fractured craters in Mare Smythii and west of Oceanus Procellarum

Transcription

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. El0, PAGES 21,201-21,218, OCTOBER 25, 1995
Floor-fractured craters in Mare Smythii and west of
OceanusProcellarum: Implications of crater modification
by viscousrelaxationand igneousintrusionmodels
R. W. Wichman
Department
of SpaceStudies,
University
of NorthDakota,GrandForks
P. H. Schultz
Department
of Geological
Sciences,
BrownUniversity,
Providence,
RhodeIsland
Abstract.Endogenicmodificationin lunarfloor-fractured
craterscanconstrainspatialvariationsin
earlylunarconditions.
Thenatureof theseconstraints,
however,depends
ontheassumed
mechanismof cratermodification.For viscousrelaxation,theextentof cratermodificationdependson
thesurrounding
crustalviscosity
andthusprovides
looseconstraints
onthehistoryof crustalheatingwithina region.For igneous
intrusion
models,theextentof cratermodification
reflectsmagmaticallydrivendeformation
andcanbe invertedto estimatebothlocalmagmapressure
andintrusiondepth.Bothmodelsindicatecleardifferences
betweenregionalconditions
at Mare Smythiiand
in thehighlands
westof Oceanus
Procel•m. The uniformlyshallowcraterdepthsin Mare
Smythiiprobablyindicatea long-livedperiodof extremecraterrelaxation,
whereasthewiderange
of modifiedcraterdepthsin thewesternhighlands
suggest
a muchshorterperiodof partialcrater
relaxation.For comparable
relaxationtimes,theaverageviscosityderivedfor Mare Smythiiis
over 10 timeslowerthantheaverageviscosityinferredfor thewesternhighlands.
Alternatively,if
modificationreflectsdeformationovercrater-centered,
laccolithlikeintrusions,
thederivedmagma
pressures
indicatea broad,uniformmagmasource
beneath
MareSmythii,whereas
thespatialvariationof estimated
magmapressures
in thewesternhighlands
suggests
thepresence
of several,
smallermagmasources.
Thederivedintrusiondepthsarepartlya functionof cratersize,butrange
from~1 to 10 km in depthfor bothregionsandmaybe slightlygreateron averagein thewestern
highlands.
Whilebothviscous
relaxation
andigneous
intrusions
canexplainthemodification
of
individual
craters,theregionalvariations
in thesederivedmodification
conditions
alsoallowfurthertestingof eachmodification
model.In particular,thecorrelation
of thelowestviscosities
or
thelongestrelaxationtimeswith thesmallestcratersin bothMare Smythiiandthewesternhighlandsseemsinconsistent
withcratermodification
by therelaxationmechanism.
The onsetof total
relaxation
at progressively
smallertopographic
wavelengths
overtimemightproducesucha trend
in Mare Smythii,buttotalrelaxationcannotbe invokedfor thewesternhighlands,
wheremany
largecratersstillpreserve
significant
fractions
of theirinitialrelief.In addition,therelaxation
of
thesmallest
cratersin bothregions
suggests
thepresence
of exceptionally
highnear-surface
thermalgradients
(~150-200K/km).Sincetheobserved
regionalvariations
in cratermodification
can
be easilyattributed
to variations
in magmapressure
asa functionof mantletopography,
we concludethatcraterfloorfracturing
in bothregionsis moreconsistent
withtheigneous
intrusion
mechanism
thanwith viscousrelaxationduringa crustalheatingevent.
Introduction
Numerous shallow craters on the Moon contain distinctive
fracturepatternsin and aroundtheir craterfloors.Thesefloorfracturedcratersare preferentiallylocatedwithin or nearthe lunar maria [Schultz, 1972; 1976a; Young, 1972; WhitfordStark, 1974], and many containminor volcanicunits [Young,
1972; Schultz, 1976a]. Moreover, despitetheir variable crater
depths,the centralpeak and craterrim heightsin suchcraters
are generally comparableto those in other lunar craters
[Schultz, 1976a]. Consequently,the floor-fractured lunar
cratersapparentlyrecordan endogenicprocessof floor uplift
and crater modification related in some way to lunar volcanism.
Although the endogenicmodificationof such craters is
widely accepted,two competingmodelshave arisenfor the
mechanismof crater modification: (1) viscous relaxation of
cratertopographyover time [e.g., Danes, 1965;Baldwin,
1968; Hall et al., 1981], and (2) surfacefailure and uplift in
responseto crater-centered
igneousintrusions[e.g., Schultz,
1972; 1976a; Brennan, 1975; Wichman, 1993]. Both mecha-
Copyright1995by theAmericanGeophysical
Union.
Papernumber95]'E02297.
0148-0227/95/95YE-02297505.00
nisms can explain the developmentof observedfeaturesin
individual floor-fractured craters [Schultz, 1976a; Hall et al.,
1981], but they have distinctlydifferent implicationsfor the
natureof local crustalconditionsduringcratermodification.
21,201
21,202
WICHMAN AND SCHULTZ: CRATER RELAXATION AND INTRUSION MODELS
In the relaxation model, low crustal viscosities allow visthe exceptionof a few, large mare-flooredcratersnear Mare
cous flow at depth to equilibrate the topographicstresses Marginis (e.g., Neper), craters outside the central Smythii
beneatha crater.The preserveddepthsof most craterson the region show little or no signsof endogenicmodification.In
Moon, however, indicate relatively high crustal viscosities contrast,no craterlargerthan20 km in diameteris unmodified
since at least the formation of the Imbrium basin [Baldwin,
insideof the inner Smythiiring scarp.The interiorcratersare
1971]. Thus viscous relaxation in floor-fractured craters either floor-fracturedor mare-filled, and they includesomeof
requires the development of locally or regionally reduced the most extensivelymodified craterson the Moon [Schultz,
crustalviscosities.If such viscositychangesare attributedto
1976a]. Many craters exhibit a characteristicstyle of crater
crustalheatingduringmare emplacement,
then the distribution modification featuring extensive floor uplift inside a wide
of floor-fracturedcratersshouldreflect the extentand intensity moat structure(e.g., Haldane).
Apollo photographsand the lunar topographicorthophoof regional heating by nearby mare volcanism[Hall et al.,
1981]. Alternatively, in the igneous intrusion model, crater tomapsprovide detailed topographythroughoutthe Smythii
modification is directly linked to the injection of mare mag- region.Thereforethe degreeof modificationin theseinterior
craterscan be quantifiedby comparingcraterdepth,diameter,
mas into breccia units beneath an impact crater. Thus floorfractured craters in this model indicate individual intrusion
rim height, and floor elevationwith the valuespredictedfor
siteswithin a regionalsystemof subsurface
magmabodiesand pristinecraters(usingrelationsderived by Pike [1980]). As
surfacemare units [Young, 1972; Schultz, 1976a]. If crater shownby Figure 2, suchmeasurements
for 74 cratersin and
modificationis related to the growth of a specificintrusion aroundthe centralmareregion(Figurelb) clearlyrevealdiffergeometry,then the recordof deformationin lunar floor-frac- ent crater morphometriesinside and outside of the central
taxredcraterspotentially can provide model estimatesfor the basin floor.
magmaticpressuresand intrusiondepthswithin suchregional
Major cratermodificationis restrictedto distanceslessthan
magmasystems[Wichman, 1993].
--200 km from the center of $mythii, a limit that closely
Dependingon the mechanismfor cratermodification,there- matchesboth the crest of the inner basin scarp (-210 km
fore, variationsin crater modificationwithin a region should radius) and the outer edge of Mare Smythii. Similarly, the
reflect spatialvariationsin either the intensityof local crustal derived reduction in total crater depthsis greatestfor craters
heatingor in the magmaticand structuralpropertiescontrol- insidethis radius(Figure 2b), and the similar floor elevations
ling intrusiongrowth.As craterrelaxationis only an indirect insideof the centralSmythiibasin(Figure2c) contrastsharply
(thermal) effect of mare volcanism, however, the d•tailed
with the rangeof elevationsobservedfor cratersoutsideof the
implicationsof each modificationmechanismfor local and basin.Last, the depth/diameterratiosfor the innermostcraters
regionalmagmatismare likely to be significantlydifferent. at Smythii are significantlylower andmore uniform thanthose
Consequently,
thesetwo modelsfor cratermodificationcan be of cratersat greaterradial distances.Craterdepthsinsideof the
testedby assessing
how the style of cratermodificationvaries inner scarpare characteristicallylessthan 20% of their initial
with crater settingwithin a single region, and by comparing value,whereascraterdepthsoutsidethe scarpare reducedby no
the distributionsof crater modification within distinctly difmore than 50% with many craters preservingtheir initial
ferent regional settings.
depths(Figure2d).
In this paper,we describetwo setsof floor-fracturedcraters
Western highlands. Another prominent concentration
in distinctlydifferent lunar settings:the central Smythiibasin of lunar floor-fracturedcraters is located nearly anfipodalto
and the highlandswest of OceanusProcellarum.We then sum- Mare Smythii in the highlandswest of OceanusProcellarum
marize the implications of viscous relaxation and igneous [Schultz, 1976a]. In contrastto Mare Smythii,this regionlies
intrusionsfor cratermodificationin eachregion,and discuss
how theseresultsvary with the distributionand geologicsetting of differentfloor-fractured
craters.
outside of any recognizedmultiring basin, and there are no
clearstructural
boundaries
delineating
the sitesof cratermodification. Instead, these floor-fracmr.
ed craterstypically occur
in groupsor clusterswithin a broadbandabout300 km wide
The Study Areas
This studyusesthe Mare Smythii region and the highlands
west of OceanusProcellarumto investigatethe variation of
crater modification with geologic setting. Both regions contain many floor-fractured craters, and these craters, in turn,
exhibit significantdifferencesin the distributionand style of
crater modification. Consequently, before modeling the
regional implications of crater modification in these study
areas,we summarizehere, for eachregion,both the settingsof
crater modification and the apparentvariations in modified
cratermorphometryas a functionof cratersize andcraterlocation. In addition,we also briefly describea regionof the lunar
farside,near crater King, to illustratethe effects of nonendogenic modificationprocesseson cratermorphometry.
Mare Smythll. The Smythii impact basin (Figure 1) is a
nearly circular,multiringedstructurewhich is centeredat ~2S,
87E on the easternedge of the lunar nearside.Mare volcanism
is essentiallyconf'medto the low-lying basin interior and to
the lavas of Mare Marginis on the northern basin rim. With
andover1200kmlong(Figure3).'Thisbandroughly
parallels
the edge of OceanusProcellaxum,but it cutsobliquelyacross
structuresthat have been identified with the outermostring of
the proposedProcellarumbasin [Wilhelm.v,1987] or, alternatively, with extendedfailure aroundthe lmbriumbasin[Schultz
and Spudis,1985;Spudis, 1993]. Sinceseveralcraterclusters
in thesehighlandsappearto be centeredon a larger central
crater (e.g., the Lavoisier and Einsteinclusters),local structural and topographiccontrolsmay be more importantfor
crater modification in this region than well-defined basin
structureslike that ohseyedat Smythii.
The floor-fracturedcraterswestof Procellarumdiffer slightly
in appearance
from the extensivelymodifiedforms found in
Mare Smythii. While a few wide floor moat featuresdo occur
west of Procellarum,they axe less commonthan at Smythii,
and polygonalfracturepatternsoccurmore frequentlyin the
central crater floors. In some instances(e.g., Repsold),fractures extend radially from one crater into another[Schultz,
1976b]. Also, Schultz and Mendenhall [1979] suggestedthat
several small (<20 lcm) floor-fractured craters inside of
21,203
Figure 1. Mare Smythii studyarea. (a) Image showingboth the floor-fracturedcratersin the basin
interior(annularstructures)
andcratersof theouterbasinring andexteriorregions.For reference,N
indicatesNeper,M indicatesMare Marginis,H indicatesHaldane,and arrowsmarka sectionof the
outerscarp(A16-M3035). (b) Sketchmapidentifyingthefloor-fractured
craters(stars)andothercraters
(triangles)of the Smythiidataset.Heavy dashedlinesdenotesectionsof the innerand outerbasin
scarps.
ent structural settings. Where small floor-fractured craters
occur independentlyin Mare Smythii, suchcratersinvariably
craters.
occureither insideof or superposed
on the rim of largerfloorThe morphometryof floor-fracturedcratersin the western fracturedcratersin the westernhighlands.Similarly, although
highlandsalso indicatesa changein crater modificationfrom there is no clear relation between crater modification and either
that observed in Mare Smythii. Although detailed stereo crater diameter or the distance to the edge of Oceanus
topographylike that used in the Smythii region is not avail- Procellarum(Figure4b and 4c), thereis evidenceto supporta
able, Lunar Orbiter imageryprovidesshadowmeasurements
(at clusteringof floor-fracturedcratersin the westernhighlands.
Most (-76%) of the floor-fracturedcratersin this data set are
sun anglesof ~6ø to ~25ø) of crater depth in 30 of the 33
cratersidentifiedby Figure 3b. These shadowmeasurements within one crater diameter of another floor-fractured crater, and
show that only a few highlandcratershave lost most of their the averagecenter-to-center
distancebetweensucha craterand
initial apparentdepth.Rather,many craterspreserveconsider- its nearestneighboris ~55 km.
able fractions of their initial topography and two depths
The King region. For reference,crater depthsand diamappearpristine(Figures4a and 4b). Thus, while a few crater eters are also described for an area on the lunar farside around
measurements match those of floor-fractured craters in the cencrater King (5N, 121E). This region lies on the edge of the
tral Smythii basin(Figure 2), most more closelyresemblethe ancientA1-Khwarizmi/Kingimpactbasin (Figure 5) and none
degradedcratersoutsideof Mare Smythii.
of the cratersstudiedexhibit fracturedfloors or any othereviLast, there is also a difference in the size and distribution of
dence of endogenicmodification. Although a broad region
the modified craters. In Mare Smythii, the floor-fractured exhibitingdark-haloedcraters[Schultzand Spudis,1979] anda
craters have a mean diameter of ~30 km and a maximum diamesinglefloor-fracturedcrater [Schultz,1976a, 1976b] lies to the
ter of -60 km. The modified craters west of Procellarum, hownorth and east of this region in the ancient Lomonosovever, have a mean diameter of -45 km and a maximum diameter Fleming basin, thesecratersalso appearto be well removed
of ~170 km. A few modified craters less than 20 km in diameter
from major mare volcanism and from the effects of recent
occur in both regions,but thesecratershave distinctlydiffer- basin-formingimpacts.Therefore this third data set should
Einsteinmay result from secondaryimpactsof melt from the
Orientale impact, rather than endogenicallymodified primary
21,204
CraterDepthsforthe SmythiiRegion
CraterShallowing
fortheSmythiiRegion
;
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RadialdistancefromSmythiicenter(kin)
Radialdistance
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Normalized
CraterAspectRatiosforSmythiiRegion
CraterFloorElevations
forthe SmythiiRegion
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ß diameter 3,45 km
mean mare elevat,on
I
ii
100.
200.
.•00.
400.
Radialdistance
fromSmythii
center(kin)
Figure 2. Crater modificationdata in the Smythii basin.(a) Crater depthsplottedagainstdistance
from the centerof Smythii.(b) Approximatecratershallowingversusdistancefrom thebasincenter,
thisvalueis derivedfromthedifferencebetweenidealcraterdepth[P/ke,1980]andtheobserveddepth.
(c) Crater floor elevationsplotted against distancefrom the basin center. (d) Observed crater
depth/diameterratio normalizedby the ideal crateraspectratio, plottedagainstdistancefrom the
Smythii center.The ideal aspectratio is determinedfrom the relationsof craterdepthto diameter
[Pike, 1980] and the observedcraterdiameter.
primarily record the effects of exogeniccrater modification
(i.e., degradationby small impactsand ejectadeposition).
The normalizedcrateraspectratios in the King region show
two distinct groups (Figure 6), with only relatively small
craters((40 km) showingsignificantchangesin depth.Larger
cratersare uniformlyunmodified,but a numberof cratersin the
smallersize range are also fairly pristine(Figure 6). Beyond
the fact that all of the shallow craters are of Imbrian age or
older, the extentof modificationdoesnot appearto be a function of crater age or geographicplacement.Most of the shallower depthsoccur to the south,but this region also contains
the highestpopulationof small craters.
different conditions [Schultz, 1976a; Wichman, 1993], but the
primary dependentvariable in these models is the changeof
crater depth resulting from floor uplift [Hall et al., 1981;
Schultz, 1976a]. Consequently,the changesin crater morphometry identified above can be inverted to constraincraterspecificmodelsfor the extent and conditionsof cratermodification by both viscous relaxation and specific intrusion
geometries[Wichman, 1993]. The basicapproachand assumptions for two such inversion models are described here, and
more detaileddescriptionsof each model are given as appendices.
Viscous
Modeling Crater Modification
Both viscous relaxation
and crater-centered
intrusions
can
theoreticallyproducea range of floor fracturepatternsunder
Relaxation
Previousworkers[e.g., Danes, 1965; Cathies, 1975] have
developed theoretical equationsfor the relaxation of crater
topographyover time with the assumption
that the lunarcrust
21,205
o
OCEANUS
--.•
PROCELLARUM
**
Figure 3. The studyareawestof OceanusProcellarum,centeredon ~80W and extendingfrom ~ION
to ~55N. (a) Major groupsof floor-fractured
cratersoccurnearthecratersRepsold(R), Lavoisier(L),
andEinstein(E), but otherfloor-fractured
cratersoccursinglyor in pairsbetweenthesegroupsandto
the west.The scalebar is ~91 km (LO IV-189-M). (b) Sketchmap identifyingthe selectedfloorfracturedcraters(stars)usedin thisstudy.Crosses
indicateotherfloor-fractured
cratersoccurringinside
Oceanus Procellarum.
behavesover long time framesas a viscousmedium.Because
the topographyof most impact cratersis essentiallyaxisymmetric, theseequationsare expressedin cylindricalcoordinates
and describethe wavelength-dependent
decayof cratertopography as a functionof time and radial distancefrom the crater
center.The only othermajor variablein theseequationsis the
crustalviscosity;consequently,theserelationsprovidea simple basis for modeling the distribution,timing and evolution
of crater modification at specific crustalviscosities[Danes,
1965; Scott, 1967].
dependent.Hence the distribution of uplift within a crater
shouldvary over time, and detailedprofiles for the initial and
presentcratertopographyare neededin orderto fully characterize the nature and extent of relaxation in a crater [Hall et al.,
1981]. Because stereographicApollo photography covers
only a small fraction of the lunar surface, however, detailed
topographicdata (pre-Clementine) are available for only a
small subsetof the lunar crater population.Third, although
cratertopographycan constrainthe distributionand magnitude
of deformationwithin a crater, both crustalviscosity(•/) and
The inversion of such forward relaxation models on the
the duration of modification (t) occur in the same term of the
Moon is less straightforward, however. First, while crater relaxation equations.Thus, without independentconstraints
topographycan record the effects of viscousrelaxation, the on the time span of floor uplift, the observeddifferencesin
equationsof the forwardmodelsactuallycharacterizethe cumu- topographybetween a pristine and a floor-fracturedcrater of
lative surfacedisplacementresulting from viscousrelaxation the samesize can only constrainthe combinationof variables
rather than crater depth. Consequently,the data used in any t/•l [Hall et al., 1981].
Despite these difficulties, Hall et al. [1981] developeda
inversionof crater topographyby relaxation are not the present crater profile but the difference at any given radius least squaresinversionof cratermodificationfor t/• l usingthe
betweenthe observedcrater profile and a model of the initial topographyof pristine lunar craters to model the initial procrater topography.Second,viscousrelaxationis wavelength- files in floor-fractured craters of the same size. The Hall et al.
21,206
WICHMAN
AND SCHULTZ:
CRATER RELAXATION
CraterDepthsWestof OceanusProcellarum
AND INTRUSION MODELS
Normalized
CraterAspectRatiosWestof Procellarum
5.5
--.
3.0
•
2.0
._o
E
._
I.$
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__ pristine½a:ers(fromPike)
ß
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© pre*Nect,
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._-
ohs, floor*fractured
ß
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f
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Craterdiameter(kin)
craterdiameter
(kin)
Normalized
CraterAspectRatiosWestof Procellarum
1.2
G
*
diameter
<20 •m
ß
diameter
20-:5 km
ß
diame{er >45 km
1.0 - ©
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,30.
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Distance
frommareedge(kin)
Figure 4. Cratermodification
datawestof Procellarum.
(a) Estimated
craterdepthsplottedagainst
cratersize;a reference
curvefor theidealdepthvaluesis alsoshown.In fourinstances,
nocraterdepth
wasderivedanda depthof zerois indicated.
(b) Derivedcrateraspectratios,normalized
by theideal
valueandplottedasa functionof craterdiameter.
(c) Normalized
crateraspect
ratiosplottedagainst
distancefromthemareedge.Notethewiderangein preserved
craterdepthsandtheapparent
independence
of cratermodification
fromproximityto themare.
inversion,however,usesdetailedcraterprofilesto producean
overdeterminedsolutionfor t/l?. Here, we simplify the relaxation equationsthroughadditionalmodel assumptions
to allow
a cruder inversion based on simple crater depth estimates
(AppendixA). Specifically,extensivecratermodificationprimarily featuresa broad,coherentuplift of the craterfloor while
preservingboth central peak and crater rim heights[Schultz,
1976a]. Thus craterrelaxationappearsto be concentrated
into
a relatively narrow rangeof long topographicwavelengths.If
this wavelengthrangeis then approximatedby the relaxation
of a single,dominanttopographicwavelengthrelatedto crater
size, a simple estimate for t/r I can be generated without
detailedmodelsof the craterprofile beforeand after modification. Instead, the amount of floor uplift and of relaxationis
constrainedby comparingthe presentcrater depth with that
predictedby the morphometricrelationsof Pike [1980], and
the quantityt/•? is derivedby insertingthis uplift into a single
equationfor relaxationat the inferredwavelengthdominating
crater topography.
Sincethe t/rI parameterdoesnot providean intuitivefeel for
the conditions of viscous crater relaxation, we also convert the
derivedt/rI valuesfor our studyareasinto representative
estimatesfor crustal viscositiesand temperatures.For this purpose, we assumethat (1) the durationof crater modificationin
each case was l0 Ma, and (2) that the relation betweencrustal
viscosity and temperatureis similar to an experimentally
determinedrheology[Sheltonand Tullis, 1981] for terrestrial
diorite.
For the first assumption,the age of crater modificationis
generallyindistinguishable
from that of nearbymare volcanism [Schultz,1976a]. In addition,the exponentialdependence
of relaxation on viscosityimplies that crater modification
WICHMAN
AND SCHULTZ:
CRATER RELAXATION
AND INTRUSION
MODELS
21,207
rocks are much drier than terrestrialcompositionsand are typically at lower confiningpressures,they shouldbe less susceptible to microscopiccreep processes[Tullis and Yund, 1989].
Consequently,if lunar rocks are stiffer than comparableterrestrial rocks,higherlunar temperatures
are neededto producethe
same deformationrates, and any temperaturesderived for the
Moon with a terrestrial theology should underestimate the
actuallunar temperature.
Igneous
Intrusions
Severaltypesof inlxusioncan conceivablyproducecratercentered deformation [Schultz, 1976a; Wichrnan, 1993], but
the coherent,level uplift of craterfloors on the Moon strongly
resemblesthe simple vertical uplift of strata observedover
many terrestriallaccoliths.Furthermore,the range and apparent evolutionof fracturepatternsin lunar cratersalso are consistent with progressivefailure over a shallow, laccolithlike
melt body [Wichman and Schultz, 1991; Wichman, 1993].
Since terrestrial studieshave developedtheoreticalrelations
for intrusiongrowth and surfacedeformationduring the different stagesof laccolith eraplacement[Pollard and Joh•on,
1973; Corry, 1988], laccolithsthusprovide a reasonablebasis
for modelingthe effectsof crater-centeredintrusions.
Laccolithiceraplacementmodelson the Earth, however,use
terrestrial
field
work to constrain
estimates for intrusion
di-
mensionsand local material properties[e.g., Johnson and
Pollard, 1973]. Consequently,similar modelsfor cratermodification on the Moon require the use of additional model
Figure 5. Apollo image showing the crater King (K, assumptions.Since erosionis limited on the Moon and since
right-center)and mostof the surrounding
studyarea(eight presentlunar gravity data cannotcharacterizethe (small) gravcraters in the southeast corner of the data set are not
iF signaturesof cratersunder ~100 km in diameter [Schultz,
shown).White lines indicateapproximateboundariesof 1976a], we estimatethe size and thicknessof the proposed
lunar topographicorthophotomaps
usedfor the measure- lunar intrusionsfrom changesin crater morphometry.For
intrusionsize, horizontalintrusiongrowth appearsto be limments reportedhere. For scale, crater King is ~75 km
ited in laccolithsafter the onsetof verticaluplift [Johnsonand
across(Apollo 16-M3000).
shouldprimarily occurduringthoseintervalsfor which crustal
viscosity is most greatly reduced [Hall et al., 1981].
Consequently,althoughthe agesof basin formationand final
mare volcanism at Smythii allow a maximum time for crater
relaxationof the order of 700-800 m.y., the majority of crater
relaxation probably occurred during those times when both
local magmatismand crustalheatingwere at a maximum. For
suchperiodsof peak mare volcanism,the derivedsampleages
for the different classesof mare basalts[Wilhelms, 1987, p.
237] indicatepulsedurationsof betweena few tensand possibly a few hundredsof millions of years.Alternatively,crater
relaxationalsocouldoccuron timescalesas shortas 1-10 m.y.
if minimum crustal viscositiesapproachedthoseof the bulk
Earth mantle [Hall et al., 1981]. Thus the values for duration
and viscositycited here are probablynot completelyaccurate,
but they are not unreasonablefor illustratingspatialvariations
in the conditionsof craterrelaxationwithin our studyareas.
Regardingour temperatureestimates,the theologicalrelations for lunar rocks are poorly known. Thus any conversion
of crustalviscosityto a model temperaturevalue mustrely on
an empiricallyderivedtheology for terrestrialrocks. The theology assumedhere appearsto describeflow behavior under
terrestrialconditionsfairly well (J. Tullis, personalcommunication, 1990); however,this theologyprobablyoverestimates
deformationin the lunar caseand thusprovidesonly a lower
boundon the modeledlunar temperaturevalues.Becauselunar
Normalized
CraterAspectRatiosnearCraterKing
1.0
ß
0
ß-
0.•
ß
ß
E
•
I).6-
ee •,
e
._•
--
© pre-Nec:arian
age
o
I).2 -
ß
Nec:arian.Irabrianage
-!- post-imbrian
age
0.0
O.
I
!
I
I
20.
40.
60.
80.
1
lOO.
120.
Craterdiameter(kin)
Figure 6. CratermodificationnearCraterKing. Observed
crateraspectratios,normalizedby the idealdepth/diameter
ratio, are plotted as a functionof crater size. Unusually
shallow craters are restricted to craters less than 40 km in
diameterand noneof the cratersin this region hasa normalized aspectratio comparableto thoseseeninside the
Srnythiibasin.
WICHMAN
ANDSCHULTZ:
CRATER
RELAXATION
ANDINTRUSION
MoD•..S
21,208
Relaxation
Parameters
fortheSmythiiRegion
Pollard, 1973; Corry, 1988]. Therefore the similarity of the
moat-bounded
lunar crater floors to the fault-bounded
strati-
1.8x•0'?
graphicuplifts over terrestrialpunchedlaccoliths[Wichman,
1993] suggeststhat crater floor uplifts on the Moon approximate the size of any underlyinglunar intrusions.For intrusion
thickness,a simple estimate is provided by the difference
between the observedand the predicted (pristine) depth of a
floor-fractured
Finally, the material propertiesgoverningdeformationover
an intrusion(Table 1) alsomust be specifiedin order to invert
the model equations.Becausethe bulk propertiesof deepseated crater floor materials are poorly constrainedon the
Moon, we assumefor this study that the responseof uplifted
crater floor materials is dominated by a coherentelastic unit
(possiblyimpact melt) with the elastic modulusof a typical
terrestrialbasalt. With these assumptions,the laccolith model
providesestimatesfor both the driving pressurein an intrusion and intrusiondepth, and theseestimatesthen can be used
to model
-
+
crater.
the distribution
and thickness
of subcrustal
mantle
.4-
+
+
+
-l..
+
+
•
++
+
i
+
o.o
-
I
lOO.
200.
300.
400.
500.
600.
700.
Radialdistance
fromSmythii
center(kin)
1.8x.0'?
meltswithin a region(seeAppendixB).
1.5x•0'?
Model
Results
Both crater modificationmodels can relate regional variations in crater modification to differencesin crustal or magmatic conditions. In addition, however, differences in crater
settingwithin a region shouldalsoproducerecognizablevariations in crater modification.Consequently,this sectionpresentsa summaryof the regional and local constraintsderived
for cratermodificationin our studyareasby the differentinver-
+
+
+
sion models.
+
+
Viscous
Relaxation
•1 + .I-4. 4'
20.
For the Smythii region, the derived values for the
parameterclearly reflect the differencesnoted earlier between
crater modification inside the central Smythii basin and outside of the inner basin ring (Figures 7 and 8). The derived
valuesinside the inner basin scarpare both much greaterand
more widely scatteredthan the t/rl valuesobservedoutsideof
the inner basin(Figure 7a). If craterrelaxationoccurredin ~10
Ma, thesedata indicate that the averagehalf-spaceviscosity
insideMare Smythiiwas well over an orderof magnitudelower
than the averageviscosityoutsideof the centralbasin during
crater modification(Figure 8). For reference,theseviscosities
in a terrestrial diorite indicate average interior and exterior
basintemperatures
of ~710øC and ~640øC,respectively.
aO.
60.
80.
100.
120.
I
140.
Craterdiameter
(kin)
Figure 7. Derived relaxation parameters(t•)for the
Smythii region. (a) Relaxationparameterplottedagainst
distancefrom the Smythiicenter.(b) Relaxationparameter
as a function of crater diameter.
mately400 km from the basincenter(Figures7a and8a). Since
this radius is locatedjust inside of the most prominentring
scarpat Smythii [Wilhelm.v,1987], someminor relaxationor
crater infilling may have occurredalong this outer basinring,
therebyindicatinga possibilityof fault-controlledmagmatism
In addition to the clear differences
between conditions
outsidethe centralbasin. Similarly, there is also a suggestion
inside and outsideof the central Smythii basin, the derived that the t/rl values inside Mare Smythii decreaseas one
inversionvalues also show several possibletrends in local approaches
the edge of the inner basin (200 km from basin
crater modificationaroundSmythii that could provide further center). This observationcould indicate a slight decreasein
detailson the sourcesand historyof crustalheating.First, the crustaltemperaturesaway from the basin center,but it is not
rangesof t/rl and viscosityoutsideof Mare Smythii are rela- supportedby the derivedviscosityvalues(Figure 8a). Instead,
tively uniform, but both data setsshow an inflectionapproxi- the central basin craters indicate fairly uniform viscosities
insideMare Smythii,and thereis an abruptincreasein modeled
viscosityacrossthe inner basin scarp.Last, while the derived
Table 1. Constants
in laccolith
modelequations.
t/rI valuesinsideMare Smythiimay not dependon locationin
Symbol Description
Value
the centralbasin,both the t/rl valuesand the inferredviscosiB
elasticmodulus
of countryrock 7.47 10lø Pa
ties in this centralbasin are clearly a functionof craterdiamek
magmayieldstrength
104 N/m2
ter (FiguresTo and8b). A similardependence
may alsooccurin
g
lunargravitational
acceleration 1.62 m/s2
the viscosity values outside of Mare Smythii (Figure 8b),
Prn magma
density
2900kg/m
3
where the derived values show a broad, diffuse trend roughly
?'m unitmagma
weight
4700kg/m2s
2
paralleling that of the cratersinside Mare Smythii. We will
WICHM
AND SCHULTZ: CRATER RELAXATION AND INTRUSION MODELS
HalfspaceViscosity
forSmythiiCraters
21,209
Lavoisier and Einstein crater clustersare only slightly lower
(-4.1x1022 P and5.3x1022P, respectively).
For reference,
1.00E+25
theseviscositiesimply temperatures
of-660-670øC in a terrestrial
•' 1.00E+24
ß
._•
ß
ß ßß
J
ß
ßß
o 1.00E+23
ß
ß
._•
ß
ß ß
ß
ß
o
•
1.00E+22
ß
.;;, ..'
ß
ß
I
' /
I
I
100
200
300
ß
1.00E+21
0
ß
I
400
500
600
700
RadialDistancefromSmythiiCenter(kin)
HalfspaceViscosityfor SmythiiCraters
diorite.
In contrast to crater modification at Smythii, therefore,
crater modification in the western highlands shows little
regionalorganizationor uniformity.Rather,the derivedinversion parametersindicatehighly variableconditionsfor crater
modification(Figure 10a). There is a slight contrastin average
viscositybetweenregionswith closely spacedfloor-fractured
cratersandregionswith moresparselydistributedcratermodification (Figure 10b), but even the clearestcrater clustersat
Lavoisier and Einstein contain viscosity values which are
comparableto the lowest viscositiesoutsideof theseclusters.
Nevertheless,the derivedtlrl and viscosityvaluesboth showa
pronouncedvariation with crater size (Figures9b and 10c),
similar to that observedinside Mare $mythii (Figures7b and
8b). Suchvariationsare clearestat the smallest(<40 km) crater
diameters,however,and thesecratersare primarily locatedin
1.00E+25
Time/Viscosity
ValuesWestof Procellarum
2.5OE-07
_>,1.00E+24
._
+
o
2.00E-07
+
• 1.OOE+23
1.50E-07
"o 1.00E+22.
1.00E-07
,
ß Craters outside central basin
iaCraters
inside
central
basin
o
1.00E+21
0
i
I
20
40
60
80
100
120
140
+
5.00E-08
[ + ++
160
O.00E+00 ,'• + -•.+,•.•+, +•
CraterDiameter(kin)
20
40
60
so
100
120
140
160
180
Craterdiameter(kin)
Figure 8. Modeledviscosityvaluesin the Smythiiregion.
(a) Derivedhalf-spaceviscositiesas a functionof distance
from the Smythiicenter,assuminga relaxationeventof 10
m.y. duration.(b) Modeledhalf-spaceviscosityas a func-
Time/Viscosity
ValuesWestof Procellarum
2.50E-07
tion of crater size.
ß--
discussthe variousimplicationsof this trend for cratermodification
later.
For the highlandswest of OceanusProcellarurn,few floorfracturedcratersindicaterelaxationcomparableto or greater
than that observed in the floor-fractured craters at Smythii.
Instead,the majorityof the derivedt/rI valuesare morecomparable to those derived for the non-floor-fractured
craters outside
of Smythii (Figure 9). Moreover, in contrastto Mare Smythii,
thereis no clear geographiceffecton the derivedvaluesfor t/rl
in the westernhighlands(Figure 9b). Although somecraters
2.00E-07
._
• 1.50E-07
ß
• 1.00E.07
5.00E-08
•jxCraters
near
Lavoi
o Craters in/near Einstein
x
•
+
x
+ Other craters
o
0.00E+00
50
1oo
150
200
250
300
350
Distanceto nearestmare(kin)
near Lavoisier and Einstein indicate extensive relaxation,
other cratersin both of theseclustersare essentiallyunmodiFigure 9. Crater relaxationmodelsfor the highlandswest
fied with very low t/rl values. The highland floor-fractured
of •us
Procellarum.For reference,the values of craters
cratersalso indicate a much broaderrange of derived crustal
in Einsteinand theLavoisierclusterare distinguished
from
more
isolated
instances
of
crater
modification.
(a)
Derived
regions of the Smythii basin (Figure 10). Last, the average
viscosities than was found for either the interior or exterior
is roughlyan order of magnitudelarger than the averagevalue
relaxationparameters(t/U) plottedagainstdistancefrom
OceanusProcellarum.(b) Derived tlrl valuesas a function
insideMareSmythii(-6.3x1021
P).Theaverage
values
forthe
of crater size.
viscosity
across
thewestern
highlands
region(~7.9x1022
P)
21,210
WICHMAN
AND SCHULTZ:
CRATER RELAXATION
AND INTRUSION
or near both Lavoisier
HalfspaceViscosityforProcellarum
Craters
MODELS
and Einstein.
Thus the inferred hetero-
geneityof crustalconditionswest of Procellarummay partially
reflect a nonrandom distribution
1.00E+25
of small floor-fractured
craters
within the region.
Finally, to illustrate the effect of simple (exogenic)crater
=Craters
in/near
Einsteindegradationon the inversion for viscousrelaxation, we have
I ßOther
Craters
alsocalculatedmodel viscositiesfor a farsideregionnearcrater
=Einstein
King. These calculations indicate an average viscosity of
• ß Craters near Lavoisier
'"" 1.00E+24
o•
0
ß
~1.2x1023P anda reference
temperature
of ~660øCfor the
1.00E+23
1:3 1.00E+22
ß
ß
ß
o
ß
?
1.00E+21
0
SO
100
150
200
250
300
350
DistancefromMareEdge(kin)
ModelViscosityVariationwithinCraterClusters
1978].
1E+25
..
©
ß CratersnearRepsold
= Craters near Lavoisier
o
ß Craters near Bartels
• 1E+24
o Craters near Einstein
ß Craters SE of Einstein
o
>1E+23
l
craters near King (Figure 11). However, the preservationof
large cratersin this region combinedwith the frequentmodificationof smallerstructures(Figure 6) contradictsthe preferential loss of long-wavelengthtopographypredictedfor viscous
relaxation.Thus cratermodificationin the King regionprobably reflects a greaterdegradationand infilling of the smaller
cratersby small impactsand distalbasinejecta[Neukumet al.,
1975]. Also, some of the smaller craters with shallow depths
may representold basin secondarycraters,which have lower
depth/diameter ratios than more recent, primary impacts
[Schultz, 1976b; Oberbeck et al., 1977; Wilhelms et al.,
Since the derived relaxation values near King are comparable to those derived for craters between the Smythii ring
scarps,it is probably inappropriateto attributemodification
of the craters outside Mare $mythii to viscous relaxation.
Endogeniccrater modification in the Smythii region apparently has been confinedto the cenl•al basin floor. In conl•ast,
the relatively minor differencebetween the derivedviscosity
averagesfor cratersin the westernhighlandsand near King
suggeststhat endogeniccrater modificationhas been limited
west
of
Oceanus
Procellarum.
Most
of
the
craters
near
o
'• 1E+22
ß
ß
Procellannnapparentlyrequirea partial relaxationeventwhich
is distinctly different from the almost complete relaxation
inferredinsideMare Smythii.
m
ß
,
1E+21
0
2o
40
60
80
loo
120
•40
•so
•80
200
DistancefromNearestLargerCrater(kin)
Igneous
Intrusion
The 1accolithinversionmodelsalso indicatesignificantdifferences between crater modification at Smythii and in the
westernhigh]ands.In particular,the derived valuesfor magmatic driving pressure inside Mare Smythii and west of
OceanusProcellarumshow distinctly different disuibutionsas
HalfspaceViscosityfor Procellarum
Craters
1E+25
ViscosityValuesin the KingRegion
"'" 1E+24
1.00E+25
0
(•
1E+23
• 1.00E+24
ß Craters near Lavoisier
13 Craters in/near Einstein
• 1E+22
ß Other craters
ß
0
• 1.00E+23
ß
1E+21
i
o
2o
40
60
80
100
120
140
160
180
o 1.00E+22
CraterDiameter(kin)
Figure 10. Modeledviscosityvaluesfor thewesternhighlands.(a) Estimatedviscosityplottedagainstdistancefrom
Oceanus
Procellarum.
Co)Estimatedviscosityasa function
0
I
•
!
,I
1
20
40
60
80
1O0
120
Craterdiameter(km)
of craterspacing
withinthedifferentcraterclusters.
(c) Figure 11. Modeledviscosityvaluesfor the farsidenear
Estimatedviscosityasa functionof cratersize.
cratergSng.
WICHMAN
AND SCHULTZ:
CRATER RELAXATION
21,211
120
ing pressurethat parallelsthe expectedeffectof cratertopography on subsurfacelithostaticpressures.Thus the modeled
intrusionsfor Mare Smythii appearto be equilibratedwith
local, near-surfacehorizontalpressuregradients.In contrast,
the deriveddriving pressures
west of Procellarumare widely
scattered,especially for those craters located outside of the
LavoisierandEinsteincraterclusters(Figure12). This rangeof
modeleddriving pressures
may be slightlyexaggerated,
since
no allowancefor craterrim degradationhas been made in the
western highlands. Nevertheless,only those pressuresin
excessof the Smythii trend are likely to reflect a lossof rim
topographyduring crater modification. The lower driving
1oo
•
ß
I•
ß
ß
©f
ß
ß
mm
m
80
13
m 60
13
ß
,•
40
ß MoatFFC insideSmythii
E
,3 Non-moat Craters inside
m 20
Smythii
(
i
i
i
50
100
150
200
250
Distance
fromSmythiiCenter(kin)
pressurescorrespond to craters with limited modification in
which rim degradationseemsunlikely.
DrivingPressuresat Procellarum
160.00
The spatial distribQtionof the modeleddriving pressures
also supportsa contrastin regionalmagmatismbetweenour
two studyareas.Inside the Smythiibasin,the deriveddriving
pressures(like the inferred crustal viscosities)are nearly
constant,with only the faintøsthint of declining valuesnear
the edge of the mare (Figure 13a). In the westernhighlands,
however, the derived magma pressuresare highly variable.
,
140.00
T
120.00
ß
100.00
13
ß
ß
80.00
ß
60.00
ß
ß
and mare
volcanism in Oceanus Procellarum (Figure 13b). Still, the
observedmagmapressuresdo suggestthat more localizedvolcanic centers may have affected crater modification.
Specifically,the driving pressureswest of Procellarumappear
to decreaseas a functionof distancefrom the largestcentral
crater within a group of floor-fracturedcraters(Figure 13c).
Sincepressuredropsaccompany
viscousflow througha feeder
dike [Johnsonand Pollard, 1973], sucha distributionof magmatic driving pressuresmight thus indicate a variation in
magma column lengths around localized magma sources.
Alternatively, since variationsin crustal thicknessshouldalso
control magma pressures,the derived driving pressuresmay
simply reflect crater-relatedvariations near the largest floorfracturedcraters in both surface topographyand the depth of
the crust/mantleboundary.(Note: althoughthe Procellarum
highlands lie in a transitional region between Oceanus
MODELS
ModeledMagmaPressuresat Smythii
a functionof size and location(Figures12 and 13). InsideMare
Smythii,cratersexhibit a relatively uniform increasein driv-
There is no clear relation between crater modification
AND INTRUSION
ß
ß
ß
O
4o.0o
ß Individual
Craters
WestofProc.
O
ß
20.00
13 Cratersnear Lavo,sier
ß
0.00
0
* Craters
,n/nearEinstein
I
,
'
I
50
100
150
200
m
!
I
250
300
350
Distance
fromMareEdge(kin)
Magma PressureVariationwithin
Crater Clusters
160.00
ß CratersnearRepsold
ß-
140.00
--
o Craters near Lavoisier
• 12o.oo
E
R.
lOO.OO
•o
Procellarum and the thickest crust on the lunar farside, data
o
o
'-
80.00
E
60.00
c3
,,-1
o
o
--
I
ModeledMagmaDrivingPressures
160
o
rn
I
o
A
"-
140
e
120
'13 40.00
._>
ß
u• 100 -
C• 80
-•.
ß
CratersinsideSmy•hii
=
Individual Craters West
of Proc.
ß
Craters near Lavoisier
o
Craters in/near Einstein
60
• 4o
ß
•
= 2o
T
•
20.00
0.00
o
0
t
I
50
100
Im
150
200
DistancefromNearestLargerCrater(km)
Topo.PressureEffect
Figure 13. Derivedmagmapressures
asa functionof locationwithinourstudyareas.(a) Deriveddrivingpressures
as
CraterDiameter(km)
a functionof radiallocationwithin the Smythiibasin.(b)
Figure 12. Laccolith driving pressuresderivedfrom the Drivingpressures
in the westernhighlandsasa functionof
crateruplift data in Mare Smythiiand the westernhigh- distancefrom OceanusProcellarum.(c) Variationof derived
lands. The solid curve shows the reduction in lithostatic
drivingpressures
withinthe individualcraterclusters.One
pressure
expectedfrom thedifferencein elevationbetweena isolatedcrater(Nernst)is notrepresented
here,as it is over
craterfloorandthesurrounding
(mean)surfacelevel.
250 km awayfromthenextnearestfloor-fractured
crater.
o
o
20
40
60
80
100
120
140
160
21,212
WIC•
AND SCHULTZ:
CRATER RELAXATION
AND INTRUSION
MODELS
ModeledIntrusionDepths
100.00
0
'-
ß UkelyInt Depths,Pro½.
1.oo -
mm•8
n UkelyInt Depths,Smythii
•0 ½.
2800 kg/m
o Te of Proc. Craters
'o
B
o
8 0
oo
0.10
o Te of SmythiiCraters
o
pM
= 3400kg/m
,
10
100
1000
CraterDiameter(kin)
Figure 14. Estimatedlaccolith depthsbeneathfloorfracUuvxl
craters.
Theminimumvaluesrepresent
thederived
effective elastic thicknesses,while the maximum values
allowfor effectsof layeringon flexuralstrength
andcorrespondto values6 timesthe effectiveelasticthickness.
Figure 15. Diagramof modelfor cratermodificationover
a laccolith.
D isthecrater
diameter;
Df isthecrater
floor
from the Clementinemissionssuggestthat the floor-fractured
diameterandapproximate
diameterof theintrusion.
Wm is
cratersoccurwithin a regionof fairly uniformcrustalthickness
the
thickness
of
the
intrusion
and
extent
of
floor
uplift;
in
(~60-70 km [Zuber et al., 1994]).)
floorupliftis equalto theinitialapparent
Turning to other model constraints,the laccolith inversion thisexample,
modelalsoprovidesestimates
for the intrusiondepth,magma craterdepth (d).T is the thicknessof the upliftedfloor
the effectiveflexuralthickness
of
columnlength, and subcrustalmelt thicknessbeneatha floor- blockandTe represents
fracturedcrater.The derivedvaluesfor intrusiondepth,how- the floor plate during uplift. Beneaththe intrusion,hc
ever,are stronglyrelatedto the craterdiameter(Figure14), denotesthe crustalcolumnheightof magmafeedingthe
sinceintrusionsize is derivedfrom the upliftedcraterfloor laccolithand dM is the depthto the baseof the magma
plate dimensions,
Becausethe averagecratersize insideMare columnin the mantle.For the hydrostaticcalculations
in
Smythii is smallerthan that in the westernhighlands,the thetext,
Pmisthemagma
density
(-2900kg/m3),
Pcis
magmasnearProcellarum
thusmay havebeenslightlydeeper thecrustaldensityandPM is themantledensity.
on averagethan thosebeneathMare Smythii.This interpretation also can be derived simply from the differencesin
observedcrater size for the two regions.Since the derived
intrusiondepthstypicallyrangefrom only a few hundredto a Smythiiindicatea commonmagmasourceof regionalextent,
cratersof the westernhighlands
apparently
few thousandmetersbeneatha craterfloor (Figure14), the the floor-fractured
likelihoodof magmasinteractingwith smallerand shallower reflect the presenceof several, smaller, discretemagma
sources.
cratersshoulddecreaseasregionalmagmadepthsincrease.
Finally, the magmaconduitlengthsderivedfrom the model
drivingpressures
and intrusiondepthsalso indicateregional
differences
betweenmagmatism
in Mare Smythiiandthe westAdditional
ModelImplications
ern highlands.If the modeledintrusionstap hydrostatic
mare
magmacolumns(Figure 15), the inferreddistributionof lunar
80.00
crustal thicknesses[Bratt et al., 1985] indicatesaverage
I=:
70.00
magmacolumn lengthsof ~35 km for the central Smythii
basin,andof ~67 km for the westernhighlands(Figure16).
Further,the subcrustal
melt thicknesses
(drnof Figure15) supporting these magma columns are strongly correlatedwith
• 60.00
•
40.00
modeledmagmapressures,
and thusexhibit a muchgreater o
O 30.00
variation in the westernhighlandsthan beneathSmythii
E
(Figure17). Althoughthe averagesubcrustal
melt thicknesses • •o.oo
=
for thesetwo studyareasare almostidentical(-8-8.5 km), the
• lO.OO
ß WesternHighlands
= MareSmythii
distributions of these subcrustal melts differ. Where the sub-
crustalmelt thicknesses
beneathMare Smythiishowonly a
broad,gentlereductiontowardthe outermare edge(Figure
o.oo
I
I
I
I
I
•
80
80
100
120
140
180
CraterDiameter(kin)
180
17a), the melt thicknesseswest of Procellarum(like the
derivedmagmapressures)
showmuchmorelocalizedvariations Figure 16. Modeledmagmacolumnlengthsfor theflooraroundindividualgroupsand clustersof floor-fracturedcraters fracturedcratersin Mare Smythiiand the westernhigh(Figure 17b). Consequently,
wherethe modifiedcratersinside lands.
WICHM
AND SCHULTZ: CRATER RELAXATION AND INTRUSION MODEL3
MantleColumnLengthsbeneathSmythii
21,213
18a), the dependenceof relaxationon topographicwavelength
actually favors the initial equilibration of larger craters.
Indeed, for comparablefir/, small craterscan remain essentially unmodifiedeven as modeledfloor uplifts in much larger
craters approachthe initial apparentcrater depths (Figure
o
lO
ß
ß
ßß
..o
Q.c:
6
CraterFloorUpliftinMareSmythii
3500.
4
ß MoatFFC insideSmythii
3000.
n Non-moat Craters inside
Smythii
50
100
150
200
2500.
250
DistancefromSmythiiCenter(kin)
'---'
Subcrustal Melt Thicknesses
beneath W. Proc.
2000.
..I-
-
._
•
•soo. -
..I-
eee
o
o
10o0.
-
500.
-
ß Cratersnear Repsold
15.00
+
m Craters near Lavoisier
initialapparentdepth
ß estimatedflooruplift
+ modeleduplift(t/q 6.31e-9)
I
O.
I
I
I
20.
O.
I
40.
!
I
60.
!
!
80.
I
I
loo.
t
J
120.
l
140.
Craterdiameter(kin)
Theoretical
FloorUpliftforCratersin a ViscousHalfspace
o
(relaxation
wavelength
definedbyfloorradius)
[]
lO.OO
3500.
cø
o
5.00
"-"
2000.
..•.
15oo.
,
,
ß
-
0.00
0
50
100
150
,'
*'
__ in,tiaJ
a•arentde•th
ß "
J..•.
upli•
for
• 3.15e-8
O'
•"
+'
200
DistancefromNearestLargerCrater(km)
o.
I
J
J
i
J.
•.uplift
for
•• 6.31
1.•e-8
I o uplift
for
e-g
I
I
I
I
I + uplift
for• 3.15e-9
,'*',
i
.
.
10. 20. 30. &O. 50. 60. 70. 80. 90. 100. II0. •20. 130. 140. 150.
Figure 17. Modeledsubcrustal
melt thicknesses
beneath
Mare Smythiiandthewesternhighlands.
(a) InferredmanCraterdiameter(kin)
fie melt thicknessas a functionof positionwithin Mare
Figure 18. Floor uplift in the Smythiiinterior.(a) Crater
Smythii. (b) Variationsin mantlemelt thicknessaround
floor upliftsas a functionof craterdiameter.Ideal, initial
individual clusters of floor-fractured craters in the western
apparent
depthsareindicatedby thecurve.Estimated
uplifts
highlands.
are shownby dotsandrepresentthe differencebetweenthe
pristineandobservedvaluesfor apparentcraterdepth.The
Implicationsfor Crater Modification
four open circles representcraterslocated on the inner,
Both models for crater modification
indicate different
mare-bounding
scarpand may be biasedby inclusionof
regional conditionsin Smythii and in the westernhighlands, scarptopographyin the crater rim height estimate.For
but theseregionsalsoreveallocal variationsin cratermodifi- reference,a predictedspectrum
of floor uplift dueto crater
cationwith both crater size and setting.Crater size and setting relaxation is also shown (crosses).(b) Theoretical floor
shouldaffect viscousrelaxation and igneousintrusionsdifferuplift due to relaxationas a functionof cratersize. Again,
ently; therefore these regional observationsprovide a basis
the solidcurvedenotesthe ideal valuesfor initial apparent
for further testingthe validity of the cratermodificationmodcrater
depth.The othercurvesrepresentprogressive
relaxels.
ation modelsat increasingrelaxationparameters.In each
Viscous
Relaxation
case,the calculateduplift at a particularcrater diameter
Although small cratersrequire less modificationto produce reflectsrelaxationof a wavelengthequalto 5.2 timesthe
the observedfloor uplifts thando largecraters(Figures2b and corresponding
craterfloorradius.
21,214
WlCHMAN AND SCHULTZ: CRATER RELAXATION AND INTRUSION MODELS
18b). Once uplift is equivalentto the initial depth, however,
little further relaxation should occur and longer relaxation
times allow comparablefloor uplifts to occur at progressively
smallercrater sizes (Figure 18b). Thus for cratermodification
during a short-livedregional heating event, relaxationshould
producea spectrumof crater modificationwith minimal floor
uplifts in the smallestcratersand near total relaxationat very
large crater diameters.Alternatively, if modification results
from a long-lived thermal anomaly, uplift can continue in
smallercraterslong after relaxationhasequilibratedthe topography of larger crater forms (Figure 18b). In this case,total
relaxationeventuallyoccursover a broadrangeof cratersizes,
and the derivedt/•l valuesincreasewith decreasing
cratersize.
Moreover, becausemodification of the larger craters occurs
early in the relaxation event, the smallest craters yield the
most representativevalues for that relaxationevent since they
are the mostrecentlyequilibrated.
Inside the Smythii basin, the near equivalenceof the inferredfloor uplifts with initial craterdepthsat all sizes(Figure
18a) requirestotal relaxationdown to craterdiametersof-20
km. Even though the observedfloor uplifts in Smythii are
compatiblewith extreme viscousrelaxation, however, this
correlationmay be coincidental.Specifically,the inferenceof
total craterrelaxationin Smythiiprimarily reflectsthe equivalence of crater floor elevations with the surroundingbasin
floor. Magmastatic equilibration with the mare of any intrusionsbeneaththesecratersalso can producesucha uniformity
of floor elevations [Schultz, 1976a]. Since the volcanically
flooded floor sectionsin many of these craters indicate that
magmashave at least partially modified presentcrater topography inside Smythii, these cratersthus provide only limited
(and nonunique) support for viscous crater relaxation in the
absenceof an associatedsequenceof smaller,partially relaxed
peraturesreflect the temperatureat d, then crater relaxation
providesa looseconstrainton local vertical temperaturegradientsduring relaxation.These thermalgradientsare smallestat
larger crater sizes (due to the greater scale depths), but the
smallest floor-fractured craters (D<20 km) in both regions
indicatemodel temperaturegradientsof between220øC/kmand
150øC/km.Consequently,for basalt solidus temperaturesof
~ 1100øC [Basaltic VolcanismStudyProject, 1981], thesegradientsimply basalticmelts at model depthsof ~5 to 7.5 km,
well within the depthrangeat whichmagmascan initiatedirect
crater modification by flexure and uplift [Wichman, 1993].
Further,since a lunar rheologyshouldbe more viscousthan
our rheologicalmodel, the implied melt depthscould be even
less than those indicated
Igneous
In
here.
Intrusion
contrast
to the viscous
relaxation
inversion,
the
observeddifferencesbetween crater modificationin our study
areasprovide qualitative supportfor deformationover cratercenteredintrusions.In particular,the derivedintrusionparameters apparentlyreflect the differences in dominant regional
structurein two ways. First, hydrostaticmagma columnson
the Moon should be sensitive to regional mantle depths
[Solomon, 1975; Head and Wilson, 1992]. Thus greater
magma pressuresshould develop at any given crustal level
over regions where the crust/mantleboundary is shallower.
Second,due to differencesin the efficiency of magma flow,
variations in lithosphericstressor crustal structurecan limit
the distribution and emplacement of subsurface magmas.
Consequently,if cratermodificationis the result of crater-centered intrusions,both the range of derived magma pressures
and the distribution
of smaller
floor-fractured
craters should
reflect the structuraldifferencesbetweenMare Smythii and the
crater forms.
western highlands.
In the western highlands, the strong dependenceof the
In the Smythii region, both the relatively narrow range of
derived t/•l and viscosityvalueson cratersize also arguesfor observeddriving pressuresand the restrictionof cratermodifitotal relaxationdown to small crater sizes.The wide range of cationto the centralbasinfloor can be relatedto a structurally
inferredcraterdepthswest of OceanusProcellarum,however,is def'med,commonmagmasourceof regionalextent.Becauseof
inconsistentwith total relaxation on a regional scale. Also, the broad, uniform mantle uplift resultingfrom basin formawhile a few cratersshow relaxationcomparableto the craters tion, little variation in magmatic conditionsor crater modifiinsideMare Smythii,many of the lessmodifiedcratersin this cation within this region would be expected.For the craters
region still indicate greater relaxation at small crater sizes west of Procellarum,however, both the highland setting and
than at larger crater sizes (Figure 9b). Consequently,the the broaderrangein derivedmagmapressures
suggestthe presobservedspectrumof cratermodificationin the westernhigh- ence of more variable mantle topography.The concentration
lands is inconsistentwith the predictedeffects of (partial) vis- of high magma pressuresnear the centersof the observed
cousrelaxation.Although enhancedrelaxationof the smallest floor-fracturedcrater clusters(Figure 13c) also supportsa corcraters in and around Einstein and Lavoisier might reflect relation between crater modification and local variations in
locally diminishedcrustalviscosities(Figure lob), suchlocal- mantle topography,and the common occurrenceof smaller
ized viscosityvariationsseem less likely for other, more iso- floor-fracturedcraterson other, largercraterrims may indicate
lated
craters
which
also
show
such enhanced
relaxation
(Figures10a and lob).
In addition,becausethe topographicstressesdriving deformationattenuaterapidly with depth[Jaegerand Cook, 1979],
crater relaxation requires viscous behavior at very shallow
crustaldepths.For a square-edged
cylindricalload of radiusRo,
half of the material flow responsiblefor relaxationin a vis-
a number of structurally controlled magma columns within
highlandimpact structures.
ConcludingRemarks
Viscousrelaxation and igneousintrusionmodels for crater
modification have distinctly different implications for
coushalf-spaceshouldoccurabovea scaledepth8 equalto regional conditions in Mare Smythii and the westernhigh~l.4Ro [Cathies, 1975]. Therefore, again equatingRo to the lands.For viscousrelaxation, the uniformity of presentcrater
observedcrater floor radii, the average floor plate sizes in depthsat all crater sizesin Mare Smythii indicatestotal crater
Mare Smythii and the westernhighlandsindicatescaledepths relaxationdown to diametersof ~20 km and a long-livedheatof-10-15
km, whereas the smallest floor-fractured craters ing event. In contrast, the wide range of preservedcrater
requireviscousflow in bothregionsat depthsof <3-5 kin.
depths in the western highlands suggestspartial relaxation
These derived scale depthsfor viscousrelaxationpresent during more transientand localized heating events.Inversion
anotherpotential difficulty. If the estimatedhalf-spacetern- of the preservedcrater topographiesfor a representativehalf-
space viscosity places average crustal viscosities in Mare
21,215
al., 1981], but suchheatingshouldbe much less likely over
Smythiiandthewestern
highlands
at ~6x1021P and~9x1022 most of the westernhighlandregion, where shallow crustal
P, respectively,but some clustersof floor-fracturedcratersin
the western highlands indicate local viscosity averages2-3
times lower than the regional average.Craters outsideof the
central Smythii basin are distinctly deeper than those in the
mare and are comparablein both morphometryand implied
viscosityto cratersnear King on the lunar farside. Since the
trendof craterdepthsaroundKing is inconsistent
with viscous
relaxation,the observedcrater depthsoutsideMare Smythii
probablyreflect modificationby crater-fillingejectadeposits
rather than crater relaxation.
For the igneousintrusionmodel,cratermodificationprimarily reflects local magma pressuresand regionalvariationsin
the associatedmagma columns.Inside Mare Smythii, the uniform derived magma pressuresprobablyindicate regionally
shallowmagmaswithin a broad, basin-centeredmantle uplift.
The apparentequilibration of magma pressureswith topographicallycontrolledlithostaticpressuressuggeststhat these
model valuesare primarily controlledby near-surfacepressure
gradients.In contrast, the derived magma pressureswest of
OceanusProcellarumapparentlyindicate a variety of conduit
lengths arrayed around a few, localized, subcrustalmagma
reservoirs.Sincethesereservoirsappearto be centeredon relatively large, crater-centeredmantle uplifts, cratermodification
in the western highlands seems to reflect regional crustal
thicknessesrather than local surface topography.Although
magmabodiesare likely to be sparselydistributedandmay be
stronglyaffectedby othercraterstructures.
Finally,although
theviscous
r•laxation
andigneous
intrusion modelshave been consideredseparatelyin this paper,
thesemechanisms
are not necessarily
independent.
Regionally
elevatedtemperaturesmay induce volcanism,whereassufficientlylarge,long-livedmagmaticintrusions
may producesufficient crustalheatingto allow viscousrelaxation.While such
combinations
can accountfor volcanismin viscouslymodified
craters,however,they do not requirerelaxationover an intrusion. Moreover,they do not addressthe apparentdifficulties
with regional viscous relaxation discussedabove. Therefore,
sincethe uniformityof craterdepthsin Mare Smythii can be
explainedby the flotationof craterfloorson subsurface
magmas as well as by viscous relaxation [Schultz, 1976a], we
believe that the regional context of floor-fracturedcratersin
both Mare Smythii and the highlands west of Oceanus
Procellarum
is more consistent with deformation
over inde-
pendent, crater-centeredintrusions than with viscous relaxation duringregional crustalheating.
The recentClementinemissionshouldprovidefurthertests
for this hypothesis.At the least, Clementinetopographydata
allow analysis of regional surface elevations near floorfracturedcratersin the westernhighlands.If thesecratersare
magmaficallymodified,thenmostof thesecratersshouldoccur
the inferred subcrustalmelt thicknesses(-8 km) are, on aver- at comparable,low elevations,and the crater clustersmay be
age, similar for the two study areas,derived magma column separatedby higher topography.In addition, the Clementine
lengthsin the westernhighlandsare much greater than those data alsomay provideimprovedcraterdepthestimatesfor the
in Mare Smythii (67 km versus35 km), and thereis a sugges- highland craters, while the improved model inversionsfor
tion that the modeled intrusiondepthsare also slightly deeper crustalthicknessprovide a strongerbasisfor testingthe relation of magmaticpressuresand crustal thicknessvariations.
in the westernhighlandsthanin Mare Smythii.
Both viscous relaxation and igneouscrater modification Nevertheless,conclusiveproof of the postulatedcrater-cenindicate regional differencesbetweenMare Smythii and the tered intrusions probably awaits future missions and the
westernhighlands.Severalaspectsof the observedcratermod- implementationof orbital radar sounders,detailed gravity
mapping via low-orbit satellites or lander/penetrator-based
ification, however, seem inconsistent with the viscous relaxation mechanism.In particular, the consistentlyenhanced seismic surveys.
relaxation of smaller craters within the western highlands
(relativeto largercraters)conflictswith the expectedeffectsof Appendix A: Modeling Crater Modification by
crater relaxation. A progressiverelaxation of shortertopo- Viscous Relaxation
graphicwavelengths
over time mightproducesuchan apparent
The characteristicequationsfor the viscous relaxation of
enhancement,but the range in both preserved crater morphologiesand relative crater depthsin this region contrasts crater topographyover time [Danes, 1965; Scott, 1967; Hall
strongly with the equilibrationof larger craters expectedto et al., 1981] describean axially symmetriccraterimposedon a
precederelaxationat shorterwavelengths.In addition,the dis- viscoushalf-space.Under theseconditions,crater topography
tribution of craters in the western highlandsappearsto be is treatedsimply as a functionof time andradial distancefrom
more consistentwith variationsin magmacolumnheight than the crater center,and if the effectsof planetarycurvatureare
with variationsin crustalviscosity.The derived highlandvis- ignored,the equationfor surfacetopographyon a uniformviscosity values show little pattern beyond a combination of coushalf-spacebecomes[Cathies,1975]
high and low viscosityvalues near major crater clusters,but
the derived magmatic driving pressuresshow a recognizable
trend of radially decreasingmagma pressuresaround these
crater clusters. This trend is consistent with both variations
in
j(r,t)=
JF(k)
e-pgt/2•lk
Jo(lcr)
kdk. (A1)
In this equation,J0 is the Besselfunctionof orderzero,fir, t) is
the topography,k is the radial wavenumberand, lettingfir,O)
representthe initial craterform,
local crustal thicknessand with increasedmagma conduit
lengthsfrom a central reservoir.Furthermore,the size of the
smallestfloor-fracturedcratersin both Mare Smythii and the
western highlands also poses a problem for viscous relaxF(k)
= lf(r,O)
Jo(kr)
r dr.
(A2)
ation. Crater relaxationin thesecratersshouldrequireviscous
0
behaviorat depthsof less than -5 km; and thesedepths,couThe decayof cratertopographyover time is describedby the
pled with the modeled viscosity values, suggestboth high
exponentialterm of equationA1, and thushas a characteristic
thermalgradients(~200øC/kin)and the presenceof fairly shallow basalticmelts (<5-8 km depth).Regionalheatingby such decaytime x(k)= 211k/pg,where//is the half-spaceviscosity,
shallowmagmasmay be plausibleinsideMare Smythii [Hall et p is the density,and g is gravitationalacceleration.Since k is
21,216
WICHMAN AND SCHULTZ: CRATER RELAXATION AIR) INTRUSION MODELS
the variable of integration,the unknownsfor an inversion of
thesetwo equationsare the viscosityand the durationof modification (t), which can be combinedinto a single parameter
t/rl, characterizingthe extentof relaxation[Hall et al., 1981].
Although the parametert/rI can be derived by an iterative
leastsquaresinversionof equations(A1) and (A2) [Hall et al.,
1981], this inversion requires detailed topographicdata for
both the floor-fracturedcrater ([(r,t)) and a pristine crater of
comparablesize (J•r,0)). Such topographicdata are presently
availablefor only a small subsetof the lunarcraterpopulation.
If crater modificationis approximatedby the relaxationof a
single topographicwavelength,however,detailedtopography
is unnecessary
to estimatet/rI. Since the primarymodification
associatedwith floor fracturingis a broad, coherentuplift of
the crater floor, the extent of modification should reflect the
changein craterdepthduringuplift, which can be constrained
by comparingshadowmeasurements
of crater depth with a
pristine crater depth indicatedby the morphometricrelations
of Pike [1980]. Although such shadow-derivedestimatesare
less precise than those derived from Apollo topographydata,
both methodsappearcomparablein accuracyfor craterdiametersgreaterthan 15 km [Pike, 1974].
Eliminationof the topographicprofile data from the relaxationmodel alsosimplifiesthe modelequations.First, because
of the flat floor uplift, crater depth can be roughlycharacterized by any point on the crater floor. For the crater center,
equationA1 thusbecomes
determinedue to the difficulty of estimatingrim heightsfrom
shadow measurements[Pike, 1977]. Thus we use a conservative estimatefor apparentcraterdepthderivedby subtracting
the initial rim height from the derivedcrater depth.This estimate assumes that relaxation
has not affected the short wave-
length topographyof the crater rim, and is consistentwith the
general similarity of crater rim heights for floor-fractured
cratersand unmodified craters [Schultz, 1976a]. Still, in cases
of extremecrater modification,this assumptionis unrealistic,
and the resultingapparentcrater depthsare negative.In such
cases, a present crater depth of zero is assumed,since the
relaxation of short wavelengthcrater rim topographyshould
require extensiverelaxation of the crater cavity as well. With
these assumptions,equation (A4) then yields the following
general relation for the relaxation parameter t/•l in terms of
the observedquantities
t/•l=Pg•,ho
] k•-
(A5)
where
k is 1.2/RfandRfistheradius
of thecrater
floorplate.
This simplified relaxation model can be testedin two ways.
First, the inversion results of Hall et al. [1981] can be comparedto the resultsof equation(A5) for the samecraters.As
shownby FigureA1, the valuesderivedfrom thesetwo inversion techniquesmatch those of the Hall et al. calculations
fairly well. (Note: for craterslike Rungeand Dumaswherethe
greatestdifferencesare observed,the inversionby Hall et al.
appearsto have been partially biasedby the inclusionof mare
or othercrater-fillingunits in the modeledcraterfloor uplift.)
Second, we can also use the derived t/h values of Hall et al. in
combination with observed floor uplift to test the assumed
sinceJo (0) = 1. Further, by concentratingrelaxation into a
valueof k in our inversionmodels. Applicationof equation
single wavelength, we can remove the integral in equation
(A4) to the relaxation models of Hall et al. [1981] resultsin
(A3). For a half-spaceof uniform viscosity,this indicatesan
effective wavenumbers that are also similar to those derived
exponential decay of topography according to the relation
from our cylindricalcavity approximation(FigureA2).
[Cathles, 1975]
•0•)
=JF(k)
e-pgt/2•lk
kdk (A3)
h(t)=ho
e-pgt/2
•lk
(A4)
Comparison
of Time/Viscosity
Inversion
Values
where h0 is the initial depthand h(t) is the craterdepthat time
t.
The solutionof equation(A4), however,still requiresa value
for k, which should be related to crater size through the
dominantwavelengthof relaxation.Cathies [1975] showsthat
the centerof a cylindrical,square-edged
hole will relax as if the
appliedload wereharmonicwith an effectivewavenumberof k
= 1.2/Ro.Therefore,sincecrater depthis essentiallyconstant
over the crater floor, the evolution of a square-edged
cylindricalcavity the size of the craterfloor providesa simple
model for the dominant wavelengthof viscouscrater relaxation. Further,we approximatethe depthof the cavity in equation (A4) with the apparentcrater depth (i.e., the crater depth
relative to the regional mean elevation,not the rim crest),
rather than the total crater depth, since the short wavelength
topographyon the crater rim shouldnot contributeto relaxation of the crater cavity.
Our inversion of crater depth for regional viscosity thus
requiresa value for bothh(t), the presentapparentcraterdepth,
andhO,the initial apparentdepth.The lattervalueis estimated
from the morphometricrelationsof Pike [1980] and assumes
that crater diameter is not significantly altered during relaxation. In the absenceof detailedtopographydata, however,the
presentvalue for apparentcrater depth is more difficult to
- + topographic
error
oHall
et
al.
(1981)
solution
•
+ Hall et al. (1981) range
o.
!
• s.
I
20.
I
I
!
I
-.
Craterdiameter(kin)
Figure A1. A comparisonof derivedrelaxationparameter
(t/TI) from our method(stars)to the valuesdetermined
by
Hall et al. (circles).Errorbarsrepresent
theeffectof a 100m errorin floor uplift on our inversionand the confidence
intervalof Hall et al. [1981],respectively.
Comparison
of DerivedEffective
Wavenumbers
.•.
4xTO'f
-
3[
c)
.
as is likely on the Moon, bendingshouldinitiate pervasive
failure at depth near the edge of the intrusion [Pollard and
Johnson, 1973]. Since suchperipheralfailure separatesthe
uplifted units from surroundingstrata, the final intrusion
thicknesscan then be related to the driving magma pressure
and to magmaticdensity[Pollard and Johnson,1973].In particular, if the uplifted roof block is totally supportedby
magmaat the end of uplift,
Pd=w,n
(•+y,,) .
2xtO'4
IO'f -,
•)
relaxation model
o Hall et al. (1981) solution
of the intrusion.
+ Hallet ai. (1981)range
o.
10.
15.
20.
25.
50.
,]5.
40.
45.
Craterdiameter(krn)
Figure A2. A comparisonof effectivewavenumberfrom
our approach(stars)andthatimpliedin theHall et al. solution by the derivedrelaxationparameterand floor uplift
(circles).The errorbarsreflecttherangeof t/rl derivedby
Hall et al. (1981).
Appendix B: Modeling Crater Modification by
Laccolithic
Intrusions
Laccolithsare, by definition,intrusionsthat evolve from an
initial sill-like form throughthe verticaluplift of overlying
strata[Gilbert, 1877; Corry, 1988]. Consequently,
the model
relationsfor deformationover a laccolithtypically incorporate a force balancebetweenmagmaticpressuresinside the
intrusion
and elastic deformation
(B2)
In this equation,k is the magmayield strength(an essentially
negligiblequantity),and Y,nrepresentsthe unit magmaweight
•.
....
21,217
outside of the intrusion.
Sincemagmapressuremustat leastequallithostaticpressure
for intrusiongrowth,deformationover a laccolithshouldprimarily reflect the intrusionsize, the strengthof the overburden, and a drivingmagmaticpressure(Pd), whichis definedas
the differencebetweenthemagmapressure
(P,n)andthelithostaticpressure(Pt) [Johnsonand Pollard, 1973].In a sill, this
drivingpressurecausesonly minor deformationthroughgeometrical stressconcentrationsat the edge of the intrusion
[Pollard and Johnson,1973]. Becauseof lateral sill growth,
however, the net upward load of magma on its overburden
In combination,theseequationsthus provide a relatively
straightforward
basisfor reconstructing
the sequenceand conditions of deformation over terrestrial laccoliths [Pollard and
Johnson, 1973]. Given values for the intrusion size and thick-
ness,equation(B2) constrainsthe magmaticpressure,P,t, and
this value is then insertedinto equation(B1) to estimatethe
effective overburden thickness under various conditions. Since
satelliteimagescannotdirecfiy constrainthe size or thickness
of a subsurfacelunar intrusion,however, the applicationof
theserelationsto lunar crater modificationrequirestwo additional model assumptions.First, we assumethat the size of an
upliftedcraterfloor plate providesan approximatesize for the
underlying intrusion since horizontal intrusion growth
appearsto be minimal after the initiation of fault-bounded,
block uplift in terrestrial laccoliths [Pollard and Johnson,
1973]. Second,the changein craterdepthduring floor uplift
providesa simple, minimum estimatefor the intrusionthickness, assumingthat peripheral failure precludessignificant
horizontalstretchingof the uplifted craterfloor units.
In addition,a rangeof modelestimatescan be derivedfor the
depth of an intrusionbeneaththe crater floor. At one end of
this range,the derivedT, valuesprovide a minimumpossible
depth for the inferred intrusions since these values reflect
deformationof each floor plate as a single elastic layer.
Discreteimpactmelt units,fallbackejectalayers,anddeeper
breccias,however,can producea crudelylayeredcraterfloor
stratigraphy[Schultz,1976a;Denceet al., 1977], whichmay
not deformas a singlelayer. On the Earth,layeredstratigra-
phies allow intrusion depthsmuch greater than the derived
effective elasticthicknesses[Pollard and Johnson,1973], and
increases in proportion to the floor area of the intrusion for the extremecaseof a sequence
of decoupledelasticlayers,
[Gilbert, 1877] and when this load finally exceedsthe rigid the effective elastic thicknesscan be theoreticallyrelated to
strengthof the crust,uplift can occurby flexure or failure of layer propertieswithin the sequence
by the sum
the overlying section.
From the analysis of Pollard and Johnson [1973], such
Bi
uplift initially occursby flexure.Therefore,if the overburden
is treatedas a layeredsequenceof elasticplates,the maximum
extent of uplift over the intrusionis related to the driving where n is the numberof layersover the intrusion,B, is the
elasticmodulususedto calculateTe, Bi represents
the individpressure,Pd, and an effectiveelasticplatethickness,
T,, by
ual elasticmodulusfor each layer, and ti is the thicknessof
5.33w,n
BT,3
layer. Thus, despitethe poor constraintson the subfloor
Pd=
a4
,
(B1) each
stratigraphyof lunar impactcraters,rudimentarymodelsalso
wherew,n is the floor uplift; a is the radiusof the intrusionand can be derived to illustrate a likely range of crater-centered
B is the elasticmodulus.While uplift is limited, suchflexure is intrusiondepthson the Moon. Sincethe lunar impactmelt and
likely to produceonly limited brittle failure over the intrusion. breccia stratigraphies are likely to contain fewer, thicker
As uplift continues,however,two responsesare possible.If layers than the sedimentarysectionshostingmost terrestrial
crustalfailure is primarilyductilein character,flexurecan con- laccoliths,we have assumedfor this study that the uplifted
tinue throughoutintrusiongrowth [Corry, 1988]. Alterna- floor sectionsare composedof no more than five layers, and
tively, if failure is dominatedby brittle or elasticdeformation, that mostof theselayers are of equivalentthickness.
T'3
=• '•t ti3'
(B3)
21,218
WICHMAN AND SCHULTZ: CRATER RELAXATION
AND INTRUSION MODELS
Finally, the derived values for magmaticdriving pressure Neukum,G., B. Konig,andJ. Arkani-Hamed,
A studyof lunarimpact
cratersize-distributions,
Moon, 12, 201-229, 1975.
and elasticoverburdenthicknessalsocan constrainthe length
of the magma column beneath an intrusion [Johnson and
Pollard, 1973].In the terrestrialcase,magmais typicallyless
densethan the crustalrocks at depth; hence,P a is simply
Apghc wherehc is the depthof the magmasourcebeneaththe
intrusionand Ap is the densitycontrastbetweenthe magma
and crustalcompositions[Johnsonand Pollard, 1973]. On the
Moon, however,marebasaltmagmasappearto be denserthan
the anorthositic lunar crust [Solomon, 1975]; thus, a nearsurfacelunarintmsionrequiresthatthebaseof the magmacolumn extendinto the lunar manfie [Head and Wilson, 1992]. In
this case(Figure 15), the extentof a magmacolumninto the
lunar mantle must balance both the height of the crustal
magmacolumnandthe drivingpressureof the intrusion,
p)ga
= apgh + Pa
(B4)
and thus varies with both local crustal thickness and intrusion
depthaswell as with the derivedmagmapressures.
Oberbeck,V.R., W.L. Quaide,R.E. Arvidson,andH.R. Aggarwal,
Comparativestudiesof lunar,martianandmercuriancratersand
plains,J. Geophys.Res.,82, 1681-1698,1977.
Pike, R.J., Depth/diameterrelationsof freshlunar craters'Revisionfrom
spacecraft
data,Geophys.Res.Lett., 1, 291-294, 1974.
Pike,R.J.,Size-dependence
in theshapeof freshimpactcraters
onthe
Moon,in ImpactandExplosion
Cratering,editedbyRoddy,DJ.,
Pepin,R.O.andMerrill,R.B.,Pergamon,
New York,pp.489-509,
1977.
Pike,R.J.,Geometricinterpretation
of lunarcraters,U.S. Geol.Surv.
Prof Pap. 1046-C, 1980.
Pollard,D.P., andA.M. Johnson,
Mechanics
of growthof somelaccolithicintrusions
in theHemyMountains,Utah,II, Bendingandfailure
of overburden
layersandsill formarion,Tectonophysics,
18, 311-354,
1973.
Schultz,P. H.,A PreliminaryMorphologic
Studyof LunarSurface
Features,Ph.D.thesis,967 pp.,Univ. of Texasat Austin,1972.
Schultz,P.H., Floor-fracturedlunar craters,Moon, 15, 241-273, 1976a.
Schultz,P.H., Moon Morphology,Univ. of TexasPress,Austin,1976b.
Schultz,P.H., and Mendenhall, M.H., On the fortnationof basinseeondarycratersby ejectacomplexes
(abstract),
LunarPlanet.Sci.
Conf.,loth, 1078-1080,1979.
Schultz,P.H., andP.D. Spudis,Evidencefor ancientmarevolcanism,
Acknowledgments.
We wishto thankS. CroftandPaulSpudisfor their
reviewsof this paper.We also thank D. Wilhelms, S. Croft, and an
anonymous
reviewerfor their commentson a previousincamarionof
thismanuscript.
Proc. Lunar Planet.Sci. Conf.,loth, 2899-2918, 1979.
Schultz,
P.H.,andP.D.Spudis,
Procellarum
basin:A majorimpactorthe
effectof lmbrium?(abstract),
LunarPlanet.Sci.Conf, 16th,746747, 1985.
Scou,R.F., Viscousflow of craters,Icarus, 7, 139-148, 1967.
Shelton,G., andJ. Tullis,Experimental
flow lawsfor crustalrocks
References
BasalticVolcanismStudyProject,BasalticVolcanismon the Terrestrial
Planets,Pergamon,New York, 1981.
Baldwin,R.B., Rille pauemin thelunarcraterHumboldt,J. Geophys.
Res., 73, 3227-3229, 1968.
Baldwin,R.B., The question
of isostasy
ontheMoon,Phys.Earth.
Planet. Inter., 4, 167-179, 1971.
Bratt,S.R.,S.C.Solomon,
J.W.Head,andC.H. Thurber,Thedeep
structure
of lunarbasins:implications
for basinformarionand
modification,J. Geophys.Res.,90, 3049-3064, 1985.
Brennan,W.J., Modificationof pre-mareimpactcratersby volcanism
and tectonism,Moon, 12,449-461, 1975.
Cathies,L.M., lII, The Viscosityof theEarth• Mantle, PrincetonUniv.
Press,Princeton,N.J., 1975.
Corry,C.E., Laccoliths:
Mechanisms
of emplacement
andgrowth,Geol.
Soc.Am. Spec.Pap., 220, 1988.
Danes,Z.F., Rebound
processes
in largecraters,
Astrogeol.Stud.Ann.
Progr.Rep.A (1964-1965),pp. 81-100,U.S. Geol.Surv.,1965.
Dence, M.R., R.A.F. Grieve, and P.B. Robertson,Terrestrialstructures:
principalcharacteristics
andenergyconsiderations,
in Impactand
Explosion
Cratering,
editedby D.J.Roddy,R.O.Pepin,andR.B.
Merrill, pp.247-275,Pergamon,
New York, 1977.
Gilbert,G.K.,ReportontheGeologyof theHenryMountains,
170pp,
U.S. Geogr.Geol.Surv.of theRockyMountainRegion,1877.
Hall, J.L., S.C. Solomon,and J.W. Head, Lunar floor-fracturedcraters:
evidencefor viscousrelaxationof cratertopography,
J. Geophys.
(abstract),Eos Trans. AGU, 62,396, 1981.
Solomon,S.C., Mare volcanismandlunar crustalstructure,
Proc. Lunar
Sci.Conf.,6th, 1021-1042,1975.
Spudis,P.D., TheGeologyofMulti-RingImpactBasins,Cambridge
Univ.
Press,New York, 1993.
Tullis,J., andR.A. Yund,Hydrolyticweakening
of quartzaggregates:
The effectsof waterandpressure
on recovery,Geophys.Res.Left.,
16, 1343-1346, 1989.
Whiffor&Stark,J.L., Intemal originfor lunar filled cratersandthe
maria?,Nature, 248, 573-575, 1974.
Wichman,R.W., Post-lmpact
Modificationof CratersandMulti-Ring
Basinson theEarthandMoonby Volcanism
andLithospheric
Failure,
Ph.D. thesis,Brown Univ., Providence,R.I., 1993.
Wichman,R.W., andP.H. Schultz,Igneousintrusionmodelsfor floor
fracturingin lunarcraters(abstract),
LunarPlanet.Sci.Conf, 22,
1501-1502, 1991.
Wilhelms,D.E., The geologichistoryof theMoon,U.S.Geol.Surv.Prof.
Pap., 1348, 1987.
Wilhelms,D.E., V.R. Obed•eck,andH.R. Aggarwal,Size-frequency
distributions
of primaryandsecondary
lunarimpactcraters,
Proc.
LunarPlanet.Sci. Conf.,9th,3735-3762,1978.
Young,R.A., Lunarvolcanism:
fracturepauemsandrillesin marginal
premarecraters,Apollo 16 Prelim.Sci.Rep.,NASASpec.Publ.,SP315, 29-89 - 29-90, 1972.
Zuber,M.T., D.E. Smith,F.G. Lemoine,andG.A. Neumann,
The shape
andintemal structureof the Moon from the Clementinemission,
Science,266, 1839-1843, 1994.
Res.,86, 9537-9552, 1981.
Head,J.W.,andL. Wilson,Lunarmarevolcanism:
Stratigraphy,
eruption conditionsandtheevolutionof secondary
crusts,Geochim.
Cosmochim.Acta, 56, 2155-2175, 1992.
Jaeger,J.C., andN.G.W. Cook,Fundamentals
of RockMechanics,3rd
ed., ChapmanandHall, New York, 1979.
Johnson,
A.M., andD.P. Pollard,Mechanicsof growthof somelaccolithic intmsionsin theHenryMountains,Utah,I, Field observations,
Gilbert'smodel,physicalproperties
andflow of magma,
Tectonophysics,
18, 261-309, 1973.
P.H. Schultz,Departmentof GeologicalSciences,
BrownUniversity,
Providence,RI 02912
R. W. Wichman,Department
of SpaceStudies,Universityof North
Dakota,GrandForks,ND 58202-9008.(e-mail:[email protected].
edu)
(ReceivedFebruary14, 1995; revisedJuly26, 1995;
accepted
July27 1995.)

fractured craters in Mare Smythii and west of Oceanus Procellarum

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