Heat Flow and Energetics of the San Andreas Fault Zone

Transcription

JOURNAL
OF GEOPHYSICAL
RESEARCH, VOL. 85, NO. Bll, PAGES 6185-6222, NOVEMBER
10, 1980
Heat Flow and Energeticsof the San AndreasFault Zone
ARTHUR
H.
LACHENBRUCH
AND J. H.
SASS
U.S. GeologicalSurvey,Menlo Park, California
Approximately100heatflowmeasurements
in the SanAndreasfault zoneindicate(1) thereis no evidencefor localfrictionalheatingof themainfaulttraceat anylatitudeovera 1000-kmlengthfromCape
Mendocinoto SanBernardino,
(2) averageheatflowis high(~2 HFU, ~80 mW m-2) throughout
the
550-kmsegment
of theCoastRanges
thatencloses
theSanAndreas
faultzonein centralCalifornia';
this
broadanomalyfalls off rapidly towardthe Great Valley to the east,and over a 200-km distancetoward
the MendocinoTriple Junctionto thenorthwest.As othershavepointedout, a localconductiveheat flow
anomalywouldbe detectable
unlessthe frictionalresistance
allocatedto heatproductionon the main
tracewere•<100bars.Frictionalworkallocated
to surface
energyof newfractures
is probablyunimportant,andhydrologic
convection
is not likelyto invalidatethe conduction
assumption,
sincethe heat dischargeby thermalspringsnearthefaultis negligible.
Explanations
for thelow dynamicfrictionfall into
two intergradationalclasses:thosein which the fault is wdak all of the time and thosein which it is weak
onlyduringearthquakes
(possibly
justlargeones).The firstclassincludes
faultscontaining
anomalously
weak gougematerialsand faultscontainingmaterialswith normal frictionalpropertiesunder near-lithostaticsteadystatefluid pressures.
In the secondclass,weakeningis causedby the event(for example,a
thermallyinducedincrease
in fluidpressure,
dehydration
of clayminerals,
or acoustic
fiuidization).
In
thisclass,
unlikethefirst,theaverage
s•rength
andambienttectonic
shearstress
maybelarge,~ 1 kbar,
but thestress
allocated
to elasticradiation(theapparentstress)
mustbe of similarmagnitude,
an apparent
contradiction
withseismic
estimates.
Unlessseismic
radiationis underestimated
for largeearthquakes,
it
is difficulttojustify averagetectonicstresses
on the main traceof the SanAndreasfault in excessof ~200
bars.The development
of the broadCoastRangeheatflowanomalysouthward
from CapeMendocino
suggests
thatheatflowincreases
by a factorof 2 within4 m.y.afterthepassage
of theMendocinoTriple
Junction.Thispassage
leavesthe SanAndreastransformfault zonein itswake;thedepthof the anomaloussources
cannotbe muchgreaterthanthe depthof the seismogenic
layer.Someof the anomalous
heat may be suppliedby conductionfrom the warmer mantle that must occur south of the Mendocino
transform(wherethereis no subducting
slab),andsomemightbe suppliedby shearheatingin the fault
zone.With no contributionfrom shearheating,extrememantleupwellingwouldbe required,and asthenosphere
conditions
shouldexisttodayat depthsof only ~20 km in thenorthernmost
CoastRanges.
If there is an appreciablecontributionfrom shearheating,the heat flow constraintimpliesthat the
seismogenic
layer is partially decoupledat its baseand that the basaltractionis in the sensethat resists
fightlateralmotionon the fault(s).As a resultof thesebasaltractions,
the averagesheafingstress
in the
seismogenic
layerwouldincrease
withdistance
fromthemainfault,andtheseismogenic
layerwouldoffer substantial
resistance
to platemotioneventhoughresistance
on the mainfault mightbe negligible.
Thesespeculativemodelshave testableconsequences.
INTRODUCTION
hapsan orderof magnitude)we can scarcelyclaim to understandthe physicsof earthquakes
or the resistance
to platemoThe simplestmodelsof pure strikeslip upper-crustalearth- tions. It is seen that with seismologicestimates of two
quakessuchas thoseon the San Andreasfault can be considindependent
relationsamongthe stresses
(for example,apparered in termsof three fundamentalstresses:
an averagecom- ent stressand stressdrop), it is in principlepossibleto estimate
ponentof shearingtractionin the directionof fault slip that the magnitudesof all three stressesfrom an estimate of the
existsat the onsetof faulting,a corresponding
componentthat magnitudeof any one of them. Measurementsof rock friction
existsat the conclusionof faulting, and an averageresisting provideadditionalusefulconstraints.
In the first part of this
stress that results in the local conversion and loss of mechani-
cal energy during an earthquake. Indirect estimatesbasedon
seismological
observationsprovide information on differences
among these generalized stressesbut not on their absolute
magnitudes. Similarly, geodetic observationsof deformation
at the earth's surfaceprovide information on ratesof accumulation and releaseof strain, but they do not generallydistinguish betweenelastic and inelasticcomponents,and in any
case,they provide no meansof extractingthe absolutevalue
of elasticstrain necessaryto estimatethe magnitudesof the
fundamentalstresses.
Although seismologicand geodeticobservations have resulted in a substantial increase in the under-
paper,weaddress
theproblemof estimating
themagnitude
of
the resistingstressfrom considerations
of the thermalbudget
of the fault zone.
It waspointedout by Bruneet al. [1969]that for the longterm averagedisplacementrates that have been documented
on the San Andreas fault, the frictional heat generation
shouldresultin a conspicuous
localheatflow anomalyif the
averagedynamicfrictionalresistance
in the seismogenic
zone
exceeded a hundred bars or so. Since no such heat flow anom-
aly had been observed,it was concluded that this stresslimit
applied. Applying seismicallyderived constraintson stress
drop and apparentstress,they concludedthat the initial (tectonic) stresswas probablylimited to about 250 bars. Addi-
standingof earthquakes,our ignoranceof the magnitudesof
the stressesprecludesan understandingof their energetics. tional heat flow measurementsand analysis[Henyey and WasWith the presentuncertaintyin thesethree quantities(per- serberg, 1971; Lachenbruch and Sass, 1973] generally
supportedthese conclusions.In a recent study of New ZeaThis paperis not subjectto U.S. copyright.Publishedin 1980by land's Alpine fault, however, Scholz et al. [1979] interpret lothe American GeophysicalUnion.
cal thermal metamorphismand argon depletion as evidence
Paper number 80B0929.
6185
6186
LACHENBRUCH
AND SASS: ENERGETICS OF THE SAN ANDREAS FAULT ZONE
O=0
y •
1
dO
= •. O(x),
t>O
thermal part of the resistanceon the assumption that the
frictionally generatedheat is transmitted by conduction (an
assumptionwe examine in a later section).
If the sliding motion of two rigid blocks with uniform relative velocity2v is opposedby an averageresistingstressR, the
rate of energydissipationper unit fault area can be written as
2vR-- D + e
(1)
where D is the average rate at which energy is consumedby
creating new surface,and Q is the averagerate of mechanical
heat generation.If R• and ß representthe portions of the total
X2
resistingstress• allocated,respectively,
to eachprocess,
then
D -- 2vR•
(2)
Q -- 2w
(3)
R = R• + •-
(4)
x
Fig. 1. Conditionsfor the problemof frictionalheatingon a strike
slip fault.
that dynamic friction in the seismogeniczone of that fault averaged at least I kbar.
Conclusionsfrom all of these studieswere basedupon heat
conduction models, which are elaborated somewhat in the
next sectionand then applied to the heat flow data presently
available near the San Andreas fault. The new data generally
confirm the conclusions of earlier studies, viz., that there is no
detectable local heat flow anomaly at the San Andreas fault
We shall first considerthe relative importanceof R•.
The Role of SurfaceEnergy
Consider
a portionof a faultsurface
of areaA thathasbeen
active for a time t during which relative displacement2vt -- 2u
has occurred.We supposethat this motion has resulted in the
creation
of newsurfaces
of areaa andsp6cific
surface
energy
•, i.e.,
trace. After consideringthe probability of heat removalby hydrologic processes,we conclude that it is unlikely and con-
D=
a•
-At
sequently,that the 100-barslimit on averagefrictional resistance probably applieswhile fault motion is in progress.We Then from (2),
then considerthe heat flow constraint in terms of generalized
a•
results on rock friction and seismic stress differences and confirm that if the constraint on total seismic radiation
R•= 2uA
is taken at
(5)
face value, the fault must be surprisingly weak even when If the newly created surfacea is representedby a gougezone
fault motion is not in progress.Following theseconsiderations of half-width B composedof cubeswith dimension b, then
of heat flow near the fault trace, we examine the broad heat
6AB
flow anomaly observed throughout the California Coast
Rangesand its implicationsfor the evolution and mechanical
behavior
of the San Andreas
RESISTING
fault zone.
STRESS AND
EFFECTS OF STRIKE
LONG-TERM
a• b
(6)
and
THERMAL
SLIP FAULTING
When slip occurs on a fault, elastic energy stored in the
earth is released.Some may appear as kinetic energy of seismic radiation that leaves the fault zone, and the remainder is
consumedlocally in overcomingthe resistanceoffered by the
fault to progressof the slip motion. (In a recentmodel by Melosh[1979],resistanceto the movingfault surfaceis reducedby
acousticoscillations.In our analysisof energetics,the acoustic
energyabsorbedin the vicinityof the fault will contributeto the
fault resistance,
and any remainder,to the radiatedenergy.)Despiteits importanceto the understandingof earthquakesand
crustal stress,the magnitude of this resistanceis unknown.
Some of the work done against fault resistancemust be allocated to the productionof heat through varioussmall-scaleinelastic frictional processes;the rest could be consumed by
other energy sinks such as metamorphic and chemical reactions or by the surfaceenergy associatedwith the creation of
new fractures and flaws. Although the nonthermal portions
are generally expected to be small, they probably should be
identified and evaluated systematically.In this section, we
shall attempt to evaluate only the effects of surface energy.
We shall then discussthe theory necessaryto evaluate the
R• -•
3•
B
b
u
(7)
Accordingto a careful studyby Braceand Walsh[1962],/Jis
in the range200-2000erg/cm2 for a wide varietyof common
rock-formingminerals.Taking b •- 1 micron(10-4 cm) and/J
'• l03 erg/cm2, (7)yields
R•
,-3x107
B(c-•)
=30
B[bars](8)
u
u
Hence for thesevaluesthe resistingstressallocatedto fracture
will not exceed30 barsunlessthe ratio of gougewidth to fault
displacement exceeds -• 10ø. For the San Andreas fault, this
ratio is probably•<10-2 (B •< 1 km, u •> 100km), whichseems
to allow us to neglect R• with some room for error in the
choices of b and/J.
It is important,to distinguishbetween surfaceenergy and
the 'fracture energy' used in models of macroscopicfracture;
most of the fracture energy ultimately appears as heat. In
studies reported by McGarr et al. [1979], specific 'crushing
energies'of about 5 x 105 erg/cm2 were determinedfrom
crushingtestson quartzite. They emphasize,however,that it
LACHENBRUCH AND SASS.'ENERGETICS OF THE SAN ANDREAS FAULT ZONE
6187
is not known how the work of crushing was partitioned
among surface energy, heat, and elastic waves.
It might be arguedthat over periodsof millionsof yearsthe
gougemight be repeatedlyhealed and refractured.Although
this could be important to the energeticsof individual events,
it seemslikely that the healing processwould releasethe surface energy as heat, and no long-term cumulative storageas
surfaceenergywould result.In what follows,we shall neglect
the contribution of surfaceenergyand use the symbolsr and
R interchangeably.
Thermal Effects
Equation (3) formsthe basisfor attemptsto estimateresisting stress(R • r) from measurementsof surface heat flow
[Henyey, 1968; Brune et al., 1969; Henyey and Wasserburg,
1971;Lachenbruchand $ass, 1973;$cholz et al., 1979]. In this
section,we presentresultsfor heat flow and fault temperature
that will be useful backgroundfor the discussionsto follow.
We considerthe thermal effectsof frictional heating by a vertical strikeslip fault in the planey = 0 in the half-spacex > 0
(Figure 1). A frictional heat sourceof strength
Q(x) = 2w-(x)
3
2
1
14
-<-----y/x•
28
42
y(krn)-•->-
0(•x2/K)-'
_
Ol ,••,c.
0•
02
x
x¾
_b
(9)
2•
startsat time t = 0, when the fault originates.From that time
46•
onward, the averageslip velocity 2v and averagedissipative
O(øC)
for• =1 HFU
resistancer(x) are both assumedto be independentof time.
Fig. 3. Surfaceheat flow q (part a) and fault plane temperature8
Consequently,the rate of heat generationdoesnot, on the average, change with time. The earth's surface x - 0 is main- (part c) for sourcestrengthdistributionshownin Figure 3b. Dimensional resultsare for x: = 14 km, K = 6 mcal/cm s øC, and X = 1.6
tained at zero temperature,the medium is homogeneouswith
thermal conductivityK - 0.006 cal/cm s øC (•2.5 W m-'
K-'), and thermal diffusivitya = 0.01 cm:/s. Thermal con-
for surfaceheat flow and fault plane temperatureare given for
duction is the only mode of heat transfer,and the fault is contwo cases:model 1, a linear increasein Q(x) from zero at the
sidered to be infinitely extended in the direction persurfaceto Q* at x = x2, with zero sourcestrengthelsewhere
pendicularto the x, y plane. In Appendix A, analytical results
(seeFigure 2b), and model 2, a sourceof uniform strengthQc
betweendepthsx, and x2, with zero strengthelsewhere(Figures3b and 4b). (For model2, the transienttemperaturedistribution throughoutthe entire medium is given, equation (A8).)
Resultsfor thesemodelscan be superimposedto describethe
effectsof any sourcedistribution Q(x) composedof step and
linear functions;a simpleusefulexampleis model3, Figure 5b.
In Figures 2-5, the resultsare normalizedby Q, the average
rate of frictional heat production between the surfaceand x2,
and q representsheat flow at the earth's surface. The well-
O8
O6
a
04
known resultsfor steadystateheat flow (appendixA, (A22b)
and (A23b)) are representedby the curveslabeled t = oo in
Figures2a, 3a, 4a, and 5a. The other curvesin partsa of these
figures represent transient states labeled in dimensionless
0
.
o• •p%
14
28
quantitieson the left, and dimensionaloneson the right (using x2 = 14 km, a = 0.01 cm2/s).The time constantis 2• =
(X2)2/4ot;
it is about1.6m.y. for x2 -- 14km, or 0.8 m.y. for x2
42
y(km)-•>-
O(Ox:/K)-'
õ
0,2 •
o•
_o?__03 _Oio =
ß t(my)
0•""
=
!
0o
230
46o
690
920
o(øc)forfi--1 HFU
Fig. 2. Surfaceheat flow q (part a) and fault plane temperature
(partc) for a linearincrease
in sourcestrength
to depthx2 (part b).
Dimensional resultsare for x2 = 14 km, K = 6 mcal/cm s øC, and X
(x:,):'/4a= 1.6m.y.
10 km. Such depthsare comparableto the thicknessof the
seismogenic
layer for continentalstrike slip faults.Within this
layer we often have reasonable assurance from microseismicitythat a substantialamountof slip occursin a narrow
zone [e.g., Eaton et al., 1970].Beneaththe seismogeniclayer,
the mode of mechanicaldeformation and heat generationis
more obscure,but fortunately,the effectof suchdeep sources
on the local heat flow anomalyis relativelyunimportant.For
example,increasingthe depthx2 of heat productionfrom 14
km to 28 km in the model of Figure 4b would increasethe
maximum heat flow anomaly by only 15% after 10 m.y. of
faulting (A23a), and near the fault the general form of the
anomaly would be changedlittle.
6188
LACHENBRUCHAND SASS:ENERGETICSOF THE SAN ANDREAS FAULT ZONE
what fraction of the relative plate motion can reasonablybe
assignedto a slip zone whosewidth is small in relation to the
thicknessof the seismogeniclayer. According to Atwater and
Molnar [1973], the relative right lateral motion between the
Pacific and North American platesaveraged4 cm?yr between
10 and 4.5 m.y. ago, and 5.5 cm/yr thereafter. Graham and
Dickinson[1978] believethat most of the motion was probably
concentratedon the San Andreas fault proper for the past 6
m.y. Analysis of geodeticdata by Thatcher[1979a] [seealso
Savageand Burford, 1973]impliesthat for the last century,localized displacementon the creepingportion of the San Andreas fault in central California probably averaged3 cm?yr,
and Sieh [1977] estimatesan average localized slip rate of
o
!
3
2
0
14
28
42
about 31/2to 4 cm?yr over the past 3400 yr in the presently
•
y/x•
y(km)
locked portion of the San Andreas fault in the Carrizo Plain
e(Ox•/K)-'
at the southernend of the Coast Ranges.At the latitude of the
0
•,Oc
0
01
02
03
04
Salton trough in southern California, Savage et al. [1979]
found that right lateral motion -,5 cm?yr was distributedover
a 120-km zone including the San Andreas, San Jacinto, and
x
Elsinore faults during the past 5 yr, and Thatcher [1979b]
found a similar broad region of strain accumulationin southb
•
28 ern California over the portion of the San Andreasfault zone
that boundsthe Mojave Block. These and other observations
suggestthat the presentrate of plate motion is typical of the
3
3•2
e(oC)
forõ=1HFU
averageover the last 10 m.y., -,5 cm?yr,and that the local slip
Fig. 4. Surfaceheat flow q (part a) and fault plane temperature 8 on the San Andreas fault presently might range downward
(part c) for sourcestrengthdistributionshownin Figure 4b. Dimen- from perhaps4 cm?yr in parts of the Coast Rangesto subsional resultsare for x2 = 14 km, K = 6 mcal/cm s øC, and 3, = 1.6 stantially smaller valuesin southernCalifornia.
m.y.
The disparitybetweeninterplateslip and fault slip suggests
that the problem of mechanicallygeneratedheat flow in the
The temperaturerise on the fault plane is shownin parts c interplate shear zone has two parts: (1) that which can be
of Figures2-5. On the upper scale,they are normalizedby the identified with frictional resistanceon a thin fault, and (2) that
'scale temperature,' Qx2/K, which is the one-dimensional associatedwith more broadly distributedinelasticdissipation
steady temperature that would result at the base of the
ø
I
s_eismogenic
layerfroma horizontal
planesource
of strength
Q there. On the bottom abscissalscalethe temperaturesare
shownin degrees
centigrade
for 0 -- 1 HFU -- 41.8mW/m•
(and X2 •---14 km, K -- 6 x 10-3 cal/øC cm s). A usefulcon-
08
version for frictional heat generationrate is
I HFU--41.8
mW/m:
• 1.32
kbar
x I cm/yr(10i
06
Asa ruleofthumb,
reasonable
models
forthevertical
distil- •
bution of frictional heating in the seismogenic
zone yield a
04
maximu_m
temperature
riseof 30-40%of thescaletemperature(Qx2/K);suchtemperatures
areapproached
in twoor
0:
three time constants,typically a few million years.
v,
Similarly,
inspection
ofpartsa ofFigures
2-5suggests
that
the maximumlong-termheat flow anomalyq(y -- O, t ----oo)
0
3
over a narrow strike slip fault is typically 60-80% of the aver-
agerate of frictionalheatingQ for reasonable
verticaldistributions Q(x) in the seismogenic
zone. Thesevalues,too, are
generally approachedin a few million years;they fall off by
an order of magnitude at horizontal distancesof about the
thicknessof the seismogeniclayer. If appreciablefrictional
heatingextendsto within a few kilometersof the surface(Figures 2 and 3), a substantialfraction of the anomaly will develop in a few hundredthousandyears,and the anomalywill
be sharply peaked. For wider fault zones,the peaks of the
heat flow curves would be subdued somewhat, but this effect
2
1
<
0
y/x•
0[.,.,•! o,q•
28
42
y(km) •
e(Ox•/K)-'
0
x!
14
01
02
03.•.•4
x•
x
[-
• M'ode,
3
'•
'•
3
23
o
46
o
69
o
920
O(øC)
for•--1 HFU
is not importantas long as the fault width is small in relation
Fig. 5. Surfaceheat flow q (part a) and fault plane temperature0
to the thicknessof the seismiclayer.
(part c) for sourcestrengthdistributionshownin Figure 5b. DimenA major problem in applyingmodelsof an infinitesimally sional resultsare for x2 -- 14 km, K -- 6 mcal/cm s øC, and 3, -- 1.6
thin strike slip fault to frictional heating lies in determining m.y.
LACHENBRUCHAND SASS:ENERGETICSOF THE SAN ANDREASFAULT ZONE
6189
I0o
'7-
I10 o
I00'
,;50..
WYOMIN
t
L,
HEAT
FLOW
rnWrn-2
HFU
IO4- ••]
>2.5
63-104-•
1.5-2.5
$1--65 ]
] O.75--1.5
0
;•00
I
i
600
i
KILOMETERS,
e,
<0
Fig. 6. A contourmapof heatflowin thewesternUnitedStates.Abbreviations:
BMH, BattleMountainhigh;EL, Eureka Low; LV, LongValley volcaniccenter;SRP, easternand centralSnakeRiver Plain;Y, Yellowstonethermalarea;and
RGR, Rio Grande Rift.
in the body of the seismogeniclayer or beneath it. If the
former is appreciable, it should be associatedwith a local
pare the observedheat flow with a referencemodel obtained
from Figure2 by selectingfault slipvelocities(2v) of 2 cm/yr
anomalyover the fault, accordingto the modelswe havejust and 4 cm/yr. The linear increaseof Q(x) with depth in this
presented;the latter may be associated
with a broaderthermal model correspondsto a simplefrictional law in which the efanomaly [seeLachenbruchand Sass,1973].
fectivenormalstressduringfault movementis proportionalto
Although
both•artsof theproblem
will bediscussed,
at overburden
pressure.
We selectQ = ,r/2 HFU sothatthe refpresent,we are interestedin limits to fault frictionimplied by erence model yields a convenientmaximum heat flow anomlocal heat flow observations.For this purpose,we shall com- aly of I HFU (A23b), and we shallassumethat the depthof
6190
LACHENBRUCH AND SASS' ENERGETICS OF THE SAN ANDREAS FAULT ZONE
TABLE 1. Summaryof Heat Flow and Heat ProductionValuesNear the San AndreasFault
Heat Flow
Designation
FS-STH
FS-AZI
FS-AZ2
SB-AZ3
FS-LB 1
FS-ACI
MB-YVW
FS-SB2
FS-SB3
FS-SB4
TR-PSA
TR-PSB
MB-PSC
FS-LH3
MB-PSD
FS-LH2
MB-PSE
MB-HVI
FS-LHI
GF-TEI
GF-TE2
GF-TE3
GF-TE4
GF-TE5
GF-TE6
GF-TE7
MB-PSF
Locality
Reference
2
Latitude
Longitude
HFU
mW/m2.
SaltonTrough
CO 71
32-48.
115-15.
3.2
ANZA A-I
ANZA A-3
ANZA A-2
L.A. Basin LB-I
Santa Ana AC-I
HW 71
HW 71
HW 71
US 71
US 71
33-30.
33-32.
33-32.
33-53.
33-58.
116-36.
116-36.
116-48.
118-02.
117-38.
1.87
1.76
1.46
1.74
1.60
78.3
73.7
61.1
72.8
67.0
Yucca Valley Water
US 79
34-13.5
116-24.2
1.12
46.9
San Bernardino SB-2
San Bernardino SB-10
San Bernardino SB-5
Palmdale Stress A
Palmdale StressB
Palmdale StressC
HW 71
HW 71
HW 71
US 79
US 79
US 79
34-15.
34-15.
34-16.
34-25.6
34-28.1
34-33.2
117-19.
117-20.
117-20.
117-51.8
117-51.2
117-42.9
1.63
1.58
1.08
1.58
1.60
1.51
68.2
66.1
45.2
66.1
67.0
63.2
118-29.
1.68
70.3
1.57
65.7
4.9
2.1
Lake HughesLH-2
HW 71
34-41.
118-26.
1.56
65.3
3.4
Palmdale StressE
Hi Vista
US 79
US 79
34-43.9
34-43.9
117-4 1.7
117-41.7
1.64
1.60
68.7
67.0
6.2
6.2
1.4
2.6
2.6
Lake HughesLH-I
Tehachapi Mt. DH-15A
TehachapiMt. DH-70
TehachapiMt. DH-14
Tehachapi Mt. DH-43
Tejon Ran. DH-43
Tehachapi Mt. DH-65, 67
Tejon Ran. DH-61, 65, 67
HW 7I
HW 71
HW 71
HW 71
HW 71
US 71
HW 71
US 71
34-44.
34-51.
34-52.
34-52.
34-53.
34-53.
34-56.
34-56.
118-24.
118-44.
118-45.
118-45.
118-46.
118-46.
118-49.
118-49.
1.72
1.48
2.21
2.03
2.02
1.83
1.30
1.36
72.0
62.0
92.5
85.0
84.6
76.6
54.4
56.9
8.7
3.6
1.64
68.7
1.93
80.8
FE-EHI
Elk
Elk
Elk
Elk
Hills 382-3G
Hills 343-4G
Hills 344-35S
Hills 372-35R
Elk Hills 326-28R
Elk Hills 385-24Z
Elk Hills 366-24Z
Temblor
La Panza TS-I
West of Bakersfield
US
US
US
US
US
US
US
US
US
BE
71
71
71
71
35-16.
35-16.
35-17.
35-17.
119-23.
119-24.
119-22.
119-28.
1.26
1.12
1.20
1.30
71
71
71
79
35-17.
35-18.
35-18.
35-21.3
119-31.
119-33.
119-34.
119-49.7
71
47
35-26.
35-28.
120-30.
119-45.
1.26
1.20
1.00
1.45
2.21
1.29
52.7
46.9
50.2
54.4
52.7
50.2
41.9
60.7
92.5
54.0
FE-VCS
FW-BHR
FE-PRM
FE-SEI
FE-MPI
FE-DMI
FE-DEI
FE-RCE
FE-MSL
1.6
1.0
1.3
1.1
117-50.8
119-26.3
FE-PT0
FE-PT9
FE-PT2
FE-PT3
FE-PT6
FE-PT5
FW-BLM
1.5
34-39.
117-45.7
FW-HT6
FW-HT2
FW-HT7
FE-PTI
3.7
34-39.1
35-04.2
FW-HT4
2.7
HW 71
34-56.1
FW-HTI
6.5
US 79
US 79
FW-MOP
1.5
1.2
0.9
Lake HughesLH-3
US 79
FW-STC
3.6
2.8
2.2
Palmdale StressD
Palmdale Stress F
FW-PR3
FW-PR4
FW-HT3
FW-HT5
#W/m 3
3.8
2.5
3.0
2.6
Maricopa
FW-USL
FW-PR2
HGU
134.
FE-MLI
FE-EH2
FE-EH3
FE-EH4
FE-EH5
FE-EH6
FE-EH7
FE-TLI
FW-TSI
FE-WB 1
FW-HAR
FW-PAT
FW-PRI
Heat Production
7.7
3.2
2.1
0.9
1.1
0.5
5.7
2.4
5.4
2.3
Harmony
US 79
35-29.5
120-58.7
1.80
75.3
2.7
1.1
Patterson et al.
PRC-2
USL 1-3
PRC-7
PRC-12
PRC-19
Hollister HO-3
Hollister HO-5
US
US
US
US
US
US
HE
HE
79
79
79
79
79
79
68
68
35-55.5
36-01.9
36-02.9
36-03.0
36-03.9
36-05.7
36-32.
36-35.
121-01.7
120-51.6
120-46.6
120-48.7
120-46.0
120-42.5
121-40.
121-27.
2.3
2.0
2.25
2.0
2.4
2.1
1.20
1.90
96.
84.
94.
84.
100.
88.
50.2
79.5
4.1
1.7
2.8
1.2
Monterey
Stone Canyon
US 79
US 79
36-36.3
36-38.4
121-54.9
121-15.5
1.56
1.79
65.3
74.9
3.8
1.6
3.5
1.5
Hollister HO- 1
Hollister HO-4
Hollister HO-6
Hollister HO-2 & 7
Hollister HO-8
Pacheco Tunnel 208
Pacheco Tunnel 210
Pacheco Tunnel 219
Pacheco Tunnel 212
Pacheco Tunnel 213
Pacheco Tunnel 216
Pacheco Tunnel 215
Ben Lomond
HW 71
HE 68
HE 68
HE 68
HE 68
US 79
US 79
US 79
US 79
US 79
US 79
US 79
US 79
36-43.
36-48.
36-50.
36-53.
36-55.
37-01.6
37-01.7
37-02.6
37-02.8
37-03.0
37-03.2
37-03.3
37-06.9
121-24.
121-20.
121-17.
121-35.
120-58.
121-18.7
121-18.4
121-15.1
121-14.2
121-12.8
121-11.3
121-10.8
122-09.1
1.71
2.30
2.30
1.70
1.40
2.03
2.12
2.14
1.90
2.10
1.60
1.63
1.61
71.6
96.3
96.3
71.2
58.6
85.0
88.7
89.6
79.5
87.9
67.0
68.3
67.4
3.4
1.4
3.1
3.1
3.1
3.1
3.1
3.1
3.1
2.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
0.9
Valley Christ. School
US 79
37-14.3
122-04.1
2.15
90.
Pescadero BHR-I
Permanente
US 79
US 71
37-14.7
37-19.
122-23.7
122-07.
2.53
2.20
105.9
92.1
4.6
1.9
3.2
1.3
SunnyvaleC-3
US 71
37-27.
122-02.
2.02
84.6
Melno Park MP-1
US 68
37-27.
122-10.
2.16
90.4
Dumbarton S.F. Bay
US 71
37-29.
122-08.
2.25
94.2
DumbartonEarthquakeI
US 79
'•7-30.6
122-07.8
2.03
85.0
Redwood City Exp.
May School
US 79
US 79
37-30.8
37-44.3
122-12.5
121-45.2
1.85
1.52
77.
63.6
LACHENBRUCH
AND SASS:ENERGETICS
OF THE SAN ANDREASFAULT ZONE
6191
TABLE 1. (continued)
Heat Flow
Designation
•
Locality
Reference
2
Latitude
Longitude
HFU
mW/m2
FE-TRI
TracyDH-2
US 71
37-48.
121-35.
0.96
40.2
FE-DA 1
Danville
US 79
37-48.1
121-56.5
1.28
53.
FE-MST
BerkeleyMSTW
US 71
37-52.
122-15.
2.00
83.7
FE-NIC
Nicasio
US 79
38-05.5
122-44.9
1.84
77.0
FW-PTR
PointReyes
US 79
38-05.7
122-53.5
1.91
80.0
FE-SEA
Sea Ranch
US 79
38-42.0
123-25.1
2.2
92.
FE-ANP
Annapolis
US 79
38-43.1
123-20.8
2.16
90.
FE-CL 1
Cloverdale
US 79
38-46.
122-58.
3.50
146.5
FE-GYS
3 Holesat the Geysers
US 79
38-48.
122-50.
10.00
418.6
FE-GUI
FE-COL
FW-PTA
FE-BVL
FE-UKI
Guinda
Colusa Basin
Pt. Arena
Booneville
Ukiah
US
US
US
US
US
38-50.4
38-53.0
38-55.7
38-59.6
39-03.4
122-12.0
121-53.7
123-42.6
123-20.8
123-09.1
0.90
0.80
1.44
1.27
1.78
37.7
33.5
60.3
53.
74.
79
79
79
79
79
FE-PVY
PotterValley
US 79
39-20.4
123-06.1
1.8
76.
FE-NOY
NoyoHill
US79
39-24.5
123-44.•8
1.8
75.
FE-WIL
CR-EG7
CR-EG8
Willitts EC- 1
Cottonwood Glade EG-7
Cold Creek EG-8
US 71
US 71
US 71
39-34.
39-42.
39-42.
123-07.
122-48.
122-53.
1.85
1.20
1.50
77.4
50.2
62.8
FE-LYN
Laytonville
US 79
39-43.8
123-30.1
1.42
60.
FE-CLN
FE-LMR
FE-SCV
FE-GBL
Covelo North
Lake Mtn. Ranch
Shelter Cove
Garberville
US
US
US
US
39-50.1
39-56.8
40-01.3
40-05.5
123-09.9
123-21.1
124-04.0
123-48.0
1.40
0.66
1.39
1.03
59.
28
58.
43.
FE-EBG
FE-KET
Ettersburg
Kettenpom
US 79
US 79
40-08.1
40-08.3
124-00.0
123-24.6
1.04
1.2
43.
50.
FE-FTS
Fort Seward
US 79
40-13.0
123-38.4
1.44
60.
FE-HON
Honeydew
US 79
40-14.4
124-07.6
1.8
75.
FE-PRA
Petrolia
US 79
40-19.4
124-16.5
1.82
76.
79
79
79
79
FE-GZB
Grizzly Bluff
US 79
40-32.8
124-10.6
1.31
55.
FE-NOS
FE-EUR
Nav. Ocean. Sta.
Eureka B-69
US 79
US 79
40-33.8
40-43.6
124-21.2
124-12.8
0.82
0.83
34.
34.7
FE-KSM
King Salmon
US 79
40-44.4
124-12.8
0.92
38.
FE-BLK
Blue Lake
US 79
40-52.6
123-58.8
1.18
49.
Heat Production
HGU
•W/m 3
2.9
5.0
2.1
1.2
0.2
0.1
2.8
2.4
1.2
1.0
ISubregions:
FS, FaultSouth;SB,Southern
CaliforniaBatholith;MB, MojaveBlock;TR, Transverse
Ranges;
GF, GarlockFault;FE, Fault
East; FW, Fault West; CR, Coast Ranges.
2CO71, Combs
[1971];HW 71,HenyeyandWasserburg
[1971];US 71,Sassetal. [1971];US 79,present
paper;BE 47,Benfield[1947];
HE 68,
Henyey[1968];US 68, Sasset al. [1968].
the seismogeniclayer (x2) is 14 km. The reference model
thereforerepresentsthe following conditions:
q---- 1 HFU--41.8mW/m 2
y--0
Q/2v -- Zavg
• 518bars
=
1035bars
t-- oo
(11a)
2v = 4 cm/yr
(1lb)
2v = 2 cm/yr
(11c)
The scaletemperaturefor use in Figure 2c is
Qx2/K = 365øC
(12a)
and the total rate of heat productionper unit length of fault is
trated in Figure 6. The westernUnited Statesis characterized
generallyby highand variableheatflow,althoughit alsocontainslargeareasof low-to-normalheatflow. High heat flow in
regionsof extensionaltectonicslike the Basin and Range
provincecan be accountedfor by the upward massflow required for plausiblerates of lithosphereextension[Lachenbruch and Sass, 1978; Lachenbruch,1978]. Some zones of low
heat flow like the continentalmargin of the PacificNorthwest
may be related to heat sinksassociatedwith subduction;others, like the 'Eureka Low' (EL, Figure 6), may be related to
systematicregionalhydrologicphenomena[Lachenbruchand
Sass, 1977].
Qx2 -- 2.2 cal/cm s
= 0.92 Mw/km
(12b)
(12c)
The part of the California Coastalregion associatedwith
the transformboundarybetweenthe North American and Pacific plates has a range of heat flows typical of most other
Accordingto theseresults,if the averageslip velocitywere
partsof the westernUnited States(Figure 6). This includes
2-4 cm?yr,we shouldexpectto seea local heat flow anomaly measurements offshore in the Southern California Borderland
of 1.0-0.2 HFU over the fault trace for each 100 bars of fric[Lee and Henyey, 1975].
tional resistance,unlessthe fault trace were very young or the
In this paper, we shall examinea data set (Table 1, Figure
frictional heat had been removed or redistributed by hydro7) that includes:the firstheat flow determinationin California
logicprocesses.
In the next two sections,we shall examinethe
(WB 1, Table 1, Benfield[1947]),subsequent
measurements
by
data on heat flow and thermal springsin an attempt to obtain
Combs[ 1971],Henyey [ 1968],Henyeyand Wasserburg[ 1971],
a limit to frictional resitancefrom this point of view.
Sass et al. [1971], Roy et al. [1972], USGS data, which until
HEAT FLOW
now have receivedonly preliminary mention in the literature
The status of published heat flow measurementsin the [Lachenbruchand Sass, 1973, 1977, 1978], and results from
westernUnited Statesas of late 1979 [Sasset al., 1980] is i!!us- somerecentdrilling in the Northern California Coast Ranges.
6192
LACHENBRUCH
AND SASS: ENERGETICS
35,•'49
OF THE SAN ANDREAS
FAULT
PTI
38ON
3•#EUR
.53
'55
120ow
.40
' 64
•76.75 .60
•.43.
.50
x
-F
_•
.59
122•W
• .60 63..50
'
Hayward-Calaveras
80-90
•"68
Palo
Colorado
,• \
San Gregorio
96 ø59
72
75
65
.
ZONE
•
.74
/
No
84-100
36øS+
96 o
122ow
ø54
'--
50
0
50
1O0
150
\•,•.oR,
42-54
200 KILOMETERS
't•154••.,
5.
4S2'54.•ock
81 MA
B••62
•
7.
85_••72
_,. .69
72 66..68
7•65
+ 35øN
116øW
\
Fig. 7. Heatflow(mW/m2) in relationto majorrecentlyor currentlyactivestrikeslipfaultsin California:a, Eureka
(EUR) to PointReyes(PTR); b, PointReyesto Maricopa(MA); c, Maricopato SaltonTroughhydrothermal
areas(STH)
(1 HFU = 41.8mW/m:).
Data from the latter two categories(designated'US 79' in
Table 1) shouldbe consideredpreliminary and are subjectto
revisionafter more detailed study. Severalheat flow determinations within a small area of the Salton Trough [Combs,
1971] have been averagedand are representedas a single
point (STH) in Table 1 and the variousillustrations.The entire data setis composedof 106independentdeterminationsat
103 distinctsites(Table 1, Figure 7) over a broad (•100 km
wide) area including the main trace of the San Andreas fault.
For most of our statistical analyses,we have excluded data
from north of Cape Mendocino (region la, Figure 8), the
Great Central Valley (EH1 through EH7, MSL, TR1, DA1,
HT7, WB1, GUI, and COL, Table 1), the Geysers region
(GYS and CL1, Table 1), and the Salton Sea Area (STH,
Table 1), leaving a core of 81 heat flow determinationsfrom
the Northern and Central Coast Ranges, the Transverse
Ranges,and the southernpart of the San Andreas fault zone.
Sites more than 100 km from the fault zone in the California
borderland [Lee and Henyey, 1975] and the Mojave Block
[Lachenbruchet al., 1978] were omitted from our analysis.
LACHENBRUCH AND SASS: ENERGETICS OF THE SAN ANDREAS FAULT ZONE
Heat flow values are shown in relation
to the San Andreas
35
N
and other recentlyor currently activefault zonesin Figure 7.
In Figure 8, the locationsof all sitesare illustratedin relation
to the main trace of the San Andreas fault and to a number of
6193
3O
subregionsto be discussed
below. The core of 81 'fault zone'
determinationsform the basisfor Figures 9, 11, and 12 and
the associatedstatisticalanalyses.
The histogramof Figure 9 indicatesa nearly normal distribution of heat flow, with a mean of 1.75 + 0.04 HFU (72 + 2
25
mW m-'), significantly
lowerthantheBasinandRangemean
20
=81
HEAN
=
SD
=
0.36
1 .75
SE
=
0.04
HFU
of 2.1 HFU [Lachenbruchand Sass, 1977, 1978] but com-
parableto the mean of 70 valuesfor the SouthernCalifornia
Borderlanddiscussed
by Lee and Henyey[1975].An examination of the heat flowreheat productiondata (Figure 10) suggeststhat despitea large amount of scatter,the mean 'reduced'heat flow qr may be comparableto that from the Basin
and Range province [see Figure 9-3, Lachenbruchand Sass,
1978].However, there is evidentlyno linear relation between
heat flow and heat production,as is found farther east in the
Sierra Nevada batholith.
The heat flow as a function
of distance normal
15
10
to the fault
is shownfor the 81 data of Figure 9 in Figure 11. Shown also
2
1
is the pattern of curves representingthe reference anomaly
q
,HFU
discussed
in the last section.As in Figure 2, the top curve representsthe steady state, and the transient curves represent
Fig. 9. Histogram of 81 values of heat flow in the San Andreas
conditionsat 8 m.y., 2.4 m.y., 0.8 m.y., and 0.3 m.y. after the fault zone (Figures 7 and 8) (excluding hydrothermal areas, STH,
start of faulting. It is seenfrom Figure 11 that even the steady GYS, CL1, Table 1, and data from the Great Valley and north of
Cape Mendocino(region lb)).
state anomaly (representinga frictional resistanceof 1 kbar
for 2v = 2 cm/yr or 0.5 kbar for 2v -- 4 cm/yr) might go almostundetectedin suchwidely scattereddata. However, Fig- jected perpendicularlyonto the San Andreasfault and plotted
ure 11 obscuresa certain amount of systematicvariation. This as a function of distancefrom Cape Mendocino along the
can be seenfrom Figure 12 in which the heat flows are pro- fault trace to a distance of 1000 km, where the surface expressionof the fault disappearsin the vicinity of the Salton
Sea.The profile of Figure 12 has beendivided somewhatarbitrarily into subregions
(seeFigure 8 and Table 2) for the purpose of discussion.Although Figure 12 has a great deal of
scatter,it showsthat north of the MendocinoTriple Junction,
wherethe San Andreasfault doesnot exist(region l a), the average heat flow is low, about 1 HFU. Southward from the
Triple Junction, the heat flow seemsto increaseover a distance of about 200 km (regions lb and 2) to averagevalues
closeto 2 HFU, characteristicof the remaining550 km of the
California Coast Ranges(regions3-6). Heat flow is significantly lower (• 1.6 HFU) farther southalongthe 150-kmfault
segmentthat boundsthe Mojave Block (region 7). South of
region 7, data are inadequateto indicate the relation of heat
flow to the fault; however, the few data available are included
in Figure 12. The high values from STH near the Salton
Trough and CL1 near the Geysersare shownin Figure 12 for
1250
350+
reference.
0
500 KILOMETERS
Fig. 8. Map of California showingthe main trace of the San Andreasfault, heat flow control,and the regionsdepictedin Figures1319. Stippled area indicatesthe approximateextent of the Great Central Valley.
In Figures 13-19, heat flow in each of the seven regions
(Figure 8) is shown(with the referenceanomaly)as a function
of distancefrom the fault trace.A casualinspectionof the individual profilesrevealsthat there is no evidencefor a thermal
anomalydue to local frictional heatingat any latitude;if such
heatingdoesoccur,its magnitudemustbe much smaller(<<1
HFU) than that representedby the referenceanomaly. Attemptingto decidejust how much local heating at the fault
tracecouldgo undetectedin an individualprofile probablyis
more a matter for judgment than for statisticsbecauseof the
uneven areal coverage,the variability from site to site in the
quality of temperature and thermal conductivity data, and
suchlocally variable conditionsas hole depth, structure,hy-
6194
LACHENBRUCH
OF THE SAN ANDREAS
FAULT
ZONE
4
4- Sedimentary
andmetamorphicrocks
13 Granitic rock
-
131313
a• a a
0
0
I
I
2
I
I
4
,I
I
6
I
I
8
I
,
10
Heatgeneration
Ao,HGU
Fig. 10. Heat flow versusnear-surface
heat productionfor the San Andreasfault zone.Referencecurvesare for Basin
and Range province(upper) and easternUnited States(lower) [Roy et al., 1968].
the condrology, and microclimate. Making allowance for some of tach suchprecisionto any heat flow measurements,
that a local anomalydoesnot exthesedetails,we judge that a local anomalygreaterthan 0.2 sistencyof the data suggests
HFU is probablyprecludedin the CoastRanges.Scalingfrom ist even at the 0.1 HFU level. However, this is the region in
our steadystatereferenceanomaly,this would imply a maxi- which Thatcher[1979b]found geodeticevidencefor a broad
mum frictional resistanceof 50-70 bars assumingthe present- shearzone, and the local slip velocitymay well be only 2 cm/
day rate of fault slip of 3-4 cm/yr; allowinga bit for dis- yr or less.Furthermore, the tectonicsof the region suggests
equilibriumandfinitefaultwidth,a figureof-* 100barswould that the main fault trace could have shiftedpositionin the last
seem reasonable.
few million years.Hence even at this location,the thermal efSome numericalsupportfor a figure of this magnitudecan fectsof frictional resistanceas large as 100barsmight possibly
be obtained if we consider the 39 heat flow determinations
go undetected.
The horizontal lines denoting mean heat flow valuesin reusedto calculatemeansfor regions3-6 (Figure 12), the portion of the CoastRangesin which the fault zone has probably gions 3, 4, and 6 (Figures 15, 16, and 18) terminate between
been in existenceon both platesfor severalmillion years.It is the easternmostdrainage divide of the Coast Rangesand the
seenfrom thesedata (Figures20a and 20b) that the difference Central Valley. As in the caseof heat flow north of the San
betweenthe mean heat flow within 10 km of the fault (Figure Andreas fault zone (i.e., north of Cape Mendocino, Figure
20a) and beyond10 km from the fault (Figure20b) is quite in- 12), the valuesto its eastin the Great Valley fall off abruptly.
significant(0.01 HFU). Accordingto a two-sampleT test for (For discussion,seeLachenbruchand Sass[1973].)
this data set, the mean heat flow within 10 km of the fault difIn summary, the California Coast Ranges representa refers from the mean heat flow beyond 10 km from the fault by gion of generally high but variable heat flow enclosingthe
less than 0.2 HFU at the 95% confidence limit.
landward portion of the San Andreas fault zone. There is no
The remarkably uniform values in the Mojave segmentof evidencethat the heat flow is greaternear the fault trace than
the fault (region7, Figure 19) deservespecialcomment.(Fol- in the surroundingterranesover a 1000-kmdistancealong the
lowing Henyey [1968] and Henyeyand Wasserburg[1971], we fault trace southwardfrom Cape Mendocino.With reasonable
exclude the single low value, SB4, Table 1, becauseof sus- assumptionsfor fault slip rate and age and assumingconpectedhydrologicdisturbances.)The total range is 1.51-1.74 duction is the only mode of heat transfer, this result suggests
HFU, and the means and standard deviations(Table 2, Fig- that the average dissipativeresistanceto motion on the fault
ures20c and 20d) are indistinguishablebetweendata setsob- does not exceed --•100 bars. The result supportsconclusions
tained within and beyond 10 km from the fault. In this region, from earlier studies[Henyey, 1968; Henyey and Wasserburg,
the two-sampleT test yields a differencein mean heat flows 1971; Brune et al., 1969; Lachenbruch and Sass, 1973]. We
within and beyond 10 km from the fault of less than 0.08 shall return to the problem of the broad Coast Range anomHFU at the 95% confidencelimit. Although it is risky to at- aly later; in the next section, we shall investigatethe possi-
I
PACIFIC PLATE
i
I
6195
i
1
......
NORTH AMERICAN PLATE
- 125
•:2.0
1
[]
MEAN
84•
[]
[]
[]
- 42
--
I
100
i
80
0
100
Fig. 11. Heatflowasa functionof thedistance
fromthemainfaulttracefor 81pointsof Figure9. Patternof curvesis
referenceanomalyfrom Figure 2a (see(1 l) and (12)).
bility that appreciable amounts of frictional heat might have
been generated and subsequently removed by hydrologic
the fault zone is removed by water flowing through relatively
permeablerocks,and it is dischargedby hot springs.
The distribution of thermal springs(those with a discharge
temperature >15øF above mean annual air temperature) is
HYDROLOGIC
TRANSPORT AND THE CONSTRAINT
shown in Figure 21 (modified from Figure 8 of Waring
ON FRICTIONAL
HEATING
[1965]). Along the main trace of the fault, spring activity is
We have seen that if heat transfer in the fault zone has been
very rare [see also Jennings,1975]. Within the Coast, Transpredominantly by conduction,then the absenceof a peaked verse, and Peninsular Ranges,there is a scatteringof thermal
heat flow anomaly suggests
that the averagestressallocatedto springs,but apart from thoseclearly associated
with the Geyfrictional heating on the fault is small (•<100 bars). If, how- sers geothermal zone north of San Francisco, their temperever, substantial amounts of frictional heat were transferred aturesare not high, and their flow rates are small, typically of
convectivelyby moving ground water, much larger frictional the order of 50 l/min or less.Many of the springsin southern
stresseswould be permissible.There are two possibilitiesfor California occurcloseto currently or recently active strike slip
removal of the hypotheticalundetectedfrictional heat: (1) it faults (for example,Elsinore,San Juan, Garlock, San Jacinto)
was dischargedat the surfaceby thermal springs,or (2) it was [Jennings,1975],but north of the San Bernardino Mountains
redistributeduniformly over a broad zone (--•100 km wide) by (i.e., north of the southernlimit of region 7, Figures 8 and 11),
no thermal springsare reported preciselyon the main trace of
someunspecifiedhydrologicprocess.
processes.
the San Andreas
Dischargeby ThermalSprings
fault.
In Table 3 we have compiled data from all of the thermal
In attempting
toreconcile
theapparent
lackof a peakedspringsthat we could find describedin the literature that lie
heat flow anomaly near the San Andreas fault with laboratory
evidencefor high mean shear stress(-• 1 kbar), someworkers
[e.g., Hanks, 1977;Scholzet al., 1979] have suggestedthat the
San Andreas fault zone is analogous to mid-ocean ridges,
where the expectedconductiveheat flow anomaly is literally
washed out by convection of seawater within permeable
rocks. By this analogy, the heat generatedby friction along
within 10 km of the 950-km length of the San Andreas fault
trace between Cape Mendocino and the southwestboundary
of region 7 [Waring, 1965; Renner et al., 1975; Brook et al.,
1979; Samreel, 1979]. The total convectivedischargeover this
distanceis 1.25 MW, 80% of which is contributed by a spring
at the southern edge of the region (Table 3). The reference
anomaly of the last section,which correspondsto a frictional
6196
LACHENBRUCH AND SASS.' ENERGETICS OF THE SAN ANDREAS FAULT ZONE
TABLE 2.
Mean Heat Flows, Standard Deviations, and Standard
The possibility remains that the heat was flushed out in
Errorsfor the RegionsIllustratedin Figures8 and 13-19
transientpulsesimmediatelyfollowingunstablelocal heating
of groundwater duringindividualearthquakes.
However,this
shouldleadto conspicuous
surfaceactivityon a scalenot generally observed,and the model leavesunexplainedthe absenceof a local heat flow anomalyover creepingportionsof
Mean
Number
Heat
Standard
Standard
Region
of
Data*
Flow
O, HFU
Deviation,
HFU
Error,
HFU
I
la
lb
2
3
4
5
17
5
12
6
14
15
6
1.23
1.01
1.32
1.66
2.06
1.87
2.17
0.33
0.22
0.33
0.24
0.22
0.31
0.17
0.11
0.10
0.09
0.10
0.06
0.08
0.07
the fault.
Lateral Redistribution
of Heat by HydrologicCirculation
If we take the broadheatflow anomalyin the CoastRange
to be 0.8 HFU over a width of 84 km (6 timesthe depthof the
6
4
1.85
0.32
0.16
seismogenic
layer), the anomalousheat losswould be equiva7
15
1.58
0.15
0.04
lent to the heat generatedlocally by 2 kbar of frictional stress
14'•
1.62
0.06
0.02
on a fault with a slip velocityof 3 cm/yr. A similarresultapplies in southernCalifornia (region 7), where the regional
*Excluding sitesin the Great Valley, stippled,Figure 8.
'•Excludingsite SB4 (seetext).
anomaly is probablybroaderbut lessintense(•0.4 HFU?)
[seealso O'Neil and Hanks, 1980].Thus the thermal budget
resistance
of 500-1000bars(dependingon slipvelocity),repre- would not be violated by very large frictional stressesif a
sentsthe generationof almost I MW of frictional heat per kil- mechanismexistedto redistributethe frictional heat broadly
ometer of fault length (13b). Hence if such stresseshad been and uniformly.
operative, hydrologic convectionwould have had to remove
Thermally driven hydrologicconvectionis not a likely canheat at the rate of almost I MW?km to account for the abdidate.The absenceof thermalspringssuggests
that modelsof
senceof a local heat flow anomaly at the fault. Stated another thermally driven hydrologic convection should have a noway, heat dischargedconvectivelyby the thermal springs mass-flowboundarycondition.In that case,hydrothermalcircould be generatedon the fault by • 1 bar of frictional resis- culation driven by the buoyancyof water heated on a vertical
tance. Allowing an order of magnitude increasefor anoma- fault plain would generallyresult in an increase(not a delously large conductiveflux adjacent to the springs[see,e.g., crease) of near-surfaceconductiveflux near the fault trace.
Olmsted et al., 1975], discharge by the spring systemsstill Further evidenceagainstthermally driven convectioncomes
would not significantlyaffect our estimatedlimits of frictional from a recentstudyby Murata et al. [1979],who concludethat
stressbasedon conductiontheory. Furthermore,sincethe dis- 'the presenceof disorderedcristobalitein shaleadjacentto the
tribution of springsdoesnot indicate a concentrationof activ- San Andreas fault suggests
that movementsalong the fault
ity on the San Andreas fault trace, there is no particular rea- have not induceda sustainedrisein temperatueof even a few
sonsto supposethat the fault is the sourceof their heat.
degreesin the shale.'
4- CLI
STH
A
CALIFORNIA COAST RANGES--
3.0
'• Mojave
Region
I
i
lb
•
i
2
I
I
i
3
I
•
4-
i
4
•
I
u_
i
5
i
I
•
'br ++
A
&++
I
I
•1
•
_
+
A
+
84 •
+
--
A
+
A
4-
4-
4-
4-
4-
A
4-
+
++
A <• 10 km fromfault
+
•
0
I
I
I
I
I
500
125
6
'll.
2.0-
-
I
I
>10 km from fault
I
I
I
1000
Distance,km
Fig. 12. Heat flow,projectedon to the main traceof the SanAndreasfault, as a functionof distancefrom Cape Mendocino(CM, Figure 8). Regionsare as definedin Figure 8. Pointsin Great Valley (stippled,Figure 8) wereexcluded.
I
PACIFIC PLATE
I
I
i ........
6197
T
+North of CapeMendocino
(Regionla)
REGION 1
[:]Southof CapeMendocino
(Regionlb)
1
3.0
o
125
2.0
84
'•
1.32
[]
[][]
i
MEAN
lb
[]
55
[]
+
MEAN la
1.0
[]
42
42
+
El
,
0 r•
,
0
I
20
I
•
,
40
Distance,km
I
60
I
I
80
I
!
100
Fig. 13. Heat flow versusdistancefrom the main traceof the SanAndreasfault, regionI (Figure 8), shownwith referenceanomaly.Horizontallinesshowmeansfor regionla (north of CapeMendocino)and regionlb (southof Cape Mendocino).
Any mechanismdevisedto accountfor a broad uniform redistribution of frictional heat by water movement must contend with the observationthat on oppositesidesof the fault
the heat flows are similar, but the hydrologic regimes probably contrastsharply. In the Coast Rangesthe San Andreas
fault is bounded on the eastby metamorphicand sedimentary
rocksof the Franciscanformation and Great Valley sequence,
which accordingto Berry [1973] are characterizedby superhydrostatic pore pressures,approaching lithostatic in many
places. On the west the fault is bounded by the Salinian
Block, a fractured granitic terrain that probably has an open
(hydrostatic)hydrologicregime [I. Barnes,personalcommunication, 1979; see also Brace, 1980]. It is difficult for us to
imaginea hydrologicsystemthat might transportheat to both
the east and the west for distances
of tens of kilometers
in
such a way as to produce similar heat flows in such contrasting terrains.
O'Neil and Hanks [1980]cite depletionof hydrogenand oxygen isotopesin a narrow band of granitic rocks adjacent to
the San Andreas fault as evidencefor profound water circulation in the fault zone. It is known that such depletion can result from interactions with ground water, which must penetrate to depths ---10 km to replace water heated during the
coolingof a pluton [e.g., Taylor, 1978].Sincethe origin of the
granitic rocks predates the origin of the San Andreas fault
(---20m.y.B.P.) by about 50 m.y., however,it is not clear that
the observed isotope depletion is associatedwith the fault.
O'Neil and Hanks estimate that the isotope exchangein this
anomalous band probably took place in the temperature
range ---100-200øC, temperatures that obtain today in the
depth range ---3-6 km. In the absenceof pervasivesurfacehydrothermal activity, for which there is no evidencetoday, the
surface from which their samples were obtained must have
undergone3-6 km of erosionsincethe isotopeexchangetook
place. It follows that unlesserosion of at least 3-6 km occurred at all of their samplesitesduring the last 20 m.y. or so,
the water circulation responsiblefor the anomaly probably
predated the fault and is unrelated to it. If such erosion did
occur,it still doesnot necessarilyimply that the anomaly is related to the fault; it could be the result of differential uplift
and erosionnear the fault, exposinga preexistinganomalous
condition that was a function of depth. In any case, the evidencefor isotopedepletion occursonly on the west side of the
fault and does not resolve the question of why heat flow is
high on both sidesin spite of the contrastinghydrologiccharacteristics.
In summary, the similarity of heat flow values and the contrast in hydrologic regimeson either side of the San Andreas
fault, taken with the absenceof appreciable convectiveheat
dischargeby springsin the vicinity of the fault make it extremely difficult to attribute the absenceof local high heat
flow to hydrologic transport in the fault zone. However, substantial undetected discharge at temperatures slightly above
ambient is a possibilityin almost any terrain, and more corn-
6198
LACHENBRUCH
AND SASS:ENERGETICS
OF THE SANANDREASFAULTZONE
-
I
I -
'i---- I
I
1
I
I
iPACIFIC
PLATENORTH
AMERICAN
PLATE
I
• 2.0
84 •
1.66
mean
69
_
1.0-
- 42
0
0
20
,
40
,
I
60
I
I
O0
Distance,km
Fig. 14. Heatflowversus
distance
fromthemaintraceof the SanAndreasfault,region2 (Figure8), shownwithreference anomaly.
prehensivestudiesof the hydrothermalbudgetof the fault
rm= /•O,'
(14a)
o,,'= o,,- P
(14b)
zone may be worthwhile.
IMPLICATIONSOF UNIFORM HEAT FLOW, FRICTIONAL
STRENGTH, AND SEISMIC CONSTRAINTS FOR
TECTONIC
STRESS
R =/•,o,,'
The foregoingdiscussion
suggests
thattheaveragefrictional
resistance
duringstrikeslipmotionin the seismogenic
layerof
•k
the San Andreasfault doesnot exceed• 100bars;it could, of
course,bemuchless.To avoida problemin notation(because
we shall discussseveraltypesof averages),we expressthis
condition generally as
average
dissipative
resistance
• 100bars= 10MPa
= -- %,,•< %,,
(15a)
(15b)
The symbolR usedpreviouslyis relatedto R and total fault
slip u by
(13)
Sincethisupperlimit is an orderof magnitude
lowerthan
• _-1•o
uRdu
u
(15c)
the dynamicfrictionthat onewouldexpectfrom the mostobviousextensionof laboratoryresultsto faults,(13) suggests The maximumstress(or 'frictionalstrength')that can be susthat specialconditionsmust prevail on the faults to account tained by a fracturedsurfaceon which the normal stressis o,
for their unexpectedweakness.In the followingsection,we is denotedby rm,porefluid pressureis P, and effectivenormal
consider
this'strength
paradox'in termsof generalized
results stressis o•'. The coefficientof (static) friction is the experifromlaboratoryexperiments
onrockfriction.It isfollowedby mentallydeterminedparameter/•. R is the instantaneous
disa section in which we consider additional constraints on fault
sipativeresistingstress(or dynamicfriction)operatingon the
stressimposedby seismicobservations.
slidingsurfacewhile motion is in progress.The coefficientof
dynamicfrictionis the parameter/•,,(15). Althoughthe experRock Friction, Fluid Pressure,and TectonicStressState
imentalbasisfor (15) is quiteuncertainand the two equations
We shall consider the relation between the heat flow con- oversimplifya very complexprocess,they provide a useful
straintand rock friction in termsof parametersfor the sim- framework for discussion.
plest frictional model, describedas follows:
The frictionalstrengthrmprovidesan upperlimit to the tec-
LACHENBRUCHAND SASS.'ENERGETICSOF THE SAN ANDREASFAULT ZONE
6199
PACIFIC PLATE
REGION 3
3.0
n
E•n I;3n
2.06
2.0
mean []
Ci
Ci
86
n
n
n
1.0
o
i
20
o
20
i
40
i,
60
i
i
80
i
!
lOO
Distance,km
Fig. 15. Heatflowversus
distance
fromthemaintraceof theSanAndreasfault,region3 (Figure8), shownwithreferenceanomaly.Horizontal'mean-line'terminates
at approximate
edgeof CoastRangeprovince.
tonic stressthat can be resolved on a fault surface and, con-
sequently,on the initial stressprior to an earthquake.The
frictionalstrengthis not constrained
by heatflow (13), and it
may be aslargeasotherconstraints
permit.The dynamicfriction R is, of course,constraintedby heat flow, but only for
thoseeventsresponsiblefor most of the displacementon the
San Andreasfault. We shallreferto sucheventsasthe 'principal events.' During principal events,the value of R may
changeif o,' changes
(evenif/•k is assumed
constant),
but its
displacement-average
R mustnot exceedan averageof-• 100
barsoverthe faultedsurface.In discussing
the heatflowconstraintin termsof rockfriction,it is usefulto distinguish
betweenexplanations
that requiresmallfrictionalstrength
and thosethat do not. In the firsttype,the fault is weak all of
the time,andin the secondtypeit mustbe weakonlyduring
principalevents(the two classes
are, of course,intergradational).
viewedfor our purposeasa reductionin R (15a) by a dynamic
reduction of either the effectivenormal stresso•' or dynamic
friction/•k.
The mostextensivebody of laboratorydata on sliding,rock
surfacescan be interpreted in terms of models of either kind.
It has been summarizedby Byerlee[1978],who showsthat for
a remarkably wide variety of rock materials (with or without
an interveninglayer of disaggregatedmaterial) the maximum
shearingstress•'mon the sliding surfaceattained during each
experimentis a simple linear function of the effectivenormal
stresso•' on that surface.To conform to (14a), we have eliminated the constantin his fit to the experimentaldata and have
adjustedthe coefficientof friction/• accordingly(seeappendix
B). This resultsin the following value:
/• • 0.75
(16)
which yields a reasonablygood approximationto Byedee's
The simplestexplanationof the first type ('permanent equationfor uppercrustalconditions
(On'< 6 kbar).
weakness')is that the fault containsintrinsicallyweak materiAfter the frictionalstrengthis reachedin laboratoryexperials, for example,water-rich clay minerals [Wu, 1978; Wang
and Mao, 1979,Summersand Byerlee,1977]or quartz grains
weakenedby the actionof water [Rutterand Mainprice,1978]
for which •-,,and henceR (15b) may neverbe muchin excess
of 100 bars. For such models the ambient tectonic stress in the
ments,failure may proceedunstablyby 'stick slip,' which is
generallyviewedas the analogof an earthquake,or by stable
sliding,generallytaken as the analog of a creep event in the
earth. In spite of the generality of the laboratory results,
$tesky[1978]cautionsthat 'we still don't know why Byedee's
law [generalizedin (14) and (16)] holdsnor why stickslip oc-
fault zonemustbe very low. Modelsof the secondtype ('transientweakness')generallyinvolve a mechanismfor reducing curs. Until we understand the deformation mechanism we
friction while fault motion is in progress.They include the will really have little confidencein extrapolatingour laboramodel of acousticfluidization [Melosh, 1979],which can be tory resultsto the earth.' Nevertheless,the simplicityof By-
6200
LACHENBRUCH AND SASS:ENERGETICS OF THE SAN ANDREAS FAULT ZONE
N. AM.
PACIFIC PLATE
PLATE
Monterey-Hollister
( U.S.G.S.
)
- 125
,• PachecoPass(U.S.G.S.)
v
3.0
CIT
I
REGION 4
- 84
I
2.0-
[]
1.87
mean
I
' 42
I
1.0-
.,.
-
o
'
40
20
0
Distance,Km
0
20
Fig. 16. Heat flowversusdistancefromthe maintraceof the SanAndreasfault,region4 (Figure8), shownwith referenceanomaly.Horizontal 'mean-line'terminatesat approximateedgeof CoastRangeprovince.
erlee'sgeneralization((14) and (16)) invitesa comparisonwith
the heat flow constrainton the San Andreas fault (13).
In experimentson polished granite, Byedee [1970] found
that R/q-m• 75%, and he commented that for other media the
ratio is usuallylarger. To the degreeof approximationof (14)
and (15), this suggests
3
/•---•
>•-4
/•
Combining(15b) and (18) and differentiating,
we obtainexpressions
for the increasein dissipativeresistance
with depth:
dR= 1.2/•--&
do3 dP.
dx
I•
dx
dx
(19a)
=0.51•'Idø'v•-•xxl
(19b)
/• Idøi
dx •xx
(19c)
=0.3
•[•k
dP
1
I•
(17)
dx
The approximation((14) and (16)) leads to an expression
for the frictional strengthof the most favorably orientedfrac- where the unprimed stressesdenotetotal values.For the case
ture in termsof the maximum (oi'), minimum (03%and aver- in which the fluid pressuregradientis normal (• 100 bars/kin;
age (o.,,g'),effectiveprincipalstresses
(seeappendixB):
by 'normal' we shall mean conditionsin an unconfmedcolumn
of water with unit specificgravity) and where the rock
q'm= 1.2 03'
densityp is 2.7 g/cm3, (17) and (19) yield
=0.50,
vg'
= 0.30i'
(18)d•-
= 0.4(Oi -- 03)
dX
d•
Equations(18) may be usedto estimatefrictionalstrength dx
q-mby insertingthe appropriateeffectivestressat the time
the appropriateaveragevaluesof effectivestressthat obtain
while faulting is in progress.We shall take the secondchoice,
since it includesthe first as a specialcase.
R (7 km) = 1070bars
vertical
(20a)
- 64 bars/km
of failure.
It mayalsobeused(with(15),(16),and(17)) dR-
tocalculate
theaverage
dynamic
friction
• provided
weinsert dx
153 bars/km
38 bars/km
R (7 km) = 445 bars
R (7 km) -- 270 bars
o•v• vertical
(2Oh)
vertical
(20c)
where the vertical stressis assumedto representthe weight of
overburden(pgx);R evaluatedat x = 7 km representsthe av-
I
I
I
I
6201
1
l
PACIFIC PLATE
NORTH AMERICANPLATE
REGION 5
125
3.0
..-.,
2.17
mean
[]
[]
91
[]
84 •
1.0
I
3O
0
10
0
10
0
Distance,km
Fig. 17. Heat flow versusdistancefrom the main traceof the San Andreasfault, region5 (Figure 8), shownwith reference anomaly.
cragcresistance
of a 14-kinscismogcnic
layer.The valuesof •
in (20) arc perhapsthe most'expectable'onesfor this extreme
rangeof tectonicstressstates.For an averageslipvelocity(2v)
of 3 cm/yr they correspond
(fromtop to bottom,respectively)
to local conductive steady state heat flow anomalies of 2.4,
1.0,and 0.6 HFU. The constraint(13) imposedby the absence
of such anomaliesimplies, however, that
dR
•'m(avg)
• 100bars
x p-p• 133b
100 bars
• •< 7•
This result saysnothing about the frictional strength •m at
the onsetof faulting unlessthe effectivestresses
in (18) were
the samebefore and during faulting. We shah assumethat this
condition is satisfiedif the fluid pressurewas unchangedduring the event. For this case, we obtain the condition of permanent weakness((13), (15b), and (17)):
"•15bars/km
(23)
(21)
The fluid pressures
(22) would then be a permanent(ambient)
conditionof the fault zone. If the uncertainvalue of/4, were
Combining this condition with (19) yields the constrainton
decreasedby a factor of 2, it would, of course, increase the
the averagefluid pressureduring faulting:
•
limit on frictional strengthproportionally, but the fluid presdP
sures (22) required for materials satisfying Byerlee's law
03vertical
(22a) would be reducedby only 10% or so. The restriction(23) on
dx >• 253bars/km
frictional strength stemsfrom the assumptionthat the fluid
dP
pressuregoverning failure is the same as the one governing
•xx>•230bars/km Oavg
vertical (22b) dynamic friction. The alternative will be discussedpresently,
but first we shah comment on explanations for anomalous
dP
•xx>•203bars/km O1vertical
(22c)
ambient fluid pressure.
The questionariseswhether the large fluid pressuresimplied by (22) could be generatedby long-termfrictional heatAccordingto (22), fluid pressureduring faulting would have ing of the fault. Water expandingat constantvolume under
to exceedthe normal value by a factor of 2 or more, irrespec- upper crustal conditionsundergoesa pressureincrease of
tive of the state of tectonic stress. This calculation illustrates
about 15 bars/øC [Lachenbruch,1980]. Hence to increasethe
the difficulty in trying to reconcilethe heat flow constraint fluid pressureby a factor of 2 from a hydrostaticstate would
with Byedee'slaw and the frictional theory of faulting. (A require an averagetemperatureincreaseof 47øC in a 14-kin
similar analysishas been madeby Steskyand Brace[1973].) seismogenic
layer. However, for a dissipativeresistanceof 100
6202
PACIFIC PLATE
REGION 6
125
3.0
I
I
,.-.,
[]
I
_o 2.0-
84 •
[]
mean
1.85
]
77
--
[]
[]
[]
[]
[]
O•0
I
I
60
I
I
40
20
0
20
40
D•stance,km
Fig. 18. Heatflowversusdistance
fromthemaintraceof the SanAndreasfault,region6 (Figure8), shownwith referenceanomaly.Horizontal'meanline' terminatesat the approximate
edgeof CoastRangeprovince.
bars(13) and slip velocityof 4 cm/yr (Q ~ 0.3 HFU, equa- 1973], which probably account for most of the cumulative
tion (10), Figures3c, 4c, 5c, and 6c) the averagetemperature fault displacement.Important contributionsto the transient
increaseon the fault plane would be only 10ø or 15oc after 10 pressureincreasecouldalsoariseif therewere relaxationof
m.y. of faulting. Hence even if the rock permeabilitywere precusorypore dilatation or dehydrationof clay minerals
in detail elsezero,thislong-termsourceof high ambientfluid pressuredoes [Raleigh,1977].Thesealternatives,discussed
not seempossible.(Thermal expansionof pore fluid during where [Lachenbruch,1980],allow failure to occurat low amevolution of the broad Coast Range anomaly is, however, a bient fluid pressure(Po), thereby relaxing the constrainton
frictional strength'rm (23) and leadingto a 'transientweakpossiblesource;it will be discussed
later.)
Berry [1973] has presentedevidencefor near-lithostatic ness' model. In this mechanism the shear stress would unfluid pressurein parts of the Franciscanformation, which dergoan initial dropfrom a staticvalue(<• •m)to R(t = O)(dethe pressure
P(t) would
boundsthe San Andreas fault on the eastin the Coast Ranges. terminedby (15b)),and subsequently,
Irwin andBarnes[1975]havenotedthatcreeping
portionsof increase
astheearthquake
proceeded.
As P(t) approached
On,
the fault occur where metamorphic fluids from the Fran- the effectivenormal stressOn'(15) would approachzero, and
ciscanformation are confined by an overlying sectionof the sowould R(t). One difficultywith the modelconcernsthe posGreat Valley sequence,and they postulatethat in suchplaces siblelimit imposedon P(t) by 03,the leastprincipalstress.As
the confined fluid is forced into the fault zone. However, the
P(t) approached03,conditionsfor hydrofracturing
wouldob-
heat flow data imply negligibledynamic friction in both the tain, and further pressureincreasemight be inhibited. This
creepingand seismicportionsand within the Coast Ranges condition can be written as
and to the south(Region 7, Figures 8 and 19) where no FranR(t) = I•, (on -- P(t))
ciscanrocksoccur.Hence it seemsunlikely that the heat flow
data can be accountedfor by speciallocal geologicconditions.
• ]'•k(On- 03)
If the small dynamic resistanceis to be reconciledwith By(24)
erlee's generalization,high fluid pressuresseem inevitable.
(We alsohavealternativessuchasthe intrinsicallyweak fault
On
or acousticfluidization,previouslydiscussed.)However, such
pressures
do not haveto be an ambientconditionof the fault
>•1-%,
(øn-Po)II
zone;theymightbe causedby transientfrictionalheatingand Under theseconditions,the minimumresistingstressR(t)
expansion
of the fluid duringlargeearthquakes
[e.g.,Sibson, wouldbe limitedby ((B6a),(15) and (17))
LACHENBRUCHAND $ASS:ENERGETICSOF THE SAN ANDREAS FAULT ZONE
I
I
!
I
I
6203
I
ß Palmdale(U.S.G.S.)
REGION 7
[] Other(U.S.G.S.)
San Bernardino
(ClT)
3.0
125
Lake Hughes(CIT)
PACIFIC PLATE
2.0
84 •
mean
1.58
,
I
60
ß I
i0
4
ß
20
0
66
20
I
I
40
Distance,km
Fig. 19. Heat flow versusdistancefrom the main traceof the San Andreasfault, region7 (Figure 8), shownwith reference anomaly.
•'k
R(t)•>0.375R(0)-• 0.375--•-,,(25a)
• 0.28%,(25b)
The averageresistingstressR, of course,would be a larger
value obtained by integrating R(t) [Lachenbruch, 1980].
Whether or not this limit (25) appliesdependsupon whether
significanthydrofracturingcan developon the time scaleof
an earthquake.
Resultsfrom the abovecalculationsare comparedin Table
4. The case'dry, P = 0' representsthe maximum stressespermitted by (14)-(18). Case 2, Table 4 may be viewed as the
transient alternative if we supposethe ambient pressureis
normal and that an increasein fluid pressureor acousticfluidizationduringslipeventscanindeedsatisfy(13), i.e., that the
resistance
can be reducedfrom an initial value R(t = 0) to
yield an averageR •< 100 bars for those eventsthat account
for mostof the slip.Case1, Table 4 represents
the caseof permanent weaknesscorrespondingto constant ambient fluid
pressure.
If the permanentweakness
resultsfrom anomalously
weak gougematerials,the assumption
(of (18) and Table 4)
that faultingoccurson the mostfavorablyorientedsurfaceis
notjustified,but effectsof the assumptionon numericalvalues
are probablyunimportantfor theseapproximatecalculations.
Hencethe lastthreecolumnsof Table 4, case1, can probably
state fluid pressuresor from anomalouslyweak fault materials. Tectonic
stress differences in the last column of Table 4
are obtained from (18), and numerical values are based on
t•k/t• = 0.75, p = 2.7 g/cm3.
The foregoing discussioncan be summarizedas follows:
1. The heat flow constrainton dissipativeresistance(13)
has strongimplicationsfor the frictionalstrength,,,, if we interpret faulting in terms of Byerlee'slaw and a frictional theory applied to a randomly fracturedupper crust.The relation
betweenR and %, dependsupon two additional variables:the
state of tectonicstressand the fluid pressure;it is most sensitive to the latter.
2. The heat flow constraint(13) requiresthat irrespective
of tectonicstressstate, fluid pressuremust be near lithostatic
while fault displacement
is in progressif Byerlee'slaw applies.
3. Such high fluid pressuremay be an ambient (steady
state)conditionof the fault zone (case1, Table 4), or it may
be a transienteffect developedduring the slip event (for example, case2, Table 4).
4. If steadystate(or if Byerlee'slaw doesnot apply, and
the fault is intrinsicallyweak), then frictionalstrength,,,, is of
the samegeneral magnitude as dissipativeresistanceR, differing only by the ratio of staticto dynamicfriction,and tectonic
stress differences do not exceed a few hundred
bars. This
('permanent weakness')alternative leavesthe anomalousfluid
pressure(requiredby faults satisfying(14)) unexplained.
5. If fluid pressureduringfaultingis transient(or if acousbe usedwhetherthe low strengthresultsfrom high steady tic fiuidizationoccurs),then ambientfluid pressures
may be
6204
Regions
3 through6
Region7
C
a
I
I
Within 10 km of fault
Within 10 km of fault
-
N =16
N=7
• = 1.99
• =1.62
SD = O.O6
SD = O.26
co
0
I
o
1
2
i
I
1
2
q, HFU
q, HFU
d
b
I
Beyond10 km
Beyond10 km
10
N=23
N=7
=1.98•
1
I
2
1.61
SD= 0.07
3
q, HFU
0
I
i
1
2
3
q, HFU
Fig.20. A comparison
between
heatflowwithin10kmof themaintraceof theSanAndreas
fault(a andc)andheatflow
•
at greaterdistances
(b andd) for regions3-6 (a and b) and region7 (c a•tdd).
normal, friction strength7,, and tectonicstressmay be large,
and low dissipativeresistance
is explainedasa consequence
of
the slip events.Difficultieswith this ('transientweakness')alternative lie in our ignoranceof the dynamics of transient
eventsduring faulting.
It might be argued that the absenceof a local heat flow
anomaly over presentlycreepingportionsof the fault implies
the condition of permanentweaknessdescribedby condition
4 aboveand that in suchplacesat least,the tectonicstressdifferencesmust be very small. However, it can be shownfrom
the resultsin appendixA that even if the resolvedshearstress
(and hencethe averagefrictionalresistance)
on the fault were
-• 1 kbar, creep at plate velocitieswould have to persistfor
more than 10,000yr before a measurableheat flow anomaly
would result. Consequently,if creep episodesof centuriesor
even thousandsof years duration were separatedby much
longer episodesof seismicdisplacement,the heat flow constraint could be satisfiedwith large tectonic stress(condition
5, above)if largeearthquakeswereresponsible
for mostof the
displacementand if they developedhigh transientfluid pressures. In the next section, we shall investigateseismological
constraints on this alternative.
inc the energeticsof the earthquakeprocessand find that
modelsof the secondtypeyieldlargequantitiesof radiatedkineticenergy,in apparentcontradiction
with interpretations
of
a largebody of seismicobservations.
We shallintroduceone
new unknown,the final elasticstress,and two new partially
known quantitiesobtainedfrom seismology,the apparent
stressand the stressdrop (defined below).
Figure22 is a schematic
representation
of the localenergy
budgetof an earthquake[seealsoAndrews,1978a].Here, 7'
and 7' are the initial and final average values of the com-
ponentof elasticshearing
stress
in thedirectionof faultslipu,
and Fis the corresponding
averagevalueof the dissipativeresistancein the directionoppositeto fault slip. The total slip
averagedoverthe faultedsurfaceis u,,. (We shahdenotethe
faulted surfaceby •, and its area by Ax.) The straightline
joiningthe averageinitial and final elasticstresses
represents
theunloadingof a linearelasticmedium;the areabeneathit is
the total elastic energy (E/Ax) released(per unit area of
slippedsurface)at the locusof faulting•. Hence
E
1
Axu,,-•(7'+ Y)
The area beneath the horizontal
Fault Energeticsand SeismicEstimatesof StressDifference
In the last section,we found that insofar as laboratory in-
(26)
line with ordinate F or the
curve r(u) (Figure 22b) is energy(E•/Az) lost from the mechanical system.Thus
formation on rock friction is concerned, there are two inter-
gradationalclassesof simplemodelsthat can accountfor the
Er -._
•.
(27)
low dynamic friction implied by the heat flow constraint:(1)
permanent-weakness
modelsin which the averagefrictional The area between the elasticstresscurve and the dissipation
strengthis also low, and (2) transient-weakness
models in curverepresents
energy(Ea/A=) allocatedto elasticradiation.
which the static friction may be an order of magnitude Consequently,
greater, the upper limit being determined by rock strength.
Ea
I ,
The first type requireslow tectonic(i.e., initial) stresses,
but
the secondtype permitslarge ones.In this section,we exam-
azu,,,
= •-(7+7')-F
(28)
124'
122'
120'
118'
6205
116'
114'
i
O
42'
OREGON
,
IDAHO
a
a
Mt Shastai '
14,161 ft
a
fee
'•
/
ß
/o
ß /
/
eI
t
/
ß
!
Wmnemucca
ß
•./
t
t
ß
?
t
ß
t
ß
ß
a
.
ß
._.*
a
ß
Reno
t
o•...
Lake
a
tt
a
%
t
ß
t
ß
N
E
tI
ß
t
*%
el
ß
,
ß
ß
Sacramento
t
./
ß
eo
I
ß
I
tt
I
a
oTonopah
38'
t
Sin Franci
t
ß
a
ß
36*
ee
e•.
ß
Angeles
e• •.•
•
ß
0
50
I
I
0
100
150
200
t
!
•
MILES
<::::)
50 100 150 200
KILOMETERS
Fig. 21. Thermal springsin California and Nevada (reproducedwith modificationsfrom figure 8 of Waring [1965]).
Heavy line is the main trace of the San Andreas fault.
Figure 22a is shownfor three differentvaluesof ?-andFigure
22b for variable
r.
sional models of the fault, in which case their intuitive meaning is clearer.
We define the average elastic stressTe and the apparent
This interpretationof areasin Figure 22 is fairly generalas
long as we define •-*, •-', and ?-respectively,as weighted aver- stress% by
agesof initial stress,final Stress,and R (15c) over the faulted
I ,
surface,the weightingfunction being the local fault slip. For
refinedmodelsof faulting in which significantamountsof enI ,
ergy are dissipatedat the propagatingedgesin complexstress
•a--•(• + •')- ?(30)
fields,the representationin Figure 22 will not, in general,provide a useful view of the sequentialvalues of the stressesat The energy balance,
any typical location. Nevertheless,the three generalized
E=E,•+En
(31)
stresses
(•-*, •-',?-)definedin thisway are usefuldescriptiveparameters,whatever their relation may be to the details of the can now be expressed((26)-(31)) as
mechanicsof the earthquakeprocess.For the purposeof disWe-- Ta -[- ?(32)
cussion,we can considerFigure 22 to representone-dimen-
6206
TABLE 3. Data on Thermal SpringsWithin 10 km of the Main Trace of the San AndreasFault
BetweenCape Mendocinoand the San BernardinoMountains
Name
Latitude
Flow
Rate
Longitude I s-•
Point Arena Hot Springs
Rocky Point Spring
Near SergentSanta Clara County
FresnoHot Springs
Tyler's Bath Springs
Arrowhead Hot Springs
Waterman Hot Springs
38052.5'
37053'
36056.8'
3608.8'
34ø13.5'
34ø11.2'
34011'
123031'
122037'
121ø33.8'
120033.5'
117029.5'
117ø14.5'
117015.5'
Temperature,
øC
0.3
0.3
0.5
1.3
0.3
3.2
0.3
44
38
25
31-36
33
94
50
Discharge,
MW
0.035
0.030
0.020
0.110
0.015
1.0
0.04
1.25
Thus the deformationenergyreleasedlocally during an earthquake is the work done by the averageoperatingelasticstress
%, which can be expressedas the sum of a part allocated to
the productionof seismicradiation, %, and a part allocated
to the production of heat, E For the transient classof models
discussedpreviously, % can be large, and since ? must be
small, this would imply large seismicradiation (i.e., large ,a).
The permanentlyweak models,on the other hand, would be
consistent with small contributions from both ? and %. In
what follows, we shall expressthe energy constraint(32) in
terms of the friction parametersof the last sectionso that the
numerical resultsobtained there can be comparedformally to
those obtained from seismology.
The relations among the seismicallyrelated stressescan be
discussedin terms of the following identity:
•(, ,+,')1,-,')- 11
Total
placementon the San Andreas fault (the 'principal events'),
we can write the heat flow constraint(13) as
Y<• 100 bars
(38)
The preponderanceof valuesof stressdrop A determinedfor
crustal earthquakes[Hanks, 1977; Kanamori and Anderson,
1975] satisfy
1 bar < A < 100 bars
(39)
Although seismicallyestimatedvalues of •-• are lesscertain,
Savageand Wood[1971]presentdata from many earthquakes
to show that within reasonablelimits of uncertainty,
1
(40)
and Kanamoriand Anderson[1975] find that on the average%
~ (1/2)A.
Substitutingupper limits given by (38), (39), and (40) in
Although seismologyprovidesno reliablemeansof estimating
the magnitudesof the three stresses
in (33), it doesprovide in- (36a) and using(37), we obtain bracketingconditionsfor the
direct estimatesof two stressdifferences[Wyss and Brune, initial stress** precedingearthquakes:
1968;Wyss,1970;Savageand Wood,1971]:the apparentstress
1
%, just discussed(30), and the stressdrop A, which is the dif(41a)
ference between the average fault stressimmediately before
and after an earthquake:
The right-hand inequality is equivalent to the result obtained
A = ** -- ,'
(34) by Brune et al. [1969] (exceptthat they used % <• 100bars inThe seismicefficiency•/is defined as the fraction of the re- steadof (40)). Their resultfor the casein which displacement
?--**-•(,
(33)
0<E%,• A<•**--?+r•+}---A
<-200
bars
leased energy that is allocated to the generationof elastic
TABLE
waves•
Ea
r/= •E
Ta
--
(35)
%+?
4.
Ambient
Conditions
Transient
Ambient
Pressure
Gradient,
dP/dx,
Combinationof (30), (33), and (34) yields
1
** - ?--%+ •-A
(36a)
1
,,_ ?m%_ •-A
(36b)
SinceF,,,•, and A are generallypositiveon physicalgrounds,it
follows from (36a) that the average initial stresshas lower
bounds given by
-
v*> r,%,•A >0
(37)
If we limit our discussions
to eventstypical of thosewhose
cumulative
effect resulted
in hundreds
Case
of kilometers
of dis-
bars/km
Effects
Initial
Dynamic
Resistance,
R(t = 0),
bars
Tectonic
Frictional
Strength,
Tm,
Stress
Difference,
O1-- 03,
bars
bars
o3 Vertical (Thrust Faulting)
Case 1
Case 2
Dry, P = 0
•>253
100
0
<•100
1070
1700
•<133
1426
2265
•<332
3565
5560
<•133
593
990
•<332
1482
2355
OavgVertical
Case 1
Case 2
Dry, P = 0
1
in Fault Zone for Three Tectonic
StressStates:Case 1. Fluid PressureDoes Not ChangeWith Time,
Case2. Ambient Fluid Pressure'Normal' and (13) SatisfiedBy
>•230
100
0
<•100
445
710
Vertical (Normal Faulting)
Case 1
Case 2
Dry, P= 0
>•203
00
0
<•100
270
430
<•133
360
570
<•332
900
1430
LACHENBRUCH
overshoot
null
locking
0
U--•-
um
b
r'/r(u) r.a •
o
f
0
U""
OF THE SAN ANDREAS
FAULT
ZONE
6207
jumping of one notch in opposingsawteeth).Savage and
Wood[ 1971]pointout that if frictionstopsthe faulting,inertia
requiresthe overshootmodel,a sufficientconditionfor which
is (40) (accordingto (42a) and(36b)).If, however,the resisting
stressvariesduringan earthquake,the physicalsignificance
of
this classificationis lost, sincethe final value, not the average
r-•shouldbe usedin (42) to relate r' to friction. This is illustrated in Figure 22b for a one-dimensionallocking model
(42c)in whichr increases
sharplyat the end of an event(dotted lines,Figure 22b). Brune[1976]suggests
that suchan increasein resistancemight result when the particle velocity
dropsbelowa criticallimit. The resistance
is sensitiveto shear
zonewidth and poredilatation,both of whichvary as particle
velocitychangesduring an earthquake;unstablepropagation
of hydrofracturesmight reduce fluid pressurerapidly, and
strengthening
due to lossof fluid pressureby dissipationof
frictional heat or Darcian flow can probablycontribute[Lachenbruch,1980].For the caseof acousticfiuidization[Melosh,
1979], rapid strengtheningmight occur in the decelerating
stagewith the lossof acousticenergy.In any case,however,
the classificationin (42) is useful for discussion;for a given
stressdrop and resistance,
•a and the seismicefficiencywill be
greatestfor the lockingmodel.Intuitively,the lockingmodel
generatesadditionalelasticradiationby its terminalimpact
againsta largehypotheticalfinal resistance.
(We make no attempt to reconcilethesesuggestions
with fracturemechanical
Um
Fig. 22. Schematicrepresentation
of relationsamongaveraged
valuesof initial stressr*, final stress¾, dissipativeresistancer• apparent stressr,,, mean elasticstressre, and stressdrop A for an event with
mean total displacementU,n.Figure 22a illustratesthe three casesof
(42), and Figure 22b showsa one-dimensionallocking model with
variable dynamic friction r.
considerationsof fault stoppage.)
In one-dimensionalmodels it is natural to equate the aver-
ageinitial stress
r* to the frictionalstrengthrm.For morerealistic two- and three-dimensional models, it is clear that the
initial stressmustequalthe strengthonly at the point at which
ruptureinitiates(and thisstrengthmay be lowerthan the laboratoryvaluebecauseof the sizeeffect);elsewhere
the stressis
is exclusivelyby uniform creep follows from (4 la) by setting
probablydeterminedby dynamicfriction [e.g., Berg, 1968;
A-ra=0:
Burridgeand Halliday, 1971].We shall assumethereforethat
the averagevalue of initial stresscan be bracketedby the
r* •< 100 bars
(4lb)
static and dynamic friction:
Theresult(4lb) isessentially
thesameasthefrictional
result
(23), sinceboth are controlledby the heat flow constraint.
However, the upper limit of 200 bars in (41a), obtained from
heat flow and seismicobservationscombined,imposesa much
more severeconstraint than rock strength (Table 4), which
limited the initial stressin models of transient weakness, dis-
cussedin the last section.Becauseof the potential importance
of the possibilityof large initial stressto the understandingof
earthquakes,we shalleliminatethe leastcertainof the seismic
constraints,the one on % (40), substitutethe limit on rock
strength(Table 4), and investigatesomeof the consequences.
Simpleearthquakemodelscan be discussed
in termsof the
relativemagnitudesof the final stressand the averageresisting
stress[seeBrune, 1976].The three possibilities,illustratedin
Figure 22a, are
r' - F< 0
-- 0
overshoot
(42a)
null
(42b)
•'m
-->-•'*>--]O[--k
'Tm
(43)
We shall consider two cases,•'m small and •'m large, corresponding respectivelyto cases 1 and 2, Table 4. The permanent low strengthin case I can result from high steady
statefluid pressureor from intrinsicallyweak fault materials.
The high strengthin case2 is a consequence
of normal ambient fluid pressure;weakeningduringthe earthquakecan be
from a transientincreasein fluid pressureor acousticfiuidization. The limiting valueson the left and right in (43) are representedrespectivelyby columns2 and 3 in Table 4. Thus in
case2, (43) becomes
(270 bars,445 bars,1070bars)
--<
r* =<(360
bars,
595bars,
1425
bars) (44)
where the valuesfrom left to right in parenthesescorrespond
respectively
to the stressstates:o• vertical,Oavg
vertical,and 03
> 0
locking
(42c) vertical. The correspondingresult for case 1 (constantfluid
pressureor an intrinsicallyweak fault) is ((23) and (28c))
If it is assumedthat the resistingstressis constant(i.e., r(u) -?-), the null model (the 'Orowan assumption'of Brune et al.
1
[1969]) attributesthe final stressto the dynamic frictional
0< K•'a,
•-A< •'•g
• -- •-• 133
bars
(45)
characteristicsof the surface.The locking model [e.g., Brune,
we shall use (44)
1976]is unrelatedto averagefriction;it could occurin a one- In evaluatingthe constrainton other stresses,
dimensional model with elastic barriers (for example, the or (45), inferredfrom frictionalproperties,the heat flow con-
6208
LACHENBRUCH
straint(38), and the constrainton stressdrop (39). The apparent stress•a, possiblythe least certain of the semimeasurable
quantities,will be retainedas a parameter.
Using the left-hand inequalityin (44) with (36), (38), (39),
(41), and (43), we obtain the followinglower limits for the
transient
case 2:
•-* - ?' •> (170 bars,345 bars,970 bars)
(46a)
120bars,295 bars,920 bars)
(46b)
•-' - F •> (70 bars,245 bars,870 bars)> 0
(0.55, 0.75, 0.90)
(46c)
(46d)
Similarly, for case1, (45) and the foregoingrelationsyield
OF THE SAN ANDREAS
FAULT
ZONE
cluding but not necessarilylimited to the principal events
('transientweakness').
3. For the class I models,the averageresolvedtectonic
stresson the fault cannotbe appreciablygreaterthan 100bars.
For the class2 models,tectonicstressis limited by the average
frictional strengthof upper crustalrocks;under normal fluid
pressurethis is -•0.4-1.5 kbar, dependingon tectonic stress
state.
4. If the principal eventsare slowcreep,permanent-weakness(type 1) models are required. However, creep eventsat
plate velocitieslasting no longer than • 10n yr are not necessarilyprincipal events(i.e., they neednot contributeappreciably to the heat flow even if the ambient stressis large).
5. Physical models for permanentweakness(type 1) include thosein which the gougematerial has anomalouslylow
friction coefficients, and those in which the friction coeffi-
cientsare normal, but the ambient fluid pressurein the fault
zone is close to the overburden pressure.Although there is
0< q'a
• 33bars
- •A < 33bars
(47b) little independent information that either of these conditions
is general in the fault zone, thesemodelsare consistentwith
the
small stress drops and apparent stresses(and, con-50bars
<
•--•A1 <_•'--y<_33bars--A
< 33bars (47c) sequently,small seismicradiation) inferred from earthquake
seismology.Models of type I require low seismicefficiency;
they are consistentwith all three typesof earthquakemodels:
locking, null, and overshoot.
6. Physicalmodelsfor transientweakness(type 2) include
Thus the transienthigh-stressalternative(case2) requires those in which the ambient fluid pressure and frictional
very large q'a(46b) in violationof (40). This leadsto a high strengthof the fault zone are normal, and resistanceis deseismicefficiency(46d)and the requirementfor a locking-type creasedduring principal events,for example, by a transient
earthquakemodel(46c)accordingto the classification
of (42). increasein fluid pressure[Lachenbruch,1980] or acousticfiuiIn contrast,the steady state pressurealternative (or the in- dization [Melosh, 1979].For suchmodels,the principal events
trinsicallyweak fault) is consistent
with the smallvaluesof
are probably large earthquakes.These models have the ad(47b) usually reported;it leads to a low seismicefficiency vantagethat the anomalousweakness(necessaryto satisfythe
(47d) and couldbe consistent
with any of the three alterna- heat flow constraint)is 'explained'asa consequenceof the slip
tives in (42) (see (47c)).
event. Only models of this type can be consistentwith large
Althoughit compoundsthe problemof fault stoppage,the ambient tectonic stressand the heat flow constraint. They
transient alternative, with initial stress-• 1 kbar and dissipative have the disadvantagethat for tectonic stresscontrolled by
resistance •0.1 kbar, is not inconsistent with the observation normal rock strength, they require apparent stressesin the
that the stressdrop A is generallysmall(•0.1 kbar). It is, how- range100bars-lkbar (depending
on tectonicstress
state).This
ever, inconsistentwith the generalinferencethat q'ais small is an order of magnitudegreaterthan the range inferred for
and, in particular,with the Savageand Wood constraint(40). crustaleventsfrom earthquakeseismology.For large tectonic
However, the physicalargumentfor the validity of (40) is stress,type 2 modelsrequire large seismicefficiencyand lockbasedon the constancyof r and doesnot necessarilyapply in ing modelsof the earthquakeprocessfor principal events.
the transient case. The questionthen remains whether the
Factors that might control the transientvariations of fluid
seismicallydeterminedquantity q'acorrespondsto the one pressureduring an earthquakeare discussed
in another paper
definedin this section,or whetherthe seismic%a'might repre- [Lachenbruch,1980].Although they might ultimately prove to
sent only a small fraction of the energy radiated from the be important to the earthquake process,if the heat flow and
locusof faulting during thoseeventsresponsiblefor most of seismicdata are taken at face value (4 la), even suchtransientthe displacementon the San Andreas fault, probably very weaknessmodelsare limited by a fault strengthof only -•200
largeearthquakes.
Only in the latter casewouldthe transient bars. In the next section,we shall investigatethe possiblerealternativeand the possibilityof large strengthand tectonic lation betweentheselocal fault stresses
and thosethroughout
stressbe viable [seealso Brune et al., 1969].
the broader interplate shearzone by consideringthe origin of
In summary,the heat flow constraint,taken with measure- the broad CoastRange heat anomaly.It is shownthat if much
ments of rock friction and seismic observations, seemsto have of the heat flow anomaly is mechanicallygenerated,it is likely
the followingimplicationsregardingstresses
on the San An- that the seismogeniclayer is partially decoupledfrom the undreas fault:
derlyingmaterialand that the resultingbasalstresses
lead nat1. If we acceptthe heat flow constraint,then resistanceto urally to a relatively weak fault, with much larger stresses
1
1-•}•0.25
(47d)
fault motionmustbe small(•<100bars- 10 MPa) duringthose
events responsiblefor most of the fault displacement(the
'principal events').
2. This condition can be satisfiedby two simple (inter-
gradational)classes
of models:(1) Thosein whichthe fault resistanceis small all of the time ('permanentweakness'),or (2)
those in which it is small only during short-livedevents,in-
elsewhere
in the shear zone.
THE
BROAD
HEAT
ENERGETICS
FLOW
ANOMALY
OF THE FAULT
AND
ZONE
The heat flow data from the San Andreas fault region have
two notable features: (1) the absenceof a local heat flow
anomaly over the 1000-km length of fault trace from which
LACHENBRUCH
6209
+ CL1
3.0
125
I
la
lb
2
i
_1'0111'3211'66,
3
2.06
4
+
,1.87
+ -IF •
2.0
/•
2.7
+
6
1.85
84
+
++½
1.0
42
•+
0
200
400
600
Distance,km
Fig. 23. Northern portion of Figure 12 showingmodelsfor the transientrise in temperaturecausedby northward migration of the MendocinoTriple Junction.CurvesA, B, C, and D correspondto modelsof equations(38a), (38b), (38c),
and (38d), respectively.Mean heat flows (in HFU) are indicatedfor each region.
data are available,and (2) the broad anomalyacrossthe Coast
Rangesextendingfor more than 500 km along the fault zone
(regions3 through6, Figures8 and 12). In the previoussection we discussed
someimplicationsof the first featurefor the
ley to the eastover a distanceof only tensof kilometers(see,
for example,Figures 15 and 18). This suggests
that the source
of the Coast Range anomaly is in the upper crust and that it
might be related to the tectonicsof the San Andreas fault
local mechanics of the main fault. In this section we shall con-
zone; however, details of the thermal transition are complicated by effectsof rapid sedimentationin the westernportion of the Great Valley. To testthe relation betweenthe fault
zone and the heat flow anomaly, we subsequentlyextended
measurements northward to and beyond the Mendocino
sider possibleimplicationsof the Coast Range anomaly for
thermal and mechanicalconditionsthroughouta broadinterplate shearzone surroundingthe main fault. The analysisis
limited to the Coast Range anomaly, becauseit is a con-
Triple Junction,where the San Andreasfault on the North
American plate should,in principle,have zero age. Owing to
the nature of the formations and the youthful topography,
confidentheat flow measurementsin this northern region (as
in many other parts of the Coast Ranges)are difficult to obtain, and this might account for much of the scatter in the
data. Nevertheless,the resultsshownin Figure 12 suggestthat
the Coast Range anomaly does,indeed, fall off to the north.
North of the Triple Junction(region la, Figure 12) the averageheat flow is about 1 HFU, consistent
with resultsfrom the
Klamath Mountains and northward along a coastal strip to
the Canadian border (seeFigure 6), the region in which suband the tectonicsof this complicatedregionhave been dis- duction is believed to be in progresstoday [see also Lachencussedby Lee and Henyey[1975];presentheat flow coverage bruch and $ass, 1977; Blackwell, 1978]. South of the Triple
there is inadequateto warrant the constructionof explicit Junction, averageheat flows seemto rise over a distanceof
models.
about 200 km (regionslb and 2, Figure 12) to valuescharacteristic of the Coast Range anomaly.
The CoastRangeAnomalyand Depthto Its Source
From plate tectonic reconstructions[Atwater and Molnar,
From heat flow measurementsin central California, we 1973],the Triple Junctionis believedto have been migrating
noted in an earlierpaper [Lachenbruch
and $ass, 1973]that northwestwardat roughly 5 cm/yr for the pastseveralmillion
the Coast Range anomalyfalls off from averagevaluesof years.Hencethe ageof the fault zone on the North American
about 2 HFU to valuesof perhaps1.2 HFU in the Great Val- plate shouldincreaseabout 1 m.y. for each50 km of distance
spicuousfeature with well-defined boundarieson the east and
north, and it enclosesa region in which most of the relative
plate motion can generallybe attributed to the main trace of
the San Andreasfault. However,the possiblewestwardextent
of the anomaly onto the continentalshelf is unknown. South
of the CoastRanges,conditionsare very complex,the shearing deformationis evidentlydistributedover a broaderzone,
and the heat flow anomaly is smaller but distributedover a
largeregionincludingthe offshoreborderlandand partsof the
Mojave Block and the Salton Trough; an island of low heat
flow occursin the southernCalifornia batholith (Figure 6)
[seealsoRoy et al., 1972].Possiblerelationsbetweenheat flow
6210
Fig. 24. Idealizedrelationsamongtectonicplatesnear the MendocinoTriple Junction(intersectionof the Mendocino
transform(M. Trans.)and the SanAndreasfault (S.A.F.)). Arrowsindicatemotionrelativeto a fixedPacificplate. Coordinate axesrefer to model in text (seealso Figure 25).
southeastwardfrom the Mendocino Triple Junction. (All of
the sitesin the arbitrary regionslb and 2 (Figure 12) were, of
course,on the North American plate as the Triple Junction
migrated northward along an offshore trench.) To obtain a
rough idea of the depth of the sourcesthat might be respon-
tive if the time constant
for Darcian
flow were an order of
magnitudegreaterthan the time constantfor heat flow, i.e., if
the permeability of overlyingrocksdid not exceed---0.1nanoDarcy [seeFigure 8, Lachenbruch,1980].A possiblesourceof
water is sedimentscrapedfrom the subductingplate. Hence it
sible for the northward transition in heat flow, we have shown is quite possiblethat the thermal evolutionof the broad Coast
the effectsof four simple one-dimensionaltransient heat con- Range anomaly could have a substantialeffect on the meductionmodels,curvesA, B, C, and D, in Figure 23. For each chanical evolution of the San Andreas fault zone through the
model the time origin is taken at the presentTriple Junction, weakening effect of high fluid pressureon mid- and upperand each anomaly is constrainedto reach 80% of its steady crustal rocks.
We can imagine two plausible mechanismsfor the anomastate value of 1 HFU at 3 m.y., which correspondsto a point
about 150 km southeastwardfrom the present Triple Junc- lous near-surfacesourceof heat in the Coast Ranges:
tion. For each model, the depth of anomaloussources(x -- d)
was adjustedto meet theseconditions;the resultsare
Temperature
(0)
Model A: constant
planesourceat x ----d; d • 3 1/2 km
(48a)
Model B: uniformsources
in 0 <_-x <_-d; d • 7 km
(48b)
ModelC: stepchangein flux at x = d; d • 11 km
(48c)
ModelD: stepchangein temperature
at x ----d; d m 20 km (48d)
The deeper the source,the greater its initial strengthmust be
and the more intense is the associatedtemperature anomaly;
for example,model C requiresan initial sourcestrengthtwice
as great as model A and a temperatureanomaly greaterby a
factor of 3. If the values of d were doubled, the horizontal
0
Os(a
)
X\x,o)
i
ß
:
(x,o)
scaleof curvesin Figure 23 would be extendedby a factor of
4. Thus as in the transitiontoward the Great Valley, a shallow
origin (•<20 km) is suggested.
Before undertaking further analysis of these results, it is
worth noting that the observedincreasein heat flow would
correspond to an increase in thermal gradient above the
sourceof >•15øC/km. The expansionof pore water at constant
volume under upper crustal conditionsleads to a fluid pressure increase--- 15 bars/øC [see,e.g., Figure 3, Lachenbruch,
OH(a)
1980]. Consequently,an increasein thermal gradient of only
,--13øC/km could increase the fluid pressure gradient by
Fig. 25. Dashedcurvesshowtemperatureat z -- 0+, Figure 24,
---200bars/km, enoughto raisethe fluid pressurefrom hydro- the initial condition for model in text.' Solid curves show initial temstatic to lithostatic. In the Coast Ranges, this could be effec- peraturewith contributionfrom radioactivityremoved.
LACHENBRUCH AND SASS; ENERGETICS OF THE SAN ANDREAS FAULT ZONE
6211
I-<-Mojave
Region-•
CoastRanges
125
3.0
84
30KM
42
1.0
I
0.5
0
I
I
250
I
500
I
750
lOOO
I
iPresentdistancefrom
Mendocino
Triple
Junction(KM)
0
5
10
15
20
25
(30)
I
(35)
Timesincepassageof Mendocino
TripleJunction(m.y.)
Fig. 26. Heat flow as a functionof distancefrom the MendocinoTriple Junctionfor selectedinitial thicknesses
a of the
North Americanplate (seeFigures24, 25, and (22)). Horizontalsolidlinesare meanheat flowsin the fault zonefor regions
delineatedin Figure 8. Horizontal dashedlinesare mean (corrected)heat flowsinterior to Great Valley. Seetext for further explanation.
1. As the North American plate movessoutheastward(relative to the Pacificplate) pastthe projectionof the Mendocino
transform(z - 0, Figure 24), its baseat depth x = a (Figure
24) slidesfrom the Gorda plate,cooledby subduction,to a re-
gion of warmer mantle material, the northernedge of the
'window' of Dickinson and Snyder [1979]. Conduction from
this material might supplythe anomalousheat provideda •<
20 km (as required by (48)).
2. A secondplausible shallow source of the anomaly is
shear-strainheating associatedwith distortion and possible
basaldecouplingof the seismogenic
layer of the San Andreas
fault zone, which originatesin the North American plate at
this location (z = 0, Figure 24).
In an earlier stage of this study [Lachenbruchand Sass,
1980] we discountedthe first possibility,sincewe thought it
unlikely that the top of the subductingplate would be at midcrustal depths(a •< 20 km) for distances~100 km from a
trench at the continentalmargin, and even if it were, low heat
flow in the Great Valley would be left unexplained.However,
preliminary resultsfrom a recent gravity study near Cape
Mendocino by Robert Jachensand Andrew Griscom (oral
communication,1980) suggestthat the North American plate
might presentlybe thin enoughin the CoastRangesto satisfy
this condition. Since an understandingof the nature of the
San Andreas fault zone might depend upon a distinction between the relative contributionsof these two processes,we
shall consider models for each.
Models
for Conductive
Heating
oftheCoast
Ranges
bya War.•
Mantle
Accordingto Dickinsonand Snyder[1979], shortly after the
Mendocino Triple Junction contactedNorth America, the Farallon plate began to disappearbeneath the continental margin, leaving a growing triangular region, the 'window,' in
which upwelled asthenospherewas left in contact with the
originalbaseof the North Americanplate. The northern edge
of the window is the inland projectionof the Mendocino
transformfault; it moveswith the Pacificplate and hasnot
been occupiedby a subductingslabfor more than 20 m.y. The
temperature in the window (region x > a, z > 0, Figure 24)
dependsupon the motion within it during that period, and
this, in turn, dependsupon how the window material has been
6212
LACHENBRUCH
where we have used a thermal conductivityK of 6 mcal/cm s
øC. In westernCalifornia, OH(a)is probablysmall, -•30øC +
We shall consideronly the most extreme case of heating 50%. Allowing 15øC for the mean annual surfacetemperature
whichoccurs
whenthemechanical
coup!ing
at x -- a (z > 0) is and assumingthe mantle solidustemperatureat atmospheric
complete(i.e., no slip); after the plate of thicknessa slidesoff pressureto be 1045øCyields
the Gorda plate, it dragsthe underlyingmantle material with
Os(O)- OM•a)-• 1000øC
(54)
it. This would generatea one-sidedburied spreadingcenterat
the inland projection of the Mendocino transform as illus- We assumefurther that the solidusgradient ¾is 3øC/km and
trated in Figure 24. Upwelling asthenosphere
at z = 0 would the thermal diffusivitiya is 0.01 cm2/s.
Equation (52) givesthe reducedheat flow at any point in
be cooledand accreteto the thickeningNorth American plate
as it moved southeastward.
the North American plate at time t after passageof the MenThe 'initial' condition (at z -- 0q-, Figure 24) for quasi-one- docino transform (provided the Farallon plate disappeared
dimensionalconductivecoolingis shownby the dashedcurves there:•rst and 'openedthe window'). In Figure 26, resultsare
in Figure 25. The temperatureOs(x) in the North American shown for selectedinitial plate thicknessesa, with the time
plate (of thicknessa) is the sumof a steadystatecontribution convertedto distancez by assumingthe relative velocity of
OH(x)from radioactivityin the plate and a linear part I'x asso- the Pacific and North American platesto have been 5 cm/yr
ciated with reduced heat flow. The temperaturein the up- for the past 10 m.y. and 2 cm/yr previously[Atwaterand Molwelling mantle below a is a linear function,0,,,-- Os(a)q- G(x nar, 1973]. Theoretical reduced heat flows have been increased0.2 HFU for radioactivity. Horizontal solid lines de- a), where Os(a)is the mantle solidus(at depth a) given by
note means(Table 2) for the variousregionsof the fault zone
Os(a)---Os(O)
q- ¾a
(49) delineatedin Figure 8. The two dashedlinesdenotemeansfor
and G is a gradient, artificially introduced to accommodate data interior to the Great Valley in regions3 and 6; thesevalheat flow from below a. The transientpart of the problem in- ueswere adjustedby 0.2 HFU for effectsof rapid sedimentavolvesthe solid lines in Figure 25, which are denoted collec- tion. The mean for the Mojave region is shownonly for curitively by Or(x,0); it is the temperaturewhose(transient)gradi- osity; it could not be accommodatedby the model for the
ent yields the reduced heat flow qr(t). The radioactive chronologywe have assumed,sinceits time origin (-•30 m.y.
B.P.) predatesthe arrival of the Triple Junction at the conticontribution is additive. Thus the initial condition is:
nental margin.
Or(X, 0) • 0(X, 0) -- OH(X
) -• FX
X< a
(50a)
It is seen that a simple model of this type fits the Coast
Range
data (solid lines, Figure 26) fairly well, provided the
= 0(0) - (GNorth American•platethicknessa wasonly about 20 km there
+ Gx - OH(a)
X> a
(50b) while subductionwasin progress.The Great Valley data fit an
initial plate thicknessa -• 40 km (dashedlines, Figure 26).
The correspondingsolution to the differential equation of
Hence accordingto the model, the rapid drop in heat flow beheat conductionwith zero surfacetemperatureis
tween the Coast Rangesand Great Valley representsa rapid
1
steepeningof subductionthere. (This model could be used
Or(X
, t)--'I'X+ • [Os(O)
-- (G- ¾)a
-- OH(a)]
also to estimatethe heat flow at a fixed point on the North
American plate following disappearanceof the Farallon plate
beneath southernand central California; for this purpose a
larger initial heat flow might be appropriate;see Pilger and
Henyey [1979].)
The foregoingmodel illustratesthat extremeconditions(for
+ •(I'-G)a -a erf•-erf•-2
(4at)!/2
(4at)!/2
example, very shallow subductionand a full-fledged spreading center in the mantle at a depth •20 km) are required to
account
for the heat flow transition in the Coast Ranges by
(*r)!/2 h
heat conductionfrom a warm mantle. The consequences
of
the model are also extreme (a 'hot line' sweepingnorthward
and the reducedheat flow at time t is given by
under the edgeof North America), and perhapsthey could be
confirmed by studiesin the Cape Mendocino area. If such
•
Os(O)
- OH(a) G- 3*
coupled to the original North American plate at their interface x ---- a.
ßIerf(4at)•/2
+erf(4at)•/2
x+a
x--a
1
1
{xlx+a (x-a)l
1 (4at)!/2
[e
-l(•-"):/(4"t)l
--e-l(•+"):/(4"t)l]
} (51)
qr(t)
=1+
I'h
qr(O)
I'
conditions do not exist, less extreme warm mantle models
ß2 a e-[•/'4"ø'1-•-)
(•!/2 (4at)!/2
ßerfc a
q-
2
a
(4at)!/•_ (•)!/2 (4at)!/:
e-[a•/4at)]
(52)
Taking the initial reduced heat flow qr(O) to be the value
today at Cape Mendocino (-•0.8 HFU) and assumingthe
steady heat flow from below a to be 0.5 HFU, we obtain
I' = 13.3øC/km
(53a)
G = 8.3øC/km
(53b)
would apply, and it is likely that a contribution from shearstrain heating (discussedin the next section)would have to be
invoked, at least in the northern Coast Ranges.Lessextreme
modelsinclude thosewith steepersubduction(for example, a
>• 30 km, Figure 26) or those in which the North American
plate becomesonly weakly coupledto the mantle (at x = a)
when it passesthe Mendocino transform(z -- 0, Figure 26),
thereby requiring lessintensedivergenceand upwelling. (If a
shouldturn out to be even lessthan 20 km, weaker-coupling
modelscould, of course,accountfor the anomaly without invoking shearheating.)
Taken literally, the model of Figures 24 and 25 leads to a
deep San Andreas fault that penetrates the entire North
6213
and velocity is continuousacrossthe projectedplane of the
main fault trace y -- 0. For physicalreasons,there must be a
transitionallayer betweenh andf, we generallyexpecth to lie
at or beneath the baseof the seismogeniclayer and j to lie at
or above the top of the fluid asthenosphere.
Anticipating the
problemof accountingfor shallowheat sources,in Figure 27b
a
we illustrate the extreme case, with h at the base of the seismo-
geniclayer and j only a few kilometersbeneathit at the base
of a 'partial decouplinglayer' with large verticalvelocitygradients.
Displacementsoccuronly in the positiveand negativez directions,and they are anti-symmetricin y. Hence our referenceframe is fixed in spaceas the primed and unprimed regions move past it in a right lateral sense.Since we are
interestedin effectsof interactionbetweenthe primed and unprimed lithosphereplates, we assumethe material at great
depth to be at rest relative to the referenceframe. In the
seismogeniclayer AA', in which uniform fault slip is permitted, we assumethat v is independentof depth, i.e., plasticdeformation or secondaryslip can occuronly acrossplanesparallel to y -- 0. We assumefurther that no distortion of the
seismogeniclayer occursbeyondy •- :l:y*. The regionsC and
b
C' are rigid and movewith velocities_+vp
characteristic
of the
respectiveplate interiors.In summary,
Ov
Ov'
ox
•ox -- 0
vO')-----v'(--y)
x< h
(55a)
all x
(55b)
vO'*)= -v'(-y*) = v•,
Fig. 27. Steadystatemodelsfor plate interactionat a transform
boundary;C and C' movewith velocityof plate interiors(+v•,):(a)
v(O+) = -v'(O-)-- Vo
minordecoupling
at baseof seismogenic
layerAA', (b) majorde-
x< h
(55c)
x< h
(55d)
couplingat baseof seismogenic
layer.
> 0
x<j
(55e)
American lithosphere,a reasonablecondition during early
stagesof the fault boundary betweenthin plates. However,
subsequenteastwardjumps of the locus of surfacefaulting
[Atwater and Molnar, 1973] may be more compatible with
-- 0
x >-j
(55/)
continuous
deformation
across the North
America-Pacific
plate boundary at depth in the thickeninglithospheres,with
shallow faulting confined to a superficialbrittle layer, partially decoupledat its base. (Shallow decouplinghas often
beensuggested
in the past;see,for example,Anderson[1971].)
Whether or not this is so, it is shown in the next sections that
h<j=• H
v, v' --> 0
x --> oo
(55g)
(55h)
In discussing
this model, we shall refer only to the unprimed
(y positive) portion, with the understandingthat the correspondingprimed velocitiesand stresses
are equal in magnitude and reversedin signunlessotherwisenoted. We shahuse
the outer normal; tractionsthat drive the fight lateral motion
of A are positive,and thosethat drive fight lateral motion of
sucha superficialfault configurationis probablynecessaryif
shearheatingis to contributeappreciablyto the CoastRange
anomaly without violating the heat flow constraint(13); the
model has testableimplicationsfor fault zone stresses.
A' are negative.
The displacements
illustratedin Figure 27 are valuesaveragedover timesvery muchlongerthan the cycleof recurrence
yet know how large a contribution is required from a frictional source,it is worth investigatingthe conditionsunder
which it could be appreciableand what they might imply
during earthquakesare as small as seismicestimatesindicate,
this shouldbe a usefulapproximation.
The complexdeformationin the regionof plate interaction,
AA', BB', DD', is a consequenceof the vertical variation in
failure and deformationcharacteristics
of the outer layersof
the earth. The stresses
?cand ?½b
exertedby C on A and B, respectively, are reactions to resistance in the shear zone
of earthquakes.
The associated
stressstateis alsoa long-term
averagecondition,and it is unchangedby the deformationasModelsfor a Mechanical Contributionof AnomalousHeat in
sociatedwith thesevelocities.The work doneon sucha systhe CoastRanges
temmustbe dissipated,
andwe shahassume
that the principal
If shearheating contributesto the Coast Range anomaly sourcesof heat and seismicradiation dissipatedin the fault
and friction on the fault is negligible,resistingstresses
mustbe zone can be accountedfor by a steadymodel of this kind. If
appreciablesomewherein the fault zone.Although we do not mostof the transienteffectsare elasticand if stresschanges
about the mechanics of the fault zone and the resistance to
plate motion at a transformplate boundary.
For this purpose, we considerthe quasi steady state mechanical models of Figure 27 in which H representslithospherethicknessand h representsthe depth to which slip on
the main fault trace is uniform
and discontinuous.
At some
depthj (Figure27a) beneathh, the mediumdeformsductRely,
AA'BB'DD'.
We shah assume that the boundaries of C and C'
have been selected so that
%, •cb> 0
(56)
6214
LACHENBRUCH
OF THE SAN ANDREAS FAULT ZONE
(57a)
va-- vb-- v•,
•A A'I
•
b
JD
(57b)
where y* is the half-width of the fault zone, and the correspondinganti-symmetricrelations apply for negativey. For
small y, (57a) is required if vois continuousat y -- 0 and v• is
not (Figure 27b), but the inequality could be reversedfor
larger y (< y*) if most of the fight lateral shearingof B were
concentratedin a thin shearzone at y -- 0, as is often assumed
[see, e.g., Savage and Burford, 1973; Hanks, 1977]. In that
case,the seismogeniclayer would be driven by the basal stress
(Figure 28b), a condition that we shall show to be incompatiblewith the heat flow constraintif there is appreciable
heat generation in the fault zone [see also Lachenbruchand
Sass, 1973].
The fault slip velocity in the seismogeniclayer is given by
•
tA
y = y*
Vo= v•,- v,,(0+)
(58a)
Vo'= v; +
(58b)
•
•
The differencebetweenv•,and Vorepresents
inelasticdeformation in A (vp,vp',Vo,andVo'aretreatedaspositivequantities.)
The long-term resistanceto plate motion offered by the
fault at y -- 0, x < h is the averageelasticfault stress•e, which
in the notation of an earlier sectionis given by
!
Fig. 28. Major alternativesfor flow of mechanicalenergyin zone
of plate interaction:(a) subcrustBB' movesslower(in right lateral
sense)than seismogeniclayer AA', which it retards,(b) BB' moves
faster than AA', which it drives. Eobsrepresentslossof heat and seismic radiation energy.Arrows denotethe directionof steadyflow of
energyfrom one regionto another.
and that the neglectedbasal traction betweenC and D is unrelated to plate interaction.
We are left with two principal optionsfor the steadyflow of
mechanicalenergyinto and throughthe zone of plate interaction(Figure 28). They are distinguished
by whetherB and
1
=+
from A and B to C.
We denotethe shearingtraction at the baseof A by ,b and
the velocityof A by va(y).The velocitya shortdistance(relative to h) belowA will be denotedby vb0')(Figure 27). Unless
vb(y)-- va(y),A will be partiallyrecoupledfrom the restof B
by thisthin zone,and energywill be dissipated
within it at the
rate ,b(vb- v•), a positivequantity, because•b will have the
sign of the velocitydifference.Accordingto (48), heat generated in this partial decouplingzone beneaththe seismogenic
layer might contributeappreciablyto the CoastRange anomaly, but heat generatedat greaterdepth (say >•20 km) probably couldnot. The rate of deformationin this zonemay be
substantial,with vb(y)continuousat y = 0 (as in Figure 27b),
or it may be slight,as in Figure 27a. Furthermorev,,may be
greateror lessthan vb,and the signof their differencecould
changethroughoutthe half-width y* of the fault zone. We
shall be interestedprimarily in the followingcase(illustrated
in Figures 27):
(59a)
-" ? -I'-'r,•
(59b)
•< 100 b + ,a
(59c)
We continueto usethe apparentstress*a and dissipativeresistance ? as positive parameters.Equation (59b) expressesthe
fact that insofar as plate motion is concerned,seismicradiation and frictional heat both representenergy dissipatedby
the mechanicalsystem.
The average(tensor)componentof sheafingstress,y• in A
is constrainedby the conditionof equilibrium:
,y:(y)
= -%- •-
B' drive(Figure28b)or resist(Figures28a and 27) the right
lateralmotionof A andA', or equivalently,whetherA andA' are
movingslower(Figure 28b) or faster(Figure 28a) than B and
B' in a right lateral sense.(The 'brittle' modelof Lachenbruch
and Sass[ 1973]is an exampleof conditionsin Figure 28a, and
the 'ductile' model is an example of Figure 28b.) Condition
(56) excludesthe possibilitythat arrowsin Figure 28 point
= 0'*+
,• dy
(60)
For purposesof illustration, we shall assumethat • is con-
stant,determinedby a plasticyield stress;
for conditions(57),
ß• is negative,and ,b' is positive,asin Figure 28a. (The caseof
ß• proportionalto (vo- v,,)hasbeendiscussed
by Lachenbruch
and Sass [1973]; T. C. Lee (personalcommunication,1979)
has pointed out that a factor of 1/2 is missing before the
bracesof equation 7 in that paper.) With this simplification,
(60) yields
Y
*y,(y)
=-%- •-*•
(61a)
and at y = y*,
y*
%----Ye- -•-Y•
(6lb)
Thus if •b is positive(Figure 28b), the greatestshearingstress
in the seismogeniclayer occurson the fault and the least on
the periphery;if ,• is negative(Figure 28a and Figures27),
the minimum occursat the fault and the maximumat the periphery.
Energeticsof Plate Interaction
Let Er be the total rate of energydissipationper unit length
at a symmetricaltransformplate boundary,and let Rr be the
LACHENBRUCHAND SASS:ENERGETICSOF THE SAN ANDREASFAULT ZONE
corresponding
resistance
(per verticalunit area)to platemo-
Combining (59c), (6lb), and (67a), we can now expressthe
heat flow constraint(13) as follows:
tion. Then for an antisymmetricshearzone,
Er-- 2hvp%
+ 2fcB%bv
v ds
-- 2Hv•,Rr
6215
(62a)
0<e=
(62b)
wherethe integralis takenoverthe boundarybetweenC and
B, and %•,is the tractionthere. Applicationof (56) yieldsa
+ -•- 1-
lower limit to plate resistance:
•'•,•<1• bars (68)
For the Coast Rangeswe selectthe follow•g values:
'
h
Rr> •%
(63)
2v•
=5cm/yr v•=0.6
2Vo= 3 cm/yr
Let Eobs
bethesumof the 'observable'
losses
of mechanically
generatedheatand seismicradiationenergy.Assuming
all of
(69)
the seismicenergyoriginateson the main fault trace,we have
Eobs---2y*Aq+ 2hvo•a
h = 14km
y,
2y*=84•
(64a)
-- 2hv•obs
v•
T =3
(64b)
whereAq is the averagevalueof the mechanically
generated
part of the broadheat flow anomaly,and Robs
is the resistance
to plate motion that is, in principle,observablefrom studiesof
heat flow and earthquakes:
which leadsto the follow•g relation(see(10)):
0<F[bars]
910Aq
[HFU]
0.4%+3(1
--
-
-
•'•,_<-100
where stresses
are expressedin bars. If the basalstress•-•,vanished, a large heat flow contribution would require a very
largeapparentstress(--•2kbar/HFU); if •-•,werepositive(FigSincethe portion of Er generateddeep within the lithosphere ure 28b), % would have to be larger still. Hence a substantial
cannot contributeto Eobs,(62b) and (64) yield a secondlower heat flow contribution from the shear zone would seem to imlimit to plate resistance:
ply basal drag on the seismogeniclayer (i.e., •-•,negative,as in
Figures27 and 28a). This requiresthat the minimum shearing
h
stressin the seismogeniclayer be the value at the main fault
y* Aq
Vo
=- • • + •'ra
(64c)
Robs
h vv vv
Rr> • Robs
(65)
Accordingto (48), Eobsshould be approximatelyequal to the
net rate at which work is done on the seismogeniclayer plus
the underlying decouplinglayer after a few million years of
transformfaulting. If we assumev•,is continuousat y -- 0 (as
in Figure 27b), then
Eobs
--•2hvvr•
+ 2f oY'V•dy
(66a)
• 2hv•%+ 2y* •,r•,
(66b)
and the maximumbe the value at the periphery% (61).
Using the equilibrium relation (61) and the energybalance
(67), we can expressthe basal and peripheral stresseson the
seismiclayer in terms of heat flow and the fault stresses
and r-)as follows:
-%,-1--• { vvif. 1---%+}
vv
-- 1- •
(70a)
{303Aq
[HFU]-3[0.6%
+ r-'I} (70b)
where •, is the averagevalue of v•,,and we have assumed•'•,to
be constant.
Combining (64) and (66) yields the energy balance for the
seismogenicand decouplinglayers:
hvv%= y*Aq + hvo%- y*•b
y* Aq
Vo
%= --h •vv+ --•',,
vv
.....
y* V•
--Robs
h vv•'•,
y* •
- -- --•'•,
h vv
(67a)
%...Ii_•_v'l-'{y'
Aq(V•,
Vo
I v-•
}
vv
.....
1 • - 910Aq
[HFU] •'
v•,
•'
v•,
%- --?
(71a)
(7lb)
(67b)
where stressis in bars in the dimensional forms, which incor-
(67c)
porate (69). It is seenthat thesestresses
are very sensitiveto
the ratio (vo/vv)of the averagespeedof the baseof the decoupling layer to the speedof the rigid plates.
For convenience,we representv•,by
The term on the left in (67a) is work doneby the plate in driving the seismogenic
layer; the first two termson the fight are
n> 0
(72a)
the heat and seismicradiation that leave the system,and the
last term is work done by the decouplingzone on the underfrom which it follows that
lying crustif •'•,is negative(Figure 28a) or on the decoupling
zone by the underlyingcrustif •'• is positive(Figure 28b). It is
(72b)
seen from (67c) that the sign of % determineswhether •-• is
vv n+l
greater or lessthan Robs,and consequently,whether (63) or
(65) imposesa strongercondition on resistanceto plate mo- Small n implies large right lateral velocitiesin the subcrust,
tion.
and large n impliessmall ones,a conditiongenerallyassoci-
6216
ated with substantialdecouplingof the seismogenic
layer (the
amountdependingon the form of Va(y)).This relationis illustrated in Figure 29 where vois shownfor n = 1/2, 1, and 2.
The solid curve labeled vavJreprese.
nts motion of the seismo-
flow anomaly for stressconditionson minor peripheral faults
will depend upon more detailed considerationsof apparent
stressand dynamic friction on suchfaults and their possible
observableseismicand geothermalconsequences.
If the pringeniclayer for a centralfault. As we have assumed•'bto be cipal interplate slip shouldoccurat the periphery of the shear
constant,the form of va(y)entersthe analysisonly throughits zone, the high stressesrequiredby the central fault would not
effecton the signof •'b(whichis the signof vb(y)- Va(y))and be eliminated; they would only be moved elsewhere [see
on the fault slip Vo.
Lachenbruchand Sass, 1980].For the symmetricalperipheral
The leastvalue of •'coccursin the physicallyunrealisticcase faults illustratedby the dashedcurve VaVa',
Figure 29, the central stress(at y -- 0) is the sameas the peripheralstress•'c(at y
of completedecouplingTo-- 0, which leadsto
-- +_y*) for the correspondingcentral fault provided n is re•'c> 910Aq [HFU] + 0.6•'a----Robs
(73)
placed by its reciprocal;under these conditions,the magniwhere stressis in bars. The greatestvalue of •'c occurs with tudesof the basal stressesare also the same.For a single pecompletecouplingat the baseof the seismogenic
layer,i.e., v-o ripheral fault (at y -- -y*), Figure 30, which approximates
• v%.Judgingfrom the measurements
of Thatcher[1959] in conditionsat the southernend of the Coast Ranges,the stress
at the oppositeside of the shearzone (y -- +y*, Figure 30) is
the CoastRanges,•a/Vp"• 0.8--0.9,whichleadsto (7lb)
the sameas that for the correspondingcentral fault (i.e., with
(74) the samen), but the basalstressis reducedby a factor of «. In
[bars]• (5-10 x 910Aq [HFU]
Hence in the absenceof decoupling,appreciableheat genera- each of thesecases,the basal stressopposesfight lateral motion would require peripheral stresses
of.several kilobars. If tion on the fault(s), for otherwise,the heat flow constraint
the averagespeedat the baseof the decouplinglayer were 1/2 would be violated.
Henceno matterwherein thesl•ear
zonetheprincipal
platevelocity(n = 1,Figure29), a conditionthatwouldrepre-
faults are located, an appreciable mechanical contribution to
the broad heat flow anomaly is possibleonly if the average
shearstressin the seismogeniclayer increasesrapidly with distance from the fault(s), a testableconsequence.
Decoupling at
the baseof the faulted blockswould generallybe in the sense
that resiststheir right lateral motion. Under theseconditions,
the unobservedmaximum stressaway from the fault(s) 0'c for
quired basalstress(70) is generallylessthan the peripheral the central fault) would determine the resistanceoffered by
stress by a factor •1/3, becoming somewhat smaller for the seismogeniclayer to plate motion. If there is an appreciable heat flow contribution,this resistancewill generallybe
larger %.
Rearranging(71a), we can expressthe heat flow anomaly substantiallylarger than Robs(68) estimatedfrom measurements of seismic radiation and heat flow. The unobserved disby
sipated energy representswork done by the decoupling layer
sent substantialdecouplingin the Coast Ranges,peripheral
stresses
are still large for modestheat flow contributions.It is
clear from (71) that the permissible
amountof mechanically
generatedheat will be limited by the conditionthat the peripheral stress•'c not exceedthe strengthof upper crustal
rocks;the stressis insensitiveto '}'aand hence to whether the
fault is weak always or only during earthquakes.The re-
Aa=f;hvp{•c1-¾ø '•-q'a --
(75)
on the material
beneath it.
The Form of the Heat Flow Anomaly;Independence
of Distance
Taking an upper limit for rock strengthunder normal fluid
pressureof 1.5kbar (Table 4), the maximumpermissible
contributionof mechanicallyderivedheat in the CoastRangesis
Aq[HFU]--0.65
1.51-• +•'a•--
+?'•-•'•(76a)
-•1-•}[HFU]
(76b)
where stressis in kilobars.This yields0.5 HFU for conditions
illustratedby n = 1 (equation(72), Figure29), 0.33HFU for n
= 1/2, and 0.1-0.2 HFU for completecoupling(n -• 1/4 - 1/
5). Thus, unlessmost of the plate motion in the interplate
shearzone is confinedto the seismiclayer (i.e., roughly, unless
n > 1), it is unlikely that shearheating can accountfor more
than about half of the steady state heat flow anomaly in the
Coast Ranges. Even this amount of heating requires substantial decouplingat the base of the layer and large stresses
at the periphery of the shearzone.
These resultsraise questionsabout stressconditionson peripheral faults. In deriving them, we assumedthat all of the
seismicenergy was generatedon the principal central fault,
equivalentto assumingthat the heat-generatingstresson minor peripheral faults is the average ambient tectonic stress
there. Implications of a broad mechanically generated heat
From the Fault
The foregoingdiscussionof energeticsdoesnot addressthe
details of the heat production processnor, indeed, whether
models of the type consideredcould reasonablycontribute a
broad uniform heat flow anomaly throughoutthe fault zone,
suchas the data from the California Coast Range suggest.
The heat flow anomaly Aq(y), discussedonly as an average
Aq in the last section,can be viewed as the sum of three contributions [seeLachenbruchand Sass, 1973]:
Aq(y) • qyz(Y)+ qb(Y)+ q(Y)
(77)
For convenience,we consideragain the centrally faulted antisymmetricshear zone, for which it is only necessaryto describethe y positiveside.The termsin (77) can be expressed
as
-•--•-y
= _h{•.e+y
• %'
dy
qyz(y)._h•.yzdVa
}dva
(78a)
qo(y)=--'}'b(Va- lib)
(78b)
.fo?q
dy= ?Vo
(78c)
Here, qyzis the rate of heat generationper horizontalunit area
resultingfrom inelasticdistortionof the seismogenic
layer (for
6217
Aq-- q----qy•+ qb
vp
•
,-
h { Y} (l-y} (80a)
•
=- f;(v•,-Vo)
%+•-•'•,
-•Vo y,
....
•
0
•' •
•
••
•
•
• •
I
=-•(v• v•)%-Vo•y
which
results
• thedesired
uniform
anomaly
(•dependent
of
• v0'• y)iftheslipvelocity
Vo
ishalftheplate
velocity
v•(80b).
There
isatriangular
m•um
at
y=0ifthe
slip
velocity
isfaster
than half the plate velocityand a maxxurn if it is slower.The
'•*
Fig. 29. Velocity of seismogenic
layer shownfor a central fault
(solidcurveVa,Va')and symmetrical
peripheralfaults(dashedcurve
Va,Va')with three different velocitydistributionsVb,Vb'at baseof decoupling layer.
possibility
ofa m•um • qy•+ qoraises
thequestion
of
whetherthis might 'hide' a more substantialcontributionfrom
fault frictionq than we haveac•owledged• defiv•g the
heatflowconstra•t ((13) and(38)) [seeLachenb•chandSass,
1973].In any case,the local anomalycouldnot exceedthe total broad anomaly of about 0.8 HFU, a conditionthat would
relax the constra•t
example,by plasticflow or subsidiaryfaulting), qois the rate
of heat generation by flow in the hypothetical decoupling
layer beneaththe seismogenic
layer, and q is heat generated
by friction on the main fault trace, discussedin detail in an
earlier section.In (78a) and (78b) we have neglectedconductivesmoothingbetweenthe sourceand the surface,justified by the approximatenature of the calculationand the fact
that the depth of the sources(x •< h) is small relative to the
width of the shearzone (2y* ,-• 6h).
From (78a) it is seenthat computationof the form of the
heat flow contribution requiresinformation on the distortion
of the seismogenic
layer not requiredin the calculationof energy balance.The heat flow anomalyis more sensitivealsoto
the y dependenceof vo,formerly enteringthe analysisas an
average, and of •, which we have assumedto be constant.
Reasonable
assumptions
regarding
the formsof Va(y
) and vby),
on fault friction to
400 bars
(81)
However,sucha minimumrequiresratherspecialconditions,
and the absenceof an observable
local anomalyin the contrastingtectonicand thermal regimesof northernand southern Californiamakesthisalternativeextremelyunlikely.
SUMMARY
We have summarized heat flow data from more than 100
sites within about 100 km of the San Andreas fault in Califor-
nia. From thesemeasurements
we havemadethreegeneralizations, the mechanicalimplicationsof which we have attempted to interpret:
1. Thereis no measurable
localheatflow anomalyalong
the 1000-kinlength of fault trace (Cape Mendocinoto San
Bernardino) from which measurementsare available.
2. The heatflowis anomalously
high(~2 HFU, ~80 mW
and of •b, which will depend upon them both, must come
m-2) throughout
thesouthern
550km of theCoastRanges,
a
from an analysisof the controllingconstitutiverelations,an
region that enclosesthe San Andreas fault in central Califoreffort beyond the scopeof this study. (Substantialdecou- nia.
pling nearthe baseof the seismogenic
layer will probablyre-
3. This broadCoastRangeanomalyfalls off rapidly toquire effectiveviscosities
<•1022P at temperatures
--•750øK,
ward the Great Valley to the east,and northwestwardover a
conditionsthat mightbe compatiblewith 'wet quartzite'and
200-km distanceto Cape Mendocino.
'limestone'but not the other mediadiscussed
by Yuenet al.
The first generalization(first discussedby Brune et al.
[1978].)Without pursuingunwarrantedrefinements,
we pre[ 1969])imposesa severeconstrainton the localenergetics
of
sent only one simple example to illustrate some general
points.
We haveshown(61)thatfor • positive,
•y•increases
asthe
the main fault, and the secondand third might containinformation on the energeticsof plate interactionand the mechanical behavior of the broad shear zone.
centralfault is approached,
andfrom(78a) and(78b)it is seen
The importance of generalization I to the mechanicsof
that both qy•and qowould generallytend to contributeto a
heat flow maximum(not observed)at y = 0. For • negative
(Figure 28a), the two contributions
tend to vary in opposite Vp
senses,and •y• is a minimum at the fault. Hence a uniform
heat flow anomalyis consistent
with a relativelyweak fault.
This is illustratedfor a simplemodelwith linear Vaand voin
whichVa> Vband hence• is negative(Va,Va'is the solidcurve
in Figure 29, and vo,vo'is the curven -- 1):
Va=V0'•(VpVoy)•
,
v•--vpyY--,
From (66),
(79a)
-Vp
y*
(79b)Fig. 30.
0
-y*
Velocity of seismogenic
layer Va,Va'for a one-sidedperipheral fault and three differentvelocitydistributionsvb,vo'at base
of decoupling layer.
6218
LACHENBRUCH
faulting dependsupon the applicabilityof two conditions:(1)
heat transfernear the fault is primarily by conduction,and (2)
work done againstresistingforceson the fault surfaceis dissipatedprimarily as heat. If both conditionsapply, then generalization 1 implies that during events responsiblefor the
preponderanceof fault motion, the average(in,stantaneous
)
resistingstresson the fault surfacesdid not exceed,--100bars;
we refer to this limit as the 'heat flow constraint.'
If heat were
removed convectivelyby water circulating in the fault zone
(in violation of condition (1)), much larger resistingstresses
would be permissible.However, we considerthis unlikely, becausethe heat dischargeof thermal springsnear the fault is
negligible and heat flows are similar on each side of the fault,
but hydrologicconditionsprobably contrastsharply. Undetected heat dischargeinto surface drainage at temperatures
slightly above ambient is a possibility that may deservefurther study. Larger resisting stressesare permissiblealso if
much of the energy dissipatedin overcomingthem is con-
sumedby creatingnew surfacesor by other energysinks(in
violation of condition2). Our estimate(basedon specificsurface energiesfrom Brace and Walsh [1962] and an average
three-dimensionalfracture spacingof 1 micron in the gouge
zone) suggests
that conversionof work to surfaceenergyis too
small by 2 orders of magnitude to affect the heat flow constraint. There is, however, a large uncertaintyin the rate of
creation of surfacearea in gouge by faulting. Other possible
energy sinks such as chemical and metamorphic reactions
should be investigated,although we considerit unlikely that
they will invalidate the heat flow constraint. Our interpretations are based on the assumptionthat the constraint is
valid.
The heat flow constraintprovidesan upperlimit (,--100bars)
to the averagedynamic frictional resistancethat obtainedduring thoseeventsresponsible
for mostof the slip on the San Andreasfault; this probably excludessmall earthquakesand isolated creep episodeslastingno more than 10,000yr. The importanceof the constraintlies in the informationit provides
on the ambient tectonic stressstate. If almost all of the slip
took place by steady uniform creep, the implications are
straightforward;the resolvedtectonicshearstresson the fault
could not, on the average,have exceeded,--100bars and consequently,tectonic stressdifferencescould not have exceeded
a few hundred
bars.
If, however, most of the displacement occurred during
earthquakes,it is the initial stressprior to the event, not the
frictional stressduring the event, that indicates the ambient
state of tectonic stress. The relation
between the two is most
easily discussedin terms of the frictional theory of faulting
wherein the initial stressis bounded above by the static frictional strengthand boundedfrom below by the dynamic friction. The frictional strength is given approximately by the
productof the coefficientof staticfrictionand the ambienteffective normal stresson the fault; the averagedynamic friction
(constrainedby the heat flow) is the productof the coefficient
of dynamicfriction and the (displacementaveraged)effective
normal stresswhile faulting is in progress.The implicationsof
the heat flow constraintare different dependingupon whether
or not the ambient effectivenormal stresspersistsunchanged
during the faulting event, i.e., upon whether the fault is weak
all the time or only during an earthquake.
If the effectivenormal stressis the samebefore and during
an earthquake, then the initial stresswill not exceedthe dynamic frictional stressby a factor greater than the ratio of the
static and dynamic coefficientsof friction, a quantity that is
OF THE SAN ANDREAS
FAULT
ZONE
probably of order unity (we have used 4/3). In this case,the
frictional strengthand the resolvedtectonic(i.e., initial) shear
stresscan be only slightlygreaterthan the • 100 barspermitted by the heat flow constraint, and the tectonic stressescannot be significantly
greaterthanthosepermittedfor steadystate
creep. Such low frictional stresses,
are, however, lessby an order of magnitudethan thoseexpectedfrom laboratory results
(Byerlee'slaw) in upper crustal rocks with normal (hydrostatic) fluid pressures.This strengthparadox can be resolved
by postulating that the fault contains materials with anomalously low staticand dynamic friction (for example,hydrated
clay minerals) or that near the fault the ambient fluid pressuresare near lithostaticand, consequently,the effectivenormal stressis very small. At present,however, there is little independent evidence that either of these conditions occur
generally on the San Andreas fault. The paradox cannot be
resolvedby explanationsof low strengththat do not also explain low dynamicfriction. For example,the strengthof small
laboratory samplesmight be much greater than the strength
of a large heterogeneous
fault becauseof the greaterprobability of the juxtaposition of randomly distributed flaws and local stressconcentrationson the latter. This does not explain
the low averagedynamic frictional resistanceimplied by the
heat flow constraint. The paradox could, of course,be resolvedwithout contradictinglaboratory results,or by assuming a changingeffectivenormal stress,if the ratio of the coefficientsof staticto dynamic friction were an order of magnitude
greaterthan we have supposed.However, this alternativeruns
into the sameobservationaldifficulty as the oneswe shall next
discuss.
If the averageeffectivenormal stresswere an order of magnitude lessduring an earthquakethan it was beforethe earthquake, then the heat flow constraintwould be consistentwith
strengthson the order of ,--1 kbar (as suggestedby laboratory
resultsfor upper crustalrockswith normal fluid pressure)and
with
ambient
tectonic
stress differences
of a few kilobars.
There are severalplausible physical mechanismsthat might
cause such large transient reductions in effective normal
stress.The fluid pressuremight increaseduring an earthquake
as a resultof frictional heatingand thermal expansionof pore
fluid or by reduction of pore volume or dehydrationof clay
minerals [Lachenbruch,1980;Sibson,1973;Raleigh, 1977],or
perhapsthe effectivenormal stresscould be reduceddynamically by 'acousticfluidization,' as recently suggestedby Melosh [1979]. However, modelsof this kind are constrainedby
implications from seismologyfor the energeticsof the earthquake process.The work done by local elastic forcesduring
an earthquake must be accountedfor by heat and seismicradiation energy.Stated another way, the averageelasticstress
operatingduring an earthquakeis the sum of a part allocated
to the productionof heat (the dynamicfrictional resistance)
and a part allocatedto the productionof seismicenergy(the
'apparent stress').It is known from seismicstudiesof many
crustal earthquakesthat the initial stresscannot exceed the
averageelasticstressby more than a few tensof bars(half the
'stressdrop'). Hence to a few tens of bars the initial (resolved
tectonic) shear stresscannot exceed the frictional resistance
(constrainedby heat flow to be • 100 bars) by more than the
magnitudeof the apparentstress.Hence modelsleadingto an
initial stressof ,--1 kbar require that the apparent stressbe of
similar magnitude; they are inconsistentwith seismicestimates of apparent stress,which are generally •50 bars. Consequently,large ambient tectonic shear stresseson the fault
are not permitted by the heat flow constraintunlessthe seis-
LACHENBRUCH
6219
mic estimatesof apparent stress(and hence of total radiated
energy) are very much in error for thoseearthquakesresponsible for most of the cumulative displacement,probably the
very large ones. If we take the thermal and seismicobservational constraintsat face value, it is difficult to justify average
tectonic shearingstresseson the fault much in excessof-,200
the foregoinginterpretationof generalizations2 and 3, mechanicalwork in this regionmustaccountfor the contribution
to anomalousheat lossin the Coast Rangesand for seismic
energyradiatedfrom the fault(s).Insofarasthe tectonicplates
are concerned,both of theseforms of energyare dissipated
and are associatedwith resistanceto plate motion.We identi-
bars.
fiedtheselosses
with the work doneby the long-termaverage
stresses
operatingthroughthe long-termaveragevelocitiesat
the boundariesof this region(the seismogenic
layer plusthe
hypotheticalunderlyingdecouplinglayer). We found that in
In addition to theseimplicationsfor the stressregime in the
immediate vicinity of the fault, the heat flow constraint has
implications for stressesin the broad shear zone surrounding
the fault when it is applied to interpretation of the broad
Coast Range heat flow anomaly. The growth of this broad
anomaly southwardfrom Cape Mendocino (generalizations2
and 3) may be interpreted as the transienteffectof the change
in thermal conditionsthat took place at the migrating Triple
Junction when subductiongave way to transform faulting.
Since the transition to the high heat flow characteristicof the
Coast Range is complete •200 km southeastof Cape Mendocino and sincethe Triple Junctionhasbeen migratingnorthwestward •50 km/m.y., this suggeststhat a steady state is
reached in •4 m.y. and, consequently,that the sourcesof the
anomaly are in the mid- and upper crust(•<20 km). This conclusion is consistentwith the rapid fall-off of heat flow toward
the Great Valley to the east. There are two simple processes
that might accountfor the anomalousobservedheat flow: (1)
conductiveheating of the North American plate from below
when it passessouthwardfrom a regionin which its baseis in
contact with a cool subductingslab to a region in which it
contactswarmer mantle material; (2) shear-strainheating associatedwith distortion and possiblebasal decouplingof the
seismogeniclayer of the San Andreas fault zone which originates near the Mendocino Triple Junction. An understanding
of the nature of the San Andreas fault might depend upon a
distinction
between
the relative
contributions
of these two
order to generate an appreciable heat flow contribution with-
out violatingthe heat flow constrainton the main fault, it is
necessarythat the (steadystate)basaltraction on the seismogeniclayerbe in the sensethat resists(not drives)right lateral
fault motion.Under thesecircumstances,
the shearingstress
on planesparallel to the fault in the seismogenic
layer is a
minimumon the mainfault and a maximumat the periphery
of the fault zone.The maximumpermissible
mechanically
generatedheatflowanomalyis limitedby howlargetheseperipheralstresses
may be and by the amountof decoupling
near the base of the seismogeniclayer. If the peripheral
stresses
are limited by the strengthof uppercrustalrockswith
normal fluid pressure(• 1.5kbar), then the mechanicalcontri-
butionto the broadheatflowanomalyprobablycouldnot exceed0.1-0.2 HFU unlessthe seismogenic
layerwerepartially
decoupled
fromthe underlyingcrustat itsbase.If the average
fight lateralvelocityof the baseof the decouplinglayer were
about« plate velocity,shearheatingcouldprobablyaccount
for about« of the steadystateheatflow anomalyin the Coast
Ranges(•0.5 HFU). Theseresultsare rather insensitiveto the
stress
allocatedto seismic
radiation0'a),andhencetheyapply
whetherthe fault is weak all the time or only during earthquakes.Similarresultsapplyto a fault zonecontainingmore
than one fault. Hence accordingto this simplifiedmodel,an
processes.
appreciable mechanical contribution to the broad heat flow
To explain the heat flow transition by the first processwithout a contribution from shearheating, extreme conditionsare
necessary,for example,shallowsubductionat a depth of only
20 km beneath the Coast Ranges and complete coupling of
the North American plate to the underlying mantle when subduction stops.This would resultin a buried one-sidedspreading center migrating northward (with the Mendocino transform) as a 'hot line' beneath western North America. The
lithosphere beneath the Coast Ranges would thicken southward (from 20 km near Cape Mendocino today) by thermal
accretion.Taken literally, the model leadsto a deep San Andreas fault penetratingthe entire lithosphere;it is too simple
to account for the inland migration of the locus of surface
faulting. Nevertheless,it accountsreasonablywell for the distribution of observedheat flow; the rapid transition toward
the Great Valley could be accommodatedby a rapid steepening of subductionto 40 km (from 20 km beneath the Coast
Ranges). If field evidence for extreme conditions of the sort
implied by this model cannot be found, it is likely that an appreciable contribution from shear-strainheating will have to
be invoked. Although this requirementis speculativeat present, it is of interest to considerits implications, when taken
with the heat flow constraint, for the mechanics of the fault
zone and plate interaction.
We consideredmodelsin which the anomalousheat is generated in a broad shear zone (correspondingto the Coast
Ranges)by distortionin the seismogenic
layer (• 14 km thick)
combined with a possiblecontribution from shear flow in a
horizontal partial decouplinglayer at its base. According to
anomalyshouldbe associated
with a rapid increasein mean
shearingstress
with distance
fromthe principalfault(s),a testable consequence.
If heat generationis significant,the
seismogenic
layer couldoffer appreciableresistance
to plate
motioneventhoughstresson the main fault were negligible;
the principal resistingsurfacewould be the horizontal baseof
the seismogenic
layer.
APPENDIX
A: GROSS CONDUCTIVE
OF FRICTIONAL
VERTICAL
HEAT
FROM
EFFECTS
A
STRIKE SLIP FAULT
We consider effectsin the half-space x > 0 of heat conductedfrom a verticaldistributionof sourcesof strengthQ(x)
commencingat t = 0 on the fault plane y - 0. The medium is
initially at zero temperature, and the surface x -- 0 is maintained at zero temperature (Figure 1).
A general expressionfor temperature 0 is obtained by integration of the transient result for continuoushorizontal line
sourceslying in the fault plane [Carslawand Jaeger, 1959, p.
261, equation 5].
O(x,
y,t)=4--• I --El--
nat
+Ei{-ya+
(x'
+x):.}-Q(x')dx'
(AI)
4at
wherethesecond
termin theintegral
represents
a negative
imagesourceas requiredto meetthe zero-temperature
condition on x = 0.
6220
The Caseof ConstantSourceStrengthin the Depth Range
(x,,x9
S(u,m) -- -•r1
For this case,Q(x) = Qc,a constant,whereXl -< x _<x2, and
Q(x) = O,where0 < x < Xl, x2 < x. A changeof variablesin
(A1) leadsto
(A1la)
v2+ 1
[tan-'
u-um2] u:m
2<<1 (A1
lb)
4•rk
o(x,y,t
) 4•t[ f{x•+x,/{4•t,l,•
Qc
• (Xl+X)/(4at)l/2• (Xl--X)/(•t)l/2
1
-• •-(1- erfm) u-• oo
.[_(m:
+f12)]
dr}
where
e•m2(v2+l
) d¾
•o
u
(A2)
(A1lc)
Tables of the exponentialintegral and the error function are,
of course, available in standard handbooks. The function S
m2= •/(4at)
(A3)
hasbeendiscussed
and tabulatedby Smith[1953]and Lachenbruch [ 1957].
The •tegral • (A2) may be •tegrated as foHows:
Applying (A9), (A10), and (A11) to (A8) yieldsthe steady
•E,(_m
•_•2)
d•=[bE,(-m
•- b•)- aE,(-m
2- a2)]
state result:
O(x,y,
oo)=
Qc
{(x2q-x)il'l[y2q-(x2q-x)2]_ (xI q-x)
(A4)
The integral on the right • (A4) may be written
ßIn [y2q-(x I q-x)2]_ (x2_ x) In [y2q-O•2-- X)2]
-2
+ (x, - x) tn Iv2 + (x, - x):1
m:+
m2
---2fab
e-m2-t•2d•
+2fab
e-m2-t•2
m2
q'fl•dfl (A5)
+2y
Itan-I
x2
+x tan2x•+x
tan_
Ix2
- x XI--X]}
Y
but
--2
be-m2-t•2d• -' -e -m2•
[erfb - erfa]
--
(A6)
and
•
Y
+ tan-•
Y
,
(A12)
Y
The temperaturein the planeof the fault is obtainedby setting y = 0 in (AS)
2f•t,
e-m:-t•:
m2
+2
fl•dfl
=2•m
,m
m
IS{mb-}- S{•,m)1(A7)
where the function S is descried below. ApplyMg (A4), (A5),
and (A6) to (A2) yieldsthe desiredgeneralresultfor the transient temperaturerise M the half-space:
-•-
(4ott)l/2
4ott
4at2 (x:x)Ei-{ (x:x)
x•+x{ (x•+x)
(A8a)
+ •I'4'•
--X)2}I
1I- erf(4at),/2
X2q-X
Xl--X
{ (X
(4at)l/2
Ei-
where
F(a; y, t) ---aEi
y2+ a2
4at
-- •
e-?/(4at)
erf •
(4at)•/2
+ 2•ryS
a
y
y' (4at)'/•
XIqX+erf(4at)•/-----X2--•X-erf(4at),/2
Xi--X•j } (A13)
+erf(4at)l/2
(ASb)
The functionsin the three termson the right in (A8b) are
respectivelythe exponentialintegral, the error function, and
the 'Smith' function; they can be representedas follows:
•o dv
E•(-u) = -
0.5772- In u - u
erf
u-=•
= •
(A9a)
e-• •
2
e-v•
dv
u
u2<< 1
u2 << I
4at
(4at),/2
Ei-
O(x,
y,t)= 4•
Qc[F(xe
+ x;y,t) -- F(x•+ x;y,t)
-- F(x 2 -- x; y, t) + F(x, - x; y, t)]
2(•r)1/2
(4at)l/2
Ei-
The factor in front of the bracesis the correspondingresultfor
an infinite plane source,and the expressionin bracesrepresentsedgeeffects,which,of course,ultimatelydominateas the
steadystate is approached.
The Caseof a Linear Increasein SourceStrengthWith Depth
For convenience, we take the linear increase to be of the
following form:
(A9b)
(A10a)
x
Q(x)= Q*•-;
Q(x) = o
XI < X< X2
o < x < x,
x2 < x
The completetransientsolutionfor this caseis unwieldy,and
(A lob) we solveonly for the temperatureon the fault plane y -- 0.
Substituting
the aboveexpression
in (A l) yields
LACHENBRUCH AND SASS'.ENERGETICS OF THE SAN ANDREAS FAULT ZONE
In the steadystate,this reducesto
• fxx2
O(x,
O,t)--4,rkx*
(x+x')2
I
_E,I_
(x'- E,{
•
4at
+ -
4at x'dx'
The transient build-up of heat flux q at the earth's surface
(x -- 0) is obtainedby differentiationof (A1):
Q..O(x,
O,t)--4at
x
(Xl+X)/(4at)1/2
q(y,
t)---1•x:e-{x':+?•/{4"'•
x,2x'
+y•Q(x')
dx'
(4at)!/2
• (xl--X)/(•t) /
(A21)
For the caseof a constantsourcestrengthQo this yields
•f(x•+x)/(4•t)
'/• f(x•-x)/(•t)
'/•
•
(A20)
Heat Flow at the Earth's Surface(x -- O)
4•rkx*
[ • (x 1+x)/(4at)1/l
8,rk
(x•
-+x)
+8x•x
O(x,
O,
oo)
_-Q*x•I I(x,_'_x')
ln'•Y
(X'x)'1
(AI4)
and a changeof variablesleadsto
,r/, ,-.,,
6221
V(Xl--X)/(•t) 1/2
From (A4) and (A6) the•tegrals with• the bracketsyieldresults of the fore:
• E
E,•t ]-E'4at
q(y,t)---Qc
(x•2+y21
( x!2+y2}l
(A22a
• 2,r
Q__sc
Inx22
+-••-• t--}oo
x,'-+y:
x E,(-•2)d•-- (4at)!/2
x
(4at)!/2
- aE,(-a 2) - •
[erf b - erf a]}
(A16)
In the firsttwo integralsof (A15), integrationby partsyields
(A22b)
For the case(correspondingto (A19)) of a linearly increasing sourceextendingfrom the surfaceto depth x,, manipulations similar to those used above lead to
resultsof the following form:
Q*{4•• e-?/•4'">
X2
q(y,
t)=2•--•x•
erf(4at),
a
E,(-•2)•
d•--• [b2E,(-b
•)- a2E,(-a
2)+e-b:- e-a:]
(A17)
(A23a)
- 2½ryS
and the final result is
•
O(x,O,t) =
I - • tan-n
•
Q*1{(x•:
_x•
)
t '-• oo
(A23b)
x2
8,rk x*
where S is the 'Smith' function describedearlier (A11).
ßIEi(-(x•+x)•-Ei
I-(x2-x)
•
APPENDIX
B:
AN
APPROXIMATION
LAW FOR FRICTIONAL
FROM
BYERLEE'S
STRENGTH
IN THE UPPER CRUST
Byedee's[1978] summary of extensivelaboratory measurementsof stresson slidingrock surfacesshowsthat for a wide
variety of rock materials,the maximumshearingstresson the
slidingsurface•m attainedduringeachexperimentcan be expressedin termsof the normalstresso. on that surfaceas fol-
+ 4at[e-(x:+x):/(4at)
-- e
• e-(X•+X):/(4at)
.{.e-(X•-X):/(4at)]
X2 t
lows:
X
a
+2•4•/--•-•,at
x•err(4at),
a+erf(4at)l
X2+X
x,+x
- erf
(4at),/-------• - erf
(4at),al
•'m= C +/•(o,,-
(A18)
where
C= 0
/• -• 0.85
if
The most useful case,in which the sourcestrengthincreases
from zero at the surfaceto Q* at depthx2, resultsin a slight C = 0.5 kbar
simplification
(by settingxl -- 0, x2 -- x*):
Q*x-•
1{(x22_x2
)
O(x,
o,t)- 8•rk
.IE,{_
(x:
+x):
-E,((x:x):'}l
4at
(B la)
0.1 kbar < (o, - P) < 2 kbar
(Blb)
/• = 0.6
if 2 kbar <(o, - P) < 15 kbar
(Blc)
Pore fluid pressureis denotedby P, and the expressionin parenthesisis effectivenormal stressdenotedhereafter by
For analytical convenience,we use the following approximation for (B 1) [seealso Zoback and Zoback, 1980]:
4at
+ 4at[e-•: +•?/•'• - e-•: -•:/{•'•]
+2•
P)
xIerf(4at),
a+erf(4at),/2
•t (A19)
x,-x
•m • •o,,'
o,,' < 6 kbar
(B2a)
0.75
(B2b)
This relation doesnot depart from (B 1) by more than about
11% for a range of effectivenormal stressfrom 0 to 6 kbar,
6222
sufficientto accommodateconditionsin the upper 15 km or so
of the crust.If we let 4, be the angle formed by the trace of the
fault and the directionof greatestprincipal stressOl, the effective normal and shearstresses
on the fault plane are given by
[e.g., Jaeger, 1962]
on the TectonicProblemsof the San AndreasFault System,pp. 136148, StanfordUniversityPress,Palo Alto, Calif., 1973.
Benfield, A. E., A heat flow value for a well in California, Am. J. Sci.,
0.'= « (0•' + 03') - « (Ol' - 03')cos20
(B3a)
Berry,F. A. F., High fluid potentialsin California CoastRangesand
their tectonic significance,Am. Assoc.Pet. Geol. Bull., 57, 1219-
rm = « (Ol' - 03) sin 20
(B3b)
245, 1-18, 1947.
Berg, C. A., Relation betweenstressdrop, fault friction, and crustal
strengthin shallowfocusstrike slip faulting, J. Geophys.Res., 73,
2217-2223, 1968.
Combination of (B2a) and (B3) yields
'
O)•
ø-2L
= 1- p, 2(sin
o.
sin 20
(B4)
Assumingfault failure occursin the most favorably oriented
fracture direction,
1249, 1973.
Blackwell, D. D., Heat flow and energy lossin the Western United
States, Geol. Soc. Am. Mem., 152, 175-208, 1978.
Brace, W. F., Permeability of crystalline and argillaceousrocks:
Statusand problems,Int. J. Rock Mech. Min. Sci., in press,1980.
Brace,W. F., and D. L. Kohlstedt, Limits on crustalstressimposedby
laboratoryexperiments,J. Geophys.Res.,85, this issue,1980.
Brace, W. F., and J. B. Walsh, Some direct measurementsof the surface energyof quartz and orthoclase,Am. Mineral., 47, 1111-1122,
1962.
0= •- •-- tan
-1
(B5a)
Brook, C. A., R. H. Mariner, D. R. Mabey, J. R. Swanson,M. Guffanti, and L. J.P. Muffler, Hydrothermal convectionsystemswith
reservoirtemperatures_>90øC,U.S. Geol. Surv. Circ., 790, 18-85,
1979.
-- 26.6ø
• = 0.75
(B5b)
which leadsto the following generalrelations[seealso Brace
and Kohlstedt,1980]:
Brune, J. N., The physicsof earthquakestrongmotion, in Seismic
Risk and EngineeringDecisions,Develop.in Geotech.Eng., 15, edited by E. Rosenbluthe
and C. Lomnitz,pp. 141-177,Elsevier,New
York, 1976.
Brune, J. N., T. L. Henyey, and R. F. Roy, Heat flow, stress,and rate
of slip alongthe SanAndreasfault, California,J. Geophys.
Res., 74,
3821-3827, 1969.
1.6
Burridge,R., and G. S. Halliday, Dynamic shearcrackswith friction
as models for shallow focusearthquakes,Geophys.J. Roy. Astron.
(B6a)
Soc., 25, 261-283, 1971.
01t
0'3t
- 4.0
(B6b)
Byedee,J. D., Staticand kinetic friction of granite at high normal
stress,Int. J. Rock Mech. Min. Sci., 7, 577-582, 1970.
Byedee,J. D., Friction of rocks,Pure Appl. Geophys.,116, 615-626,
1978.
Oavg
!
0.64
(B6c)
Cardwell, R. K., D. S. Chinn, G. F. Moore, and D. L. Turcotte, Fric-
tional heatingon a fault zonewith finite thickness,Geophys.
J. Roy.
Astron. Soc., 52, 525-530, 1978.
where
Oavg
t •---'
«(01
! "['03t)
(B7)
Thus the frictional strength(B 1) can be expressedin terms of
the effectivenormal stress,the greatest,least, and averageeffectiveprincipal stresses
and the differencein horizontalprincipal stressesas follows:
rm'--'0.75 o,'
(B8a)
= 1.2 03t
(a8b)
= 0.30 Ol'
(B8c)
= 0.48Oavg'
(B8d)
---0.40 (o, - 03)
(B8e)
Carslaw, H. S., and J. C. Jaeger,Conductionof Heat in Solids,386 pp.,
Oxford University Press,New York, 1959.
Combs,J., Heat flow and geothermalresourceestimatesfor the Imperial Valley, in CooperativeGeological-Geophysical-Geochemical
Investigations
of GeothermalResourcesin the Imperial ValleyArea of
California, pp. 5-27, Education ResearchService, University of
California, Riverside, Calif., 1971.
Dickinson,W. R., and W. S. Snyder,Geometryof subductedslabsrelated to San Andreas transform, J. Geol., 87, 609-627, 1979.
Eaton, J. P:, W. H. K. Lee, and L. C. Pakiser, Use of micro-earth-
quakes in the study of the mechanicsof earthquake generation
alongthe San Andreasfault in centralCalifornia, Tectonophysics,
9,
259-282, 1970.
Graham, S. A., and W. R. Dickinson, Evidence for 115 kilometers of
right-slip on the San Gregorio-.Hosgrifault trend, Science,199,
179-181, 1978.
Hanks, T. C., Earthquakestressdrops,ambient tectonicstresses
and
stresses
that drive plate motions,PureAppl. Geophys.,
115,441-458,
1977.
Acknowledgment. We are very grateful to Robert Jachensand Henyey, T. L., Heat flow near major strike-slipfaults in California,
Andrew Griscom for advisingus of the unpublishedresultsof their
Ph.D. thesis, Calif. Inst. of Technol., Pasadena, Calif., 1968.
recent gravity study near Cape Mendocino. In addition, we thank Henyey,T. L., and G. J. Wasserburg,
Heat flow nearmajor strike-slip
ThomasHanks, Barry Raleigh, Wayne Thatcher,Malcolm Johnston,
faults in California, J. Geophys.Res., 76, 7924-7946, 1971.
JamesSavage,Joe Walsh, and Tanya Atwater for helpful discussion Irwin, W. P., and I. Barnes,Effect of geologicstructureand metamorand suggestions.
phic fluidson seismicbehaviorof the San Andreasfault systemin
central and northernCalifornia, Geology,3, 713-716, 1975.
REFERENCES
Jaeger,J. C., Elasticity,Fractureand Flow, Methuen, London, 1962.
Anderson, D. L., The San Andreas fault, Sci. Am., 225, 52-68, 1971. Jennings,
C. W., Fault map of California,scale1:750,000,Calif. Geol.
Andrews, D. J., Application of rupture propagationtheoriesto earthMap Set., map 1, 1975.
Johnson,A. G., R. L. Kovach, and A. Nur, Fluid-pressurevariations
quakes, U.S. Geol. Surv. Open File Rep., 78-380, 33-70, 1978a.
and fault creep in central California, Tectonophysics,
23, 257-266,
Andrews, D. J., Coupling of energy betweentectonicprocesses
and
1974.
earthquakes,J. Geophys.Res., 83, 2259-2264, 1978b.
Kanamori, H., and D. L. Anderson,Theoretical basisof someempiriAtwater, T., and P. Molnar, Relative motion of the Pacific and North
cal relationsin seismology,Bull. Seismol.Soc.Am., 65, 1073-1095,
American plates deducedfrom sea-floorspreadingin the Atlantic,
1975.
Indian, and south Pacific Oceans,in Proceedingsof the Conference
LACHENBRUCH
AND SASS:ENERGETICS
OF THE SAN ANDREASFAULT ZONE
Lachenbruch,A. H., Thermal effectsof the ocean on permafrost,
Geol. Soc. Am. Bull., 68, 1515-1530, 1957.
Lachenbruch,A. H., Heat flow in the Basin and Range Province and
thermal effectsof tectonicextension,Pure Appl. Geophys.,117, 3450, 1978.
Lachenbruch,A. H., Frictional heating,fluid pressure,and the resistance to fault motion, J. Geophys.Res., 85, this issue, 1980.
Lachenbruch,A. H., and J. H. Sass,Thermo-mechanicalaspectsof
the San Andreasfault system,in Proceedings
of the Conferenceon
the TectonicProblemsof the San Andreas Fault System,pp. 192205, Stanford University Press,Palo Alto, Calif., 1973.
Lachenbruch, A. H., and J. H. Sass, Heat flow in the United States
6223
Sass,J. H., D. D. Blackwell,D. S. Chapman,J. K. Costain,E. R.
Decker, L. A. Lawvet, and C. A. Swanberg,Heat flow from the
crustof the United States,in PhysicalProperties
of Rocksand Minerals,edited by Y. $. Touloukian,W. R. Judd, and R. F. Roy,
McGraw-Hill, New York, in press,1980.
Savage,J. C., and R. O. Burford, Geodetic determination of relative
plate motion in central California, J. Geophys.Res., 78, 832-845,
1973.
Savage,J. C., and M.D. Wood, The relationbetweenapparentstress
and stressdrop, Bull. Seismol.Soc.Am., 61, 1381-1388, 1971.
Savage,J. C., W. H. Prescott,
M. Lisowski,andN. King, Deformation
acrossthe SaltonTrough,California,1973-1977,J. Geophys.
Res.,
and the thermal regime of the crust,in The Earth's Crust, Geophys.
84, 3069-3079, 1979.
Monogr. Ser., vol. 20, edited by J. G Heacock,pp. 626-675, AGU,
Scholz,C. H., J. Beavan,andT. C. Hanks,Metamorphism,
argondeWashington,D.C., 1977.
pletion,heat flow, and stresson the Alpine fault, J. Geophys.
Res.,
Lachenbruch,A. H., and J. H. $ass,Models of an extendinglitho84, 6770-6782, 1979.
sphereand heat flow in the Basin and Range province, Geol. Soc. Sibson,R. H., Interactions
betweentemperature
and pore-fluidpresAm. Mern., 152, 209-250, 1978.
Lachenbruch,A. H., and J. H. Sass,Heat flow and energeticsof the
San Andreas fault zone, U.S. Geol. Surv. Open File Rep., 80-625,
47-146, 1980.
Lachenbruch, A. H., J. H. $ass, and $. P. Galanis, Jr., New heat flow
resultsfrom southernCalifornia (abstract),Eos Trans. AGU, 59,
1051, 1978.
sureduringan earthquakefaultingand a mechanism
for partial or
total stressrelief, Nature, 243, 66-68, 1973.
$ieh, K., Study of Holocenedisplacement
historyalong the southcentralreachof the San Andreasfault, Ph.D. thesis,219 pp., Stanford Univ., Stanford, Calif., 1977.
Smith, R. C. T., Conduction of heat in the semi-infinite solid with a
shorttableof an importantintegral,Aust.J. Phys.,6, 127-130,1953.
Lee, T. C., and T. L. Henyey, Heat flow through the southernCaliforStesky,R. M., Rock friction-effectof confiningpressure,temperature,
nia borderland, J. Geophys.Res., 80, 3733-3743, 1975.
and pore pressure,PureAppl. Geophys.,
116, 690-704, 1978.
McGarr, A., S. M. Spottiswoode,and N. C. Gay, Observationsrele- Stesky,R. M., and W. F. Brace, Estimation of frictional stresson the
vant to seismicdrivingstress,stressdrop,and efficiency,J. Geophys.
SanAndreasfault fromlaboratorymeasurements,
in Proceedings
of
Res., 84, 2251-2261, 1979.
Melosh, H. J., Acoustic fiuidization: A new geologic process?,J.
Geophys.Res.,84, 7513-7520, 1979.
Murata, K. J., T. W. Dibblee, Jr., and J. L. Drinkwater, Thermal ef-
fectsof largebodiesof intrusiveserpentiniteon overlyingMonterey
shale; Southern Diablo Range, Cholame area, California, U.S.
Geol. Surv. Prof Pap., 1082, 1979.
Nut, A., and J. D. Byedee,An exacteffectivestresslaw for elasticdeformation of rock with fluids,J. Geophys.Res., 76, 6414-6419, 1971.
Olmsted, F. H., P. A. Glancy, J. R. Hatrill, F. E. Rush, and A. $.
VanDenburgh,Preliminaryhydrogeologicappraisalof selectedhydrothermal systemsin northern and central Nevada, U.S. Geol.
Surv. Open File Rep., 75-56, 1975.
O'Neil, J. R., and T. C. Hanks, Geochemical evidence for interaction
along the San Andreas and Gatlock faults of California, J.
Geophys.Res., 85, this issue,1980.
Pilger, R. H., Jr., and T. L. Henyey, Pacific-North American plate interaction and neogene volcanism in coastal California, Tectonophysics,57, 189-209, 1979.
Rennet, J. L., D. E. White, and D. L. Williams, Hydrothermal convection systems,U.S. Geol. Surv. Circ., 726, 5-57, 1975.
Richards,P. G., Dynamic motionsnear an earthquakefault: A threedimensional solution, Bull. Seisrnol.Soc. Am., 66, 1-32, 1976.
Roy, R. F., D. D. Blackwell,and E. R. Decker, Continental heat flow,
in The Nature of the Solid Earth, edited by E. C. Robertson, pp.
the Conference
on TectonicProblemsof the SanAndreasFault System,pp. 206-214, StanfordUniversityPress,Palo Alto, Calif., 1973.
Summers,R., and J. Byedee,A noteon the effectof fault gougecomposition on the stability of frictional sliding, Int. J. Rock Mech.
Min. Sci. Geornech.Abstr., 14, 155-160, 1977.
Taylor, H. P., Jr., Oxygenand hydrogenisotopestudiesof plutonic
granitic rocks,Earth Planet. Sci. Lett., 38, 177-210, 1978.
Thatcher,W., Systematicinversionof geodeticdata in centralCalifornia, J. Geophys.Res., 84, 2283-2295, 1979a.
Thatcher,W., Horizontalcrustaldeformationfrom historicgeodetic
measurements
in southernCalifornia, J. Geophys.Res., 84, 23512370, 1979b.
Wang, C.-Y., and N.-H. Mao, Sheafingof saturatedclays in rock
joints at high confiningpressures,
Geophys.
Res.Lett., 6, 825-828,
1979.
Waring, G. A., Thermal springsof the United Statesand other countriesof the world, U.S. Geol.Surv.Prof. Pap., 492, 1965.
Wu, F. T., Mineralogyand physicalnatureof claygouge,PureAppl.
Geophys.,116, 655-689, 1978.
Wyss,M., Stressestimatesfor South Americanshallowand deep
earthquakes,J. Geophys.Res., 75, 1529-1544, 1970.
Wyss, M., and J. N. Brune, Seismicmoment, stress,and sourcedi-
mensionsfor earthquakesin the California-Nevadaregion, J.
Geophys.Res., 73, 4681-4694, 1968.
Yuen, D. A., L. Fleitout, G. Schubert,and C. Froidevaux, Shear de-
506-543, McGraw-Hill, New York, 1972.
formationzonesalongmajortransformfaultsandsubducting
slabs,
Rutter, E. H., and D. H. Mainprice, The effect of water on stressreGeophys.J. Roy. Astron. Soc., 54, 93-119, 1978.
laxation of faulted and unfaulted sandstone,Pure Appl. Geophys., Zoback,M. L., and M.D. Zoback,Faultingpatternsin north-central
116, 634-654, 1978.
Samreel,E. A., Occurrenceof low temperaturegeothermalwatersin
the United States, U.S. Geol. Surv. Circ., 790, 86-131, 1979.
Sass,J. H., A. H. Lachenbruch, R. J. Munroe, G. W. Greene, and T.
H. Moses,Jr., Heat flow in the westernUnited States,J. Geophys.
Res., 76, 6376-6413, 1971.
Nevada and strengthof the crust,J. Geophys.
Res., 85, 275-284,
1980.
(ReceivedFebruary 27, 1980;
revisedMay 2, 1980;
acceptedJune 25, 1980.)

Heat Flow and Energetics of the San Andreas Fault Zone

Transcription

Similar documents