in these areas require
understanding of deltaic sedimentation (Stanley et al., 2004). The second reason is that
other major deltas such as the Mississippi, Mekong, Rhine-Meuse, Rhone and Fraser
have become areas of large habitation. Human development in these areas, together with
collateral activities that these bring, transportation infrastructure and industry
development, requires understanding of delta proceses such as sediment deposition/
erosion, subsidence and avulsion. Also, there are major environmental problems related
3
to land loss because of subsidence and sea level rise in some of the populated deltas (e.g
Allison, 1998, Cecini, 1998, Sanchez-Arcilla et al., 1998, Stanley and Warne, 1998).
Ancient deltas studies are important because deltas contain potential resources such as
hydrocarbons, coals or ore deposits. Large quantities of hydrocarbons (40%) have been
estimated to be stored in delta deposits (Tyler and Finley, 1991). Coal deposits are also
commonly associated with ancient delta environments (Ryer, 1981).
Three distinct geomorphological/ sedimentological parts have been differentiated within
deltas. These are the delta plain, delta front and prodelta, and these are formed regardless
of the dominant processes that build a delta (Figure 1.1). These sub-environments have
Figure 2.1. Examples of river-dominated, tide-dominated and wave-dominated modern
deltas, from Bhattacharya and Walker (1992). Note that delta front is present in all delta
types but has different plan view geometries.
specific sedimentological and architectural characteristics that make them distinguishable
within the larger delta assembly. The delta front is by far the most variable subenvironment with large differences from one delta type to the other.
4
1.3
Delta Front
The delta front represents the part of the delta that has the highest sedimentation rate. The
high sedimentation rates specific to delta fronts are due to river effluent deceleration
basinward from the river mouth. The physical processes associated with the river effluent
have been described in numerous studies (Albertson et al., 1950, Bates, 1953, Wright,
1977, Nemec, 1995, Allen, 1997). The sediment settling in front of the river mouth is a
result of the momentum decrease of the river water due to the friction between river and
basin water (Bates, 1953). Three types of river effluent can be distinguished based on the
relative density between river and basin water, these are: hypopycnal flows, when the
river water is less dense than the basin water; homopycnal flows when the river water has
approximately the same density as the basin water; and hyperpycnal flows when the river
water density is higher than the basin water.
Despite the fact that the delta front has been recognized as a distinct environment since
early studies (Barrell, 1912, Fisk, et al., 1954) there are few studies (Willis et al., 1999,
Willis and Gabel, 2000, Lee et al., in press) that specifically addresses sedimentology and
facies architecture variability of delta fronts. The wide spread definition of the delta front
as “a narrow zone with the most active deposition within a delta, consisting of a sheet of
sand, and occurring within the effective depth of wave erosion, 10 m or less” given in the
American Geological Institute geological glossary (Jackson, 1997) is impractical and
erroneous for a multitude of modern and ancient deltas. This definition is also confusing
because the same definition can be used for shoreface and it uses relative, qualitative,
terms like “narrow”, and “most”. Delta front deposits do not form sandy sheet like
deposits all of the time; wave erosion depth is related to delta front slope and basin wave
5
energy (wavelength, amplitude) and is improper to use for delta front definition. Barrell
(1912) differentiated delta deposits into topsets, subdivided in subaerial topsets (delta
plain) and subaqueous topsets), foresets and bottomsets (Figure 1.2). Subaqueous top set
deposits were depicted as almost horizontal beds, dipping gently basinward, which are
separated by foresets at the depth of the fair wave erosion. These topsets correspond to
delta front deposits following the AGI glossary definition.
Figure 2.2. Formation of delta topsets, foresets and bottom sets. B - Topsets, foresets,
bottomsets relationship function of discharge and sea level variation (from Barrell et al.,
1912).
In ancient deposits, the delta front is recognized as a large-scale coarsening-upward
facies succession that passes from fine-grained prodelta facies upwards into shoreline
facies, and are typically sandstone dominated (Bhattacharya and Walker, 1992, Elliott,
1996). Delta front deposits were depicted in different studies as part of a larger delta
6
deposit and internal architecture oversimplified for a better understanding of the entire
delta system (Bhattacharya 1991, Bhattacharya and Walker, 1992, Tye et al., 1999,
Rodriguez, 2000, Tye and Hickey, 2001), but detailed studies dedicated to delta front
architecture are missing. This dissertation deals with several key aspects of delta front
facies architecture and formative processes.
1.4
Publication Status
The current (August 2005) publication status of each chapter is:
1. Chapter 2: Accepted by Journal of Sedimentary Research. Co-authored with Janok P.
Bhattacharya.
2. Chapter 3: To be submitted to Geosphere. Co-authored with Janok P. Bhattacharya,
Robert J. Stern, Matthew I. Leybourne and Stephen K. Boss.
3. Chapter 4: To be submitted to Sedimentology. Co-authored with Janok. P.
Bhattacharya.
4. Chapter 5: To be submitted to Journal of Geophysical Research. Co-authored with
John F. Ferguson.
CHAPTER 2
TERMINAL DISTRIBUTARY CHANNELS AND DELTA FRONT
ARCHITECTURE OF FLUVIAL-DOMINATED DELTA SYSTEMS
2.1
Abstract
Using modern and ancient examples we show that fluvial-dominated deltas formed in
shallow basins have multiple coeval terminal distributary channels at different scales.
Sediment dispersion through multiple terminal distributary channels will result in an
overall lobate shape of the fluvial-dominated delta that is opposite to digitate Mississippitype, but similar to deltas described as wave-dominated. The examples of deltas
presented show typical coarsening upward delta front facies successions but do not
contain deep distributary channels, as have been routinely interpreted in many ancient
deltas. We show that shallow water fluvial-dominated delta front deposits are typically
capped by small terminal distributary channels, the cross sectional area of which
represents a small fraction of the main fluvial “trunk” channel.
Recognizing terminal distributary channels is critical in interpretation of fluvialdominated deltas. Terminal distributary channels are the most distal channelized features
and can be both subaerial and subaqueous. Their dimensions vary between tens of m to
km width, with common values of 100-400 m and depths of 1-3 m, and are rarely incised.
The terminal distributary channels orientation for the same system has a large variation
with values between 123º (Volga Delta) and 248º (Lena Delta). Terminal distributary
7
8
channels are intimately associated with mouth bar deposits and are infilled by
aggradation and lateral or upstream migration of the mouth bars. Terminal distributary
channel deposits have characteristic sedimentary structures of unidirectional effluent flow
but also show evidence of reworking by waves and tides.
2.2
Introduction
Many ancient subsurface examples of river-dominated deltas deposited in shallow
intracratonic seaways are depicted as thick, narrow, branching shoestring sandstones,
interpreted as distributary channel complexes, which lack fringing delta front sandstones
(Busch 1959, 1971; Cleaves and Broussard 1980; Rasmussen et al. 1985; Bhattacharya
and Walker 1992; Figure 2.1). In interpreting these examples, the passive margin, shelf
Figure 2.1. Pennsylvanian Booch delta, from Busch, 1971. Extremely thick, elongated
sand bodies interpreted as fluvial dominated delta through analogy with modern
Mississippi Delta. Note that the fringe lobes are missing at the basinward end of the
elongated features.
edge Mississippi bird-foot delta has been historically used as a modern analogue, which
may be inappropriate giving the peculiar environmental conditions of the Mississippi.
More recent studies have reinterpreted many of these deeply incised “distributary
9
channels” as incised valleys (Willis 1997; Bowen and Weimer 2003). A re-evaluation of
fluvial-dominated deltas that have multiple distributaries is needed to reconcile these
differences in interpretation.
In this paper we will reconsider the scale and the presence of channelized deposits that
commonly lie at the top of delta deposits using modern fluvial-dominated deltas as well
as ancient examples. To address this problem, our focus will be on the terminal
distributary channels, which are the most distal channelized features of a distributive
system. This study shows that fluvial-dominated deltas formed in shallow water basins
typically exhibit a lobate shape with multi-scale coeval terminal distributary channels.
Unfortunately, there are limited examples of small terminal distributary channels
described in ancient deposits (Olariu et al. 2005) despite their presence in many modern
deltas (Figure 2.2). We suggest that the lack of recognition of these features is a result of
a lack of criteria for identification and indicate the need for a revision of existing facies
model of delta fronts in fluvial-dominated deltas, especially those formed in shallow
water basins.
Terminal distributary channel formation and their relationship with coeval mouth bars
has been described for modern deltas by Axelsson (1967), Zenkovich (1967), Baydin
(1970), van Heerden (1983), van Heerden and Roberts (1988) and DuMars (2002), but no
attempt to describe a typical depositional succession nor indicate facies architecture has
been made. Distributary channels described in ancient delta front deposits and
reinterpreted by us as terminal distributary channels provide detailed data related to
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sedimentary facies architecture (Bhattacharya et al. 2001; Olariu 2002; e.g. Chidsey et al.
2004). The delta front was described as a sheet of sand by Fisk et al. (1954), but recent
studies (van Heerden and Roberts 1988; Tye et al. 1999; Rodriguez et al. 2000;
Bhattacharya et al. 2001; DuMars 2002; Overeem et al. 2003; Olariu et al. 2005) show
that both modern and ancient delta fronts have a complicated morphology, consisting of
multiple terminal distributary channels, subaqueous levee deposits and mouth bars. Few
studies have been dedicated to delta front deposits, despite the key importance of this
delta sub-environment to understanding delta growth and facies architecture.
This paper:
1) presents a new paradigm for interpretation of ancient fluvial-dominated delta front
deposits that have multiple terminal distributary channels at different scale, which is
opposite to the Mississippi type that has only a few large distributary channels;
2) document the large variation in terminal distributary channels dimensions and
orientation (within the same system), and discuss formation and evolution of terminal
distributary channels based on modern examples; and,
3) set the basis for recognition of terminal distributary channels in ancient delta front
deposits based on sedimentary facies architecture;
2.3
Scales of Channels
There is huge variability in the scale of channel-like features, from small elongate
ephemeral scours to canyons but there is also a complete continuum between these scales.
In this section we discuss the relative size of the channels that are likely to be recognized
in deltas and their position within delta systems.
12
2.3.1
Fluvial “Trunk” Channel
Valleys typically form in areas undergoing degradation and erosion. Such large areas
define and form drainage basins and the general pattern of rivers within these coalesce to
form larger “trunk” rivers (Figure 2.3). The “trunk” channel is defined as the largest
channel of a fluvial-distributive system. “Trunk” rivers also commonly occupy valleys
(e.g. the Mississippi Valley). A fluvial channel is maintained both because it is confined
within an erosional valley or depositional levee and due to its downslope gradient, even
where slopes are exceedingly low, such as 3x10-4 for typical meandering rivers to 2x10-54x10-5 for the lower Mississippi and Amazon (Olsen 1993). In the case of deltas, the
“trunk” channel feeds the distributive system that starts at the apex. The apex represents
the point downstream from where the general pattern of the flow form distributary
channels (Figure 2.3).
Figure 2.3. Sketch with formation of distributary systems due to unconfined, low variable
gradient conditions. Sn - slope normal to the flow direction; Sd - slope down flow (main
direction of the flow), dashed lines represents contour lines. (A) Topographic map of a
distributive system indicates similar gradients (arrows) away from the main direction of
the main "trunk" valley. When a confined flow (channel) reaches an open area, flow
tends to spread but still will form channels due to subtle topographic differences.
13
2.3.2
Distributary Channels
Distributary channels are described from deep sea fans (Damuth et al. 1983; Posamentier
and Kolla 2003), alluvial fans (Prior and Bornhold 1990) and delta plain and form when
the main channel reaches an area with low lateral gradient variability (Figure 2.3).
Gradient values in a distributary system might be similar to the lower part of the ”trunk”
channel, but the gradient variation normal to the stream direction is similar to the
downstream gradient, in contrast to tributary systems where gradients normal to the
stream direction are typically higher (Figure 2.3). Because delta plain gradients are small
and sedimentation rates are high, the direction of distributary channels can be changed
easily by aggradation or differential subsidence and compaction, such that the gradient
will be steeper in other directions and might capture part of the flow creating a new
distributary channel (Figure 2.3).
In many modern deltas, the discharge from the “trunk” channel is split into a few major
distributaries (Figure 2.2), each with different discharges. The main distributaries will
bifurcate farther downstream and with each bifurcation, the discharge and sediment load
is split between newly formed channels. As a consequence of this successive splitting, the
distributary channels become smaller in the downstream direction. Yalin (1992) indicate
that with each bifurcation or avulsion the channel width and depth will change as
Bk+1§0.7Bk and hk+1§0.8hk respectively, where B is channel width, h is channel depth and
k is channel order. For a large delta system (Volga Delta, Lena Delta) distributaries can
rejoin forming a delta pattern similar to braided or anastomosed rivers (Morisawa 1985).
However, in a distributary system there should be more bifurcations than joins overall,
14
which generally results in an increasing number of smaller distributary channels
downstream (Morisawa 1985).
2.3.3
Terminal Distributary Channels
Terminal distributary channels are formed within a delta at the very end of a distributive
channel system. Terminal distributary channels start subaerially from the last subaerial
bifurcation and extend subaqueously to the last channelized expression on the delta front.
Terminal distributary channels represent the most active part of the delta and are
intimately associated with mouth bars.
We use the term “terminal distributary channel” rather than “n”-order channel to describe
these channels because it is typically impossible to count the numbers of channel splits in
ancient systems given the scarce data relative to the detailed morphology of ancient
deltas. Even in large modern delta systems with hundreds of bifurcations, it can be
difficult to accurately count the order of channels, since some channels are only
seasonally active.
Because the terminal distributary channels are formed through multiple successive splits
from “trunk” channel they are shallow and narrow compared with the fluvial “trunk”
channels of the same delta system (Figure 2.2). The distributary system ultimately
changes from the feeding “trunk” river channel to the smallest terminal distributary
channels, in a reversed pattern of the drainage basin (Figure 2.2).
2.4
Terminal Distributary Channel Examples
Modern (Atchafalaya, Wax Lake, Volga, Lena) as well as ancient (Panther Tongue,
Perrin, Ferron) examples of terminal distributary channels are presented in the following
15
section to build a conceptual model about how terminal distributary channels evolve, and
to describe their resulting delta front facies architecture. We include reinterpretation of
the previously published data, analysis of aerial images from modern deltas and new
outcrop measurements from several ancient deltas. Modern examples allow us to extract
the distribution and dimension of specific morphometric features and allow a process
based analysis of the formation of terminal distributary channels. The modern examples
have been chosen from deltas that are fluvial-dominated and have multiple distributary
channels. Ancient examples were selected based on the presence of small channelized
features within delta front deposits. The ancient examples provide log insight about facies
architecture and cross-sectional facies variability.
2.4.1
Modern Deltas
Atchafalaya Delta.--- The modern Atchafalaya Delta, formed after 1950 (Roberts 1980;
Tye and Coleman 1989), progrades into the 3 m deep Atchafalaya Basin. The delta
became subaerially exposed following an extreme flood in 1973 (Roberts 1980).
Subsequent aerial images show major morphological changes within only few years
(Figure 2.4). Subaerially exposed mouth bar growth indicates significant upstream
accretion as well as lateral migration of the mouth bars (Figure 2.4). Downstream
accretion is predominant, but upstream and lateral accretions are the dominant controls
on the discharge and sedimentation through the associated terminal distributary channels.
Cross-sections
16
Figure 2.4. (A) Atchafalaya Delta location (arrow). (B) History of subaerial delta
evolution and mouth bar growth, based on maps (from van Heerden 1983). The arrows
emphasize the migration of the bars, the length represents the degree of growth.
Downstream migration forms and extends the channels while the lateral and upstream
migration infills and closes channels. The channels on the right part of the delta have a
primarily sinistral migration, whereas channels on the left side of the delta lobe have a
primarily dextral migration.
through the delta, based on vibracores (van Heerden 1983; van Heerden and Roberts
1988) show a general coarsening up pattern. In a dip section (Figure 2.5A), landward
inclined beds are interpreted to form during upstream growth of bars. These upstream
inclined surfaces have a slope of 0.001 (1m/ km) versus 0.0005 (0.5 m/ km) for the
17
Figure 2.5. (A) Dip oriented cross section through eastern Atchafalaya Delta mouth bar
deposits (data from van Heerden 1983). (B) Dip oriented section through moutbar
deposits (modified from van Heerden 1983). (C) Variation of terminal distributary
channels profiles through time, the arrows from 1:1 profiles indicate accretion, or lateral
infill as in exaggerated profiles. For cross section and profiles locations see Figure 4.2.
basinward dipping surfaces. Successive aerial images, as well as successive bathymetric
surveys of the terminal distributary channels (van Heerden 1983; van Heerden and
Roberts 1988), indicate that the channels are infilled by aggradation, and lateral and
18
upstream bar growth (Figures 2.4, 2.5B, C). Terminal distributary channels are extremely
shallow (Figure 2.5C), less than 2 m deep, with width-to-depth ratios of a few hundred.
The cyclic pattern of terminal distributary channel formation has been repeated but
neither advance nor incision of the deeper “trunk” channel has occured. Four phases of
delta lobe evolution have been distinguished (van Heerden 1983; van Heerden and
Roberts 1988; Roberts 1998): (1) prodelta/distal bar (subaqueous platform) formation; (2)
distributary-mouth bar and subaqueous levee formation; (3) subaerial levee and channel
elongation; and (4) upstream accretion and lobe fusion.
Wax Lake Delta.---The Wax Lake Delta is similar to the Atchafalaya Delta, in that the
water is derived from a branch of the Atchafalaya River and also discharge into
Atchafalaya Bay (Figure 2.4A). The Wax Lake Delta was formed at the end of the Wax
Lake outlet, dredged in 1942 by the U.S. Corps of Engineers (Roberts 1980). The delta
has a similar morphology to the Atchafalaya Delta, with multiple terminal distributary
channels separated by mouth bars (Figures 2.2 and 2.6B). Cross-sections based on
vibracores do not allow reconstruction of bedding surfaces (Majersky et al. 1997), but
thicker sand deposits occur in a landward direction (Figure 2.6C) and suggest upstream
accretion.
A morpho-hydrological study of the Wax Lake Delta related to channel flow velocities
and suspended sediment variability, concluded that sediment flux and deposition is
highest at the distributary talweg where the mouth bar is formed (DuMars 2002). Our
analysis of channels profiles indicate that channel cross-sectional areas decrease
19
Figure 2.6. For Wax Lake Delta location see Figure 2.4A. (A) Location of channel
transects (from DuMars, 2002) and vibracores with sand thickness in meters (from
Roberts 1998). (B) Isopach of sandy deposits. (C) Terminal distributary channels
sections, with characteristic profiles and area (modified after duMars 2002). Triangle and
square dots indicate profiles used for Figure 2.6D. (D) Terminal distributary channel area
variations in downstream direction, for profile location see Figures 2.6A and C. (E)
Typical geometry of Wax Lake Delta terminal distributary channels cross-sections with
10 times vertical exaggeration and without vertical exaggeration.
20
basinward following each channel split. The area decreases at different percentages with
each split (Figures 2.6D and E). Despite this decrease, no change has been observed on
terminal distributary channel cross-sectional area or geometry during the subaerial to
subaqueous transition. Subaqueous channels extend basinward at least 3-4 km (Figure
2.6D). The sum of all small terminal distributary channels represents a larger crosssectional area than the initial channel, requiring lower overall velocity associated with
terminal distributary channels discharge. The overall loss of flow velocity results in high
sedimentation in the terminal distributary channel area. As in the Atchafalaya Delta,
terminal distributary channels on the Wax Lake Delta are extremely shallow (Figure
2.6F) with width-to-depth ratios of a few hundred.
Volga Delta.---The modern Volga and Lena deltas allow the analysis of terminal
distributary channel dimensions and distributions in a continental-scale fluvial-dominated
delta. The Volga Delta built into the Caspian Sea (Figure 2.7A), a closed basin with sea
level variations up to 15 cm/ year. The present Volga Delta has about 800 terminal
distributary channels (Kroonenberg et al. 1997; Alekseevskiy et al. 2000; Overeem et al.
2003) that coalesce upstream into a single “trunk” channel (Figure 2.2). An increasing
number of distributary channels were formed in the lower delta plain from 200 at the end
of the 1800’s to 1000 by 1980 during sea level fall and delta progradation (Figure 2.7B).
This happened with coeval channel abandonment in upper parts of the delta
(Alekseevskiy et al. 2000). Incision and increased discharge through the main distributary
channels and a decrease in the number of distributary channels in the upper delta plain
during sea level fall (Alekseevskiy et al. 2000) can be attributed to slight slope changes,
21
despite a relatively constant slope of 5 cm/ km in delta plain and offshore area
(Kroonenberg et al. 1997; Overeem et al. 2003).
Figure 2.7. Modern Volga Delta. (A) Location. (B) Modern sea level changes (modified
after Alekseevskiy et al. 2000), with indication of relative number of terminal distributary
channels; on the right map, each color represent the relative extent of the delta at different
stages. (C) Map of recent sediments in the delta front area, (modified from Belevich
1969). The unvegetated dry areas have been exposed since the 1930 sea level fall. Top of
the figure shows percent of total discharge in different areas; the second and the fourth
areas have together 23% of discharge.
The density of channels along the shore line is up to 6 channels per km (Kroonenberg et
al. 1997; Overeem et al. 2003). The terminal distributary channels average 1-3 m deep
(Kroonenberg et al. 1997), like the Atchafalaya and Wax Lake examples, and are rarely
wider than 10-20 m (Overeem et al. 2003). The flow velocity and suspended sediment
concentration vary with position within delta front area, and this is reflected by
sedimentation pattern and superficial recent sediment distribution in front of the delta
(Figure 2.7C). The sediment distribution indicates that sediments derived from terminal
22
distributary channels form narrow ribbon patterns in front of the channels, but commonly
these merge together (Figure 2.7C).
A sedimentological study of the modern and recent delta front deposits, based on a large
auger dataset (Overeem et al. 2003), indicates that terminal distributary channels have
low to moderate sinuosity and contain the coarsest deposits in the system (fine sands
0.12-0.21 mm). The spatial variability of channel deposits in the subsurface is as high as
in the modern delta with tens of meters wide ribbons. Terminal distributary channels
initially build subaqueous levees, a few kilometers long and tens of meters wide, with
maximum topography of 1-2 m. Mouth bar deposits are relatively thin (less than 1 m)
with a coarsening upward trend for regressive (forced regression) periods and fining
upward for the transgressive period (Overeem et al. 2003).
Lena Delta.---The Lena Delta progrades into the Laptev Sea. The delta evolution was
highly influenced by tectonic activity during last the 80,000 years (Are and Reimnitz
2000; Schwamborn et al. 2002). The Lena Delta has not been studied in detail, like the
Atchafalaya and Caspian examples, but from analysis of the present morphology (Figure
2.2) multiple terminal distributary channels can be observed. Most of the “trunk” channel
(“Lena pipe”) discharge is taken by the Trofimovskaya distributary toward the east
(61%). This distributary also has most of the active network of terminal distributary
channels (Figure 2.2), and is associated with the most actively subsiding part of the delta,
the eastern part. Subsidence does not favor bifurcation directly but increases slope and
thus increases discharge, which is reflected in a larger number of bifurcations. Terminal
distributary channels are extremely shallow, in the seaward part of the Trofimovskaya
23
Channel (Figure 2.8A) with water around 1 m deep for a few km offshore (Are and
Reimnitz 2000).
Figure 2.8. Distributary channels variations in Lena Delta. (A) Measurement locations.
(B) Variation of channel width after each bifurcation. (C) Width ratio between new and
old channel for each bifurcation. Values larger than 1 appear due to channel joins or areas
with shallower channels. Also all values seem to be overestimated, since measurements
follow the largest branch. (D) Plot of subaerial mouth bar width and the adjacent
distributary channel. (E) Frequency distribution for terminal distributary channels widths
and inter-distributary channel distances.
24
Changes in distributary channel width were measured on a satellite image of the Lena
Delta (Figures 2.8B, C). The channel width decreases by splitting but at different rates
than was predicted by the Yalin (1992) equation, Bk~0.7Bk+1. The differences appear
because the theoretical estimations were made for equilibrium channels, which
distributary channels are not. The measurements of terminal distributary widths and interchannel distances, along the delta shoreline (Figures 2.8D) indicate that 200-400 m wide
terminal distributary channels are the most frequent (Figures 2.8E). Inter-channel
distances of 200-500 m are the most frequent with another high frequency at 800 m
(Figure 2.8E). The channel width and inter-channel distances may also be biased by the
satellite image resolution, which can not resolve less than about 100 m wide channels.
2.4.2
Ancient Deltas
Campanian Panther Tongue Delta.---Exposures of the Cretaceous Panther Tongue
delta in Spring Canyon in central-northeast Utah, in the Book Cliffs, are oriented at
different angles relative to paleoflow. Depositional strike and dip exposures of up to 30 m
high cliffs through proximal delta front deposits allow the 3-D facies architecture to be
mapped (Olariu et al. 2005; Figure 2.9). On strike-oriented cliff faces, terminal
distributary channels were interpreted based on 3-D bedding diagrams, ground
penetrating radar (GPR) profiles and sedimentary sections (Olariu et al. 2005). The
channelized features have low topography, with less than 4 m of relief, and are tens to
hundreds of meters wide. Erosion of the channels into adjacent deposits is rare and
typically appears only on one side of a given channel (Figures. 2.9A and B). The lateral
migration and aggradation of the same terminal distributary channel compensates for
differential topography. The lateral migration is in the order of hundreds of meters.
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During each lateral migration, the channels aggrade a few meters (Figure 2.9C). The
channels are infilled with fine to medium sandstone with structureless, trough-cross
laminated or parallel laminated beds. Associated with terminal distributary channels are
mouth bar deposits which are mostly formed from parallel and massive fine sandstones
(Figure 2.9D). Interbedded with the sandstone beds are silt to very fine sandstone beds
with rippled or highly bioturbated tops. Ichnofacies (Olariu et al. 2005) represent the
Skolithos or proximal Cruziana assemblages (Pemberton et al. 1992). Mouth bar deposits
infill the channels as they migrate laterally. On dip oriented sections, beds are inclined in
a basinward as well as landward direction (Figures 2.10B and C). The upstream inclined
beds are mostly structureless to parallel laminated, fine- to medium-grained sandstones.
These are interpreted to represent upstream growth of bars (Olariu et al. 2005), which
infilled terminal distributary channels. From a limited number of dip oriented exposures
it is difficult to evaluate bar migration direction precisely and it is probable that bars
migrated laterally as well as in the upstream direction, as observed in the modern
Atchafalaya Delta. The slope of upstream inclined beds is around 12 degrees relative to
the top of the outcrop which corrected for regional structural dip corresponds to an angle
between 2 and 7 degrees (Olariu et al. 2005). On an adjacent cliff face (Figure 2.10B) we
measured seaward delta front clinoforms dips of between 1 and 8.2 degrees, which is in
general less than the upstream inclined surfaces (Figure 2.10C), but steeper than the
range of modern delta front slope values (Coleman and Wright 1975).
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Pennsylvanian Perrin Delta.---The Perrin Delta prograded into a Pennsylvanian
cratonic basin, and is part of the Placid Formation of the Canyon Group that consists of
four thick limestones with interstratified clastic deposits (Brown et al. 1990). Delta
deposits representing parts of the Perrin Delta crop out west of Wizard Wells, Texas
(Figure 2.11A). According to Brown et al. (1973), the Placid Formation consists of “high
constructive” (i.e. fluvial-dominated) elongate deltas, which are composed of highly
contorted, superposed channel-mouth bar and distributary channel sandstones. A
photomosaic of the Wizard Wells outcrop oriented at a high angle to paleoflow (Figures
2.11B and C), shows low topographic channelized features. Growth faults and contorted
beds present on the photomosaic (Figures 2.11C and D) are syn-depositional features
associated with delta front slides, similar to the Mississippi (Coleman et al. 1998).
Channelized features are infilled mainly with trough cross-stratified fine sandstones with
mudchips and plant fossils. Secondary, parallel or massive beds are also present (Figures
2.11E). Parallel laminated beds are interpreted as mouth bar deposits and are finer than
cross-stratified or massive beds. Classification of the channels as terminal distributary
channels rather than fluvial channels is based on the presence of structureless sandstone
deposits, fining up, turbidite type beds indicating waning flows, and wave ripples, which
suggest a shallow water setting. Erosional cut bank of the channels are present only on
one side, and mouth bar migration infill the channel on the other side. These observations
are similar to the terminal distributary channels seen in both the Panther Tongue and the
modern examples described earlier.
Turonian Ferron Delta.---Large continuous outcrops of the Turonian Ferron Delta from
east-central Utah have been extensively studied as outcrop analogs for fluvial and wave
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30
dominated delta reservoirs (Barton 1994; Gardner 1995; Corbeanu et al. 2001; Chidsey et
al. 2004).
Based on outcrop observations, the Ferron Sandstone has been separated into 7 major
stratigraphic cycles (Ryer 1981) with different stacking patterns. Subsequent studies
(Barton 1994) distinguished upward-coarsening facies successions separated by minor
flooding surfaces, and were interpreted as delta front deposits. The first three seaward
stepping progradational deltaic parasequences are interpreted as river dominated (Barton
1994). Given the relatively low number of bifurcations and limited number of distributary
channels or channels belt mapped by different authors within the Ferron Delta,
Bhattacharya and Tye (2004) suggested that all the parasequences have a strong wave
influence. The first parasequence is indeed composed of multiple stacked and laterally
extensive mouth bar deposits (Barton 1994; Gardner et al. 2004; Garrison and van de
Berg 2004) indicating a strong river influence, but these studies do not indicate the
geometry of terminal distributary channels associated with the mouth bars. Barton (1994)
described the mouth bar deposits to consist of bar front, bar flank and bar crest
subdivisions. Bar front deposits have characteristics of delta turbidite deposits, including
convoluted strata, massive and thin graded beds exhibiting sharp bases and incomplete
Bouma sequences, variable bioturbation, common ripple lamination and HCS. Draped
mudstone is laminated and contains plant debris and bioturbation. Bar flanks represent
the area between the bar front and the bar crest where the influence of waves is stronger;
the characteristic sedimentary structures are massive to planar laminations, wavy
laminations and HCS. Bar crest facies consist of amalgamated, unidirectional, high-angle
cross-strata with poorly sorted material containing clay clasts and organic matter. Bar
31
crest facies consist of numerous reactivation surfaces and scour-and-fill structures. These
deposits have a lenticular geometry that thicken over short distances into a lenticular
coarse-grained channel fills with distinct erosional bases. We suggest that the bar crest
facies, interpreted by Barton (1994) as the product of shallow channelized flows, and
represent terminal distributary channel facies.
Eocene Battfjellet Deltas.---Extensive outcrops of the Eocene Battfjelet Deltas in
Spitzbergen shows large, complete clinoforms on the paleoshelf edge (Steel et al. 2000;
Plink-Bjorklund et al. 2001; Mellere et al. 2002). Facies described from the deltas include
laminated and massive sandstone with erosional base and rip-up clasts and coal debris
that indicate scours and channels (Plink-Bjorklund et al. 2001; Mellere et al. 2002). Also
current ripple and planar laminations intercalated with shales were interpreted as mouth
bars (Mellere et al. 2002). The Battfjellet deposits were interpreted as shelf edge deltas
containing abundant hyperpycnal flow deposits dispersed into the basin through multiple
terminal distributary channels (Mellere et al. 2002). The terminal distributary channels
which were connected to the distributary system are named by Mellere et al. (2002) as
slope channels since delta front is prograding over shelf slope. The terminal distributary
channels are up to 5 m deep ,50-200 m wide and can be as narrow as 40 m on the distal
slope (Mellere et al. 2002), but their distribution was not mapped in detailed. The water
depth for the active channels was about 50 m, that is considerable deeper than the
previous examples.
32
2.5
Summary of Terminal Distributary Channel Examples
2.5.1
Terminal Distributary Channel Dimensions
All the delta examples presented above have shallow and narrow terminal distributary
channels and that represent a small fraction of “trunk” channels as the channel crosssection decreases downstream due to multiple bifurcations (Figure 2.8). Terminal
distributary channel widths vary between tens of m to km, but the most common width
observed was in range of 100-400 m (Figures 2.4, 2.6, 2.8). The depth of terminal
distributary channels ranges between 1 and 3 m, with a common width to depth ratio of
about 100. No dimensional changes were observed in the transition from subaerial to
subaqueos channels (Figure 2.6). Within modern shallow-water deltas there are typically
tens to hundreds of active terminal distributary channels and the channel density reached
up to 6, 4 and 3 channels/ km for the Volga, Lena and Atchafalaya deltas respectively.
2.5.2
Terminal Distributary Channel Orientation Relative to the “Trunk”
Channel
The number of distributary channels increases from delta apex to the shoreline (Figure
2.2) and the number of active terminal distributary channels also increases as the deltas
prograde. With increase of terminal distributary channel numbers the angle range relative
to the “trunk” channel axis also increases (Figure 2.2). The terminal distributary channel
orientations range between 123° for the Volga Delta and 248° for the Lena Delta (Figure
2.12). The median orientation of terminal distributary channels might be at a high angle
relative to the main “trunk” channel; 50° in case of the Atchafalaya Delta (Figure 2.12).
Preferred channel orientation might be due to local tectonic factors such as higher
33
subsidence. In the case of a high angle between the “trunk” channel and the terminal
distributary channels median (Figure 2.12), this might be the result of basin topography
and/ or regional geological structures.
Figure 2.12. Orientation of terminal distributary channels in modern deltas; overall range
of terminal distributary channel orientations (ß) and the angle between median orientation
of terminal distributary channels and the "trunk" channel (Į). “n” represents the number
of terminal distributary channels measured Zero is North for all the deltas. See Figure 2.2
for entire distributive pattern.
2.5.3
Terminal Distributary Channel Formation and Evolution
Formation of terminal distributary channels is related to channel mouth processes. Mouth
bar deposits form as the flow condition at the channel mouth change from confined to
unconfined and velocity decreases (Albertson et al. 1950; Bates 1953; Wright 1977). The
34
initial mouth bar will form close to the channel axis and will bifurcate the channel flow
(Figures 2.4, 2.5 and 2.6).
Based on modern examples presented several stages of terminal distributary channel
evolution have been differentiated and are closely related to mouth bar evolution (Figure
2.13). In phase one, new terminal distributary channels are formed by extension of
Figure 2.13. Conceptional formation and evolution of a terminal distributary channel mouth bar system (modified from Axelson 1967; Baydin 1971; van Heerden 1983).
Three main phases of evolution have been distinguished: (1) formation of new terminal
distributary channels and mouth bars; (2) mouth bar migration and terminal distributary
channel extension; (3) terminal distributary channel abandonment.
35
subaqueous channel levees, widening of the channel and bifurcation of the flows because
of mouth bar formation (Figure 2.13). In phase two, the growth and migration of a mouth
bar (lateral and upstream accretion) forms terminal distributary channels at different
scales.
In phase three, preferential mouth bar accretion and filling of terminal distributary
channels will reduce the flow velocity and sediment discharge through that channel,
which eventually will be abandoned. Some of the terminal distributary channels bifurcate
again and form another generation (order) of terminal distributary channels (Figure 2.13).
These evolutionary phases become faster or slower in different areas of the delta as a
consequence of gradient changes through time because of deposition or allocyclic factors.
With each new cycle of mouth bar formation, the terminal distributary channels become
shallower and frictional processes of the river effluent (Wright 1977) increase as the
system tries to carry bedload (sediment in traction and saltation) farther into the basin.
Because mouth bars grow laterally, terminal distributary channel cross-sections become
smaller and grain size decreases as flow capacity decreases after a critical stage is
reached. Concomitantly with flow decrease in one terminal distributary channel, the flow
is diverted toward another active terminal distributary channel or a new one is formed.
This process might have a short recurrence time even a few years as was observed in the
case of Atchafalaya Delta (Figure 2.4).
The cyclicity of mouth bar and terminal distributary channel formation and evolution are
controlled by: (1) the relative ratio of bedload to suspended load, (2) the amplitude of
seasonal river discharge variation, and (3) the accommodation space (depth of the basin)
relative to river sediment load. The cycle of lobe evolution is shorter for rivers with high
36
bedload, high amplitude of discharge variation and with low accommodation (e.g.
shallow water).
2.5.4
Terminal Distributary Channel Sedimentary Facies
In the previous examples (Figures 2.9, 2.10 and 2.11) upward-thickening and coarsening
delta front deposits have terminal distributary channels facies interbedded with mouth
bars deposits. In general, mouth bars have different sedimentary structures compared to
terminal distributary channels (Table 1). Terminal distributary channels have the coarsest
grain sizes with common trough-cross beds and rip-up mud chips. The ancient outcrop
Table 2.1. Characteristic facies for terminal distributary channels and mouth bars in
ancient deposits.
Facies\
Location
Terminal
Distributary
Channels
Mouth Bar
Campanian Panther
Tongue (Olariu et al.,
2005)
Fine to medium
sandstone; massive,
trough cross stratified
and parallel laminated;
variable bioturbation
intensity with high
bioturbation at the top
of the beds; drag casts.
Fine sandstone parallel
and massive laminated;
very fine sandstone to
silt; highly bioturbated
silty tops.
Pennsylvanian Perrin
Delta (this study)
Turonian Ferron Delta
(Barton, 1994)
Trough cross stratified
fine sandstone,
secondary parallel or
massive; mud chips and
plant fossils are
common, load casts and
drag casts are common.
Convoluted strata, massive
and thin graded beds, sharp
bases, variable bioturbation.
Common ripple lamination
and hummocky cross
stratification. Laminated
mudstone with plant debris
and bioturbation.
Amalgamated, high angle
cross strata, clay clasts and
organic matter.
Parallel laminated or
massive very fine
sandstone, low
bioturbation.
examples indicate that sedimentary structures from terminal distributary channel facies
partially overlap the mouth bar, but the geometry of beds is different. More tabular beds
with graded grain size variation are observed for mouth bars, while terminal distributary
channels have variable low topography, might have erosional boundaries, and are
bounded by lower topography planar beds (Figures 2.9 and 2.11). Channel incision into
37
previous mouth bar or delta front deposits is very modest within the modern and ancient
deltas presented. Erosion of terminal distributary channels was commonly observed only
on a single side (Figures 2.4, 2.5, 2.9 and 2.11), and is probably produced by lateral
channel migration. Trough cross-beds are formed by confined flow on the backside of the
bar in terminal distributary channels. Because terminal distributary channels are
decreasing in size basinward it is expected that terminal distributary channel facies
should be more common in the proximal delta front with mouth bar facies occurrence
increasing in the distal delta front.
2.6
Discussion
The presence of terminal distributary channels has implications for the facies architecture
of fluvial-dominated deltas and interpretation of ancient delta deposits.
2.6.1
River-Dominated Delta Facies Architecture
The modern Mississippi Delta is typically presented as the classic fluvial-dominated delta
(Galloway 1975; Coleman and Wright 1975). Other fluvial-dominated deltas with
different morphology, which are seldom used as modern analogs, include the modern
Volga, Lena and Atchafalaya Bay deltas. All these deltas are fluvial-dominated since they
prograde into basins with low tides and low wave energy. These aforementioned deltas
have tens to hundreds of small terminal distributary channels (Figures 2.2, 2.4, 2.6, 2.7
and 2.8) and do not have large “finger like” sand bodies (Fisk 1961) but rather small
mouth bars merged together within an overall lobate shape (Figures 2.4, 2.6C, 2.9, 2.10
and 2.11).
38
The previous Mississippi delta lobes have been mapped as lobate and interpreted to have
multiple terminal distributary channels, despite the fact these terminal channels were not
mapped in detail (Frazier 1967). In the Pleistocene Lagniappe Delta, a network of small
distributary channels that build a succession of overlapped lobes has been inferred
(Roberts et al. 2004). The distinction between elongate (deep water) versus lobate (shoal
water) fluvial-dominated deltas was made by Fisher et al. (1969). The difference is
interpreted to relate to accommodation. The Mississippi is a shelf edge delta, prograding
into deep water and the recurrence time for terminal distributary channel bifurcation and
lobe switching is long (hundreds to thousands years), mainly because of compaction,
allowing channels to extend and to accumulate relatively coarse sediments as elongate
sand bodies. Other shelf-edge deltas that form mouth bars and delta distributaries
disperse the sediments through multiple small terminal distributary channels which
extend to the slope as a function of the steep gradient (Steel et al. 2000; Plink-Bjorklund
et al. 2001; Mellere et al., 2002). The presence of multiple terminal distributary channels
on the Eocene Battfjellet deltas in Spitsbergen (Steel et al. 2000; Plink-Bjorklund et al.
2001; Mellere et al., 2002) compared to the modern Mississippi Delta might be related to
the higher percent of bedload and more frequent hyperpycnal flows in the case of
Spitzbergen deltas.
Shoal-water deltas typically are lobate and have more outlets than deep-water deltas,
compared to their discharges. This reflects a much shorter recurrence interval of
bifurcation and avulsion, typically less than 100 years. In the case of the Atchafalaya and
Wax Lake deltas, each has more than 10 terminal distributary channels (Figure 2.2)
formed in less than a century. Fluvial-dominated delta classification needs to include
39
deltas with multiple terminal distributary channels with patterns similar to the modern
shallow-water deltas presented (Figure 2.2) or older Mississippi Delta lobes. Sand body
Figure 2.14. Comparison between digitate versus lobate river dominated deltas. (A)
Strike cross section through lobate river dominated delta compiled from modern
examples (Wax Lake Delta, Atchafalaya) for horizontal scale and from ancient examples
(Panther Tongue, Perrin Delta) for internal architecture. (B) Bar finger deposits of a
digitate delta (Fisk 1961); note that active channel is about 20% of sandbody thickness.
(C) Vertical section through digitate delta, for location see Figure 2.14B. (D) Vertical
section of a lobate river dominated delta (modified after Barton 1994). Note the thickness
differences between digitate (C) and lobate (D) vertical sections.
40
distribution of fluvial-dominated delta can also have a lobate shape, similar to wavedominated deltas as presented by Coleman and Wright (1975). The lobate sand body of a
delta is built by coalescence of multiple terminal distributary channels and mouth bars
(Figures 2.7, 2.9 and 2.11) and has different facies architecture from the elongate or
digitate deltas that are more commonly described for subsurface fluvial-dominated deltas
(Figure 2.14). The two types of deposits do not necessarily have significant differences in
the succession of vertical facies but the architecture is different with significant
difference in facies thickness. Lobate river deltas have high lateral variability with
multiple terminal distributary channels interbeded with mouth bars, while in digitate
deltas the channel is stable and generates stacked mouth bar deposits. Elongate deltas
typically produce thicker deposits than lobate river deltas, because in the latter, the
sediments are spread out into the basin (Figure 2.14).
2.6.2
Implications of Multiple Terminal Distributary Channels Presence on Delta
Front Deposits
Distributary number in different delta types. --- In fluvial-dominated deltas, channel
bifurcation and avulsion are common because sediment deposited at the river mouth is
not removed by basin processes and the growth rates of mouth bars are high. Strongly
wave-modified deltas tend to have only a few distributary channels for the simple reason
that waves remove material supplied to the coastline, thus inhibiting progradation and
channel bifurcation (Bhattacharya and Giosan 2003; Bhattacharya and Tye 2004). In tidal
deltas, tides maintain a reduced number of distributaries by increasing sediment
dispersion because of amplification of the river current, especially during ebb tides.
41
However, in a delta, low-order, delta plain distributary channels can be stable for long
periods (i.e. enough time for initially straight channels to become highly sinuous) and
have high preservation potential due to high sedimentation rates associated with large
accommodation space. The cause for the presence of multiple relatively stable large
distributaries might be that the channel gradient is similar among distributaries, and their
relatively long path to the basin requires a long time to change the channel gradient in
order to capture a more significant part of discharge than other distributaries.
In contrast, terminal distributary channel evolution is more dynamic and is controlled by
mouth bar growth and migration. Mouth bars usually fill the terminal distributary
channels by narrowing the channel section from a single side (Figures 2.4, 2.5, 2.9 and
2.11).
Because processes of terminal distributary channel and mouth bar formation are not well
understood, most numerical modeling programs, which mainly use process based
equations, have a simplistic approach for sediment source changes. Most programs use
stochastic methods (Syvitski and Daughney 1992; Slingerland et al. 1994) or lateral
migration of a single channel (Tetzlaff and Harbaugh 1989) to describe the change of
sediment source within a delta, which commonly is expressed as distributary channel
bifurcation or avulsion. The model proposed in this paper indicates that numerical models
of dispersive systems also need to incorporate coeval multiple-scale terminal distributary
channels.
Sand body geometry. --- The number of terminal distributary channels will control the
distribution of sediment in the delta front area and as a consequence sand body geometry,
as well as the overall shape of the shoreline. In the case of multiple terminal distributary
42
channels, the distribution of sediments into the basin is rather more linear and will form
an “apron” of sand deposits.
Sand body geometries associated with modern deltas were described by Coleman and
Wright (1975) but they do not indicate the number of terminal distributary channels
associated with different sand body morphologies. If we associate the number of terminal
Figure 2.15. The shape of sand bodies for the main energy factors encountered in delta
systems and expected number of terminal distributary channels. The color pattern
represent the relative thickness of deposits, thicker deposits are darker.
43
distributary channels with typical sand bodies from modern deltas (Figure 2.15), it is
clear that elongate, Mississippi type sand bodies are rather unusual for river-dominated
deltas, but are more common for tide-dominated systems or even for highly asymmetrical
wave-influenced systems. This reflects the reworking capacity of mouth bar deposits and
the possibility of relatively stable channels for a long time. A low number of bifurcations
can be found in wave-dominated systems with only one or two stable distributaries,
followed by tide-dominated deltas with a few to tens of terminal distributary channels
(Figure 2.15). Actually the most tide-influenced deltas has many tidal channels but only
1-2 active distributary-mouth outlets which might be stable for 1000’s of years (Tanabe
et al. 2003). Fluvial dominated systems may have multiple (hundreds) terminal
distributary channels and a lobate shape (Figures. 2.2 and 2.15) similar to that described
by Fisher et al. (1969) as shoal-water fluvial-dominated deltas. The lobate shape of the
sand bodies is formed because of successive bifurcation, avulsion and increasing angle of
dispersion. The orientation of terminal distributary channels may show a large variation
within the same system. From the apex angle, which can be up to 180 degrees in the case
of the Lena Delta (Figure 2.2), it can be deduced that distributary channels in the same
systems can be oriented at angles of more that 180 degrees (Figure 2.12).
When the distributary system (i.e. delta) is not able to adjust to the increased friction, the
main channel will avulse and a new distributive system (sub-delta) will be formed. This
is a fundamentally autogenic process that drives avulsion in distributive depositional
systems and causes lobe switching. In reality, compaction and tectonics interfere with
autogenic processes in the distributive system. The position of the high discharge channel
within the system can change suddenly or can be stable for a longer time than can be
44
predicted only from river mouth processes (e.g. Mekong). Tidal reworking has allowed
the distributary channels of the Mekong to be stable for over 1000 years (Tanabe et al.
2003).
Mississippi Delta as an analog. --- Use of the Mississippi delta as a modern analog to
interpret ancient delta deposits (Fall River, Booch) might be erroneous. Because of the
analogy with the Mississippi delta, sand bodies with elongated patterns were interpreted
as fluvial-dominated deltas (Figure 2.1). Most of the deposits interpreted as deltaic (Fall
River, Booch) have recently been reinterpreted as incised valleys (Willis 1997).
The main argument against interpretation of elongate sand bodies as delta distributaries is
that a single delta deposit has a lobate shape with decreasing grain size away from the
source and it is not an isolated sand body without its fringing lobe. The elongate shape of
the sandstone can be explained by migration of successive lobes basinward, but this
model is difficult to accept without environmental conditions similar to the Mississippi,
or without strong structural control (e.g. Bhattacharya and Willis, 2001). In fact, the
Mississippi is an exception rather than a common analog for most ancient deltas because
it drains a continent, discharges into a basin with a narrow shelf and recently has been
largely held in place by the US Army Corps of Engineers.
2.6.3
Implications for Interpretation of Ancient Deposits
Recognizing ancient terminal distributary channels within fluvial-dominated delta
fronts.---The delta front is the most dynamic deltaic setting. Processes acting on the delta
front, which produce and define the architecture of deposits, are distinct from processes
in adjacent deltaic areas; therefore, the resulting deposits have distinct characteristics
compared with coeval delta plain or prodelta deposits. Mouth bars and terminal
45
distributary channels are the main component of fluvial-dominated delta fronts and
describing the formation and evolution of these is critical for understanding (1) the
dominant processes (i.e. fluvial vs. wave vs. tides) of sediment partitioning and (2)
heterogeneities associated with delta growth.
However, identification of terminal distributary channels in ancient delta deposits is not
trivial because of (1) the relatively low topopgraphic expression of these features and (2)
of the different types of sedimentary structures (i.e. fluvial and marine) which creates
complex facies interfingering (Figures 2.9, 2.10, 2.11 and Table 1).
Sedimentary facies distinction of terminal distributary channels.---Mouth bar
deposits are inseparable from terminal distributary channels deposits because the mouth
bars infill the channels. There are also examples of passive, mud filled distributary
channels caused by flow decrease and channel abandonment in Atchafalaya Delta (van
Heerden and Roberts 1988).
Terminal distributary channel deposits are influenced by marine basin processes, such as
waves and tides. Commonly, the influence of basin factors appears upstream of the last
bifurcation. We still name these channels as terminal distributary channels because, in
ancient deposits, the influence of basin factors indicates that the channel is relatively
close to the shoreline (the end of a delta-distributive system). Thus, in ancient systems,
terminal distributary channels can be distinguished based on the presence of sedimentary
structures associated with basinal processes (waves, tides). Garrison and Van der Berg
(2004) separated proximal and distal distributary channels in outcrops of the Cretaceous
Ferron Delta based on relative position, approximately 10 km, to paleo-shoreline. This
approach might be useful where detailed paleogeographic reconstructions are available,
46
but it is still desirable to rely on the presence of sedimentary structures such as symmetric
wave ripples, HCS and flaser bedding, rather than to a given distance from the shoreline,
which might be highly variable for any given delta. Tidal signatures might be confusing
in macro-tidal environments were tides can occur upstream as far as the apex of the delta.
The presence of wave-formed sedimentary structures are the most useful to distinguish
the sub-aqueous part of terminal distributary channels.
Characteristic features of terminal distributary channel deposits are an assemblage of (1)
continuous channelized flows with trough cross-beds, mudchips, and continental-derived
organic matter, (2) flow waning structures with graded (turbidite type) beds, structureless
sandstone beds and mud-capped sandstone beds, (3) sedimentary structures associated
with waves (symmetric ripples, hummocky cross-stratification) and tides (e.g. flaser
beding; Table 1). High energy marine ichnofossil assemblages of Skolithos or proximal
Cruziana also may be associated with terminal distributary channels deposits. The
ichnofacies distribution appears to be cyclic, with highly bioturbated beds associated with
periods of low discharge (Olariu et al. 2005).
Recognizing and preservation of small scale terminal distributary channels,
implication on distinguishing wave- by river-dominated deltas. --- In subsurface
settings, terminal distributary channels, while potentially important in controlling
complex facies architecture, are typically too small to map or resolve within a mapped
delta lobe. Despite mapping of large-scale valley and “trunk” rivers in the Dunvegan Fm.
(Plint and Wadsworth 2003; Figure 2.16A) or Ferron Sandstone (eg. Chidsey et al. 2004)
these typically are shown as stopping tens of kilometers landward of the shoreline. Based
on thousands of well logs, outcrop and core data, fluvial and wave-dominated delta types
47
Figure 2.16. (A) Fluvial – trunk system in Dunvegan River lacks details of distributary
pattern because distributary channels are too small to image (from Plint and Wadsworth
2003). (B) Example of a tributary-distributary system, Volga basin. The tributary pattern
is an order of magnitude larger (tens to hundreds of times) than the distributary pattern,
the main "trunk" valley connects the two patterns, modified (after Payne et al. 1975)..
48
approximately 40-50 km from shoreline. Comparison of the Dunvegan with the modern
have been interpreted and mapped within different lobes of the Dunvegan Formation in
the Western Canadian Sedimentary Basin (Bhattacharya 1991, 1994; Bhattacharya and
Walker 1991; Plint 2000; Plint and Wadsworth 2003). Plint (2000) indicated that the
successive deltas prograded hundreds of kilometers into a shallow water basins. The
resolution of the data for the Dunvegan Formation (Bhattacharya and Walker 1991;
Bhattacharya 1994; Plint 2000; Plint and Wadsworth 2003), however, does not allow
mapping of terminal distributary channels in the subsurface and only the deeper “trunk”
rivers can be mapped (Figure 2.16A). These cannot be mapped farther seaward than
Volga drainage basin and delta network (Figure 2.16B) shows that the incised valley
network cover a large area (hundreds of time larger than the delta) and has deeply-incised
valleys while the delta-distributary part of the same system cover a smaller area and is
composed of channels too small to resolve (Figures 2.2 and 2.9). In shallow water basins,
such as the Cretaceous Western Interior Seaway, rivers with relatively high discharge like
the Dunvegan, will form deltas that have multiple small terminal distributary channels
hundreds of meters wide and a few meters deep. The presence of multiple terminal
distributary channels will form sand bodies or shorelines similar to wave-dominated
environments. The paleogeographic conditions suggest formation of multiple distributary
channels and probably the same lobe was successively fluvial-dominated followed by a
period of wave reworking and lobe switching.
Misidentification of distributary channels and incised channels due to sea level fall. -- Ancient delta deposits are commonly associated with a coarsening-up facies succession
with channelized deposits at the top (Eliott 1978; Bhattacharya and Walker 1992;
49
Reading and Collinson 1996; Figure 2.14). When channelized deposits are not present at
the top of a deltaic succession, it is sometime assumed that these were ravined during
subsequent transgression (Bhattacharya and Willis 2001; Burger et al. 2002). In the
modern examples presented no significant incision has been observed, the scenario with
“incised” distributary channels at the top of a delta happens only in the case of sea level
fall or a sudden increase in discharge. In the case of still-stand periods or sea level rise,
while the delta progrades into the basin, a network of shallower terminal distributary
channels will be developed and no major incision occurs (Figure 2.14). In the case of
Achafalaya and Wax Lake deltas (Figures 2.4 and 2.6) there was no progradation of the
major distributary but rather progradation was associated with formation of smaller
terminal distributary channels. As a consequence of non-incision of distributary channels
into their own delta front deposits during sea level still stand or rise, the top limit of delta
front deposits in a vertical succession is represented by the base of incision of large
distributary channels, which do not represent delta front deposits, or by subaerial
exposure. The major distributaries might incise in the case of a major avulsion, like that
between major Mississippi lobes (i.e. St. Bernard, Teche, Lafourche) but in these cases
they incise within deposits of a previous lobe and not within their own deposits. The large
incised fluvial channel deposits, usually described as distributary channel deposits, more
likely represent a subsequent fluvial incision due to sea level fall or a major avulsion.
2.7
Conclusions
(1) Fluvial-dominated deltas have multiple, terminal distributary channels and there is no
such thing as one-scale of distributary channel. In shallow basins, fluvial-dominated
deltas might have hundreds of small terminal distributary channels. Terminal distributary
50
channels are: (i) shallow and narrow channelized features relative to the main distributary
channel and are intimately associated with mouth bars; (ii) have a large variability of
orientation relative to the trunk channel; (iii) have low topographic expression; (iv) are
rarely incised through previous deposits; and (v) sedimentary structures of terminal
distributary channel represents a combination of fluvial and basinal processes (Table 1).
(2) Formation and evolution of mouth bars and terminal distributary channels are part of
an autocyclic process. Mouth bars are initiated due to bedload deposition and are formed
from the coarsest deposits carried by the river. The mouth bar might migrate (grow)
downstream, upstream, or laterally. Upstream and lateral migration of the bar controls
evolution of terminal distributary channels.
(3) Terminal distributary channels are contained within delta front deposits. Fluvialdistributary channels incise previous delta deposits only in the case of sea level fall or
huge increase in discharge. Barring such an allocyclic control, the channel will avulse
laterally and will start building another delta lobe. This is a fundamentally autogenic
avulsion process, unrelated to the growth of alluvial ridges or other upstream
mechanisms.
(4) The number of terminal distributary channels increases for deltas with high sediment
discharge formed in basins with low accommodation space. The result of increasing the
number of terminal distributary channels is that sand bodies will have a lobate shape
because of decreasing distance among channels and fusion of proximal mouth bar
deposits. All deltas have multiple terminal distributary channels if development of these
is not inhibited by high basin energy such as waves or tides.
51
For ancient fluvial delta deposits modern analogs need to be chosen mainly from deltas
with multiple terminal distributary channels if the paleogeography suggests high
discharge rivers which infill shallow basins.
(5) In shallow water basins fluvial-dominated deltas will have multiple tens to hundreds
of terminal distributary channels that are coeval. The multitude of small channels that
will tend to distribute sediments radial will form an overall lobate geometry sand body
opposite to Mississippi elongate sand bodies but similar in shape to wave-dominated
deletas.
CHAPTER 3
REMOTE SENSING OF HYPERPYCNAL PLUMES: RED RIVER-LAKE
TEXOMA SYSTEM, TEXAS AND OKLAHOMA, USA
3.1
Abstract
We use satellite remote sensing to study sediment-laden waters of the saline upper Red
River flowing into Lake Texoma to distinguish hyperpycnal (bottom-flowing) from
hypopycnal (top flowing) or homopycnal plumes (total water column). Hyperpycnal
plumes can be distinguished using remote sensing because different electromagnetic
wavelengths penetrate to different water depths. Near-infrared imagery shows the turbid
front closest to the Red River delta, whereas images using deeper penetrating visiblewavelengths show the turbidity front farther away from the delta, indicating a sinking
(hyperpycnal) plume. The Red River/ Lake Texoma system may be a unique modern
system because abundant evaporite deposits in the watershed make Red River water
saltier than Lake Texoma and hyperpycnal plumes may be permanent. High total
dissolved solids combined with higher suspended sediment concentrations in the Red
River result in dense water that produces hyperpycnal flows upon entering Lake Texoma.
Existence of permanent hyperpycnal plumes in Lake Texoma enlarges the known
spectrum of lake hyperpycnal river plumes from rivers that have frequent hyperpycnal
plumes to rivers that have permanent hyperpycnal plumes. The presence of a modern
natural permanent hyperpycnal system raises the question of how common such system
52
53
were in the past. The resulting deposits are expected to be similar to those described from
short lived hyperpycnal flows.
3.2
Introduction
Suspended sediments are carried by rivers into lakes and seas by hypopycnal (buoyant),
homopycnal (neutrally buoyant), and hyperpycnal (negatively-buoyant or sinking)
plumes (Bates, 1953; Wright, 1977; Nemec, 1995; Mulder et al., 2003; Figure 3.1).
Figure 3.1. Possible types of plumes formed by river effluent into a basin. A- Hypopycnal
plume. Common for rivers that discharge into marine basins. B- Homopycnal plume.
Common for rivers that discharge into fresh water lakes. It is an instable instable
condition that will transform into hyper- or hypo-pycnal plume. C- Hyperpycnal plume.
Common for glacial rivers that discharge into fresh water lakes. Higher river density can
appear because of higher suspended sediments, temperature or dissolved salts into river
water.
54
Hypopycnal plumes, generated by low density fresh river water, are generally regarded as
the most common way that suspended sediments are dispersed into saline – thus denser seas (Bates, 1953; Wright and Coleman, 1974; Nemec, 1995). Hyperpycnal plumes are
relatively uncommon but can be generated when high density river water flows into a
lake with lower water density. Greater water density of inflowing water might be
induced by high suspended sediment concentration (SSC), high total dissolved solids
(TDS), or colder water, and will respectively be referred to as particle-laden, hypersaline,
or thermal hyperpycnal flow. Recent studies of marine deltas suggest that hyperpycnal
plumes may be much more common than previously thought and there is hence renewed
interest for documenting and understanding hyperpycnal plumes (Johnson et al., 2001;
Warrick and Milliman, 2003, Mulder et al. 2003).
Hyperpycnal flows are common where rivers discharge into lakes (Forel, 1892, Bell,
1942, Lambert et al., 1976; Weirich, 1984) but also sometimes form where rivers flow
into seas as well (Wright et al., 1988; Mulder and Syvitski, 1995; Johnson et al., 2001). In
freshwater lakes, rivers have to overcome a small density difference (considerable less
than 1g/ L) in order to form hyperpycnal flows (Forel, 1892, Mulder and Syvitski, 1995).
River-derived deposits represent a significant part of lake fills (Sly, 1978) and much of
this may be deposited hyperpycnally. Hyperpycnal plumes represent the most efficient
way for a river to deliver sediment into a basin because these transport higher
concentration of suspended sediments than hypopycnal plumes and sometimes farther
from the river mouth taking advantage of basin slopes (Bell, 1942, Kassem and Imran,
2001; Johnson et al., 2001).
55
Understanding the importance and frequency of hyperpycnal flows is important for
understanding sediment dispersal in basins near deltas. For some systems it has been
suggested that hyperpycnal plumes carry 98-99% of the total sediment load during floods
(Mertes and Warrick, 2001) and 25-60% of total annual sediment (Warrick and Milliman,
2003).
Direct observations of hyperpycnal flows are rare in marine settings, but have been long
documented in lakes (Forel, 1892, Bell, 1942, Weirich, 1984). Semi-permanent
hyperpycnal flows have been reported for glacial lakes. During melting periods, glacial
waters are denser than the lake because they are colder and have greater SSC (Thompson,
1975). In marine settings, hyperpycnal plumes are typically documented by salinity,
temperature and suspended sediment concentration (SSC) measurements associated with
flood-related discharges (Wright et al., 1988; Johnson et al., 2001), or based on discharge
records correlated with sediment load (Mulder and Syvitski, 1995). Other indicators of
lacustrine hyperpycnal flows are observation of density and velocity distribution in front
of river mouths and observation of resulting turbidite deposits (Lambert et al., 1976,
Sturm and Matter, 1978, Weirich, 1984).
For most rivers flowing into the ocean, Mulder and Syvitski (1995) suggest hyperpycnal
flow recurrence times of centuries to millennia, with only nine rivers worldwide able to
create annual hyperpycnal plumes; this is based on estimation of river SSC relative to
basin salinity. Nevertheless, sediments deposited by hyperpycnal plumes are inferred for
several ancient deltaic deposits (Mutti et al., 2000; Plink-Bjoerklund et al., 2001; Olariu
et al., in press). Recent studies on modern river plumes discharging into the ocean
(Warrick and Milliman, 2003; Johnson et al., 2001) and experimental results (Parsons et
56
al., 2001) suggest that hyperpycnal flows are more frequent than earlier studies
suggested, and may occur in rivers with relatively low SSC (~1g/L). In lakes, seasonal
hyperpycnal flows are commonly inferred (Forel, 1892, Bell, 1942, Chapron et al., 2002)
but so far (to our knowledge) no permanent hyperrpycnal plumes have been reported.
In this paper we describe a lacustrine system that has a permanent hyperpycnal river
plume, where the Red River feeds into Lake Texoma. The plume is generated by a
combination of mixed particle-laden flows and saline density flows. In order to better
estimate hyperpycnal plume frequency in marine and lacustrine settings, a simple method
is required. We test a novel remote sensing method for identifying hyperpycnal plumes
on Lake Texoma and we suggest that the technique should be applicable to the study of
hyperpycnal plumes in marine shelf settings.
3.3
Remote Sensing Applied to Differentiate Turbid River Plumes Geometries
Commonly, remote sensing data are correlated with in situ measurements of total
suspended sediment, light attenuation and/or chlorophyll content (Woodruff et al., 1999),
or used to quantify relationships between suspended sediment concentrations and
reflectance (Curran and Novo, 1988; Baban, 1995). This paper represents the first attempt
(to our knowledge) to use satellite remote sensing and the differing penetrations of visible
and near infrared (VNIR) imagery to study river plume geometry. Studies of river plumes
have linked reflectance or DN with SSC to estimate suspended sediment distribution
(Curran and Novo, 1988; Baban, 1995) but plume geometry was not addressed, although
Baban (1995) noted variations in turbidity on different Landsat bands. Deng and Li
(2003) quantified SSC variation with depth in the Changjiang Estuary but did notconsider
river plume geometry.
57
Water absorbs electromagnetic radiation, but different VNIR wavelengths penetrate to
different depths (Gordon and McCluney, 1975; Kowalik et al., 1994; Baban, 1995;
Jensen, 2000). Penetration depth also depends on the quantity and type of suspended
sediment. In extremely clear water, such as in the Sargasso Sea, the shortest VNIR
wavelenghts (blue) can penetrate more than 50 m (Gordon and McCluney, 1975, Jerlov,
1976). In the case of turbid water (> 1g/L), penetration is diminished because of
reflection and absorption by suspended sediment and organic matter and can be less than
1 meter, such as is found in estuaries (Gordon and McCluney, 1975; Jerlov, 1976).
Multispectral satellite imagery can be used to ‘sound’ water bodies using VNIR energy
because each band records energy received in narrow intervals across this part of the
electromagnetic spectrum. The digital number (DN) of each band corresponds to the
surface reflectance registered over a given wavelength interval and allows comparison of
the signal received by each band for the same area. For sediment-laden plumes in water
more than a few m deep, the reflectivity of each band increases with suspended sediment
concentration (SSC) (Jensen, 2000). The DN of each band represents the reflection of
VNIR by the summed suspended sediment from the water column penetrated. Combining
the two characteristics from above, (1) the different penetration of each band and (2) the
correspondence between SSC and the reflectance (or DN value) we can produce images
that represent the location of the upper surface of turbid water at different depths, if this
is sufficiently shallow.
Our hypothesis is that differential penetration of visible bands (Figure 3.2A) will result in
a diagnostic pattern that can be used to map the turbid upper surface in a dataset which
can in turn be used to distinguish two plume-type patterns (Figure 3.2B). The turbid
58
Figure 3.2. Theoretical patterns of remote sensing images for different types of river
plumes. A- Cross sections through plume area with relative water depth penetration for
different bands of ASTER (band 3 - 0.76-0.86 ȝm, band 2 - 0.63-0.69 ȝm, band 1 - 0.520.6 ȝm). B- Map view pattern for different ASTER bands (wavelengths) and for each
plume type. Because VNIR penetrates clear water to different depths, different band
images represent slices at different depths. The turbid river water edge appears at
different locations in the case of a hyperpycnal plume because of the different penetration
of the bands, whilst for homopycnal and hypopycnal plumes the edge turbid water will
appear approximately in the same location.
upper surface of the plume appears at different locations in the case of hyperpycnal
plumes because the interface plunges basinward. For homopycnal and hypopycnal
plumes the turbid plume will appear at approximately the same depth in all wavelengths.
In this study, we used different bands of the same ASTER (Advanced Spaceborne
Emission and Radiometer Reflection; http://asterweb.jpl.nasa.gov/) image to evaluate the
geometry of the turbid Red River plume as it feeds into Lake Texoma.
3.4
Regional setting
Lake Texoma is located on the border between Texas and Oklahoma in the south-central
USA (Figure 3.3). After impoundment in 1944, the Red and Washita rivers formed a long
and narrow lake (Figure 3.3). The Red River contributes two thirds of Lake Texoma
water with an average discharge into the lake of 91 m3/s, whereas the Washita River
59
flows at an average discharge of 48 m3/s (USGS Surface-Water;
http://waterdata.usgs.gov/nwis/sw).
Figure 3.3. Study area location. A- Red River and Washita drainage basins. Area with
Permian evaporites is taken from geologic maps of Texas and Oklahoma. B- Lake
Texoma. Dark grey shows growth of the Red River delta (1945-2003).
The Red River flows eastward from its headwaters in northern New Mexico, West Texas
and Oklahoma to the Mississippi. It is over 900 km long upstream of Lake Texoma, with
a 79,700 km2 drainage basin (USGS Surface-Water; http://waterdata.usgs.gov/nwis/sw).
A large part of the drainage basin exposes easily dissolved Permian evaporites (Figure
3.3). Interaction of groundwater and river water with these evaporites results in Red
60
River waters being very saline (up to 32.4 g/L TDS) at USGS 07297910 gauge station
(Prairie Dog Town Fork Red River near Wayside, TX; http://waterdata.usgs.gov/nwis/rt).
The high TDS has restricted human development along the Red River and results in water
with a higher than normal density. The study of the Red River Delta and the associated
plume in Lake Texoma represents a large controlled experiment, because the most
important features of the system: basin topography, river discharge and lake level are
known over the 60+ year life of the system.
The smaller Washita River has fresher water than the Red River and also fresher than the
lake. The weighted TDS values to discharge shows that Washita river has 382 mg/L at
USGS Dickson station, Red River has 1045 mg/L at Gainesville gauge station while the
Lake Texoma water at Dennison Dam has 887 mg/L (Figs. 7 A and C). Also, the lake
water is less salty because lake salinity is heavily weighted to periods of peak river
influx, when salinity of river water is low. The considerably less salty (< 1g/L TDS)
water of Lake Texoma results from a mix of both river discharges over a period of about
8 months. This is the time over which the summed average discharge of the Red and
Washita rivers replaces the entire lake water.
3.5
Methods
In this study we incorporated remote sensing images, historical records, in situ
measurements and lake water samples. There are several satellites that collect VNIR
imagery, have good temporal resolution and have sufficient spatial resolution for imaging
river plumes (Landsat, ASTER, SPOT, MODIS). In this project, we used ASTER data
because its spectral ranges are appropriate for turbid water studies and because it has
excellent spatial resolution (15 m). In this project we have used digital numbers (DN) in
61
imagery analysis because (1) transformation of DN into reflectance does not change the
overall imagery pattern, and (2) ASTER data available for the area have not been
processed for correct water–leaving reflectance values. Density slicing was applied to
ASTER visible and near infrared bands: band 1 (0.52-0.60 μm, corresponding to visible
green), band 2 (0.63-0.69 μm, visible red) and band 3 (0.76-0.86 μm, very near infrared).
In general, the depth of penetration into water and thus potential imaging depth should
increase in the order, band 1>band 2>band 3. The density slice-intervals have been
selected based on the characteristic DN values of turbid river water and clear lake water.
The DN values between characteristic river and lake values have been assigned as
intermediate (Figure 3.4). The characteristic river and lake water DN values were
measured in the same area for all bands analyzed (Figure 3.4). A color code was used for
characteristic values of DN to differentiate turbid river from relatively clear lake water
(Figure 3.4). Dark blue represents relatively clear water, green represents turbid water
and blue-green represents water with intermediate turbidity.
In order to be able to distinguish between plume suspended sediment and bottom
reflections (1) multi-temporal satellite images were analyzed with the river plume under
different forcing conditions (Figure 3.5) and (2) a bathymetric survey was conducted
using Knudsen Kel-320 B/P dual frequency (28/200 kHz) EchoSounder and a Trimble
Pathfinder Pro-XRS GPS on October 12th 2002.
Physical properties of river water (TDS and SSC) measured at the Gainesville gauge
station (USGS Surface-Water; http://waterdata.usgs.gov/nwis/sw) were compared with
lake water measurements at Denison Dam gage station (Figure 3.3) to evaluate historical
river density variations relative to the lake. TDS was measured as residue after 180°C
62
evaporation. River water suspended-sediment grain-size measurements were taken from
the USGS data base. The Gainesville gauge station is approximately 30 km upstream of
Lake Texoma, resulting in delays of 1-2 days before arrival of this water at the lake.
Figure 3.4. Methodology to establish different type of water on remote sensing images.
A- Location of the areas selected on the false color (ASTER 321) images from September
20th 2000 and September 26th , 2002. B- Distribution of the digital number (DN) values
for lake and river water for the images from figure 3A. For lake and river water it was
established a threshold value of DN, and the values between has been mapped as
intermediate water. On the 2002 image in Band 3 a bimodal distribution can be observed,
this appears because the image has a vertical banding in this particular ASTER 1A
unprocessed data.
63
Physical parameters were not measured continuously at Gainesville station, so
correlations between TDS, SSC and river discharge could only be established for the
periods 1967-1983 and 1966-1986, during which time TDS and SSC respectively were
recorded. Discharge has been measured at Gainesville continuously since 1936. These
correlations with discharge are sufficiently robust to allow TDS and SSC to be
extrapolated for the life of the lake.
To better estimate river plume geometry, water samples were collected on September 28th
2003 from different depths in front of the delta (Figure 3.3) and analyzed for SSC. Water
samples were collected in 0.5 liter bottles, filtered using 0.45 μm filter paper, dried and
weighed. Temperature, TDS, specific conductivity and pH of the plume water were also
measured using a Quanta Hydrolab Multiprobe.
3.6
Results
ASTER imagery collected on September 20th, 2000, June 12th, 2001, September 26th,
2002 and August 30th, 2004 over Lake Texoma show a pattern where the Red River
turbidity edge in band 3 is closest to the distributary channel mouth whereas the turbidity
edge appears further from the distributary channel mouth on bands 2 and 1 (Figure 3.5).
This pattern matches our theoretical model (Figure 3.2B) and is interpreted to indicate a
hyperpycnal plume. Although the discharge at Gainesville during the image acquisition
was high (200 m3/s on June 2001) the same pattern was also observed on September 20th
2000 at a discharge of just 3.5 m3/s, September 26th, 2002 at a discharge of just 4 m3/s
and August 30th, 2004 at 20 m3/s discharge (Figure 3.5). Comparison of the bathymetry
map in front of the channel (Figure 3.6) with the turbidity images indicates shallow water
64
in the area where high reflection (turbid-river water) has been distinguished on images at
different times. The shallow area corresponds to the area over the active mouth bar that
has high SSC. However, the plume has different locations on images collected at
Figure 3.5. Time series of ASTER satellite images of Red River plume on June 3rd 2001.
In the columns are data from September 20th, 2000, June 12th, 2001, September 26th, 2002
and August 30th, 2004. Images collected on different bands; A- Band 3 (0.76-0.86 μm).
B- Band 2 (0.63-0.69 μm). C- Band 1 (0.52-0.6 μm). For each band, density slices were
built with distinct colors for river, lake and mixed water. Grey represents land area. BRed River discharge prior and during image acquisition. Discharge was measured 30 km
upstream of the mouth therefore an average one day delay was considered. Note that
discharge is on a logarithmic scale. C- Lake level variations prior and during images
acquisition.
65
different times under different discharge regimes, indicating that the pattern observed on
images is given by suspended sediments rather than bottom or re-suspended sediment
reflections. For comparison of bathymetry with remote sensing imagery we compare the
DN variation along a dip oriented profile in front of the Red River channel (Figure 3.6).
Penetration depth for each band depends on SSC, but the order remains the same, with
the order Band3-Band2-Band1 from shallowest to deepest. Comparing bathymetric
Figure 3.6. Lake bathymetry in front of the Red River Delta based on data collected on
October 12th, 2002. Note that in front of the main river channel there is a shallow water
platform.
profile with DN profiles indicates that the river plume plunges in the relatively shallow
area of 2 m water depth (Figure 3.7). On the image collected in 2002 when the lake level
was 1m lower than the conservation pool (Figure 3.5C) and the discharge was also small
66
Figure 3.7. Digital number (DN) variation along a dip-oriented profile. A- Location of
profile on ASTER321 images collected at different times. B- DN profiles with threshold
levels (horizontal lines) used to differentiate turbid river water (light green) from clear
lake water (dark green). Band 3 of the 2002 and 2004 data appear sawlike because it is
unprocessed ASTER 1A level. C- Bathymetry along the same profile. For location see
Figure 3.5. Note that the according to DN profiles, the river water plunges in shallow
water areas.
67
(4 m3/s) it might be inferred that the transition from turbid to clear water overlies the
transition from mouth bar to deeper water, and it might be possible that the pattern is
partially given by lake bottom reflections. In fact it is almost certain that the 2000 image
shows bottom reflections, because (1) the lake level was 1.7 m lower than the
conservation level which made the water depth over the mouth bar area less than 0.5 m,
(2) SSC was low facilitating deeper penetration, and (3) high reflectivity (DN value)
appears over the mouth bar in Band 2 (Figure 3.7B), which corresponds to visible red.
The higher reflectance in the ASTER red band over the mouth bar might indicate a strong
bottom reflection because the bottom of the Red River is red.
However, DN profiles show different locations of the turbidity front for different bands
and rule out the possibility that bottom reflections affect all the acquired images under
different lake/ river conditions (Figure 3.7). Along the lake shore beside the channel
mouth delta, images vary less variable discharge and here the reflection pattern can be
created by lake bottom given the relatively shallow water and lake level variations
(Figure 3.6).
Comparison of TDS data for Gainesville and Denison Dam stations indicates that lake
TDS and SSC is rather constant (Figures 3.8A and B), whereas large variations in Red
River TDS and SSC are observed. River variations show that TDS decreases with
increasing river discharge, whereas SSC values increase (Figures 3.8C and D). These
TDS-SSC decrease relationship reflect control by rainfall, whereby large amounts of
precipitation dilute highly saline groundwater base–flow, whereas, the consequent high
runoff results in high sediment loads. In general Red River water has higher average TDS
than Lake Texoma (Figure 3.8A) and also has higher SSC than lake water (Figure 3.8B),
68
Figure 3.8. Total dissolved solids (TDS) and suspended sediment concentration (SSC) of
the Red River (at Gainesville) and Lake Texoma (at Denison Dam). A- Comparison
between TDS of Red River and Lake Texoma. TDS values for Lake Texoma are
commonly around 1 g/L whereas Red River TDS vary with discharge and can be up to 7
g/L. B- Comparison between SSC of Red River and Lake Texoma. SSC for Lake Texoma
are < 1 g/L while Red River SSC varies with discharge and can be > 20 g/L. C- TDS
variation with discharge (Q) in Red River water. D- SSC variation with discharge in Red
River water. E- The density differences (ǻȡ) between lake and river water (1945-2005).
The density difference between lake and river water is negative. Lake density was
calculated assuming the density of fresh water at 20° C with the values of 0.5 g/L SSC
and 1.3 g/L TDS. River water density was calculated assuming 25° C with SSC and TDS
calculated as a function of discharge according to regression functions (Figures. 3.8C and
D). Note that the river water is always denser than lake water even considering the
maximum values measured for TDS, SSC and permanently colder (by ~5°C) lake water.
69
which suggests that river water is generally if not invariably denser than the lake. At high
discharges, high SSC creates denser particle-laden hyperpycnal flows, whereas at low
discharges, the high TDS concentrations increase density and generate hypersaline
hyperpycnal flows with low particle concentration. This yields a permanent regime of
hyperpycnal Red River plumes (Figure 3.8E) that nevertheless has a dual character.
The water samples and physical measurements collected on September 28th, 2003
(discharge of 7 m3/s) and June 19th, 2004 (discharge of about 60 m3/s) indicate an overall
decrease in SSC away from the river but or increase towards the bottom, as expected for
a hyperpycnal plume (Figure 3.9). Plume water physical measurements (TDS, specific
conductivity, temperature dissolved oxygen and pH; Figure 3.9) indicate that higher
values of SSC are not merely the result of sediment resuspension but are the result of
river water continuing to flow below lake water. Different patterns of river/ lake water
mixing that appear on Figure 3.9 are due to different diffusion coefficients of measured
physical properties (SSC, TDS, specific conductivity, temperature, dissolved oxygen) and
the relative difference for lake and river water for each. Figure 3.9D represents an
obliquely-oriented profile in front of the river mouth and indicates distinct river water
that has higher SSC, TDS, specific conductivity and temperature, which plunges below
lake water. Meanwhile, relatively high dissolved oxygen (DO) and pH do not indicate an
change of lake isoline pattern. Close to the river mouth, SSC values do not vary much
with depth, but farther lakeward the bottom 1 m water layer has higher SSC (Figure 3.9).
A distinct turbid water layer at the bottom of the lake can be followed from the river
mouth on profiles measured in front of the river (Figures 3.9C, D, G and H). These rules
out the possibility that high suspended sediment concentrations observed in shallow
70
71
Figure 3.9. Physical measurements in Lake Texoma in front of the Red River. ALocation of measurements stations and profiles plotted in Figs. 8A to H. B- River
discharge prior and during September 28th 2003 sampling. C- Physical measurements
variations along a side-mouth profile on September 28th, 2003 D- Physical measurement
variations along an oblique profile in front of the main channel on September 28th, 2003.
E- Physical measurements variations along a cross-lake profile on September 28th, 2003.
F- River discharge prior to and during June 12th, 2004. G- Physical measurements
variations along an oblique profile in front of the main channel on June 12th, 2004. HPhysical measurements variations along a side-mouth profile on June 12th, 2004.
72
water are due to bottom resuspension except by hyperpycnal flow. A profile on the
margin of the river mouth indicates a more homogenous pattern of lake water body with
slightly stratification of DO and pH (Figure 3.9E).
Our interpretation of a hyperpycnal plume in Lake Texoma is supported by remote
sensing imagery and is consistent with inferred density of river and lake water from
USGS gage station data. Analysis of SSC data and physical measurements collected from
the river water plume also indicates a distribution of river-derived suspended sediment
that fits the hyperpycnal interpretation.
3.7
Discussion
The methodology described in the present paper shows that river plume geometry can be
studied, based on mapping the location of turbidity plume front on different bands of
satellite imagery. Because remote sensing data generally cover large areas with good
temporal resolution, distinguishing river plume geometry with our method should allow
estimation of modern hyperpycnal plumes frequency in lakes and marine settings.
However, the method needs to be used cautiously with multi-temporal images.
Penetration depth depends on the SSC concentration and because of this the model shown
in Figure 3.2 will change with discharge (Figure 3.10). For the same system, SSC in the
mixing zone water column increases as discharge increases, allowing only in the shallow
parts of plume geometry to be observed during high discharge periods. Nevertheless,
during high discharge episodes, the general order of penetration depth for each band
should be preserved (Figure 3.10).
The existence of hyperpycnal river plumes in Lake Texoma suggests that natural rivers
flowing into lakes can result in hydraulic regimes that are characterized by long-lived, if
73
not permanent hyperpycnal plumes. Recognizing permanent hyperpycnal river plumes
also raises the questions of how commonly these formed in the past, if such systems are
possible in marine settings, and whether or not it is possible to distinguish such deposits
Figure 3.10. Relative penetration of remote sensing bands into turbid river water and lake
clear water. A- Profile during low suspended sediment concentration. B- Profile during
high suspended sediment concentration. Note that relative penetration depth is lower in
the water river than in the lake and also during high discharge (higer suspended sediment
concentration) penetration depth is lower than during low discharge (lower suspended
sediment concentration).
in the rock record. Normally, standing bodies of water are at least as salty as the rivers
that flow into them, but the Red River-Lake Texoma system presents a case where the
lake is fresher than one of the rivers that flow into it. Certainly, systems where rivers
have high TDS combined with more SSC and rivers that drain watersheds with salt-rch
evaporite deposits could increase the hyperpycnal plume frequency. A possible example
of the latter might have existed on the rim of the Delaware Basin during Permian time
(Harms, 1974) may have resulted in hyperpycnal plumes. Most probably the combination
74
of elevated TDS and SSC to create hyperpycnal plumes will result in a hyperpycnal
plume with dual character, (1) during floods with high SSC when considerable sediment
volume is delivered into the basin and (2) during low discharge with low SSC but high
TDS. These two modes should affect sedimentation differently. Sediments deposited in
association with SSC-driven hyperpycnal flows should reflect a higher sedimentation
rate. .In the case of TDS-driven hyperpycnal flows, sediments are still deposited under
the plume and erosion is less probable, given the relatively low shear stresses associated
with low discharge.
The presence of permanent hyperpycnal plumes also raises questions about how different
these deposits are from occasional flood-generated hyperpycnal deposits (Mulder et al.,
2003). We expect that in continuous hyperpycnal flows the waxing and waning beds
characteristic of flood hyperpycnal deposits will have transitional contacts that will
depend on the river hydrograph. Graphs of discharge vs. SSC during floods can have
different shapes (Mulder and Syvitski, 1995) and because of this, these cap the coarser
high discharge deposits and will form sequences similar to those described by Mulder et
al. (2003), despite the fact that at low discharge hyperpycnal plumes will deliver low
quantities of sediments. Red River suspended sediments (Figure 3.11) shows
considerable quantities of silt size particles but during high discharges up to 60% can be
sand. The coarse sediments (sands) will be deposited near the river mouth but silts and
clays will be carried and deposited farther into the lake even during low discharge.
Because the flow is permanently hyperpycnal, the deposits will result in a stacked normal
and inverse successions, with coarse beds formed during high river discharge. During low
75
river discharge only clay will be deposited. A challenge will be to distinguish between
hyperpycnal and hypopycnal mud within a succession because both cap coarser deposits.
Figure 3.11. Suspended sediment grainsize distribution at different discharges measured
at Gainesville USGS gauge station. Red distribution curves represent measurements
during a single flood, small dashes – before peak discharge, large dashes during peak
discharge and continuous red line after peak discharge.
3.8
Summary
1. Different wavelengths of VNIR penetrate different water depths. Comparison of
ASTER bands allows the plume turbidity edge to be located and this can be used to infer
plume type. In the case of hyperpycnal plumes, the turbidity edge will appear at
progressively basinward positions in deeper penetrating bands, whereas homopycnal or
hypopycnal plumes show no change in the position of the turbidity edge for different
wavelengths.
2. Based on remote sensing data, historical measurements and lake water samples it is
concluded that the Red River plume is hyperpycnal where it flows into Lake Texoma.
76
This is a peculiar situation reflecting the unusually high density of Red River water which
drains evaporites in its drainage basin.
3. Measurements of SSC and TDS at different Red River discharges show that these vary
inversely and predictably, with high TDS at low discharge and high SSC at high
discharge. Field measurements of plume water collected during low and medium
discharge in the delta front area confirm that elevated turbidity near the lake bottom is
river derived and the presence of a hyperpycnal plume.
4. The presence of permanent hyperpycnal plumes in the Red River-Texoma system
suggests that natural permanent hyperpycnal flows can exist. High TDS in rivers that
drain extensive evaporites could increase the frequency of hyperpycnal flows in ancient
marine or lacustrine basins. The resulting deposits will not be different from successions
formed from flood hyperpycnal deposits.
CHAPTER 4
INTERPLAY BETWEEN RIVER DISCHARGE AND LAKE BOTTOM
TOPOGRAPHY IN A HYPERPYCNAL LACUSTRINE DELTA, RED RIVER,
LAKE TEXOMA, TEXAS/ OKLAHOMA, USA.
4.1
Abstract
This paper studies the influence of basin topography with progradation direction and
changes in delta morphology of the hyperpycnal Red River Delta. The Red River water
creates a hyperpycnal plume, which is the main process that builds the delta. Because the
river plume is hyperpycnal, topography has a strong influence on deposition. Higher river
water density is created by higher total dissolved solid (TDS) values in Red River water
than Lake Texoma into which it builds. In addition, the density contrast is increased by
high suspended sediment concentration (SSC) during high discharge events.
The presence of steep basin lateral slopes deflects hyperpycnal river plumes and
subsequently changes overall delta progradation direction before the delta is able to reach
the opposite bank. This study of multi-temporal aerial and satellite images indicates that
the hyperpycnal delta follows the steepest gradients, which correspond to the pre-dam
river talweg, bypassing shallow parts of the lake. A numerical model for the hyperpycnal
plume trajectory indicates plume deflection during low or high discharge events, toward
the deepest part of the basin. The magnitude of plume deflection is a function of river
discharge and basin-side gradients. Plume deflection can vary between 10 and 80 degrees
77
78
from the channel axis toward the old river talweg. The high deflection appears in the case
of maximum basin side-gradients of 12.8 degrees and in conditions of low river
discharge. During low discharge periods the Red River Delta had a lobate shape with
multiple terminal distributary channels while during high discharge periods the Red River
Delta had an elongate shape with a single large distributary channel.
4.2
Introduction
This paper represents a study of a hyperpycnal lacustrine delta that links the delta
progradation direction with the interplay between river discharge and lake topography
and investigates how delta morphology changes with river discharge.
Basin topographic influence on clastic deposits is widely recognized in deep water
turbidite deposits (e.g. Lomas and Joseph, 2004), but studies that demonstrate
topographic control on deltas are sparse. The topographic control on turbidite deposits is
obvious, since the turbidity currents flow along the basin bottom. For deltas, topographic
influence is less important in cases where river effluent has a hypopycnal character (i.e.
buoyed above basin water; Bates 1953, Wright and Coleman, 1974, Nemec, 1995).
Hyperpycnal plumes (i.e. where the river effluent sinks below the basin water) may be as
frequent as seasonal as in the case of the Huanghe River (Prior et al., 1986; Mulder and
Syvitski, 1995). In spite of being relatively rare events in some modern rivers that feed
marine basins (Mulder and Syvitski, 1995), during hyperpycnal flow events, large
quantities of sediments are delivered to the basin compared with periods of normal
hypopycnal flows (Warrick and Milliman, 2003). Bay-head, fjord-deltas and glaciolacustrine deltas are environments where conditions for hyperpycnal flows are commonly
encountered because of high sediment load and lower temperature of river waters.
79
Topographic influence on delta deposits in fjord environments has been suggested by
previous studies (Gustavson, 1975, Gustavson et al., 1975, Syvitski and Farrow, 1983,
Hansen, 2004) but there is a lack of detailed reports that link delta progradation direction
and underlying topography.
Understanding influence of topography on sedimentary deposits, especially in deltas that
have high sedimentation rates, is important for a successful interpretation of depositional
remnants (Martinsen, 2003). Delta depocenter migration and major distributary avulsions
are other important aspects that are insufficiently addressed and may be aspects where
understanding basin topographic controls on delta progradation might bring a significant
contribution.
In this paper, an analysis of the hyperpycnal Red River lacustrine delta will be made.
Firstly, it will be shown that data collected indicate a permanent hyperpycnal flow of the
Red River into the Lake Texoma (Olariu et al., submitted). Secondly, the morphology of
the delta plain and changes in progradation direction through time will be discussed.
Thirdly, the magnitude of lake topography (basin-floor gradients) on hyperpycnal flows
will be analyzed using a numerical model based on velocity evolution of the river plume.
The study of the Red River Delta formed in Lake Texoma represents a large natural
flume and is especially useful because the main inputs of the system: basin topography,
river discharge and lake level are known. Despite the fact that Lake Texoma represents
an engineering construction, the Red River has a natural regime with minimum
anthropogenic intervention upstream of Lake Texoma.
The main contributions of the paper will be to: (1) quantify the influence of basin
bathymetry (pre-delta topography) on delta progradation direction; (2) discuss the
80
changes of delta plain morphology with river discharge; and, (3) evaluate delta
progradation rates under different discharge.
4.3
General settings
Lake Texoma is located on the border between Texas and Oklahoma in the south-central
USA (Figure 4.1A). The Red River originates from Tierra Blanca Creek, New Mexico
and discharges into the Mississippi River. Lake Texoma is a large artificial dam-lake that
Figure 4.1. Study area location. A- Red River and Washita drainage basins. Area with
Permian evaporites is taken from geologic maps of Texas and Oklahoma. B- Lake
Texoma. Dark grey shows growth of the Red River delta (1945-2003).
81
was built for flood prevention, river flow control and hydroelectric power. After dam
impoundment in 1944, the Red River and Washita River water flooded the previous river
valleys forming a long and narrow lake (Figure 4.1B). The lake has an area of 588 km2, a
maximum length of approximate 70 km (along the talweg), and a maximum depth of 34
m near Denison Dam, with an average water volume of 3.29x109 m3 (Dennison Dam,
http://www.swt.usace.army.mil/projects/pertdata/laketexoma/laketexoma.htm; Figure
4.1B). The lake has two main tributaries, the Red River and Washita River. There are
several other small creeks, although these do not have major hydrographic significance.
The Red River contributes two thirds of Lake Texoma water with an average flow into
the lake of 91 m3/s, whereas the Washita River flows at an average rate of 48 m3/s. The
Red River flows eastward from its headwaters in northern New Mexico to the
Mississippi. It is over 900 km long upstream of Lake Texoma, with a 79,700 km2
drainage basin (USGS Surface-Water; http://waterdata.usgs.gov/nwis/sw). A large part of
the drainage basin exposes easily dissolved Permian evaporites (Figure 4.1A). Interaction
of groundwater and river water with these evaporites results in Red River waters being
very saline. The high total dissolved solids (TDS) has restricted human development
along the Red River and resulted in water with a higher than normal density. The study of
the Red River Delta and the plume it forms in Lake Texoma represents a 60 year long
experiment in which historical data of the system has been recorded.
4.4
Methodology and Data Used
Different types of data have been used to study and quantify Red River Delta
progradation and river plume dynamics, including aerial and satellite images, river
discharge measurements, pre-dam topographic maps, bathymetric surveys, physical
82
measurements, and water samples in front of the delta. Data used in this paper has been
collected at various times since Lake Texoma was built in 1944 (Figure 4.2). The data
collected were used to study (1) the nature of the Red River plume, (2) areal and “linear”
delta progradataion, (3) delta morphology changes, and (4) magnitude of plume
deflection due to lake topography.
Figure 4.2. Data type used in this study and the time intervals when were colected (thick
black line). The smallest black line represent a single day. For the exact dates see the
text.
4.4.1
Aerial Photos and Satellite Images
Bands 1, 2 and 3 of ASTER satellite images have been previously used to evaluate the
turbidity of the river plume in front of the Red River delta (Olariu et al., submitted). Each
band has a different wavelength and energy and penetrates water at different depths
(Gordon and McCluney, 1975; Kowalik et al., 1994; Baban, 1995). Based on this
principle, different bands of the same data set were compared to evaluate position of the
turbidity front at different depths in the subaqueous delta front area. The analysis of
imagery using the different penetration principle allows the differentiation of hyperpycnal
flows from homopycnal and hypopycnal flows.
83
Multi-temporal aerial photos and satellite images were used mainly to study delta
progradation (Table 4.1, Figure.4. 2). The images were selected at a resolution that allows
observation of delta progradation as well as morphological changes of the subaerial delta.
Morphological observations were focused on (1) delta shape, (2) location, number and
size of distributary channels, and (3) presence of active distributary channels relative to
the preexistent drainage network. Successive images have been compared in terms of
delta plain area and “linear” progradation rate (i.e. the rate at which the river mouth
advances into the lake), as well as evaluating the morphologic changes that occur
between images. The area of the subaerial delta (delta plain) has been adjusted for each
image according to lake level on the day that image was captured. Lake levels were
registered daily at Denison Dam by the US Army Corps of Engineers (http://www.swtwc.usace.army.mil/DENI.lakepage.html). For morphologic observationsof the delta,
different bands were used to enhance images of the delta/ water contact: band 4 for 1984
and 2001 satellite images and band 5 for 1991 and 2000 Landsat data were used to
enhance water/ land contrast. Due to high absorption of the electromagnetic spectra, NIR
(near infra-red) and SWIR (short wave infra-red) bands can distinguish water from land.
4.4.2
Historical Measurements
River discharge also has been considered. River discharge measurements at the last gauge
station (Gainesville) on the Red River upstream of Lake Texoma, has been taken from
the USGS database. Discharge measurements are available starting from 1934 to the
present and cover the entire period of delta evolution (Figure 4.2). The gauge station is
approximately 30 km upstream and because of this, a delay of approximately 1-2 day is
expected between Gainesville station and the Red River Delta. The 1-2 day delay time is
84
Table 4.1. Red River Delta characteristics on successive aerial and satellite images.
Date of
image
acquisition
Lake elevation
(m)
Abs
olut
e
Relative
to the
conserva
tion pool
(188.1
m)
- 4.3
River
dischar
ge
during
image
acquisit
ion
(m3/s)
River discharge
since last image
acquisition
Avera
Peak
ge
discharge
(m3/s) (m3/s)
Delta
plain
area
(m2)
Delta
morphology
3.28
3 peaks
over 1000
no
2 over 1000
Delta
progradation
Obser
vation
s
(Imag
e type)
Area
(km2)
Lin
ear
(m)
Subaqueous delta
-
-
BW
aerial
photo
no
Subaqueous delta
-
-
Lobate with
multiple terminal
distributary
channels
Lobate with
multiple terminal
distributary
channels
Lobate with a
single large
distributary
-
BW
aerial
photo
BW
aerial
photo
8.22
(since
Begin
ning)
1.68
~60
00
BW
aerial
photo
727
-1.84
810
2.77
553
BW
aerial
photo
Color
aerial
photo
Lands
at 321
0.06
333
0
Lands
at 321
-0.18
106
0.3
0.06
682
1.56
111.
3
Color
aerial
photo
Lands
at 321
Lands
at 321
-3.32
570
4.31
42.6
-0.33
71.3
Nov 21st
1952
183.
8
Oct 20th
1955
187.
5
-0.6
112.1
86.1
since
01/01/
1945
73.7
Feb 27th
1976
186
- 2.1
12.77
65.4
3 over 2000
9 over 1000
-
Nov 22nd
1976
186.
4
- 1.7
15.51
48.7
No major
peaks
8.227
Sep 21st
1981
186.
1
-2
10.22
54.9
4 over 1000
11.26
March 7th
1982
187.
3
- 0.8
18.57
115.7
No major
peaks
6.65
August
15th 1984
186.
1
-2
9.8
107.7
10.57
Aug 19th
1991
187.
6
- 0.5
28.1
158.9
1 over 2500
More over
1000
1 over 6500
1 over 3000
More over
1500
Feb 17th
1995
187.
1
-1
20.44
134.9
2 over 1500
1 over 3000
12.3
July 2nd
1997
Aug 19th
2000
188.
3
187.
2
0.2
98.3
185.8
16.28
- 0.9
5.6
71.5
1 over 4000
1 over 2500
1 over 3000
June 3rd
2001
September
20th 2002
188.
1
187.
3
0
84
63.8
2 over 1000
15.04
-0.8
5.35
43.53
1 over 500
15.44
October
17th 2004
187.
1
-1
52.3
34.97
1 over 500
14.03
11.11
15.16
Delta has more
distributary
channels
Elongate with a
single large
distributary. A
secondary
distributary also
active.
Elongate with a
single distributary
Elongate with a
single distributary
Elongate with a
main distributary
and a secondary
one
Elongate, a single
distributary
Elongate with a
main distributary
and a secondary
one
Elongate with a
main distributary
and a secondary
one
Aster
321
Aster
321
Aster
321
85
important for considering turbidity observations on satellite images, but the time delay is
not critical for determining overall delta progradation through time or deltaic facies
architecture. A series of physical parameters have been registered at Gainesville gauge
station (Figure 4.1), among which are total dissolved solids (TDS) and suspended
sediment concentrations (SSC). The physical parameters were not been registered
continuously but only for short periods, TDS in 1965, 1977-1986 and 1995, and SSC
from 1975 to 1987 (Fig. 2). The values were correlated with river discharge for the
periods that have been recorded. Based on correlation functions, the values of TDS and
SSC with discharge for the entire period of delta evolution based on daily river discharge
records were extrapolated.
A USGS topographic map of the Lake Texoma area, published before the impoundment
of the lake (USGS Topographic map – Denison Quadrangle, 1901), has been digitized
and used to extract initial (pre-delta) water depth and estimations of Red River valley
slopes that represent the initial lake topography. Typical basin slopes were used for
numerical modeling to qualify the magnitude of plume deflection.
4.4.3
Field Data Collection
To establish the type of river plume (hypopycnal vs. hyperpycnal) SSC measurements in
the river plume were determined from water samples collected in 0.5 liter bottles, filtered
using 0.62 ȝm filters and weighed. Samples were collected at different river discharges
and at different locations and depths. Also, physical properties (temperature, specific
conductivity, TDS, pH) of river plume water were measured at different locations using a
Quanta Hydrolab Multiprobe. The measurements were reported by Olariu et al.
(submitted).
86
In order to calculate modern delta front slopes at different locations and to observe
morphology of the delta front and prodelta, a detailed bathymetric survey using a
KNUDSEN KEL-320 B/P ECHO SOUNDER dual frequency (28/200 kHz) was made in
2002. The modern delta front slope data was used to estimate the shoreline variation
during lake level changes and to correct the calculations for delta plain area.
4.4.4
Numerical Model
For estimation of plume deflection due to basin topography, a simple physical model to
calculate the trajectory of a moving hyperpycnal plume on an inclined plan has been
used. For the plume trajectory computation only the axis of the plume that flows on an
inclined plane right from the mouth has been considered (Figure 4.3). To estimate the
plume direction at different locations, plume velocity evolution has been evaluated both
along channel and normal to the channel axis, in the x and y directions respectively. The
velocity along the x and y axis is given by the equations
vx = voe
§ x·
−K¨ ¸
©h¹
(1)
where K is friction coefficient, K =
g
C2
and
v y = C h sin α (2)
equation (1) is valid for an effluent when only the friction at the bottom is considered
where ux is the average plume velocity at some distance x, uo is the initial plume velocity
at the river mouth, K is a friction coefficient that is a function of Chezy coefficient (C), x
is the distance from the mouth and h is the average plume thickness. Chezy coefficient
values were calculated as C=1.49 Rh1/6/n (McCuen, 1998, p.138), where Rh is the
87
Figure 4.3. Deflection of a hyperpycnal plume flowing on an inclined (lateral) plane. The
plume has initial velocity vo in the x direction and, after a time flowing on an incllined
slope will have velocity vx and vy after x and respective y directions and the plume
velocity will be deflected with angle ȕ See text for the equations that control velocities
after x and y directions.
hydraulic radius and n is Manning’s roughness coefficient. Equation (1) has been given
by Wright and Coleman (1974) for frictional plumes without considering friction with the
ambient water and diffusion processes. Equation (2) represents the velocity of a steady
uniform flow down an inclined plane with an angle Į (Allen, 1997).
From equations (1) and (2) deflection (deviation from the channel axis) at a given
distance can be estimated using the following equation:
gx
1
2
y = C h sin α xe hC
v0
(3)
Initial velocity used in the numerical model was approximated based on channel
dimensions and historical river discharge from United States Geological Survey (USGS)
database.
For approximation of delta progradation rates as a function of discharge, the volume of
suspended sediments at a given discharge that will be dispersed in front of the delta has
been considered. The distance over which sediments are dispersed has been estimated
from 200 m at low discharge to 5 km at high discharge, these values are estimated based
88
on the observations of Tye and Coleman (1989) on hyperpycnal flows in Grand Lake.
The thickness of the newly formed bed over the delta slope will make delta shorelines to
prograde.
4.5
Results
4.5.1
River Plume - Hyperpycnal Flow
The type of the river inflow is important in relation to the basin topography. When the
river plume is hypopycnal (buoyant) or homopycnal (neutral) the influence of basin
topography on the flow is minimal, but if the river plume is hyperpycnal (negatively
buoyant) the basin topography will affect the river effluent. Olariu et al. (submitted)
indicate that the Red River plume is permanently hyperpycnal. Using the principle that
different electromagnetic wavelengths from visible-near infrared spectrum penetrate at
different depths, hyperpycnal river plumes have been differentiated on satellite images at
different river discharges (Olariu et al., submitted).
During two lake surveys, water samples were collected in front of the delta and analyzed
for SSC values. Physical measurements were also made for a better estimation of the
river plume geometry. The 2003 and 2004 survey results indicate a decrease in suspended
sediments away from the river but concentrated above the bottom corresponding to a
hyperpycnal plume. Close to the river mouth, vertical SSC values do not vary
considerably but at locations farther in front of the delta, the bottom 1 m water layer has a
higher SSC. Analysis of SSC data type on the river plume geometry corroborates that the
Red River is a hyperpycnal plume most of the time.
89
The satellite imagery and field measurements represent punctual data and can not be
confidently used to conclude that the hyperpycnal flows are permanent. To asses the type
of river effluent through time we estimated the density of river water relative to the lake
water. Physical properties of river water measured at Gainesville gauge station were
compared with lake water measured at Dennison Dam gauge station (Olariu et al.,
submitted). Red River water has higher total dissolved solids (TDS) than lake water at
Dennison Dam. River water also has higher suspended sediment concentration than lake
water. Higher values of TDS in the river water are due to the presence of dissolved salts
formed by chemical weathering of Permian evaporate beds in the Red River watershed.
Plots of discharge versus TDS and SSC show that TDS values decrease with increasing
river discharge while SSC values increase (Figures.4.4A and B). Because of the opposite
TDS and SSC variations with discharge, the river water has a permanently higher density
than the lake water, and forms a hyperpycnal plume most of the time (Figure 4.4C). At
high discharges (over 100 m3/s) the high SSC creates conditions for hyperpycnal plumes.
For low discharges the high TDS concentrations contribute to creation of a hyperpycnal
plume.
4.5.2
Red River Delta Progradation
Delta progradation direction, morphology and progradation rates represent the interplay
between river discharge and topography. The orientation of terminal distributary channels
and direction of delta progradation with respect to the pre-dam drainage network are
documented on time series images. Red River delta progradation and evolution into Lake
Texoma is discussed below, focused on three points: (1) lake topography control on delta
90
Figure 4.4. Physical measurements, total dissolved solids (TDS) and suspended sediment
concentration (SSC) of the Red River water (at Gainesville gauge station) and Lake
Texoma water (at Dennison Dam). A- TDS variation with discharge in Red River water.
B- SSC variation with discharge in Red River water. C- Variation of the sum of TDS and
SSC in Red River water through time. Can be observed that the summed values are over
3000 mg/l permanently.
91
progradation direction, (2) morphology changes with discharge and (3) rates of
progradation.
Lake Texoma basin topography influence on Red River delta progradation.--Successive images of the Red River delta (Figures 4.5A to O) show a deflection of
progradation direction before the delta reached the opposite shore of the lake. The Red
River delta bypasses some parts of the lake in the NW part of the images (Figure 4.5) that
have more than 2 m water depth. In Figure 4.5 it can be seen that the delta followed the
old river talweg, the entire old drainage over the lake area is drawn.
On the images from the 1950’s (Figures 4.5A and B) the deltas were mainly subaqueous
but preferential sediment deposition (more turbid water) can be seen toward the western
bank of the lake. On the 1976 images (Figures 4.5C and D) the delta prograded along the
old river talweg along the western bank but subsequently cutted off a meander and
continued to prograde northeastward again along the old river talweg. Levee deposits
extended northward infilling accommodation from the old talweg in an “upstream”
direction. On the 1981 and 1982 images (Figures 4.5E and F) the main terminal
distributary channel is oriented eastward, taking advantage of the slope from an old
tributary valley. On the 1984 image (Figures 4.5H) the delta has two terminal
distributaries roughly pointing toward the location of the old river talweg. On Figure 4.5J
the delta has a single main terminal distributary channel that is placed over the old
talweg. The 1991 image (Figure 4.5I) follows a large flood in 1987 that had peak
discharges over 6500m3/ s (Figure 4.5G). On the images from 1991 to present (Figures
4.5I to O) the river had a single terminal distributary channel that seems to
92
Figure 4.5. Delta progradation and morphology changes on successive satellite and aerial
photos. Aerial images on: A- November 21st, 1952, B- October 20th, 1955, C- February
27th, 1976, D- November 22nd, 1976, E- September 21st, 1981, F- March 7th, 1982,.GRed River discharge for 1945-2005 period. Note that the scale is logarithmic. Aerial
images on: H- August 15th, 1984, I- August 19th, 1991, J- February 17th, 1995, K- July
2nd, 1997, L- August 19th, 2000, M- June 3rd, 2001, N- September 26th, 2002, O- October
17th, 2004.
93
94
locally take advantage of some of the old tributary valleys. On Figures 4.5M to O one of
the small levee channels that is oriented toward the old river talweg, is reactivated.
The pre-lake drainage network influences the position of terminal distributary channels
and the delta progradation direction. The explanation is that the gradient differences of
the side slopes of the basin in front of the delta control delta progradation. The pre-dam
topography, digitized from a pre-dam topographic map represents the initial lake (basin)
topography (Figure 4.6). The delta mainly followed the old river talweg reflecting the
fact that the hyperpycnal plume follows the steepest gradient. As a consequence, river
derived sediments are deposited predominantly toward the middle of the lake.
Figure 4.7 and Table 4.2 summarize the delta lobe positions (progradation stages) from
different images relative to the old river talweg. Successive images show that the delta
prograded mainly along the old river talweg. However, there are some exceptions that
need to be mentioned. From stage 1 to stage 2 the delta cuts off an old meander and did
not follow the old talweg at this stage (Figure 4.7). In stage 2 the delta prograded in 2
directions, in an upstream direction (stage 2.1) and a downstream direction (stage 2.2).
The latter continued in stage 3 as the slope was higher. During stage 4.1 progradation was
controlled by an old tributary while stage 4.2 was controlled by the old river talweg. In
stage 5 there were two progradation directions, along river talweg (stage 5.1) and straight
toward an old tributary (stage 5.2). This time the delta prograded beside the old river
talweg, most probably because of high discharge (Figure 4.5G) combined with an area of
relatively gentle lake slopes (Figure 4.6). However in the latest images (Figures 4.5 M to
95
Figure 4.6. A- Lake Texoma initial bathymetry extracted from a topographic map (USGS
Topographic map – Denison Quadrangle) surveyed before lake impoundment. B - Table
with values of lake topography slopes. For location see Figure 4.6A.
96
Figure 4.7. Summary variation of Red River delta progradation direction compared to the
old river talweg. Six main stages were differentiated based on (1) location relative to old
river talweg and (2) relative discharge during the period that one particular stage was
formed. Dark to light gray color represent stages from old to young.
Table 4.2. Description of delta progradation stages relative to the old river talweg.
97
O) a reactivation of the distributary associated with the stage 5.1 delta was observed. This
might indicate the beginning of the reoccupation of the old river talweg.
Coriolis force can contribute to the deflection of the delta lobes, as was described in the
hyperpycnal Huanghe Delta (Wright et al., 1990). The deflection also can be due to
northern streams or deflection of the main stream from the northern shore of the lake, but
in the Red River Delta, Coriolis force and lateral streams effects seem to be secondary to
topography.
Delta plain morphology changes with discharge.---For delta morphology we used a set
of aerial photos and satellite images of the delta (Table 4.1). Each image acquisition time
was also indicated on the Red River discharge chart (Figure 4.5G) allowing us to
compare discharges to delta morphology. Because the lake level was different for each
image we extracted a typical slope of the delta front from the bathymetry survey data
(Figure 4.8) and corrected the shoreline position on each image, considering the
conservation lake level of 188.1 m as the average. Some shallow features like mouth bars
(Figure 4.8C) might appear on images acquired during low lake levels.
Analysis of delta morphology, correlated with river discharge history and lake level
change, indicate major changes in the shape of delta plain and number of distributaries
over short periods (Figure 4.5). Important features related to the moment when the image
was collected and observations on delta morphology are summarized in Table 4.1.
Because river floods contribute the most sediment to the delta, we will make reference to
the large peak discharges and also to the average river discharge for the period between
images (Table 4.1).
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Since 1952, three main morphologies have been observed: (1) an initial subaqueous delta,
(2) a lobate delta and (3) an elongate delta. Initially, on 1952-1955 images, despite the
lake level being 4 m lower than the average (in 1952) the subaerial delta can be observed
only on the narrow N-S oriented part of the river. This indicates that at this time, the delta
was mainly subaqueous in the wider part of the lake (Figure 4.5A and B).
Figure 4.8. Lake Texoma bathymetry in front of the Red River Delta based on the
echosound data collected on October 12th, 2002. A- Bathymetry in front of the delta. BDetailed bathymetry in front main river channel. Note that a subaqueous mouth bar was
formed. C- Echosound profiles that shows channels and mouth bar. Typical slope values
of the delta front were extracted to correct subaerial delta area for the lake level changes.
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The lobate delta morphology was observed initially on two 1976 images, but also on the
successive images of 1981 and 1982. The February 27th, 1976 image shows a lobate delta
with multiple terminal distributary channels (Figure 4.5C). At the beginning of the lake
bend the delta prograded in two directions. The first direction was toward the north,
filling the old river talweg, which was abandoned. The second direction was toward the
northeast, which represents a cut off of the old river meander. The delta cut the old
meander taking advantage of the higher slopes toward the old river talweg. Toward the
northwest, the delta prograded along the old river talweg with only a visible crevassesplay deposit oriented toward the north. On the November 22nd, 1976 image, the delta
morphology was still lobate but more active terminal distributary channels can be
observed than on the previous image. The terminal distributary channels have an
orientation range of 180 degrees. (Figure 4.5D) with a large distributary toward the
northwest that subsequently will be abandoned.
However, on the September 21st, 1981 image, one of the distributary channels is larger,
taking advantage of the slope toward an old river tributary valley (Figure 4.5E). No
morphologic changes were observed on the March 7th, 1982 image (Figure 4.5F) but, on
the northern side of the delta the shoreline seems to be smoother than on previous images.
After 1981, peak discharges increase, with more frequent discharges over 1000 m3/s and
higher maximum peak discharges (Figure 4.5G). The discharge variation might be related
to El Nino variations (NOAA-CIRES Climate Diagnostics Center,
http://www.cdc.noaa.gov/ENSO/enso.current.html). As a consequence of overall
discharge increase, on August 15th, 1984, the Red River delta has more terminal
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distributary channels and with a preferential lakeward extension of the channels (Figure
4.5H). A large sandy mouth bar also can be distinguished (Figure 4.5H).
By far the largest discharge observed since 1944 was in June 1987, when river discharge
exceeded 6500 m3/s. An elongate delta was observed on August 19th, 1991 showing the
Red River Delta extended to the northern side of the lake. Also the main flow is now
oriented west - east along the northern shore of the lake. Abandoned deposits from
previous terminal distributary channels can be distinguished and also new terminal
distributary channels were formed (Figure 4.5I).
On February 17th,1995 the delta was still elongate along the northern shore with a single
large distributary channel prograding on the direction of the old river talweg. A spit,
which was also distinguished on the previous image, encloses a previous gulf of the lake
(Figure 4.5J).
On July 2nd, 1997, the main channel extends along the northern shore of the lake (Figure
4.5K). Terminal distributary channel oriented north-south can be distinguished. Probably
these are abandoned but on the image they are filled with water due to high lake level
(Table 4.1).
On the August 19th, 2000 image, the delta is elongated with the main distributary parallel
to the northern shore. The delta prograded eastward instead of following the river talweg
probably due to high discharge combined with the high gradients of one of the old
tributaries to the main valley (Figure 4.5L). The south levee of the main channel is larger
than the north one. The previous gulfs of the lake, situated at the north of delta, are
isolated. An old secondary terminal distributary channels is reactivated.
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On June 3rd, 2001 image, the delta has a similar morphology to that on the previous
image. The difference is the widening of the south channel levee, probably due to
preferential deposition on that side. The secondary small terminal distributary channel
observed on the previous images is still active (Figure 4.5M). On the September 20th,
2002 image the delta morphology did not change but the right levee of the main terminal
distributary channel grew (Figure 4.5N). On October 17th, 2004 image (Figure 4.5M) the
delta is still elongated but the secondary terminal distributary channel seems to be active.
Two periods of delta evolution have been distinguished, the first period, before 1981,
with relatively low river discharge (multiannual average value), and the second period
after 1981, with relatively high discharge (multiannual average value). The discharge
variability is reflected in the shape of the delta. During low discharge periods the delta
exhibited a lobate shape, but during high discharge the delta was elongated with a single
main distributary channel.
Progradation rates.--- The study indicates high progradation rates, with an average of
250 m/ year since 1944, when the lake was impounded. Progradation rates are mainly
dependent on river discharge.
Quantitatively, the area of subaerial delta growth for each image has been measured and
the area increase for each interval is plotted in Figure 4.9B. Corrections for lake level
have beeen made considering an average slope of 0.01 in front of the distributary channel
and 0.02 lateral to the active channel along the delta shoreline (Figure 4.8). Subaerial
delta area growth indicates that in at least two cases, area decreased, despite corrections
made for the lake level. The negative values can be explained by: (1) oversimplification
of the method by choosing a unique delta front slope; (2) the lake elevations are reported
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Figure 4.9. Red River Delta progradation into Lake Texoma for 1944- 2004 period. AProgradation of the main distributary channel into the lake. B- Subaqueous Red River
delta area through time. C- Red River yearly discharge average. D- Multivariate El Nino/
Southern Oscilation (ENSO) index. From NOAA-CIRES Climate Diagnostics Center
(http://www.cdc.noaa.gov/ENSO/enso.current.html). E- Initial depth of the lake Texoma
in the area where is located the main active distributary.
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at Denison Dam which is 45 km (lake length) downstream of the delta and if we assume a
water slope of 1cm/ km (10-5) for a 45 km distance, which might produce an error of +0.45m in lake level estimation; and (3) after periods of high discharge followed by low
discharges the sediments will subside and/ or are dispersed by waves that will decrease
overall subaerial delta area. A linear progradation (advance of the river channel mouth)
for different intervals also has been computed (Figure 4.9A). Channel progradation is
positive at all times but at a varying rates that have an overall decreasing trend, which can
be attributed to low discharge and/ or increasing basin (lake) accommodation. Delta
progradation rates (Figure 4.9A and B) are controlled by river discharge (Figures 4.5G
and 4.9C) and accommodation (Figures 4.6A and 6.9E). High rates of progradation can
be linked with an increase in overall river discharge Figure 4.9C). The increase in river
discharge appears because of climate variation. High Red River discharge shows a good
correlation with El Nino/ Southern Oscilation index (warm phase) (Figure 4.9D). Despite
increasing water depth the high progradation rates for the interval 1984-1991 (Figure
4.9E) can be explained through increasing discharge (Figure 4.9C). The relatively steady
increase in channel length despite low discharge after 1997 (Figure 4.9C), can be
explained by the relatively constant basin depth (Figures 4.6A and 4.9E).
Despite high sediment discharge and average progradation rates of 250 m/ year, it is
estimated that it will take more than 200 years for the river to fill the lake. This time span
for the lake life was calculated using yearly average volumes of suspended sediments
divided by the lake volume. If the delta bypass some parts of the lake (Figure 4.7) or
increases in discharge, the delta will reach the dam earlier.
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4.5.3
Numerical model experiments on hyperpycnal plume deflection
Red River delta progradation deflection from the along channel direction occurs because
the direction of the hyperpycnal plume is affected by a lateral sloping plane (Figure 4.3).
Because the hyperpycnal plume has to flow perpendicular to the old valley slope, it is
affected by gravitation and follows a curved trajectory (Figure 4.3). To quantify the
plume deflection it has been considered a frictional river effluent flow to which the initial
velocity decreases (Wright and Coleman, 1974). The final plume trajectory has been
computed considering velocity variations along the x and y directions with equations (1)
and (2). The resulting plume trajectory is described by equation (3) and will depend on
the initial plume velocity and the side–slope gradients. For the range of initial velocity we
considered the possible Red River discharge through a typical Red River channel size
that varies between 0.5 depth and 100 m width at low discharge and 2m depth and 325 m
width at high discharge. For the range of the side slope we estimated slopes from the predam topographic map (Figure 4.6B). Slopes were found to vary between 0.005 (0.33o)
and 0.22 (12o).
In the case of low discharge (5 m3/s) with an initial velocity of 0.1 m/ s and steep lateral
slope (~12degree) the plume will be deflected 80 degrees from the flow direction (Figure
4.10). In the case of high river discharge (6500 m3/s) with an initial velocity of 10 m/s
and low lateral slope (0.33 degree) the plume will be deflected approximately 8 degrees
(Figure 4.10). In our model, we did not include mixing, dilution and frictional processes
that will affect the distance that the river plume protrudes into the lake.
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The most probable river velocities will be around 1m/ s and the lateral slopes of about 1
degree (Figure 4.10). In this case the plume will be deflected about 45 degrees at 200 m
from the mouth (Figure 4.10). The deflection increases with distance from the mouth as
Figure 4.10. Result of plume deflection numerical model. A- The magnitude of
hyperpycnal plume deflection for the given parameters (minimum, average and
maximum) of the Red River/ Lake Texoma system. The blue line shows the plume
deflection calculated for 1991-2004 period. B- Comparison of numerical model of plume
divergence with observed Red River main distributary channel position for 1991-2004
period.
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the velocity along channel (x) direction decreases (Figure 4.10). In both cases of low or
high discharge, the sediment delivery by the river in front of the delta will follow the
steepest gradient and therefore the delta will tend to infill the deepest parts of the basin
first.
However, at low discharges the plume will advance into the lake less than during high
discharge periods and as a consequence the plume will flow less over lake topography but
over its own prodelta deposits and because of theis deflection will be more probable
during the high discharge periods (Figure 4.11). The approximation of daily progradation
at a given discharge (Figure 4.11B) based on volume of sediment dispersed by the Red
Figure 4.11. Delta progradation with discharge under topographic influence. A- Variation
of progradation direction as a function of basin slopes and discharge magnitude. BComputation of progradation rates as a function of discharge for Red River/ Lake
Texoma conditions. Computations were made for flood discharge (a), average discharge
(b) and low discharge (c). Note that progradation vary over four order of magnitude form
cm/day at low discharge to tens of meters/day during the flood.
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River into Lake Texoma per day indicates a wide range from cm/ day to tens of meters/
day. Variation of progradation rates and plume deflection vary with initial velocity
(discharge) and slope (Figure 4.11A).
The progradational model has been compared with the main Red River channel trajectory
for the 1991-2004 interval (Figure 4.10B). Plume deflection has been considered only for
the periods with over average discharge. This assumption has been made because at low
discharge is considered that the river effluent flow only over delta front and prodelta
deposits without being deflected by the lake topography. We considered an initial 0.02
lateral slope over which delta prograded and later a gentler slope of 0.01 as delta
prograded. Comparison (Figure 4.10B) between the modeled trajectory and observed
channel trajectory shows similar trends, the differences might indicate that other unmodeled processes are involved in the delta deflection. The differences that appear (a
more curved observed trajectory) are caused by an oversimplification of the basin slopes
and using a single threshold for the plume deflection (average discharge).
4.6
Discussion
4.6.1
Conditions for delta deflection
Results of this study can be applied only in specific delta systems that (1) can produce
hyperpycnal flows, (2) form in basins with significant topographic differences, and (3)
has large discharge variability. Since in nature not all conditions are ideal and transitions
between extreme cases occur, a multitude of intermediate situations might appear.
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4.6.2
Hyperpycnal deltas
Studies of deltas are mainly focused on marine deltas, either modern (Broussard, 1975,
Giosan and Bhattacharya, 2005) or ancient (Coleman and Wright, 1975, Broussard, 1975,
Giosan and Bhattacharya, 2005). The main reason for this is that lacustrine deltas are
generally small, compared with marine deltas, and as a consequence are environmentally
or economically less important than marine deltas. Generally, lacustrine deltas have short
evolution periods, as lakes are usually filled in extremely short time periods (thousands to
tens of thousands years) compared to geological ages. There are exceptions when modern
large lakes represent remnants of marine basins such as Lake Baikal of the Caspian Sea,
large glacial lakes Great Lakes or are associated with rifting like East African lakes
(Bohacs et al., 2003).
One of the main differences from marine deltas is given by the fact that the basin (lake)
water is usually fresh and because of this hyperpycnal river underflows are common. This
problem has been addressed to studies of sedimentation from river plumes (Akiyama and
Stefan, 1984) or numerical models of river deltas (Akiyama and Stefan, 1984, Kostic and
Parker, 2003). Attention has been also given to river generated turbidites into lakes
(Ludlam, 1974, Lambert et al, 1976).
Most marine deltas have hypopycnal river plumes (Bondar, 1971, Wright, 1977, Nemec,
1995, Mulder and Syvitski, 1995), but in some cases hyperpycnal plumes can be formed
(Wright et al., 1986, Warrick and Milliman, 2001). By far less common for marine deltas,
hyperpycnal plumes can be formed due to excess of SSC (Wright et al., 1988, Mulder and
Syvitski, 1995) and presence of brackish coastal water. In hypopycnal flows, common in
marine deltas, (Wright, 1977, Mulder and Syvitski, 1995, Nemec, 1995) topography has
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limited influence on delta progradation direction, and basin processes (waves, currents)
are more significant in dispersing sediment.
However, hyperpycnal deposits have been described in ancient and modern marine
systems (Mulder et al., 2001, 2003, Mellere et al. 2002, Olariu et al., 2005). The
permanent hyperpycnal river flows into Lake Texoma appear because of the higher river
water density relative to lake water. The density difference needed for river water to form
a hyperpycnal plume has been reported to be as low as 0.0003 in a Laitaure Lake
(Axelsson, 1967), value that is permanently exceeded in the Red River/ Lake Texoma
system (Fig. 4C). In the Red River case, the permanent hyperpycnal plumes are created
by a combination of high river salinity and suspended sediment concentration.
4.6.3
Basin topography influence on delta progradation
The influence of the slope on marine hyperpycnal flows has been observed in two
dimensional unsteady models for the Eel River (Imran and Syvitski, 2000). The model
results show that Eel River hyperpycnal flows have a tendency to flow toward the
adjacent Eel Canyon, taking advantage of the steepest gradient. However, influence of
basin topography on hyperpycnal flows are expected to occur in bayhead deltas where the
flooded valleys have steep side-gradients and closed or semi-closed conditions create
brackish to fresh water bays. Fjords are another environment with conditions for
topographically influenced hyperpycnal flows. Fjords have steep lateral side-gradients
and rivers that discharge into these have periods with high SSC during seasons of ice
melt (Gustavson, 1975, Hansen, 2004).
In deltas that form in shallow bays with low topography like the Atchafalaya, Colorado,
Guadalupe and Wax Lake Deltas (Donaldson et al., 1970, Kanes, 1970, van Heerden and
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Roberts, 1983, Roberts, 1998) a preferential progradation direction will not exist and
lobate deltas with multiple terminal distributary channel will form (Olariu and
Bhattacharya in press). The lobate shallow deltas will prograde through successive
avulsions infilling the entire low accommodation from low topographic basins rather than
prograding after a preferential path given by topography.
Some studies of basin topographic influence were made on turbidity flows (Kneller et al,
1991, Kneller, 1995, Amy et al, 2004) but these relate the topography to changes in flow
conditions and in different type of deposits produced. Turbidity flows on tortuous paths
in areas of high topography on different modern slopes, and related stratal geometries,
have also been described by Smith (2004). The difference betweeh turbidite and
hyperpycnal deltas is that the first ones have higher energy and might surpass higher
slopes but have a more discontinuous occurrence.
4.6.4
Discharge variability and delta progradation
In general, a delta progrades over its own prodelta deposits and as a consequence, the
slope over which new sediments are deposited is gentle, with only small variations. Some
changes might appear when the delta progrades into a narrow basin with steep slopes,
such as a fjord, narrow bay or a flooded valley lake like in our study.
A condition for the delta to “feel” the topography is for hyperpycnal plume to flow
farther than delta front and prodelta. The large discharge variation of the Red River
between 2 m3/s and 6500 m3/s with an average of 100 m3/s indicate that this condition is
fulfilled in this case. The morphologic variations of the Red River delta from lobate to
elongate, (Figure 4.5) are related to river discharge (Figure 4.5G). The observed average
delta progradation of 250 m/ year is high, but higher progradation rates have been
111
reported for other lacustine deltas (Tye and Coleman, 1989) in the Grand Lake Delta (2
km/ year) and the Lake Fausse Point Delta (500m/ year). The difference is given by the
fact that the Grand Lake and Lake Fausse Point deltas prograde into 2 m deep lakes while
the Red River Delta builds in a 6 to 9 m water depth. Because the Atchafalaya basin is
very shallow where the deltas are also more effective in filling the entire lake. However
the delta also bypassed some lake areas (Tye and Coleman, 1989). However, the
relatively high progradation rates of the Red River appear because of plume confinement
toward the old river talweg and restriction of sediment dispersal.
The similarities reflect similar processes and conditions with common hyperpycnal flows
within a basin that has a distinctive elongate deep part. However, differences appear
between morphology and progradation rates of the Atchafalaya (van Heerden and
Roberts, 1988), Wax Lake (Roberts, 1998), Grand Lake, Lake Fausse Point (Tye and
Coleman, 1989) and the Laitaure delta (Axelsson, 1967) and the Red River Delta.
Another difference is that the Red River has a relatively high discharge within a narrow
basin with a well defined deep region, while for the other deltas mentioned, the river
discharges into a wider but still relatively shallow water basin. Because the basin is
shallow, frictional processes are more important and these deltas will build multiple
terminal distributary channels (Olariu and Bhattacharya, 2005) and will have a lobate
shape during their evolution.
In the Red River Delta all three conditions required for a strong topographic influence are
present: hyperpycnal flows, high topography and high discharge variability. Under these
conditions, the Red River delta does not build straight in front of the river filling the
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accommodation but diverges toward the deeper parts of the basin (Figures. 4.5 and 4.7).
The delta thus bypasses some lake areas despite the relatively shallow water setting.
4.7
Conclusions
1. Deltas that have common hyperpycnal plumes, form in basins with variable
topography, and have significant discharge variability, are expected to be deflected by
under the topographic influence.
2. Red River/ Lake Texoma represents a system that has permanent hyperpycnal flows,
that prograded into a flooded valley and has significant discharge variations (between 2
and 6500 m3/s). As a consequence the Red River Delta is strongly deflected by Lake
Texoma lateral slopes.
3. The Red River delta mainly followed the old river talweg as it prograded. The old river
talweg represented the steepest slope available for the hyperpycnal river plume. Some
exceptions occurred when the delta cut off a meander, infilled the old talweg in an
upstream direction, or prograded toward an old tributary.
4. The morphology of the Red River delta changes with the discharge. During period of
low discharge the delta had a lobate shape, while during high discharge periods the delta
had an elongate shape.
5. During low discharge (lobate delta shape) the system switches the distributary channel
location often. During high discharge periods the delta had tendency to prograde straight
because of flow inertia, but it was deflected because of a basin topography.
6. A numerical model shows that the plume can be deflected more than 80o at low
discharges over high lateral slopes (12o). The model as applied to the Red River Delta
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system, indicate a deflection of 30o for 1991-2004 period that is similar with deflection
observed on the aerial images.
CHAPTER 5
STRATIGRAPHIC INVERSION USING A GENETIC ALGORITHM: LESSONS
ABOUT NON-UNIQUENESS
5.1
Abstract
Quantitative predictions of geological data can be made for a number of important
sedimentary environments. These approximate and ad hoc models are difficult to verify
and validate. An important problem involves the fitting of model parameters to geologic
data. Inverse modeling is a widespread practice in geophysics, which produces estimates
of model parameters from observed data. The primary interest is the non-uniqueness of
inverse models; any given data can be fit to a range of model parameters. This paper
presents an analysis of non-uniqueness in the inversion of a river delta model.
Usually inversion procedures are cast in the form of optimization problems with respect
to data misfit. The data misfit can be measured by correlation of a synthetic well log with
an observed well log. The inverse problem for the delta model can be solved by
application of a genetic algorithm to maximization of well log correlation. Nonuniqueness is explored by the creation of a large number of optimal models. These
models can be “linearly close” and parameters may simply “trade off” or they may cluster
into distinct classes.
A set of “known” parameters for the delta model is specified and bed thickness logs are
computed at distinct locations. The genetic algorithm inversion generates hundreds of
114
115
models, all of which produce similar logs. The models are then analyzed using cluster
analysis, principal components analysis and graphic displays.
5.2
Introduction
Clastic sedimentary deposits represent a large part of basin infilling and the resultant
stratigraphy. Stratigraphic numerical modeling is used to gain insight about basin infilling
sedimentary processes, as well as the resultant stratigraphy. Numerical models can be
evaluated in a forward or inverse sense. In stratigraphical modeling, forward models are
more often used (e.g. Cross, 1990, Harbaugh et al., 1999), inverse models have been
introduced relative recently (Bornholdt and Westphal, 1998).
Forward models start from given parameters and predict the state of the system based on
the knowledge of the processes involved. The mathematical model is built based on a
conceptional model and numerical evaluation and is used as a predictive tool (Fig. 1).
The conceptual model on which the forward model is based may rely on observations
and/or empirical relationships among different geological observations. The comparison
of the forward model results with observed data is often made qualitatively (Cross, 1990;
Slingerland et al., 1994).
Inverse modeling is the reverse process of forward modeling, the mapping of data space
into parameter space. Partial knowledge of the state of the system is used to estimate
parameters and their associated uncertainty. Inverse modeling is not a method often used
in stratigraphy but is an essential element of geophysical theory (Parker, 1994). For
stratigraphy, it is difficult to analyze the inverse problem because most of the forward
models use ad hoc and quasi-empirical approximations to describe sedimentary
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processes. (Cross, 1990; Tetzlaff and Harbaugh, 1989; Pirmez et al., 1998; Syvitski et al.,
1998; Harbaugh et al., 1999; Paola, 2000).
Stratigraphic inversion has been applied mainly to two-dimensional (cross section) data
sets (Bornholdt et al., 1996; Cross and Lessenge, 1999) and parameters such as
subsidence, sea level, sediment supply and topography were estimated. The inverse
model presented here embodies small to medium scale processes and the observed data is
three-dimensional bed thickness variations. The inversion extracts parameters related to
sediment dispersion into the basin, like flow velocity, channel dimension, and diffusion
coefficients over time intervals of tens to hundreds of years.
In this paper the inverse problem will be solved using a random search method from the
extensive family of genetic algorithms (Goldberg, 1989). Genetic algorithms are used for
optimization problems in diverse scientific fields (Goldberg, 1989; Mitchell, 1996) and
were recently introduced into stratgraphic modeling by Bornholdt et al., (1999). One of
the most important aspects of inverse problems, and the focus of this paper, is parameter
resolution and uniqueness. The lack of uniquess of model parameters, which produce
similar stratigraphy, has significant implications for geological interpretation and model
building.
The present paper:
(1) Presents a method of stratigraphic inversion using a genetic algorithm for
optimization.
(2) Applies the inverse methodology to synthetic, computer generated, data (representing
successive bathymetric surveys or well logs).
117
(3) Analyzes the resultant multi-variable model population, each member of which fits
the data.
(4) Discusses the non-uniqueness of the possible solutions with implications for
geological modeling.
5.3
Forward and Inverse Modeling
5.3.1
Forward Modeling
Forward modeling simulates processes and computes the observable responses of a
system having some specified initial condition and configuration. Mathematically
speaking, the parameter space is mapped into the data space. In stratigraphic forward
modeling, given an initial configuration of a sedimentary basin, the evolution of the basin
is simulated and infill characteristics predicted (Figure 5.1). After some comparison of
Figure 5.1. Chart indicting the relationships of forward and inverse modeling. There are
steps common to forward and inverse modeling such as "Parameter" estimation, and
"Observed Data" that is used for "Data Error Analysis". "Parameter Modification" may
be specific to the particular numerical model or it may be general.
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the model output to geologic observations, the initial set of parameters might be adjusted
based on geologic intuition, informed by experience. In the case of stratigraphic models,
Cross and Harbaugh (1990) observed that different parameter sets can produce similar
simulation results and therefore a non-unique relationship to any actual field data.
Forward stratigraphic models use a complicated mix of multiple interacting processes
described by partial differential equations and empirical relationships (Syvitski et al.,
1988; Tetzlaff and Harbaugh, 1989; Pirmez et al., 1998; Syvitski et al., 1998; Grajdeon et
al., 1999; Paola, 2000). Deltas (areas where a river discharges into the basin) are the most
active part of a sedimentary basin. Deltas are characterized by high sedimentation rates
where continental derived sediments are delivered into the basin. Because of the
importance of deltas in the formation of stratigraphy, a number of basin stratigraphic
models make use of delta sedimentation (Overeem et al., 2004). Most of the forward
stratigraphic models, regardless of scale, use a localized sediment source (river) and
mechanisms for sediment dispersion. Present delta forward models consider discharge,
sediment load, topography, subsidence, sea level and basin energy as parameters which
control the stratigraphy (Overeem et al., 2004).
5.3.2
Inverse Modeling
Inversion is the process of finding a set of parameters (a model) that will produce results
similar to observed data through forward modeling (Parker, 1994). Note that the word
model is used in a larger sense to refer to the mathematical formulation of the forward
model and in a smaller sense to refer to a particular parameter set of the forward model.
This ambiguous use of the word model is common in the literature. The data space is
mapped into the parameter space (Figure 5.1). Stability means that points which are close
119
together in one domain, map into points which are close together in the target domain.
Since the forward process relating parameters to data is stable, the inverse process is
usually not stable. Inverse problems are usually cast as optimization problems, where the
goal is to choose parameters, such that some observed data is matched by similar
theoretical data. Parameters are found by optimizing a scalar measure of the "fit" between
the theoretical predictions from the model and the observed data. This scalar measure of
fit, known as the objective function, is a function of the N model parameters. Many
different choices of misfit measures are available, which can either increase (correlation
type measures) or decrease (error type measures) with improved fit. In cases where the
inverse relationship between the objective function and the parameters is linear (and
easily expressed as a mathematical function), the inverse problem can be computed and
analyzed directly. In practice, it is more common to encounter a nonlinear relationship,
for which the inverse problem must be solved iteratively, possibly using a linear
approximation locally in the parameter space.
Inversion is based on searching for extrema, one or more minima (or maxima) of the
objective function in the parameter space. There are many optimization and search
methods including gradient-based, enumerative or random search. Gradient-based
methods navigate the parameter space by following gradients in the scalar objective
function. Partial derivatives of the objective function, with respect to the parameters,
must be computed. These methods may fail to search adequately in the case of nonlinear
inverse relationships, which can have multiple extrema. The ad hoc nature of
stratigraphic forward models prevents easy estimation of the partial derivatives, since the
forward model is usually not easily expressed as a mathematical function. In the case of
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enumerative methods, objective function is evaluated exhaustively on a sufficiently fine
grid in the N-dimensional parameter space. For N larger than two or three this is usually
much too costly in terms of computational effort to be practical. A "random walk" can be
used to explore the parameter space, making use of objective function information, with
out the computation of derivatives. This random search can balance the conflicting
requirements of efficient generation of "good” models and exhaustiveness. Genetic
algorithms are a class of random search methods.
Finding a single set of parameters that produce an adequate fit to the data is never the
only objective of inverse modeling. There are two kinds of "errors" which affect the data
misfit: statistical error or "noise" associated with the observations, and resolving errors
related to the inherent smoothing and stability of the forward model. The physics of the
process itself contributes the resolving errors, even in the case of "perfect" error-free
observations. The resolving errors are associated with the smoothing in the forward
direction and instability in the inverse direction dichotomy. Real observations are never
free of errors, in part because of measurement imprecision and in part due the presence of
un-modeled processes. These causes are usually modeled statistically as a random noise
process. Since the parameters are estimated from a random function (the observed data)
they must also have random behavior and an associated parameter variance. This paper is
primarily concerned with the resolving error.
In the discrete linear inverse case, it is possible to construct an operator known as the
resolution matrix (Wiggins, 1972; Kennett and Nolet, 1978) from the forward model
operator (which can also be represented as a matrix). When the resolution matrix
multiplies a parameter vector a smooth average parameter vector results from the linear
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combination of the individual parameters with each other. All parameter vectors that fit
the data can be averaged to a single unique average parameter vector. This average set of
parameters is representative of the possible parameter vectors and should not be
interpreted as the necessarily "correct" parameter set. In the linear case, the resolution
matrix will not depend on the data values, but may depend on the relative locations of the
data in space and time as well as the physics of the model.
Inverse theory as a highly technical subject, requiring rather advanced mathematics in its
understanding (Parker, 1994). The random search methodology however provides a
means of addressing the subject of non-uniqueness and resolution from the point of view
of two elementary concepts from multivariate statistics: cluster and principal component
analysis. The random search is designed to cover a bounded range of the N-dimensional
parameter space. A sufficiently large population of M parameter vectors is uniformly
distributed over the region. The M points randomly move around the parameter space
taking advantage of information gained concerning the objective function. Good search
methods do not necessarily always move points toward, but sometimes permit points to
move away from optimal solutions. After a large enough number of such moves, the
search will have generated a sufficient number of parameter vectors that fit the observed
data within some acceptable error. In nonlinear inverse problems these successful
parameter vectors may form distinct clusters that represent very different classes of
possible models. The points may also fall on loci through the parameter space that
represent "trade-offs" among the parameters. For instance a family of successful
parameters vectors might be generated by increasing one parameter, while
simultaneously decreasing another.
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The recognition of clusters and determination of their membership is the subject of
cluster analysis. There are a huge number of cluster algorithms. For the purposes
discussed here, variants of the k-means algorithm (Hartigan, 1975) have proven to be
effective when combined with a method for identification of the number of clusters, k.
Within a cluster it may be possible to assume linear behavior. Principal component
analysis transforms the N-dimensional covariance matrix for a unimodal cluster into a
diagonal matrix. The coordinate rotation which accomplishes this task optimally
combines the interdependent parameters into new independent variables. Additionally the
number P of independent variables may be less than N. When the number P of
independent variables is determined, the resolution matrix for the cluster can be
constructed from the rotation matrix. This connection between principal components
analysis and the resolution matrix in inverse theory was recognized by Wiggins (1972) in
one of the original papers on discrete linear inverse theory. The non-uniqueness has two
levels: discrete parameter vector classes, which are not linearly related, and linear, tradeoff resolution represented by a resolution matrix. After the random search, more or less
standard methods of multivariate statistics can be applied to the resulting model
population to characterize the parameter variance error (the probability distribution) and
the resolution error.
5.4
Inversion of a Numerical Delta Model
5.4.1
A Numerical Delta Model
The forward model of Syvitski et al. (1988), described by Slingerland et al. (1994), is
investigated in this paper. This model of deltaic sedimentation assumes time independent
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conditions of sediment distribution, discharge, channel dimensions and diffusion
coefficients, and a succession of bathymetric maps are produced. The model is scaled for
small to medium size basins (1 to 10 km) over time periods of tens to hundreds of years.
The model limitations result in reasonable computer power requirements by 2005
standards. The time limitations are consistent with the conceptual model assumptions. It
would be unrealistic to assume constant conditions for time periods over a thousand
years. The forward model has three main components.
The first component is the modeling of flow in a turbulent jet with resulting bedload and
hemipelagic sedimentation (Figure 5.2). The flow velocity in the offshore direction (xdirection) (Figure 5.2A) is computed using distinct velocity equations for zones of flow
establishment and fully established flow within turbulent jet. Albertson et al. (1950) and
Bates (1953) developed a theory of turbulent jet flow. Velocities in the alongshore
direction (y-direction) (Figure 5.2B) are obtained from the continuity equation for fluid
flow using an implicit finite difference method (Slingerland et al., 1994).
Second, plume sedimentation is considered as a suspended particulate matter
concentration change within the plume. Sediment rains out of the plume according to a
first order differential equation, with settling rate proportional to grain size. The program
considers a discrete distribution of four grain sizes (coarse, medium and fine silt and
clay) with different settling rates. Figures 5.2C and 5.2D show the transit time of
suspended sediment and the rate of suspended sediment removal from the plume.
Bedload dumping is computed in the channel mouth area where the plume velocity is
similar to channel velocity. Bed load is deposited in this area as the velocity decreases
with expansion into the open basin.
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Figure 5.2. Variation of forward model parameters and resultant output. (A) The
velocities in turbulent jets in x (offshore). (B) The velocities in turbulent jets in y
(alongshore) directions. (C) The transit time, the time that sediments are suspended in the
plume. (D) The rate of hemipelagic rain (removal of sediments from the plume). The
typical model output is represented by basin bed elevation. (E) The basin elevation after 9
time 8 year steps. (F) The basin elevation after 10 time 8 year steps. The difference
represents the thickness of deposits formed in an 8 year interval.
Thirdly, down-slope mass movements are modeled as a diffusion process, depending on
bed slope and which satisfies the conservation of mass. The two-dimensional diffusion
equation for the bed elevation is considered with anisotropic diffusivity (greater in the
alongshore direction) (Slingerland et al., 1994). The partial differential equation is solved
by the implicit Crank-Nicholson finite difference method.
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The finite difference methods in steps 2 and 3 require a two-dimensional spatial grid. The
model is strictly symmetric about the y-axis through the river channel mouth. Each of
these three processes is applied, in order, at each discrete time step to advance the
solution forward in time. The river mouth is redefined as the basin fills. Some care must
be exercised in the choice of space and time grid steps, depending on the size of the
various rate parameters in the model.
The forward delta model is computed with parameters similar to those for the Rhine
River delta in Lake Constance, Switzerland proposed by Slingerland et al. (1994). These
parameters (Tables 5.1 and 5.2) are based on historical measurements (Muller, 1966) and
geological intuition.
Table 5.1. Parameters used for synthetic model.
Parameter
Symbol
Value Units
Flow Velocity
u0
0.28
m/s
Channel Width
b0
200
m
Channel Depth
h0
4
m
x-Diffusion
kx
1x10-8
m2/s
y-Diffusion
ky
2x10-5
m2/s
Dumping Rate
d
6x10-9
m/s
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Table 5.2. Grainsize characteristics of the modeled sediment.
Grain Size Concentration Settling Time Constant Sediment Density
kg/m3
s
kg/m3
Coarse Silt
0.150
5760
1750
Medium Silt
0.050
14400
1600
Fine Silt
0.050
28800
1500
Clay
0.054
43200
1400
The model results along a dip-oriented profile are compared with observed profiles
(Muller, 1966) in Fig. 3. The geometry of the modeled clinoform beds is seen to be
similar to that measured in the lake (Figure 5.3).
Figure 5.3. Observed and modeled clinoforms. (A) Observed clinoforms of the Rhine
Delta in Lake Constance (modified after Muller, 1966). (B) Delta clinoforms generated
with delta-forward model described in the test. See Figure 5.2 for profile location. The
modeled clinoforms are produced over approximately the same time interval and have
similar geometry to observed clinoforms of the Rhine Delta.
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5.4.2
Genetic Algorithms
Genetic algorithms (Holland, 1975) have been inspired by evolutionary biology, where
natural organisms adapt themselves to the environment through modification of a genetic
code. Natural adaptation represents an optimization problem of a multivariate process
using only basic operations, such as reproduction (crossover, mutation) and fitness
evaluation. There is a large family of related random search algorithms, rather than a
single genetic algorithm. These methods are largely used in engineering and computer
science for evolutionary computing and machine learning optimization problems
(Goldberg, 1989; Mitchell, 1992). In geosciences, applications have been primarily in
geophysical inverse problems (Stoffa and Sen, 1991; Gallager et al., 1991; Gallagher and
Sambridge, 1994) and later on stratigraphic modeling problems (Bornholdt and Westphal,
1998). A genetic algorithm is particularly suitable for stratigraphic inversion because it is
a powerful optimization tool with little dependence on the mathematical or computational
details of the forward model.
Genetic algorithms work with the coding of the parameter set into a bit "string", most
often binary coding is used (Goldberg, 1989, Mitchell, 1992). The search is conducted
from a population of points, rather than a single point in the parameter space. As a
consequence, the result will not be a single best solution, but a best-fit population.
Genetic algorithms use objective function information, not derivatives or other auxiliary
knowledge. Probabilistic and not deterministic transition rules are used to move between
points in parameter space.
In the inversion experiment, a genetic algorithm is used to invert for six parameters: flow
velocity, channel width, channel depth, dumping rate, diffusion coefficient in the x-
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direction (normal to the shore) and diffusion coefficient in the y-direction (along shore).
For each of the six parameters, 16 bit binary coding is used so that there are 216 = 65,536
possible values for each parameter. That gives 79x1027 possible models in the parameter
space. The parameter ranges for the inversion experiments are presented in Table 5.3.
The "observed" data will be produced using the parameter values in Tables 5.1 and 5.2.
Table 5.3. Possible range values of the initial parameters.
Parameter
Range
Units
Flow Velocity
0.1 < u0 < 1
m/s
Channel Width
200 < b0 < 400
m
Channel Depth
2 < h0 < 5
m
x-Diffusion
0.5x10-8 < kx < 3x10-8
m2/s
y-Diffusion
1x10-5 < ky < 4x10-5
m2/s
Dumping Rate
3x10-9 < d < 14x10-8
m/s
Initially 200 random parameter vectors (i.e. models) are generated uniformly throughout
a hypercube in the parameter space. Each model is evaluated using the numerical
procedure discussed above and the response is compared to observed data to determine
the "fitness" (Figure 5.4). New models need not be better than the best model in the
current generation. This produces resistance to become trapped in a local optimum. The
algorithm iteratively generates successive populations using three operators:
reproduction, crossover and mutation. In the reproduction operation, strings are chosen
for reproduction randomly, but according to their fitness values. Fitness is defined in this
case as the sum of the correlation between synthetic well logs generated from a specific
model (or string) and the “observed” well logs. For reproduction a steady state method is
iteratively applied and the two models with the poorest fit are replaced (Davis, 1991;
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Goldberg, 1989). Crossover is the operation in which strings are randomly combined. A
random location on the string is chosen and both strings are split and recombined to
create new strings. Crossover is applied with a probability of 0.8, so that 20% of the time
no crossover occurs. Through the mutation operation strings are randomly altered. With a
probability of 0.04 individual bits are "flipped" from 0 to 1 or vice versa. Through
successive iterations (Figure 5.4) the population fitness will improve and a final
population with good overall fitness will result.
Figure 5.4. Flow chart of steady state reproduction genetic algorithm.
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5.4.3
Observed Data and Objective Function
Comparing the observed data with the numerical model results and evaluation of the
fitness is fundamental to the optimization process. The output of the forward model is a
succession of basin floor bathymetries with time. The observed data could be for example
bed thickness, for a particular time interval, in a set of wells. Data of this type can be
extracted from the successive bathymetric maps produced by the forward model. The
bathymetry difference represents the thickness variation within a given time interval.
The basin is strictly symmetric in this formulation so that sample points (i.e. wells) are
located in half of the basin (Figure 5.5A). Deposition versus time (Figure 5.5B) is
different for each well according to the position relative to the river mouth. At the
beginning, the river mouth is relatively far in a landward direction and sediment
deposition at the well is slow. After a period of time, with deposition, the river mouth
(sediment source) passes the well and the deposition curve becomes flat again, reflecting
non-deposition (Figure 5.5B).
The "well log" represents the bed elevation at each time step or the bed thickness
sequence. The objective function is the sum of the correlations between the observed and
predicted logs. This function should be maximized for best data fit (or high fitness in the
genetic algorithm). The maximum correlation for a single well is 1, when the well logs
for the observed and modeled results are the same. The maximum correlation is equal to
the number of well logs (sample points); four in the case illustrated in Figure 5.5. The
observed data for this paper is also generated by the forward model using a particular
parameter set (Tables 5.1 and 5.2).
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Figure 5.5. (A) Location of control data (observation wells) on the synthetic model with
x, y coordinates. The model has the symmetry axis along the middle of the basin
(channel) and because of this we sample only half of the basin. The colors indicate bed
elevation after 88 years of deposition. (B) Evolution of bed elevation at each well
location over the modeled time interval. Time steps are at 8 years intervals. Each well has
a different period of deposition according to the location relative to the river mouth (see
text for discussion).
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5.4.4
Genetic Algorithm Performance
The genetic algorithm is an effective tool to maximize the objective function (Figure 5.6).
A steady state reproduction method is used that iteratively replaces the two worst fitting
models. Because of this approach, the model population converges relatively fast. In
some genetic algorithms the models are replaced randomly and that does not guarantee
improvement in each iteration, which results in a slower convergence rate (Goldberg,
1989). During our testing we observed that smaller initial populations converge faster.
Finally we observe that a population of 200 models reaches a very good correlation after
approximately 1700 iterations (Figure 5.6).
Figure 5.6. Genetic algorithm performance. Fitness improvement with genetic algorithm
during an inverse model run on a population of 200 models. There are 9 observation data
sets (wells) and the maximum fitness is 9. The histograms show distribution of the fit in
the model population after different numbers of trials.
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5.5
Inverse Modeling Results
The inversion methodology was tested with different population sizes and with more or
fewer iterations. It was concluded that an initial population of 200 explores the parameter
space adequately and after 6000 iterations it will converge to a stable population. The
results also depend on the number and location of the wells. The results using an array of
4 wells (Figure 5.5) are shown in Figure 5.7 as histograms of the marginal distributions
for the inverted parameters. Each marginal distribution is the projection of the sixdimensional multivariate distribution onto a single dimension. The mode or expected
value parameter vector for the final population of 200 models does not need to be
approximately coincident with the “actual” model used to generate the "observed" data
(Figure 5.7A). The parameter distributions for the "good" models that have a fit greater
than 3.95 out of 4 during 14 runs of 6000 iterations each are plotted in Figure 5.7B. The
mode for the distribution is close to the actual model (red lines), but with a large spread
in the range of possible values.
To understand the relationships between parameters and the possible “trade off” we
calculate cross-plot errors and the resolution matrix. The resolution matrix was obtained
from a principal component analysis (Davis, 1986) of the good model population (fitness
greater than 3.95). For a population of M models in N parameters the eigenvalues and
eigenvectors of an N x N covariance matrix are found. This analysis suggests that only 4
(out of 6) parameters are nonzero in the principal axis coordinate system. The R or
resolution matrix is found by multiplication of the truncated eigenvector matrix with its
transpose (Kennett and Nolet, 1978). Rows of the resolution matrix are plotted in Figure
5.8. A perfectly resolved parameter would have a delta function in its row, the degree to
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Figure 5.7. Results of inversion using 4 wells (control points); me-mean, md-median, stdstandard deviation, n-number of models. (A) Distribution of parameter values of a final
population of 200 models after 6000 iterations, all the models have a fit over 3.99. (B)
Distribution of parameters values for the models with the fit over 3.95 from a maximum
of 4 from 14 succesive runs with 6000 iterations.
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Figure 5.8. Resolution matrix for all models (74220) resulting from inversion with four
control wells that have a fit greater that 3.95. Variables are uo-initial velocity, bo-channel
width, ho-channel depth, kx-diffusion coefficient normal to the shore, ky-diffusion
coefficient alongshore, d-dumping coefficient. The resolution matrix indicates how well a
parameter can be solved independently. There is a large dependence between initial
velocity and channel width. Diffusion coefficients and dumping coefficient are solved
independently by the other parameters. For detailed discussion see the text.
136
which parameter values are averaged due to loss of resolution is indicated by the breadth
of the function plotted in a given row. The values of the R matrix indicate how much
correlation (normal or inverse) exists between a parameter and all the other parameters.
For example in Figure 5.8, initial velocity has a large inverse (negative) correlation with
channel width. In the case of the diffusion coefficient normal to the shore (x-direction) it
is delta like, indicating an independence of this parameter value relative to the other
parameters. The resolution matrix depends on the forward model itself and also on the
distribution of sample points. Poorly distributed sample points can also reduce resolution.
Error cross-plots for pairs of parameters (Figure 5.9) have been calculated in order to
Figure 5.9. Crossplot parameters pairs. The graphs indicate the fit for each possible value
of the parameters. The maximum fitness is dark red, the white point are the values of a
population model of 200 after 6000 iterations. Magenta dot is the original value. Note
that the color scale is different for each graph.
137
promote understanding of the resolution question. The cross-plots have been calculated
using an enumerative method; error was computed varying two parameters over the
parameter space; holding all of the other four parameters constant. The error measure, the
summed well correlation, is then contoured. Topographic trends in these contour maps
(Fig. 9) show a negative correlation between initial velocity (u0) and channel width (b0)
and depth (h0) and between channel depth (h0) and width (b0). A positive correlation
exists between diffusion coefficient alongshore (ky) and channel width (b0) and depth
(h0). Diffusion coefficient normal to the shore (kx) has no correlation with initial velocity
(u0) or other parameters and it might have any possible value for the same initial velocity
(Figure 5.9).
5.6
Dependence on the Well Locations
We test how sensible the results are relative to the position of the control points in the
basin (wells). Three distinct possible distributions of 9 wells have been considered
(Figure 5.10). The marginal histograms for models with fitness greater than 8.95 from 15
runs are plotted in figure 5.10. As in the case of inversion using 4 wells, the diffusion
normal to the shore (kx) was poorly resolved. When the wells are distributed along a line
normal to the shore (Figure 5.10B) the resolution matrix shows that channel width is
better resolved than the other arrays.. Standard deviation for all parameters are higher
than in case of normal distributed wells but the the parameters distributions have even
larger standard deviations in the case of an array oriented parallel to the shore. In the case
that wells are distributed along a line parallel to the shore, (Figure 5.10C) the parameters
that are still relatively well resolved are initial velocity (u0) and diffusion coefficient
alongshore (ky) (Figure 5.10C) Dumping coefficient (d), channel width (b0) and depth
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(h0) are almost uniformly distributed.. The results of inversion using different arrays
indicate that initial velocity (u0) and diffusion coefficient alongshore (ky) are the least
sensible to the distribution of wells while dumping coefficient (d), channel width (b0) and
depth (h0) are highly dependent on the well array. Diffusion normal to the shoreline (kx)
is not resolved properly regardless by the well array.
Figure 5.10. Distribution of different arrays of 9 wells into the basin and the resolution
matrix for the best models (from 15 runs) with a fit over 8.95 from 9. (A) Normally
distributed wells. (B) Wells distributed normal to the shoreline. (C) Wells distributed
alongshore. When the control wells are normally distributed into the basin, the
parameters are overall better solved. In the case when the wells are distributed normal to
the shore, channel width is better solved. In the case when the wells are distributed
parallel to the shore, the velocity and coefficient diffusion along the y direction is better
solved.
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5.7
Discussion and Conclusions
To perform stratigraphic inversion with the forward model used in our study we need
accurate time measurements in vertical well logs, which are closely spaced (hundreds of
meters to kilometers). Studies of Quaternary deltas (Masuda and Iwabuchi, 2003, Tanabe
et al., 2003) have limited numbers of wells (two or three) with accurate time
measurements that are widely spaced at tens of kilometers. The type of data discussed in
this study is not generally available, but could be produced, at least in principle, for a
particular delta. Seismic reflection data, wells and cores or historical bathymetric maps
might be used to produce invertable data sets.
Solutions to the inverse problem are non-unique and a range of parameters can generate
similar bed geometry. This was demonstrated by the inversion of synthetic data, based on
a known parameter set. Similar results were obtained for different sampling densities
(number of control wells). The results presented in this paper are specifically derived
from the Syvitski (1988) type delta model, but some of the conclusions should generalize
to any formulation that adequately captures the dynamics of delta formation. The use of
the genetic algorithm optimization and multivariate analysis of the model population
would work in the context of any reasonably efficient numerical modeling scheme. The
inversion procedure can estimate a most probable model (not necessarily the correct
model) as well as assess the parameter accuracy and the range of non-uniqueness (which
should cover the correct model).
The presence of non-unique models, which produce the same geometry, has implications
for geological interpretations and reservoir modeling. If there are multiple flow and
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transport conditions, which can generate the same stratigraphy, these need to be
considered when paleogeographical reconstructions are made.
For example a significant trade off was observed between flow velocity and channel
dimensions. Despite the multiple possible models the most likely can be chosen by taking
into consideration other conditions, which are external to the model, such as the position
of the river mouth relative to a mountain range (closer would have higher flow velocities
due to increased gradient).
CHAPTER 6
CONCLUSIONS
6.1
Concluding Remarks
Delta front deposits represent the key building block for any delta assemblage.
Continental derived sediments carried through the fluvial system and delivered to the
basins are filtered during its pass through a given delta system. Sediments delivered by
fluvial channels in deltas are partially retained in delta plain, delta front and prodelta
areas. Delta plain sedimentation is mainly active during the floods through levee and
overbank deposits. In contrast, sedimentation in the delta front and prodelta are
permanently active but the sedimentation rates vary with river discharge. Delta fronts are
important because they retain the coarsest sediments in deposits of the system due to
channel mouth processes. This controls the evolution of the entire delta dispersal system.
This study shows that delta front deposits are more than just a “sheet of sand” as is
generally defined, and have complex internal facies architecture. Some of the features
that were rarely described in ancient deltas are the presence of small terminal distributary
channel deposits and upstream inclined mouth bar surfaces that reflect landward
accretion. Also basin topography affects the way that sediments are dispersed into the
basin and this might create specific paths for delta progradation.
The main findings of this dissertation, are listed below, followed by suggestion for future
research and application of the results of this study.
141
142
6.2
Summary
The main contributions of this dissertation are:
1. Delta fronts of fluvial-dominated deltas that form in shallow water basins have
multiple coeval terminal distributary channels. The resulting delta front facies
architecture will have the characteristic coarsening upward signature but is nevertheless
distinct from the classical model of fluvial-dominated Mississippi type “bird-foot” deltas.
The shallow fluvial-dominated deltas have thinner overall delta front deposits that extend
laterally and contain deposits of shallow terminal distributary channels interbedded with
mouth bar deposits. The Lafourche lobe of the Mississippi delta has been previously
interpreted as a lobate fluvial-dominated delta (Frazer, 1967).
2. Because of the presence of multiple coeval small terminal distributary channels that
deliver sediment to the basin, the resulting shoreline morphology will be lobate. The
lobate shape of the delta deposits might be erroneously interpreted as wave-dominated in
subsurface based only on lobate sand bodies shapes as was described by Galloway
(1975). This misinterpretation might appear especially in cases when only low resolution
subsurface data is available, which makes it impossible to identify and map small
terminal distributary channels that have dimensions below typical subsurface data
resolution.
3. Incision of distributary or terminal distributary channels into their own deposits is less
probable without allocyclic forcing (i.e. sea level change, uplift). Lateral erosion related
to channel migration of channel erosion due to flood events is possible, but these are
small adjustments to the short period discharge variation.
143
4. Remote sensing can be used as a method to identify river plume geometries. The
method is based on the fact that (1) visible- near infrared bands penetrate water at
different depths and (2) the reflectivity intensity is given by the suspended sediment
concentration in the water column. Because the images of each band represent depth
slices that reflect water properties, hyperpycnal plumes will show the turbidity front at
increasing distances from the river mouth, while homopycnal and hypopycnal plumes
will appear approximately in the same location.
5. Using the remote sensing method combined with plume water measurements and
historical measurements of physical properties of river and lake water it was established
that the Red River forms a permanent hyperpycnal plume into Lake Texoma. The
permanent plumes result from higher river water density that is the result of a
combination between high total dissolved solid (TDS) values during low discharge and
high suspended sediment concentration (SSC) during high discharge. The inverse relation
of TDS and SSC with discharge result in a permanent hyperpycnal plumes with dual
character, hypersaline plumes during low discharge and sediment-laden plumes during
high discharge.
6. The presence of permanent hyperpycnal plumes in Lake Texoma causes lake
topography to have a considerable influence on the lacustrine Red River delta
progradation. The Red River delta bypassed some parts of the lake following the old river
talweg that represented the highest available slope. The magnitude of topographic
influence on hyperpycnal plumes is controlled by basinal slopes and river discharge.
7. The Red River delta prograded at significant rates of 250 m/ year since 1944 when it
started to form. River discharge controls the delta progradation rate but also delta
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morphology. On multi-temporal aerial photos and satellite images it has been observed
that the delta had a lobate shape with multiple distributaries following periods of low
discharge and forms an elongate shape with a single large distributary channel during
high discharge periods.
8. The use of genetic algorithms for delta inverse stratigraphic models is a powerful tool
given the fact that forward stratigraphic models uses nonlinear equations that can not be
inverted using derivative-based methods. The inversion results using a synthetic model
indicate that statistically a solution can be found. However, there are multiple sets of
initial parameters that will produce identical delta stratigraphy indicating non-uniqueness
of the solution. Because of the non-uniqueness, the single-run forward models that
produce stratigraphic models that are “similar” to observed data should be avoided.
9. The exploration of the inverse solution using multiple control data arrays indicate that
the result is better constrained when the controls are evenly distributed into the basin. The
poorest constrained solution was found while using an array that uses control data
oriented predominantly parallel with the delta channel direction (normal to the shore).
6.3
Future Work Related to the Results of this Project
During the work on the papers that represent Chapters 2 to 5 more problems related to the
delta front and in general to delta deposits were unearthed. These topics are briefly
discussed below and might represent future directions of research.
6.3.1
Delta Distributary Channel Networks
In Chapter 2 implications of multiple coeval terminal distibutary channels to the fluvialdominated delta front architecture have been discussed. One of the aspects mentioned but
145
not detailed in Chapter 2 referred to the distinction of well developed distributary
networks in modern deltas but never described from ancient deltas (Frazier, 1969,
Roberts et al., 2004). A possibility to overcome the lack of data for ancient deltas is to
extract quantitative data from modern distributary channel networks and use the data as
input for a stochastic method to populate subsurface mapped lobes of ancient delta
deposits when the resolution of data is low (below resolution required to identify small
terminal distributary channels). The stochastic model will build distributary channel
networks with similar probabilistic distributions to modern deltas.
The data can be quantified after a method described by Morisawa (1985) with dimensions
measured on the circles with the centrum in a distributary network apex and with radius
at percent increments from maximum extension of the network (Figure 6.1). The data
Figure 6.1. Example of a delta distributive system with typical morphometric
characteristics that can be extracted from a distributary pattern, modified from Morisawa
(1985).
146
extracted for each distance from the apex will represent: number of channels, distance
between channels, bifurcation angles, and when possible, channel dimensions (width or
depth). The preliminary data measurements on modern deltas indicate that some common
characteristics exist for all distributary channel networks. The maximum number of
channels is reached at a distance of 60-80% from the apex (Figure 6.2). However, some
other morphometrical measurements, such as bifurcation angle, seem to be characteristic
for each delta. The measured results can be normalized to the entire distributary channel
Figure 6.2. Number of distributary channels of shallow water fluvial-dominated delta
distributary systems as a function of distance from the apex. Note that the maximum
number of distributaries appear at 60-70% distance from the apex and seems to be
consistent for all deltas measured.
network length, width and apex angle. In the case of a mapable ancient delta lobe, where
a distributary channel can be only inferred, based on the lobe dimensions, this can be
populated with distributary networks with similar statistics as in the modern. Such an
approach should be used cautiously because some of the morphometrical dimensions of
147
the distributary network depend on distinct characteristics such as system grainsize,
discharge regime, basin energy, or basin morphology.
6.3.2
Hyperpycnal Red River Plume into Lake Texoma
The study of facies architecture of the Red River Delta into Lake Texoma should be
made and linked with the results presented in Chapter 3 and Chapter 4. There are three
aspects that can be followed giving preliminary results of Chapter 3 and Chapter 4 that
(1) the Red River has a permanent hyperpycnal flow and (2) topography and river
discharge controlled delta morphology and progradation direction.
Conclusions of Chapter 3, that the Red River has a permanent hyperpycnal plume, should
be reflected in a succession of “turbidite” like deposits with alternate gradual transitions
from coarse to fine to coarse deposits. A coring program through the Red River delta
deposits should reveal the vertical and lateral variation of hyperpycnal deposits. For a
better understanding of bed geometries, high resolution seismic and/ or electro-metric
surveys should be made. The findings of such a study should be focused
on the fate of the large volume of coarse grained deposits that were related to high peak
discharges indicated on Figure 4.7. The subsurface delta facies architecture should also
reflect the transition from a low discharge lobate delta with multiple terminal distributary
channels to elongate delta with a single large distributary, as was observed on multitemporal imagery.
Basin topographic control on delta architecture should be reflected in significant
thickness variation in the strike direction. Asymmetrical development of beds due to
topography has been observed in turbidite deposits (e.g. Lomas and Joseph, 2004) but not
described in deltas.
148
6.3.3
Topography Influence on Delta Progradation
The results of Chapter 4 can be applied to study the Danube Delta internal architecture.
The area of the Danube Delta that now represent the “fluvial delta” (Panin, 1976, 1989,
1996) was an embayment of the Black Sea at the beginning of the Holocene (Figure 6.3).
Figure 6.3. Actual morphology of the Danube Delta, with location of wells (Liteanu and
Pricajean, 1963) used for cross sections. The delta area represented by green was a bay at
the beginning of the Holocene.
The initial Danube Bay was similar to Red River/ Lake Texoma. The Black Sea had
alternate fresh and brackish water (Liteanu et al., 1961) and because of this the Danube
149
probably had common hyperpycnal flows. Mulder and Syvitski (1995) erroneously
attributed the modern Danube as a river that never forms hyperpycnal plumes, estimating
exaggerated salinity in the basin based on the latitude of the delta. Pre-delta topography
in the Danube Bay area (Figure 6.4) indicates the presence of pre-delta drainage that
probably controlled the initial delta progradation.
Figure 6.4. Topography of predeltaic sediments in Danube Delta area based on well data
from Liteanu and Pricajean (1963).
A sequence stratigraphic interpretation of Danube Delta deposits, based on well data
(Figure 6.3) (Liteanu and Pricajean, 1963), suggest existence of multiple deltaic lobes or
150
parasequences (Van Wagoner et al., 1991). In my reinterpretations I used sequence
stratigraphy as a conceptual framework for interpretation, but allostratigraphic
terminology to designate mapped units (NACSN, 1983). In the Danube delta
accommodation depends on sea level changes as well as subsidence, which has a
significant tectonic component.
On two reinterpreted dip-oriented sections four allomembers separated by flooding
surfaces were differentiated (Figure. 6.5). Below the deltaic deposits, fining upward
successions of alluvial deposit are interpreted to represent the infill of the initial Danube
Bay.
The topography at the top of colluvial-prodelta deposits, bellow allomember 1, shows a
ridge in Mahmudia-Maliuc area (Figure 6.4). This ridge influenced progradation of
allomember 1 deltas. These are limited toward the south but follow the maximum
gradient (Figure 6.4) and prograded in the middle of the paleo-Danube Bay. The
transgression following allomember 1 flooded the entire Danube Bay but previous delta
areas of allomember 1 represent shallow water regions. Allomember 2 deltas prograded
in different direction than the delta lobes of allomember 1 and this happens because of
differential compaction around the older delta lobes.
The reinterpreted sections indicate paleo-topographic influence (i.e. Mahmudia ridge,
Chilia-Murighiol ridge) and tectonic control on progradation pattern and thicknesses of
deltaic lobes. The allomember thickness distribution suggest that allomember 1 followed
the pre-existeing talweg while the successive allomembers followed a compensation
model prograding to the side of the previous deltaic lobe.
The subsurface morphology is difficult to link with present day morphology when the
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152
active distributaries reached the open basin with low lateral topographic variability and
the brackish water of the Black Sea diminishes hyperpycnal plume frequency. The
conditions during delta progradation into the Danube paleo-Gulf were different with
considerable topographic influence.
6.3.4
Delta Front Sedimentation Rates and Depocenter Migration
A literature search has been made to find data collected from modern and ancient systems
that can be used to run the inversion program described in Chapter 5. Unfortunately
ancient data commonly lack the required spatial and temporal resolution to be able to
invert. Modern core data generally has the temporal resolution required but usually, cores
that have detailed analysis and descriptions are at large distances and the surfaces
between are merely extrapolated interpretations that are not reliable for a numerical
model.
However, the most appropriate and complete data seems to be represented by successive
(at decadal interval) bathymetric surveys in front of modern deltas. The study of
historical bathymetric maps in Danube and Mississippi deltas suggest a complex
evolution of delta front depocenters.
The isopach maps built in front of the Pass a Loutre distributary, in the Mississippi Delta
based on bathymetric maps from 1875, 1933 and 1965, indicate extremely high
depositional rates, up to 0.5 m/ year in some areas (Figure 6.6). These high sedimentation
rates are mainly related to sediment mass transport processes (Coleman and Prior, 1980).
An interesting study will be to asses the variability of depocenter switching that has been
153
Figure 6.6. Isopach maps in front of Pass a Loutre distributary of Mississippi delta. AIsopach map based on bathimetry differences between 1875 and 1933 maps. B- Isopach
map based on bathimetry differences between 1933 and1965 maps. A lighthouse has
been used as local coordinate origin. With black and white dashed lines are emphasized
the channel axis for south and north pass respectively. Note that sedimentary depocenter
(red color) moved from South to North.
154
observed in front of different secondary terminal distributary channels (Figure 6.6). The
front of the Sf. Gheorghe distributary of the Danube Delta shows migration of the
depocenter under a strong longshore current. Quantification of depocenter migration and
3-D variation in these deltas and in some other deltas where historical maps are available
Po Delta in Adriatic Sea or Rhone Delta in Mediterranean Sea, can contribute to a better
understanding of heterogeneities associated with delta deposits.
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VITA
Cornel Olariu was born in Bucharest, Romania, on April 28, 1971. He graduated in the
summer of 1995 from University of Bucharest, Faculty of Geology and Geophysics with
a Bachelor of Science degree in Engineering Geology. He worked from 1995 to 2000 as a
researcher at GEOECOMAR in Bucharest. He joined the graduate program of University
of Texas at Dallas, Geoscience Department in fall 2000 to work under the supervision of
Dr. Janok P. Bhattacharya and earn a MS title in summer 2002. After 2002 graduation he
continued his graduate studies at the University of Texas at Dallas.

Olariu, C. - Quantitative Sedimentology Laboratories

Transcription

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