JOURNAL OF GEOPHYSICALRESEARCH,VOL. 90, NO. B5, PAGES 3701-3732,APRIL 10, 1985
ClusteredImpacts' Experimentsand Implications
PETER H. SCHULTZ
Lunar and Planetary Institute, Houston, Texas
DONALD
.E. GAULT
Murphys Centerof Planetology,Murphys, California
Impact by clustersof projectilesrather than a single projectile can result from several processes'
atmosphericbreakup,tidal breakup, and ejectafrom a large primary impact. Experimentshave been
performedin order to establishthe characteristics
of sucheventsover a wide rangeof impact velocities
(15 m/s to 6 km/s). At very low impact velocities(15-200 m/s), clusteredimpacts were produced by
launchinga groupedprojectilesof aluminumshot,steelshot,iron filings,and sand.At moderateto high
velocities(0.8-6 km/s), pyrex sphereswereshatteredabovethe target during passagethroughaluminum
foil or paper,therebyforminga well-definedclusterof fragmentsof overallradiusre.The ratio of the overall
radiusrcof theclusterto theradiusrsof a solidimpactorof thesamemassprovidesa measureof thecluster
dispersion.Sandand compactedpumicetargetswereusedin orderto comparequalitativelythe additional
effectof slightdifferencesin target strength.The experimentsreveal marked contrastsbetweenimpacts
by clustersof projectilesand impactsby a singlesolid body. "Tight" clusters(r•/r.• < 3) displacea factor
of 2 lessthan a singleimpactorof the samemass,"open"clusters(r•/rs -9) displacea factor of 5 lessmass,
and "dispersed"clu_sters
(r•/rs > 20) displacea factor of 10lessmass.This reductionin crateringefficiency
islargelyexpressed
asa shallowcraterwith an aspectratio (diameter/depth)aslargeas30 for openclusters.
The sizeand velocityof the cluster(as well as the densityand strength•ontrast betweenthe impactor and
target)can dramaticallyaffectcrater morphology.Open clustersimpactingcompactedpumiceproducea
flat, hummockyfloorwith an incipientmultiringpattern,whereasa tightclusterimpactingthesametarget
producesa centralfloor mound. Oblique impactsby symmetricalclustersform a characteristicarray of
V-shapedridgespointinguprange.The apex angleof the ridgesdependson the clusterdispersionand
impact angle.Inventoriesof postimpactprojectilematerial revealthat the projectileis largely retainedon
the surfaceand spreaddownrangefrom the impact direction.The amount of projectilematerial retained
on the surfacesincreaseswith decreasingimpact angle(from the horizontal) and with increasingstrength
of the target relativeto the projectile.Clusteredimpact cratersand lunar secondarycratersbear striking
similaritiesovera broad rangeof morphologicfeatures.On this basisand on the basisof reasonablemodels
of ejectacurtain structure,we suggestthat theseexperimentsprovide new cluesfor understandingejecta
emplacementaroundlarge lunar impact craters.When the ejectacurtain around large impactsis viewed
as a thick wall of debris and clusteredimpactorsare viewed as a unit sectionof such a curtain, then
experimentalresultsindicate that the continuousejectafacieseven for lunar craterslarger than 100 km
couldcontainas much as 90% primary material. Sucha conclusioncontrastswith many existingmodels
that derivemixingratiosimplicitly basedon single,noninteractingimpact events.Beyondthe continuous
ejectafacies,impactingclustersof ejectaprovide a physicalbasisfor understandingthe wide variety of
secondarymorphologiesand the large rangein spectralsignaturesof primaYymaterial in crater rays.
1.
INTRODUCTION
Previous studies of the impact process generally have
considered
the effectsof a singleprojectile.Impactsby clusters
of projectiles,however,shouldoccurunder a.variety o!
conditions.The atmospheres
of Mars, Earth, and Venushave
been shownto fragment meteoroldsbelow a certain size
focuseson the latter process. Although there are obvious
implicationsand applicationsto high-velocityevents, these
aspectswill be treated in a subsequentcontribution.
Secondarycraterprocesses
generallyhavebeencalibratedby
single-bodyor two-bodyimpactsinto relativelyhomogeneous
quartz-sandtargets[Oberbeck, 1975;Oberbeckand Morrison,
1974; Oberbecket al., 1975]. Such studieshave clearly shown
that the excavatedmassgreatlyexceedsthe impactingmassby
a factor of 200 at laboratory scales;thereforesecondarycrater
ejecta should be dominated by local rather than transported
material [Oberbeck 1975; Oberbecket el., 1975]. H6rz et el.
[ 1977,1983]and Hiirz [ 1982]haveexamineddepositsof the 26-
dependent
on thestrength
andvelocityof theobject[Baldwin
and Schaeffer,1971; Tauberand Kirk, 1976;Passeyand
Melosh, 1980;and Melosh, 1981].The impactby suchhighvelocityclustered
objects
mightaccount
for unusual
terrestrial
craters[Roddy,1976;Melosh,1981;Lambert,1982],thereby
havingimplications
for understanding
craterson otherplanets km-diameter terrestrial Ries crater in detail and also have
[Melosh, 1981; Schultzand Gault, 1983]. Low-velocity emphasized the important role of secondary cratering.
clusteredimpactsalsomay characterize
secondary
cratering However, severalcontradictory observationsto single-body
processes
[Schultzet al., 1980].The presentcontribution secondarycrateringand theoreticalconsiderationssuggestthat
someenigmasremain.First, possibleballisticallytransporte
d
•Nowat Department
of Geological
Sciences;
BrownUniversity, materialscan be identified in secondarycratersassociatedwith
Providence,Rhode Island.
impactbasins[Schultzand MendenhaH,1979]and in spectral
signaturesof crater rays [Saunderset al., 1976] at distances
Copyright
1985bytheAmerican
Geophysical
Union.
where locally excavatedmaterial should dominate the signature. The latter observationhas been more recentlyconfirmed
Paper number4B1375.
by spectraldatafor ejectafrom Copernicus[Pieterset al., 1982].
0148-0227
/ 85/ 004B-1375505.00
3701
3702
SCHULTZAND GAULT:CLUSTEREDIMPACTS
4.0
i
I
Preliminary laboratory experiments have indicated that
clusteredimpactscan significantlyreducecraterefficiencyand
can affect crater morphology[Schultz and Mendenhall, 1979;
Schultzet al., 1980;Schultz,1981].The presentpaperreports
l
%*-0
these results in more detail. We divide our discussion into six
3.0
•
sections.Sections2-5 consideronly the experimentalresults,
includingexperimentalprocedure,crateringefficiency,crater
morphology, and ejecta dynamics. Section 6 focuseson the
relevanceandpossibleimplicationsof the resultsfor planetary-
•ooø- •_SAND
o•
2.0
scale processesthat are then summarized in the conclusion
Ottawa Flint Shot (Schmidt, 1980)
No.
140-2•
section.
Sand
Compacted Pumice
2.
1.0
-9
I
I
I
EXPERIMENTAL
PROCEDURE
Three differentapproaches
were usedto producemultiple
impacts: rocket-launchedshot, air gun launched shot, and
of a brittle projectile
Fig. 1. Crateringefficiency(M/m = displaced
mass/projectile
mass) clusteredfragmentsproducedby passage
asa functionof thegravity-scaled
dimensionless
parameter(•r2= 3.22 througha thin diaphragm.The first two approaches
permitted
gr/v2,where
gisthegravitational
acceleration,
r istheprojectile
radius, sampling the distribution of projectile material; the last
and v is the impactvelocity)for sandand compactedpumicetargets.
approachprovided a more controlledcluster of impacting
Leastsquares
fits to the datagivelog (M/m) = -0.45 log •r2-0.172 for
-8
-7
-6
-5
LOG %
fragments.
sandand log (M/m) = - 0.518log •r2 - 1.0162for pumice.
Second,dark crater rays crossinglight and dark units on both
the moon and Ganymede indicate that locally excavated
material may not completely mask ballistically transported
material [Schultz, 1976; Poscolieriand Schultz, 1980]. Third,
theoreticalconsiderationssuggestthat the mediansizeof ejecta
is not simplyproportionalto cratersizeowingto both the peak
shockhistory and the long residencetime in the craterprior to
excavation [Schultz and Mendell, 1978; Schultz et al., 1981].
Both factors increasecomminution and may contributeto the
very nonblockycharacterof ejectaaround lunar craterslarger
than about2 km in diameter[Schultzand Mendell, 1978].Thus
crater ejectamay be composedof swarmsand clumpsof fine
debrisin additionto (or ratherthan) largeindividualfragments.
I
shapedsabot,therebyreleasing
the projectiles.
The velocityof
impactwasdeterminedby an industrialstrobeilluminatingthe
projectiles
in a time-exposed
photograph.Thissetupproduced
impactvelocities
rangingfrom 15to 20 m/s. Thetargetmaterial
was no. 24 moist sand (i.e., sand passedthrough a no. 24
standardsievewith 70%of thegrainssmallerthan0.5 mtn).The
moistureresultedfrom ambient atmosphericconditionsand
clearlyaffectedthe cohesion,internalfriction, and densityof
the target material. No effort was made to characterize these
targetproperties.The multipleprojectilesincludedfine quartz
sand,steelshot(0.45 cm in diameter),and glassshot(1.0 cm in
I
ALUMINUM
"o
The rocket-launched
impactsformedthe exploratoryphase
of this effort. A solid fuel model rocket enginewas launched
verticallydownwardalongguidewiresfrom a heightof 12 m.
About 1 m abovethe target, a barrier stoppedthe rocket and
I
I
PROJECTILE
DIFFERENT
TARGETS
Pb-shot
target
(6.0)
PROJECTILE
@
(DENSITY)
hollo• nylon sphere (0 087)
)l( nylon(2 1)
z•.• target
(1.6)
Glass-shot
pyrex
(22)
ß
alum,num (2 8)
ß
steel (6 2)
ß
cadmium (6 9)
PUMICE
TARGET
•
DIFFERENT
PROJECTILES
@@
-9
-8
-7
-6
-5
LOG •r2
Fig.2. Crateringefficiency
for differentprojectile/target
densityratios.Thedensitycontrastbetween
projectile
andtarget
haslittle effecton the scalingrelationsfor impactsinto differentdensitytargetsor differentdensityprojectiles
into thesame
target.Densityisgivenin gramspercubiccentimeter.
Thecompacted
pumice
targethasa density
about1.28g/cm3.Least
squaresfit for pumicedata giveslog (M/m) = - 0.539 log •r2-1.243.
SCHULTZAND GAULT: CLUSTEREDIMPACTS
3703
diameter)with total launchedmassrangingfrom 58 to 72 g. For
comparison, solid body impacts were also made. These
projectiles were thin-walled oblate spheroids containing
albumen (eggs, 4.5 x 5.8 cm) with temperature-controlled
IMPACTING
solid
BODIES
clustered
viscosities.
All impactsweremadeu.nder ambientatmospheric
,mpact angle
ß
vertical
(90
ø)
©
oblique (60*)
0
obhque
(45*)
conditions.
The secondand third approachesutilized the NASA Ames
Vertical Gun Range (AVGR) facility [seeGault and Wedekind,
1978].For lowerimpactvelocities(50-200 m/s), compressed
air
(up to 21 bars) was usedto launcha 4.7-cm-diameterpolyethelenesabot. Total launch sabot massranged from 75 to 160 g,
but the releasedimpactor massranged from 8 to 116 g. Holes
nearthe end of the air gun launchtube and deflectorsredirected
and dispersedescapedcompressedair behind the sabot. This
designpreventedinteraction betweenthe cratering event and
compressed
air, asconfirmedin thefilm records.The projectiles
were launchedat variousimpact anglesinto no. 40 sand(sand
smaller than 420/am) in the 2.4-m-diameter vacuum chamber
of the AVGR. Clustered projectiles included 0.318-cmdiameter aluminum shot, 0.159-cm-diameter steel shot, iron
filings, sand, and sand-water mixtures. Solid body projectiles
included solid nylon spheres, hollow nylon spheres, and
puttylike material. Projectile velocity measurements,cluster
dispersions,and kinetic energydistributionswere determined
from high frame rate movies (8000 frames/s). Becausethis
launch technique resulted in a range of impact velocities by
individual projectileswithin a given cluster, the sum of the
kineticenergyof the clusterhadto bedeterminedby the number
of individual projectilesimpactingat velocitiesmeasuredfrom
the high frame rate movies.An effectivevelocityof the cluster
was then determined
from
this measured
cumulative
i
i
i
i
ß solid body • =2 8
ß hollow aluminum
6 =0 59
@ hollow nylon • =0 09
0 cluslered impac!
(.) effechve solid body
3.0
-
_
(')•o
•o
6,=0.06
_
i
I
-8.0
I
i
-7.0
I
I
-6.0
I
I
-5.0
,1
I
-4.0
3ß.............. -•o•
2,
-9
•,._e':::::::::::::-:.-_:?_.,o
•
•
i
-8
i
-7
-6
I
-5
•
,,
-'
LOG •r2
Fig. 4. The effectof obliqueimpact angleson the crateringefficiency
of clusteredimpacts by broken pyrex into pumice. As in Figure 3,
arrows
indicate
change
in•r2if thecluster
radius
(rattler
thantheradius
of an equivalent masssolid body) is used. The 1-6 (830540, 830539,
830534, 830536, 830531)indicate ranking of clusterradius. Increasing
numbersindicateincreasingclusterradius(correspondingto decreasing
clusterdensity):0.8, 2.4, 2.8, 3.8, 5.4, and 8 cm, respectively,for data
points 1-6. Data points7 (830541) and 8 (830546)correspondto solid
pyrex and nylon spheres,respectively,whereasdata points9 (830549)
and 10(830548)representhollownylonspheres.Obliqueimpact(point
5) by a very low densityclusteris more efficientthan a vertical impact
(point 6) owing to the greaterinterfragmentspacing.This effect does
not occur for 45ø impacts 2 and 4 since the interfragment spacing
remains close enough that individual fragments do not dominate
excavation.Impact anglesat 30ø resultin surfacerougheningwithout
a measureableor meaningfuldisplacedmassratio. The line represents
the best fit to the data shown in Figure 2.
kinetic
energyand the impactor mass.
The third techniqueusedthe AVGR powder and two-stage
light-gasguns. The powder gun provided launch velocities
between 1 and 2 km/s, whereas the light-gas gun produced
velocitiesabove4 km/s. Pyrex projectileswereshatteredduring
4.0
2• •---'L--•------22'•o--"•©
1
-3.0
LOG •r2
Fig. 3. Cratering efficienciesfor low-densityand clusteredimpacts
into no. 40-120 sandcomparedwith solid body impactsas shownin
Figure 1. Low-densityimpactsby hollowaluminumprojectiles(0.59 g/
cm3) showlittle variationfrom singleimpactor.Very low-density
impactsby hollow nylon projectilesand clusteredprojectiles,however,
are consistentlyless efficient than single-bodyimpacts. Although
clusteredimpacts are about 5 times less efficient than single-body
impactsof the samemass,incorporationof the clusterradiusinto the
dimensionlessscaling parameter •r2 moves the data closer to the
nominal single-impactorrelation. The effective cluster density /5eis
givenin gramsper cubiccentimeter.The line correspondsto the best
fit for the data shownonly in Figure 1 for sand.
passagethrough paper (2.5 mil) or aluminumfoil (1 mil).
Groovesin the launchbarrel spinthe sabot,therebyseparating
the sabotand projectileduringlaunch;consequently,
this spin
disperses
thefragmentsafterbreakupbycentrifugalforce.Two
differentpowdergun barrelsprovideda 1:25.4and 1:33twist
(revolution:distance
in centimeters).The light-gasgun barrel
has a 1:91.4 twist. Increaseddistancebetween the paper/foil
and target increased the lateral dispersion of the pyrex
fragments.High frame rate cameras(10,000 frames/s) recorded
the dispersion at impact and provided images of cluster
configurationsfor velocitieslessthan 1.6 km/s. Additionally,
in separatetests,aluminum witnessplatesrecordedthe lateral
dispersion at impact and revealed the size and spatial
distribution of the cluster fragments.Impact velocitieswere
determinedfrom the preruptureprojectilevelocitiesestablished
by sequentialbreakingof photobeams.Comparisonsbetween
prerupturevelocitiesandthe cloudof fragmentsrecordedin the
high frame rate moviesindicate that the passagethrough the
thin foil reducesthe impact velocityby lessthan 10%.Appendix
A providesfurther discussionof the velocity,spatialdispersion,
and size distribution of fragments produced by this launch
technique.
3.
CRATERING
EFFICIENCY
3.1. Effect of Projectile and Target Density
The resultsof clusteredimpactsmustbe placedin the context
of single-body impacts for the same impact conditions.
Consequently,this sectionconsiderscratering efficiencyas a
function of a dimensionlessparameterrelated to projectilesize
3704
3.0
SCHULTZAND GAULT: CLUSTEREDIMPACTS
i
I
i
,
IMPACTING
BODIES
SOLID
,
solid
clustered
CLUSTERED
,,
impact angle
tures from A1 projectiles impacting sand. Figures I and 2
together demonstrate that marked departures of cratering
efficiencyfor clusteredimpactsrelativeto singleeventsmustbe
viewed in terms of fundamental differencesin the impact
• ß vertical
(90
ø)
O
oblique (45 ø)
A
oblique(30ø)
processand/or the effect of projectile configuration(e.g.,
I•
oblique (15 ø)
diameterto length ratio of projectilecluster).
3.2.
ClusteredImpacts and Cratering Efficiency
For purposesof discussion,clusteredimpactsare arbitrarily
groupedaccordingto the maximum lateral dimensionrcof the
ensembleof projectilesrelative to the radius rs of a single
projectileof the same massand density."Tight" clustersare
-6.0
-5.0
-4.0
-3.0
-2.0
definedhere for clusterswhererc/rs< 3, "open"clustersfor 3
LOG •rz
< re/rs< 10, and "dispersed"clustersfor r•/rs > 10. Appendix A
Fig. 5. The effectof obliqueimpactangleson thecrateringefficiency
of clusteredimpacts(aluminumand steelshot)into sand.The general summarizeshow rc is determined.Figure 3 showsthat vertical
trendsobservedin Figure4 for higherimpactvelocitiesinto pumiceis impacts by an open cluster of pyrex fragments into sand
also observedhere. Data in parentheses
indicatehigher-densitysteel consistently
displaceabout a factor of 5 lessmassthan a singleshotand longejectaclouds.The dashedline represents
the bestfit to
body impact of the same mass. Becausethe independent
the data shownin Figure 3.
variable•r: includesthe projectileradius,the appropriate•r: for
a clusteredimpact shouldincludethe observedradiusreof the
ensembleof fragments.Such an approachviewsthe impacting
and impact velocity, as discussedby Schmidt and Holsapple clustersas a singlebut low-densityprojectile, an assumption
[ 1980].First, we establishsuchrelationsfor the targetsusedin frequentlyusedin theoreticalsimulationsof the sameproblem
clustered-impact
experiments.Second,we examinethe effects [e.g., O'Keefeand Ahrens, 1982].This approachalsoillustrates
of different target and projectile densities on cratering that very early time complexitiesassociatedwith individual
efficiency.
fragmentsimpactingnearlysimultaneously
arelostat late times
Schmidt
andHolsapple
[1980]andHolsapple
andSchmidt in crater growth, for sufficientlyclosely spacedfragments.
[1982] suggested
that a setof dimensionless
parametersdefines Figure 3 showsthat usingthe overallclusterradiusbringsthe
dependent and independent variables controlling impact datafor clusteredimpactscloseto the nominal•r2efficiencyline
cratering.Of interesthereis the relation betweenthe dependent for single-bodyimpactsof the samemass.It shouldbe noted
1.0 -
variablesof crateringefficiencydefinedas the ratio between
displacedmassM and projectilemassm and the independent
variable •r2calledthe gravity-scaledsizedefinedas
-3.0
i
i
1
•r2= 3.22gr/v•
where g is the gravitational acceleration,r is the projectile
radius, and v is velocity.The displacedmassis definedby the
product of bulk target densityand the measuredvolumeof the
crater referencedto the preimpactsurface.Gault and Wedekind
[ 1977]pointedout that a singlefunctionalrelationmay not be
c6rrectover an extendedvelocityrange,but it is usedherefor
convenience.Also of interestis the ratio betweentarget •txand
projectiledensitytip.
Figure I showsthe •r2 efficiencyrelation for two different
targetsof no. 140-200sand(i.e., sandgrainswith sizesbetween
105 pm and 149/•m that will passthrougha no. 140sievemesh
but will be retained in a no. 120 sievemesh), and compacted
pumice (finer than 105 /•m) from Mono Craters, California.
The slightlydifferentslopesfor thesematerialsprobablyreflect
the different angles of internal friction and cohesion.These
differencesare of no further applicationhereexceptto provide
a qualitative effect of different strength targets. Appendix
Tables BI-B3 provide the detailed impact conditionsfor the
data shownin Figure 1.
Figure2 confirmsthe preliminaryconclusions
of Schmidtet
al. [1979] and Schmidt[1980] that projectileor target density
haslittle, if any, effect on crateringefficiency.Projectileswith
densities
ranging
from0.087to6.9g/cm3impacted
intopumice
showedno consistentor significantdeparturefrom projectiles
of a singledensityimpactedinto the sametarget. Likewise,
impactsby projectilesof one densityinto targetswith densities
ranging
from0.47to 0.8g/cm3showed
nosignificant
depar-
2.0
6 • 09
1.0
-
ß HIGH-STRE
NGT•
• CLUSTERED
IMPACTS
23
"•'•"
o LOW-STRENGTH
MOIST
0.0
-6.0
-5.0
-4.0
SAND
-3.0
-•.0
LOG •r2
Fig. 6. Comparisonof crateringefficienciesfor clusteredand weak
bodiesimpactingverticallyinto no. 40 sand,moistsand,andcompacted
pumice at low velocities(20-200 m/s). The •r2 term for clustered
impactsincludestheclusterradiusratherthanthe equivalentsolidbody
radiusof the samemass.Numbereddatacorrespondto projectileswith
differentstrengths.Data points 1 (3031) and 2 (4445)representthinwalledoblatespheroidswith low and highviscosity,respectively.
Point
3 (5152)indicatestightly clusteredsandand 4 (3940)represents
a solid,
competentimpactorof the samesize.At very low velocities(<20 m/s),
impactsinto moistsandshowno changein crateringefficiency.Point
5 (830546)representsa solid nylon impactor,whereas6 (830548)and
7 (830549)indicatehollownylonspheres
impactingcompactedpumice.
Data points8 (830602)and 9 (830601)correspondto sand-embedded
plaster and a puttylike plastic impactingthe sametarget. Projectiles
that were deformedat impact tend to have slightlyhigher cratering
efficiencies
relativeto the undeformednylon impactors.
SCHULTZ AND GAULT: CLUSTERED IMPACTS
3705
that Figure3 includesdata from a varietyof launchtechniques projectilesand projectiles
filled with hardenedplasterof Paris
and fragment characteristics (aluminum shot, pyrex
(Figure6) produced
littlechangein crateringefficiency
at very
fragments).
low velocities(20 m/s).
Clusteredimpactsinto compactedpumice producecraters
The subsequentexperimentsat the AVGR providedaddivery similar to those in sand. Figure 4 includes results for
tionaldatafor fiveprojectiles
of contrasting
strengthimpacting
broken pyrex impactingat velocitiesfrom 1.3 to 2 km/s. For
compactedpumiceat higher velocities(---200m/s). The solid
vertical impacts the cratering efficiency is reduced as the
nylonprojectile(point5) wasundeformed
by theimpactandis
dispersion
is increasedevenaftercorrectingrr2for the observed consistent
with the efficiencies
resultingfrom hollow nylon
sizeof theclusterat impact.Highlydispersed
clusteredimpacts impactors
(points6 and7). Projectiles
thatunderwent
complete
(re/rp• 25) displacenearlyan order-of-magnitude
lessrelative disruptionareindicatedby points8 and9, bothof whichexhibit
massthan a solidbody projectileof the samemass.As discussed a slight increasein efficiency.Projectile8 was a mixture of
in Appendix A, sucha dispersioncan be approximatedas a plasterandsandthat wascompletelyshattered.Projectile9 was
cloudof debriswithan effective
densityof 1.9x 10-ng/cm3. a puttylikesphere("Ductseal")that was flattenedat impact
Correctionsfor sizesof suchdispersedclustersleavecratering with an insignificant
fraction(<0.1%) of the projectileejected
efficienciesreducedby a factor slightly lessthan 2 but are from the crater.As will be discussed
in the followingsection,
adequatefor openand tight clusterscorrespondingto effective the crater morphologiesproduced by plastically deformed
densities
greater
than10-3g/cm3.
impactors (putty and albumen) underwent fundamental
Figure4 alsoincludesdata for obliqueimpactsinto pumice. changes,eventhoughthe crateringefficiencywas relatively
For the samemassprojectile(sameprerupture radius) and the unaffected.
same impact velocity, oblique impacts result in reduced
4. CRATER MORPHOLOGY
crateringefficiencies.However, the displacedmassratios for
45ø and 60ø impactsappearto be slightlyhigher than vertical
The appearanceof cratersproducedby clusteredimpactors
impactswith the sameapproximateclusterdiameters.Such a
changes,
to first order, with the dispersionof the impacting
trend is reversedfor impactsat angleslessthan 45ø, but these
fragments.
In thissection,we first considera typicalexample
resultscouldnot be shownin Figure4 becausethe craterprofile
in orderto focuson relevantparameters.Second,we reviewthe
wasvery shallowand irregular.The slightincreasein cratering
betweenclusterdispersion
andcratermorphology
efficiencyfor 450-60ø impactsbut decreasebelow 45ø can be systematics
for
vertical
impacts.
Third,
we
look
at
obliqueangleimpacts
understood as a combination of the effects of fragment
which
have
relevance
for
planetary
secondarycratering
penetrationandeffectiveimpactarea.The effectiveimpactarea
Fourth, theseresultsare comparedwith impactsby
increases
asthe secantof the impactangle.However,penetra- processes.
The diameter-to-depth
tion depth and crateringefficiencydecreasewith decreasing singlebodieswith differentstrengths.
ratio,
rim
profile,
and
herringbone
patterns
are specifically
impact angle [Gault and Wedekind, 1978]. Eventually, the
discussed
because
such
parameters
may
provide
diagnostic
slightincreasein scouringactionwith smallerimpact anglesis
cluesfor impactson planetarysurfaces.
outweighedby the reduction in cratering efficiency due to
energy lost in ricocheted fractions. Figure 4 shows that
correctionsto rr2 using the observedcluster radius result in
4.1. Appearanceand Crater Profile
displacedmassratios evengreaterthan the nominal solid body
The differencein appearancebetweena singleimpactorand
projectilesfor the 60ø impact angles.
The effect of impact angle on crateringefficiencyin sand is clusteredimpactorsis easily recognizedin the stereoviews of
shown in Figure 5. These data representvery low velocity Figure 7. Both impactswere made under comparablecondiimpacts (100-200 m/s) of aluminum, steel shot, and water tionswith the only major differencebeingthe physicalstateof
impact. The resultsare similar to the more controlledimpact the projectile. Four major differencescan be identified. First,
conditionsillustratedin Figure4 for pumicewith the exceptions the shallowfloor of the clustered-impactcrater is surrounded
that higher-densityfragments(steelversusaluminum) and long by a ring depression.Such a profile is consistentlyformed for
wherere/rs> 10. The ring depressionresults
streams of material tend to result in greater net cratering clusterdispersions
in
a
subtle
multiring
pattern (Fig. 8). Second,the diameter-toefficiency.Thesedata are indicatedby parentheses.
depth ratio (aspect ratio) is clearly increasedfor clustered
impacts,and this observationwill be discussed
quantitativelyin
3.3. Projectile Strengthand Cratering Efficiency
a subsequentsection. Third, the raised rim for a clustered
A clusterof projectilescan be consideredas a body of zero impact appearsto be exaggeratedin relief relative to a solid
strength. Consequently, several exploratory low-velocity
bodyimpact.This exaggerationis partly the resultof the fourth
impactswere made with objectshaving different strengthsin
major difference:the thinning of ejectawith distancefrom the
order to seethe effecton crateringefficiencyand morphology. rim of a clusteredimpact is more rapid than that for a singleFigure 6 includesresultsfor thin-walledprojectilescontaining body impact. Such differencesare further illustratedin a crossalbumen (eggs) impacted into sand and different strength sectionedview of a clusteredimpact in Figure 8.
projectilesimpactingcompactedpumice.The former prelimiFigure 9 shows the effect of cluster dispersionon crater
nary seriespermitted changingprojectile strength simply by
morphology for vertical impacts into compactedpumice. As
heating, and the results provided impetus for the latter
intuitivelyexpected,the lessdispersedthe cluster,the deeperthe
experimentsat the AmesVertical Gun Range.The experiments crater. Perhapslessintuitive, however,is the sequencefrom a
with thin-walled impactorswere done under ambient atmos- pittedand hummockyfloor, with an incipientmultiringpattern
pheric conditionswith relatively high humidity. Such condi- to a moundedfloor. A singlefloor pit typicallyformsfor a lowtionsresultedin an increasein the angleof internal friction and velocity (<4 km/s) single-body impactor into compacted
cohesionrelative to dry sand, thereby decreasingcratering pumice.This sequence
is not simplythe resultof the largeangle
efficiency[see Schmidt, 1980]. Impacts by the albumen-filled of internalfriction characteristic
of pumice.Impactsinto sand
3706
SCHULTZ
ANDGAULT:
CLUSTERED
IMPACTS
Fig. 7a
.......
•.•...
%...,,,,•.., ;•...;?""":*"'•
,.'?--.,:
.•;.-5;:
...
ß
....-..
Fig. 7b
Fig.7. Stereo
views
ofclustered
(Figure
7a)andsingle-body
(Figure
7b)impacts
intocompacted
pumice.
Theclustered
impact
(830526)
inFigure
7awas
produced
bya0.635-cm
pyrex
sphere
ruptured
bypassage
through
thin(1.0mil)aluminum
foil.Impact
velocity
was1.77km/switha lateral
dispersion
of7.0cmatimpact.
Thecrater
hasa shallow,
flatfloorwith
a narrow
raised
rim(rim-rim
diameter
of 13.5cm).Beyond
therim,ejecta
areconcentrated
inradialandsubradial
spikes.
Thesmall
isolated
craters
were
produced
byunburned
powder
grains
anddidnotinterfere
withtheformation
oftheprincipal
impact.
Figure
7bshows
a crater
(820503)
produced
by2.01km/spyrex
sphere
0.635
cmindiameter.
Therim-rim
crater
diameter
is20cm.Thesingle-body
impact
produced
a deepcraterwitha broadrimanduniformly
distributed
ejecta.
produce
a similarsequence,
although
tightlyclustered
impacts
intosandproduce
cratersresembling
loosely
clustered
impacts
into pumice.Figure10illustrates
thispointfor two clustered
impacts
withnearlyidentical
dispersions
insandandin pumice.
The craterin pumicehasa shallowfloor encircled
by a moat,
featurenot observedby Quaideand Oberbeck[1968]. If a
tightly clusteredimpactexpendsmostof its energyand
momentumnearthe surface,then a grossanalogycan be made
betweenthe statichalf-buriedexplosivecrateringexperiments
and the resultspresentedhere.
whereasthe crater in sandhas a slightlymoundedfloor.
Fortson and Brown [1958] and Piekutowski [1975] have
experimentally
produceda similarvarietyof cratermorpholo- 4.2. Aspect Ratios
giesbyhalf-buried
explosions
in layeredsand,andQuaideand
To first order,both the shallowness
of the craterand the
Oberbeck[1968]producedsimilarmorphologies
by impacts
appear
todepend
onthedispersion
oftheclustered
into similar targets. Piekutowski's [1975] experiments, morphology
Cluster
dispersion
isrelated
totheeffective
density
however,produceda centralmoundevenin unlayeredsand,a impactors.
SCHULTZAND GAULT:CLUSTEREDIMPACTS
3707
.:.
...•...,•-.:.•-•:.
,-.::..,.c•.•.... •. ..':......:•
*::•:,..•:
½:'5:•::..•:•.;:•'•:•--.':•:
........
•::•:;':::
...
::.:• ' •'.Y
'• ................
:.•:..:.
-:.
........ ';-:%
•
"7::
":'-.
.. "'-':':
::.•.•
..
•......
........
ß
.;
•
' •:'•"
.....
::½.;::.
• .• ß;: ..;:.'.':::':
..-•'
•'-...*•:.•......
<:::....
-....
:":""::-•.•::'•
:½
...... ':•:77'"•."
-.-•-:•.
%-.•:?--:½;•:•;•?-..:.½:•:.•
.•:•.?;
.....'-:..'
-.....•v:-::..
' •d:<.;.....
.....
•.
•.-::•--•
:•.-•.•::.:•;;•.:..::...'.;...'::-.:'.'•
.•;•"•:•&•-•{•:%"":•:•.;
......'•'-...'"'-
: •,•'::•4::%:•'•::
.?"
'•:':':•-:•
•',:':•:•:•:•
..........
'" 7-•:.•-•'::'"•-:'..
ßß•.•.'.-• •7'••':•:.
•:• '.•':.d
:•'•:."•"";.•:..
• "i•..'•.......
::'.
....?
;::.•.•.:....•.•
:•::--•:.•:,:.:•;•;•.•.,•.---.,.....z•:.............:•::
•;.:•½•::•:•.
:•--...:...,.:•...',½:•;.•:•
--:.:.•-:;..
.•:..
:•.•:.•..:-.;:.- :-...:•:•..•.•.•;•-.-• %•-:•':
'.........
..•.
.........................
,..:•:;.::..:•
.....
.......•
.........................
•. .•......................
.......
•-•,..-•:•,,
'-----•
....':'::::•:'½•:'
,-:.-.•
........
•:•:',•.:-•,
..............
.........
':•:•':"'
........... "•:,•
'..........
$'"
•.... •:"•'"'•:'•'*:
"':'•: '"':"
'"'*'::;';
..............
'" ' ' "<':::'"'•"
;*½•:'"
•:'"•':"•* ...........
%;:::•':?':":•":
......::•::"%:)4•"
':'"•:•"
::':• .... '"
:':....;.;'
....'-•;•:",:.:,:...:.':;..•
...........
Fig.8. A cross-sectioned
viewof a hypervelocity
clustered
impactintocompacted
pumice.The0.635-cm-diameter
pyrex
sphere
wasshattered
duringpassage
through
a 2.5-milpieceofpaperandimpacted
witha velocity
of4.83km/sandcluster
dispersion
of8cm(821231).
Therim-rimdiameter
isabout17cm.Suchimpacts
produce
atypicalhummocky
floorcomposed
of compactedpumicesurroundedby a moat.
/J•,where the launch massis divided by an estimatedvolume of
the cluster at impact. As discussedin Appendix A, cluster
volume is determined from the observedlateral dispersion
recorded in the high frame rate photographs and from
aluminum witness plates placed at the target surface. Photographsof clustersin flight indicate a relatively sphericalshape,
therebyjustifyingan approximateexpressionof r3 for
calculating all cluster volumes. Figure 11 shows the relation
betweenthe aspectratio (diameter-to-depth)and the projectiletarget density ratio for both sand and pumice targets. Also
shownsymbolicallyare the crater morphologiesfor solid body
and clusteredimpacts.The aspectratio clearly increaseswith a
decreasingprojectile-target density ratio, but another inde-
4.3. EjectaDistributionand Rim Profile
Figures7-10 revealthat the morphologyof the crater rim
from clusteredimpactsappearsmore ridgelike than the rim
from single-bodyimpacts.This appearanceresultsfrom a very
rapid radial thinningof ejectathicknessdemonstratedboth in
the profiles of Figure l0 and in the transparency of the
preimpactsurfacetexture shownin Figures7a and 9.
Figure 14 showsthe normalizedejectadecaycurvesfor some
typical results of impacts into pumice and sand and clearly
revealsthat clusteredimpactsconcentratemost ejectanear the
crater. Such near-rim concentration of ejecta might be
explainedby the cumulativeeffectsof three processes.
First,
individual fragmentscomprisingan impacting cluster would
correlation.
produce small craters with limited ejecta distributions if
Clusteredimpactorscontrastwith single-bodyimpactorsnot isolated. A single-bodyimpact into sand typically has about
only becausethey have low effectivedensitiesbut alsobecause 2/3 of the total ejectedmasswithin two craterradii of the rim
[StOffler et al., 1975]. If a clusteredimpact is viewed as an
the time betweenfirst and last arrival of the impactor cloud can
be appreciable.Sincethe poorestfitting data in Figure 11 tend ensemble of individual fragments, the collective ejecta
to havethehighestandlowestimpactvelocities,bothprojectile- distribution should be more restrictedin range. Such a view,
targetinteractiontime and densitycontrastmay be important. however, is a gross oversimplificationsince the integrated
The time for the projectileto completecontactwith the target crateringefficiencyfor all individualfragmentsfar exceedsthe
is simplythe projectilediameterdividedby the impactvelocity. observedcrateringefficiencyof theclusteredimpact;indeed,it
Figure 12 showsthat inclusionof this variable significantly would exceedthe crateringefficiencyof a single-bodyimpact
decreasesthe scatterfor clusteredimpacts.Moreover, similar of the same total mass. Nevertheless,such a view provides a
crater morphologiesnow occupywell-defined domains in limitingcase.Second,theshockandrarefactionwavesresulting
contrastwith Figure 11. Impacts by single-bodyobjectsinto from clusteredimpactorsare muchmorecomplicatedthan the
pumice(Figure 12a)exhibit nearlyconstantaspectratioswith wavesfrom a singleimpactor. Interactionsmay significantly
reduce the total energy expended in excavation and ejecta
the exception of the very weak projectile (i.e., puttylike
impactor)and the hollow nylonspheres.Thesetwo exceptions deposition.Third, the multipleinteractionsamongejectafrom
closelymatchthe relationestablished
for clusteredimpactors. the crater of each fragment in the clusterresultsin a random
Impacts by weak or hollow projectilesinto sand also can be distributionof ejectawith a net upwardbulk trajectorythereby
accommodated
(Figure 12b). Figure 13 illustratesa variety of resemblingan adiabaticallyexpandinggascloud.At late times
crater morphologiesand profilesthat resultfrom single-body (crater is •80% complete),the classicalinverted cone-shaped
impactorsof different strengths.Although flat-floored craters ejectacurtaindevelops,but lessejectacomprisethe upperejecta
are not produced, mounded-floor geometries are evident. curtaindueto earlytimeinteractionsof the high-velocityejecta.
The changein craterdimensionswith clusterdispersionis
Postimpactexcavationsrevealthat moundsare not the result
of accumulationsof projectilematerial on top or beneaththe illustratedin Figure 15. Low-velocityimpacts(150-200 m/s)
surface.
with about the samekineticenergyproducedeepercavitiesand
pendent variable seems to be required to improve the
3708
SCHULTZAND GAULT: CLUSTEREDIMPACTS
:. •
ß:
..........
• ---4,•
......•:•:•--.-.-•
::::.,•..:•?.,>:
.•c•i•.;:::.,•.•..,•!:•.%½,,:•:•.::•,,•,,.?..•?•:•.:-.•:.•:v•,,•:•:•,.•
-.... :••••
Fig. 9a
Fig. 9. The effectof impactordispersionon cratermorphologyfor high-velocity(Figure 9a) and low-velocity(Figure 9b)
impacts.Each crater was producedby 0.635-cmpyrex spherethat rupturedby passagethrough2.5-mil paper. In Figure
9a the top example (821231) resultedfrom a 4.83 km/s impact into compactedpumicewith a lateral dispersionof 8 cm;
the middle example (821225) with a 1.8-cmspreadat 4.23 km/s; and the bottom example(821226) with a 1.5-cmspread
at 4.06 km! s. As clusterdispersiondecreases,
the craterfloor area reduceswith a changefrom an incipientmultiringprofile
to a mounded floor. In Figure 9b a similar changein morphologyoccursfor low-velocityimpacts(<2 km!s) as cluster
dispersiondecreases.The example at top (830531) representsa 1.5 km/s impact with a dispersionof 16.0 cm; the middle
example(830526),a 1.77km! s impactwith a 7.0-cmdispersion;and the bottomexample(830534),a 1.45km! s impactwith
a 5.5-cm dispersion.The moundedfloor of the 1.8-cmdispersionhigh-velocityimpact and the 5.5-cmdispersionlow-velocity
impact is similar, therebysuggesting
that velocityas well aseffectiveimpactordensityis important. Accompanyingprofiles
are scaledsuchthat apparent crater diametersare the samewith a factor of 2 vertical exaggeration.
higher rims with decreasingclusterdispersion(i.e., increasing
effectivedensity).Crater diameter, however,remainsapproximately constant, although very dispersedclustersproduce
larger diameters. High-velocity (4.0-4.8 km/s) impacts
apparentlyhavea differenttrend. Both craterdiameterand rim
height remain essentiallyconstant, whereasthe crater depth
increaseswith decreasingclusterdispersion.In otherwords,the
aspect ratio dramatically decreaseswith decreasingcluster
dispersion,but the rim height remainsnearly constant.Future
experimentswill be performed to confirm thesetrends and to
pointswhereejectadynamicsand distributionof projectile
explore the cause.
materials are considered.
Suchapparentlycontradictoryresultssuggesta possible
differencein impactphysicsfor low and high-velocity
events.
Low-velocityimpactsdisplaceconsiderable
targetmaterialby
compression,
whereashigh-velocityimpactsproduceshock/
rarefractionwaves,comminution,
andwasteheatreflectingthe
transfer of kinetic energy. Discussionsabove noted that
clustered
impactssignificantlyalterthehighervelocityfractions
of ejectathroughinteractingrarefractionwavesandinterejecta
collisions. Discussions below will elaborate further on these
SCHULTZ AND GAULT: CLUSTERED IMPACTS
3709
Fig. 9b
4.4.
$poked and Herringbone Patterns
A feature common to all low-velocityclusteredimpacts at
normal incidenceis the developmentof a spiked pattern of
ridgesextendingradially and subradiallyfrom the crater rim.
High-velocityclusteredimpactsdo not producethis pattern.
The number of spokesdo not appearto dependon the number
of impactingfragmentsin the cluster.Thousandsof fragments
produceabout 20 well-definedspokes.High frame rate movies
revealthat the spokesresultfrom filamentary stringsof ejecta
that developat relativelylate times(seebelow).
For nonverticalimpacts(Figure 16) the spokesform acute
anglesdirecteddown range,therebyresemblingthe "herringbone" pattern of secondaryimpactson the moon. Figure 17a
illustrates the systematicchange in this pattern and crater
profile with impact angle,and Figure 17b illustratesthe effect
of cluster dispersion. Six distinctive features are observed.
First, the herringbonepattern generallysubtendssmallerapex
angles with smaller impact angle. Second, the herringbone
pattern commonlybendsdownrangewith increasingdistance
from thecraterrim. Third, thezoneof maximumejectadeposits
forms a downrangefan for modestimpact angles(<60ø from
the horizontal)that doesnot occurfor singleimpactorsexcept
for very low (<10ø) impact anglesas shown by Gault and
Wedekind[1977]. Fourth, little ejectaare depositeduprange
even at modestimpact angles(<60ø). Highly oblique (<15ø)
single-bodyimpactorsproduceasymmetricbutterfly wing
ejectapatternswith little ejectain the uprangeand downrange
(except for the fan) directions. Fifth, the crater rim becomes
pronounced downrange and eventually absent uprange as
cluster dispersion increases, and sixth, the crater floor is
asymmetricwith the deepestportionoccurringuprange.Both
of theselatter featuresalso occur for singleimpactorsbut
requiremuchlowerimpactangles[Gaultand Wedekind,1977].
The progressivechangein crater morphologywith cluster
dispersionis shownin Figure 17band underscoresthe contrast
betweensingleand multiple impactors.
Figure18quantifiesthesystematic
changein theherringbone
pattern with impact anglefor two differenttypesof clustered
impacts.For low-velocity(100 m! s) aluminumshotin sand,the
3710
SCHULTZ
ANDGAULT:CLUSTERED
IMPACTS
Fig. lea
Fig. 10b
Fig. le. Profilesof cratersproduced
by clustered
pyrexfragments
impacting
at highvelocity(Figurelea) andlowvelocity
(Figure10b)intocompacted
pumiceandno. 140-200sand.In Figurelea theupperprofile(821231)resulted
fromanimpact
at 4.8 km/s with a dispersion
of 8 cminto compacted
pumice,whereasthelowerprofile(830203)resultedfrom an impact
at 4.35km/s withidenticaldispersion
intosand.In Figure10btheupperprofile(830526)resulted
from 1.77km/s impact
witha 7.e-cmdispersion
into compacted
pumice,whereas
thelowerprofile(830608)resulted
froma 1.6km/s impactwith
an 8.5-cmdispersion
intosand.Compacted
pumicehasgreatercompressive
andshearstrength
thansand,therebyproducing
a differentmorphology.
The high-velocity
impactsinto eithercompacted
pumiceor sandtendto producemoundedcrater
floorsfor the samedispersion
at impact.The craterprofilesare scaledsuchthat the apparentdiameteris the samewith no
vertical exaggeration.
apex angle of the principal herringboneridge decreasesfrom
near 45ø to near 30ø as the impact angledecreases
from 45ø to
30ø (from the horizontal). The higher-velocity (1.5 km/s)
broken pyrex impacts into pumice produce the same trend.
Figure 17 showsthat at a 30ø impact angle,the brokenpyrex
3.0
I
clusterdoesnot form major herringboneridgesbut doesform
a thick fan zone, which may be equivalent.Minor ridges,
however, do extend from the rim with large apex angles.
Additionally, Figure 18 indicatesthat the uprangezone of
ejectaavoidancegenerallybecomeswider (i.e., the apex angle
I
I
1
CRATER
PUMICE
]
PROJECTILE MORPHOLOGY
ß solid
2.0
+ central
pit
©
clustered
¸
bowl-shaped
G
hollow
•
centralmound
--
v•4 km/s
r-q "fiat" floor
A•
1.0
I
i
-3
-2
I
1
-1
0
LOG
Fj•.
2.0
I
i
i
I
B
II
-4
-3
-2 LOG(6n,
6,) '1
0
1.0
Fig. 1lb
Fig. 11. The effectof projectile/target
densityratio on theaspectratio andmorphologyof impactsinto compacted
pumice
(Figure1la) andsand(Figure1lb). Theaspectratio(diameter/depth
-- D/d) decreases
for clustered
impactsintocompacted
pumicebut is uncorrelated
for impactsinto sand.Leastsquares
fit for onlytheclustered
impactdatainto pumiceandsand
gives,respectively,
log(D/d) -- -0.38 log(Sp/St)
+ 0.541(correlation
coefficient
of-0.970)andlog(Sp/6t)- -0.0398 log
+ 1.016(correlationcoefficientof-0.167). Identifitieddatapointsin Figure11a represent
thefollowingimpactors:
plastically
deformable
sphere
(A), weakandbrittlesphere
(B),andhollowthin-shelled
nylonspheres
(C). Identifieddatapointsin Figure
1lb represent
thefollowing:hollowaluminumsphere(A) anda hollowthin-shelled
nylonsphere(B). Theenclosed
numbered
datain Figure1lb indicateimpactsbya varietyof projectile
typesintomoistsandandcorrespond
to identifications
in Figure
6.
SCHULTZ AND GAULT: CLUSTERED IMPACTS
3711
3.0
pit lbowll .... ded
CRATER
MORPHOLOGY
PROJECTILE
ß sohd
2.0
+ central
pH
© cluslered
(• hollow
(3 bowl-shaped
• central mound
--
CI
•
"flat"
4 km/s
2.0
i
1
i
i
i
i
"fial" floor
1.0
1.0
I
-7
-6
1,
-5
I
I
-4
-3
0
-2
-1
0
-6
I
I
I
[
I
1
-5
-4
-3
-2
-1
0
LOG [(2r/v) '(•5,j•Sp)|
1.0
LOG [(2r/v)'(/•,/•)]
Fig. 12a
Fig. 12b
Fig.12. Thecombined
effects
oftarget/projectile
density
(•t/•p)andtimeforprojectile-target
contact
oncrateraspect
ratio
andmorphology.
Theprojectile-target
contacttimeis givenbytheprojectile
diameter2r dividedby theimpactvelocityv.
Figure12ashows
thatbothcratermorphology
andaspect
ratiofor clustered
andweakimpactors
systematically
varywith
thecontacttimeandtarget-projectile
densityratio.Competent,single-body
impactors,however,areuncorrelated
withthese
parameters
andform pittedcraterfloors.The leastsquares
fit appliesonlyto clustered
impactors
represented
by open
symbols:
logDid = 0.267log[(2r/v)' (St/$p)] + 2.072(correlation
coefficient
of 0.981).Letteredsymbols
areidentified
in
Figure1la. Figure12balsoshowsgoodcorrelation
for impactsinto sandin contrastwith Figure1lb. The letteredand
numbered
datapointsareidentifiedwithFigurelib. Theleastsquares
fit (including
pointB) gives:logDid = 0.148log
[(2r/1)).(•t/•p)] -[-1.318(correlation
coefficient
of 0.849).
referred to the downrange axis becomessmaller) with smaller
impact angles. Single-body impacts (Figure 18) produce
relativelysmallzonesof avoidanceuprange,therebysuggesting
that cluster dispersionalso may control the ejecta patterns.
Figure 19 explicitly demonstrates this fact and shows a
systematicchangein the zone of ejectaavoidanceuprange,the
apex angleof the principal herringbonepattern, and the apex
angleof the downrangeejectafan zone.
Oberbeck and Morrision [1974] produced herringbone
patternsexperimentallyby two adjacentsimultaneousimpacts
and demonstratedhow such patterns result from the simple
interactionof the two expanding,cone-shapedejectacurtains.
The resultspresentedhereindicatethat the herringbonepattern
can also be producedby much more complicatedinteractions
of hundreds to thousands of small impactors. Four other
significant differencesbetween clustered and double impacts
can be cited that might prove useful as diagnosticclues for
clusteredimpacts on planetary surfaces.First, simultaneous
double impactsproduceherringboneridgeswith apex angles
muchlargerthan thosefor clusteredimpactsat the sameimpact
angle. Second,herringboneridgeswrap around the uprange
rim at modestimpact angle(45ø), whereastwo-body impactsdo
not develop such a pattern to the same degree. Third, many
herringboneridges can develop around the same crater for
clusteredimpacts,whereastwo-bodyimpactsare dominatedby
a singleseptumdividing each crater. Fourth, the herringbone
ridgesbend downrangein clusteredimpactsat 45ø (seeFigure
resemblesthose craters previouslydescribedexcept that the
axis of syymmetry does not parallel the impact direction.
Oberbeckand Morrison [1974] found the sametype of offset
for two-body impacts.
5.
EJECTA DYNAMICS
AND DISTRIBUTION
PROJECTILE
OF POSTIMPACT
MATERIALS
The evolution of the ejecta plume for clusteredimpacts is
significantly different from plume evolution for single-body
impacts.In this sectionwe comparesuchdifferencesfor vertical
and obliqueimpactsat velocitiesfrom 1.3 to 1.8 km/s. A more
detailed discussionof ejecta dynamics with comparisonsat
higher impact velocities (6 km/s) will be considered in a
separatepaper. A preliminary account,however,can be seenin
the work by Schultz and Gault [1983]. The qualitative
examinationhere is intendedto place the precedingdescriptionsin the contextof the crateringprocess.Also in this section,
we examine the distribution of projectile material resulting
from a clusteredimpact.Suchconsiderations
haveimportant
implications
for understanding
thelateraltransport
of primary
ejecta,themixingprocess,
andthespectral
signature
of primary
materialfollowinga low-velocitysecondaryimpact.
5.1.
EjectaDynamics
For any given dispersion, vertical impact by clustered
consistently
producesa verydistinctivesequence
of
17b).Althoughtwo-bodyimpactsalsoproducethisdownrange projectiles
bendingof the herringbonepattern, the inflection is restricted
to the distal endsof the ejecta.
The clusteredimpactsproducedby shatteredpyrex spheres
form a relativelywell-definedcloudof projectiles.This may not
bethe configurationfor eitherprimary or secondaryimpactson
planetary surfaces. Consequently, an experiment was performedwith the rupturingdiaphragmorientedobliquelyto the
flight direction. Figure 20 shows that the resulting crater
plume growth. Figure 21 permits comparison of such a
sequence
(Figure2lb) with a single-bodyimpacthavingabout
the same massand velocity (Figure 21a). The entire cloud of
projectilesimpactswell within one frame of the high-speed
sequence,i.e., the interframe time interval of 0.1 ms, and an
expanding amorphouscloud is quickly formed. This cloud
eventually forms a well-defined boundary inclined at a low
angle (<15ø) from the surface.This ejecta curtain gradually
3712
SCHULTZ AND GAULT: CLUSTERED IMPACTS
Fig. 13. The effect of projectilestrengthon crater morphologyfor low-velocityimpactsinto compactedpumice.The
exampleat top (830546)wasproducedby a 1.9-cmsolidnylon sphere(7.84 g) impactingat 204 m/s. The crater profile (with
the projectileremoved)hasa distinctivebut characteristic
pit on the floor. Impactat 176m! s by a hollownylonsphere3.75
cm in diameter(2.46 g) produceda pronouncedcraterfloor mound(examplein middle,830549).Comparisonbetweenthese
two exampleswould suggestthat projectiledensitymight be the controllingparameter,but the bottom example(830601)
alsowith a moundedfloor wasproducedby a puttylikesphereabout 3.75 cm in diameter(51.9 g) impactingthe sametarget
at 136 m/s. The flattenedprojectilewas removedfor the illustration and profile. The relative crater dimensionsin the
photographsare preserved,but the profilesare scaledto the sameapparentdiameter (no vertical exaggeration).
range ejecta and the ejecta curtain progressivelyincreasein
angle from the horizontal to about 40ø for a 45ø incoming
shapedejectaplumeis quicklyestablished
in a single-body impactor. At very late time the ejecta curtain becomes
impact. The ejectadepart the target at an angle of about 45ø, symmetrical(uprangeand downrange)and resemblesa vertical
which remains relatively constant throughout crater growth.
impact. Within the first few frames,clusteredimpactsinitially
The regultingejecta plume simply advancesoutward in a produce an amorphous cloud of ejecta that evolves into a
manner describedby Gault et al. [1968] and Oberbeck et al.
prominentdownrangetrajectorythat resemblesthe early time
[1975].
sequencesof a single-bodyimpact. The downrangeejection
Clustered impacts at oblique angles also produce very anglefor a 45ø impactoris approximately30ø. This anglefor
distinctive
ejecta plumes
(Figure21d).Thesequence
for a single a 60ø and 30ø obliqueimpact is 40ø and 18ø, respectively.A
impactor revealsa very low angledownrangecomponentof symmetricalejecta plume never develops,and the event is
ejecta(Figure21c). Theejectaplumeisinitiallyveryassymmet- dominated by a downrange plume without an uprange
ric with most material ejecteddownrange.With time, down- component.At very late stages,filamentary stringsof material
steepenswith time and dissolvesinto filamentaryraysthat are
emplacedasthe spokesshownin Figure 17. In contrast,a cone-
SCHULTZ
ANDGAULT:CLUSTERED
IMPACTS
3715
slitted barrier [see Oberbeck and Morrison, 1976]. The
measuredejectacurtain thicknesses
at the baseare about 7% of
the apparentcrater diameter within 1R of the rim and 10% at
greaterdistances.The thicknessof the baseof the ejectacurtain
does not becomethinner at greater distancesfrom the crater,
but the spatialdensityof the curtain is reduced.Thus the ejecta
curtain maintainsa finite width throughout depositionand is
composedof many individual ejectafragmentswhichreducein
number with increasingdistancefrom the crater rim.
At laboratory scalesthe back edge of the ejecta curtain
arrives about 20 ms after the leading edge. At much broader
scales the time between first and last arrival
.m,.....'...:?..,.f,:.,•*:i,,.-.::..,:.,,.w:-.:q:•='
...:x...:.•.'..:"--..,...:...,*•.,.:".:...
<,'.:.•,'.,,,,x....
..... •,•,•,':'.::..,:'::'
:.::q..,...•.'.:.x....::...':'
'......' ".......
...•.,....."
:
..':.:: ".
:..:,,'...'•:
Fig. 16a
of material
at a
given distancefrom the crater would become much greater,
thereby increasing the interference with secondary crater
formation by individual ejectablocks.If we geometricallyscale
laboratory ejecta curtain thicknessto planetary-scalecraters,
then a 100-km-diametercrater may havean ejectacurtain about
6 km thick and an Imbrium size basin about 30 km thick (for
precollapsecavity diametersof 60 and 600 km, respectively).
An alternative estimate of ejecta curtain thicknesscan be
basedon thicknesses
of ejectadeposits.If the excavationcavity
of a large planetary-scalecrater growsin the samemanner as
a laboratory impact into sand [see Grieve et al., 1981; Croft,
1981; Schultz et al., 1981], then ejecta thickness increases
approximately
as Rs/•at a givenrelativedistance
from the
craterrim [seeSchultzand Gault, 1979;Housenet al., 1983].
Near the crater rim (within 0.5R) the ejectacurtain thickness
can be related to the thicknessof the emplacedejectadeposit.
"'"';"'•;":':':1•;'
---." .-..'.½.-.
'.......
,.
... .
•.:•.
-.
:"7'.
}:.;.
;,•:'b.:'"'*
...
...
...:.,..::
.,.}'"
.,::.:
•.• .:•--.
......
ß 'i.,)';:
'
,,
,
ß•
.
•?:.
...
, :•
..,•
,..
Fig. 16b
Fig. 16. Comparisonbetweenverticaland oblique(45ø) impactinto
compactedpumicefor comparablevelocitiesand dispersions.
Vertical
clusteredimpactorsproduceradial and subradialspokes(Figure 16a,
830526)for 1.77km! s impactand 7.0-cmdispersion.The 45ø oblique
impactor(Figure 16b,830538)producesa patternof V-shapedridges
(arrow above)pointinguprangefor 1.62 km!s impact and a 6.3-cm
dispersion(normal to impactdirection).The distalendsof the ridges
benddownrange(arrow below).In addition,a narrowdownrangefan
of concentratedejectadevelops.
ejectaat a giventime formsa conicalejectacurtain.Beforethe
crater has reached its maximum size, the trajectoriesin the
ejecta curtain are approximately parallel to the curtain
boundary;after crater formation, trajectoriesbecomemore
normal to the curtain boundary. Consequently, the ejecta
curtainrepresents
an outwardmovingwall of debris.The ejecta
curtain has been studied in the laboratory (D.E. Gault,
unpublished
data, 1975)by positioninga horizontalplatesuch
that only one half of the growingcavity is exposed,thereby
slicingthe ejectacurtainand permittingmeasurements
of the
ejecta curtain thickness. This technique minimizes the
interejecta
collisionsproducedby experiments
incorporatinga
Suchanapproximationisanoversimplification
dueto scouring
and subsequent
flow of the deposit;nevertheless,
this assumption providesan order-of-magnitudeestimate.The average
ejectadepositthickness
at 0.3R from therim of thelunarcraters
Jehan(4.6 km diameter)and Hadley (5.7 km) is about 130 and
150 m, respectively(Lunar Topo photo maps). A 60-km
precollapsediameter crater (Copernicus?)has a depositof
primary ejecta material about 500 m thick near the present
postcollapserim as extrapolated by scalingrelations and
observed for lunar craters. The minimum ejecta curtain
thicknesst, is relatedto the ejectadepositthicknesst•, by t• =
t, sin0, where0 isthe angleof impactwith respectto the surface.
Both laboratory [Gault et al., 1968] and theoreticalmodels
[e.g.,seeOrphalet al., 1980]indicatean ejectacurtaininclined
about 45ø from the surface. Therefore the minimum ejecta
curtain thickness for a 100-km-diameter
crater is about 700 m.
Modelsof ejectionfavoredby Oberbeck[1975]suggest
impact
anglescloserto 15ø, thereby indicatinga minimum ejecta
curtain thickness of 2 km.
Estimatesbasedon ejecta depositthicknessesare significantly smaller than those provided by scalinglaboratorymeasuredejectacurtainthicknesses
because
the curtainis not
simplyan in-flightblanketof debriswith densityequivalentto
the final deposit.For example,at 0.3R from the rim of a 30cm-diameter laboratory crater in sand, the observedejecta
thicknessis about 2 mm. Thus the observedwidth of the ejecta
in the curtain (10% of the crater diameter)at this distanceis
about 10 times the thicknessof the deposit. The extrapolated
curtain thickness of the same bulk density for a 100-km-
diametercrater becomes7 km for 45ø ejection/impactangles
and 20 km for 15ø ejection/impact angles:valuesconsistent
with the previousmethod that simply scalesejecta curtain
thickness as a function
of crater diameter.
The relative width of the ejecta curtain, therefore, is thin
3716
SCHULTZ AND GAULT: CLUSTERED IMPACTS
ß
:::.
•.•::.•:
•;•;•::::::::•..•/:.•::.;•:.::.::•.•
:.•:.•
..:::•::::•:...•.:
::..:•:..:
:.:::::::::::::::::::::::::::
::::::::::::::::::::::::::::::::::•:
.•:...:.
•:.:..:.:.:
::.•:
•:•
.•,,,,
•:.:•.•...:....:....:...:
.:...•
.:...
:•......:....:.:..:::......•.•:
.....
Fig. 17a
Fig. 17. Cratersproducedby clusteredprojectilesimpactingwith three differentangles(Figure 17a) and four different
dispersions
(Figure 17b).Clusteredimpactsat increasingly
obliqueanglesconcentratethe ejectadownrangeand reducethe
crateringefficiency(Figure17b).The oblongcratershapereflectsthe ellipticalpatternof impactingfragments.In contrast
with single-body
impactorsthe asymmetryin cratershapeandejectadistributionoccursat highanglesfrom the horizontal.
The top example(830531)resultedfrom a verticalimpactat about1.9krn/s with a dispersion
of 16crn;themiddleexample
(830536),from a 1.56kin/s impactat 60ø with 14-cmdispersion;
andthebottomexample(830535),from a 1.47kin/s impact
at 15ø with 12-crndispersion.The last exampledid not provide a meaningfulprofile. The radial and subradialspokes
producedin verticalimpactsform V-shapedridgespointinguprangein obliqueimpacts.Figure17bshowstheeffectof cluster
dispersionon cratermorphologyfor similarimpactvelocitiesat 45ø. The dispersiondecreases
from top to bottom:7.6 cm
(830538);4.9 cm (830539);1.6cm (830540);and unbroken,i.e., 0.635-cmsphere(830541).The respectiveimpactvelocities
are 1.62, 1.44, 1.46, and 1.55 km/s. The herringbonepattern becomesmore obtuseas the clusterdiameterdecreasesand
disappears
for tightclusters
withaneffective
density
greater
thanabout0.03g/cma.Nevertheless,
eventightlyclustered
impactorsproducea distinctively
asymmetric
ejectapatternat 45ø impactanglesthatisverysubtlefor single-body
impactors.
The accompanying
profilespreserverelativesizesbut havea twofoldverticalexaggeration.
compared to the crater diameter, but for a large crater the
absolutewidth becomesappreciable.As a result,the potential
time for interactionbetweenincomingprimary ejectaand the
secondarycratering processbecomesappreciable.For example, at 0.3R from the postcollapserim of a 100-km-diameter
lunar crater(60 km precollapsediameter),thetime betweenfirst
and last arrival of material in the curtain is about 25 s. Thus at
a given ballistic range we should expect interaction between
secondaryejecta and later arriving primary ejecta. Laboratory
impactsby a clusterof fragmentsasdescribedin the preceding
SCHULTZAND GAULT: CLUSTEREDIMPACTS
3717
Fig. 17b
Ejectasizes. The sizedistribution of ejectawithin the ejecta
discussions
can be viewed as a small sectionof the impacting
ejectacurtain. In contrast,independentformation by a single curtain at a givenrangeis not yet known. Althoughthe
noninteractingimpactor requiresthe ejectacurtain to contain maximum block size on the rim of lunar craters increases with
size [Moore, 1971], this probably does not reflect the median
a singleblock.
3718
2OO
150-
SCHULTZ AND GAULT: CLUSTERED IMPACTS
i
I
I
APE;.••,••ANGL
EV
single AI
+ \
simulatethe excavationstageof hypervelocityimpactcratering
sincethe extremelyhighpeak shockpressures
shatterthe target
out to near the rim prior to excavation. This simulation is
inappropriate,however,for secondarycrateringexceptwhere
the preimpact target also has low strength. The amount of
shock-inducedpulverization at low velocities is much less
important than mechanical failure. Early researchers in
explosion cratering used the term "compressioncraters" to
I
+
broken pyrex
.50-
....
I
-I•
I
___o
-
describe
the formation
of secondaries
around
terrestrial
explosioncraters [Roberts, 1964]. Scaling relations basedon
either impactsinto sand or high-energyexplosionsinto rock,
I
I
I "ø--,-1 ......... •2
o
i
therefore, overestimate the cratering efficiences produced
20
30
40
50
60
70
o
1o
during low-velocitysecondarycratering.
IMPACT ANGLE (degrees)
Summary. As crater sizeincreases,both the absolutewidth
Fig. 18. The effectof impactangleon the apexanglesof V-shaped
of
the ejecta curtain and the number of ejecta fragments
ridges(the herringbone
pattern)for clustered
impacts.Threetypesof
impactorsare shown:singlesolid-bodyaluminumspheres
into sandat composingthe curtain increase.As a result, secondaryimpact
200 m! s (crosseddot); clusteredaluminumshotinto sandat 100m! s cratering near the crater rim (within continuous deposits)
(solid traingles, solid circles); and clusteredpyrex fragmentsinto cannot be viewed as the summationof individual impactsbut
compactedpumice at 1-2 km/s (open triangles,open circles,open
as an ensembleof clustereddebris.The laboratory experiments
squares).Trianglesrepresentthe apexanglesfor the zoneof avoidance
described
in the precedingsectionsprovidean analogyfor this
uprange,whereascirclesindicatethe principalherringboneridge.The
opensquaresindicatethe apex angleof the downrangefan of ejecta. processwhere the tight clustersrepresenta unit column in an
Clusteredimpacts consistentlyproduce a herringbonepattern that ejecta curtain. At greater distancesfrom the crater rim, the
forms a relatively small apex angle at a given impact angle in ejectacurtain doesnot necessarilybecomenarrower but on the
comparisonwith a single impactor and the double impactorsof
averagebecomeslessdenseand brokeninto clumps,asperhaps
Oberbeckand Morrison [ 1974].
typified in laboratory experimentsfor the open clusters.Thus
secondaryimpacts may be more directly analogousto the
laboratoryclusteredimpacts.Geometricdispersalof the ejecta
block sizeat any given relative range. Maximum block sizeon curtainis proportional
to r2,andat largedistances
(r > 5R),
the rim is related to spallation processesand failure along noninterfering impacts by individual fragments become
preexistingflaws (e.g., joints and faults) under relativelylow possiblebut not to the exclusionof clusteredevents.
peak shockpressuresat the final stageof excavation.Moreover,
The low velocities(<1 km/s) of mostlunar secondaryimpacts
absoluteblock sizeis largelycontrolledby absolutepeak shock dictatefurther cautionin simplyapplyingthe resultsof single
pressures.If ejectionvelocityis relatedto peak shockpressure, impactsinto low-strengthsand targets.Low-velocityimpacts
thenejectaballisticallytransportedto the samedistancerelative reducethe degreeof shockdamageto the target and increase
to the crater size will be subjectedto greater absolutepeak the importanceof in situ target strength.Conditionsobviously
shockpressures[seeSchultzand Mendell, 1978;Schultzet al., occur where single-bodyimpacts into loose sand provide an
1981; Croft, 1981]. In addition, the residencetime of shocked appropriate analogy for secondary cratering, but such
materials
inthecraterpriortoejection
increases
asR•/2,thereby conditionsmust be recognized.
On the basis of the precedingdiscussionthere is a strong
potentially increasing the degree of mechanical breakup
[Schultz and Mendell, 1978]. The increasedimportance of
comminutionfor large cratersmay contributeto the general
absenceof large blocks(<2 m) around freshlunar craterslarger
i
i
i
200[
than one crater radii from the rim, as indicated in highresolutionphotography,in the thermal infrareddata [Schultz
and Mendell, 1978], and in the radar reflectanceobservations
150
[ Thompsonet al., 1981].
\\
To illustrate further the most likely physicalstate of ejecta,
we can considerthe size of ejecta necessaryto producelunar
100
basin secondaries.Scaling relations used by Oberbeck et al.
[ 1975] require blocks6 km in diameter to producea secondary
crater 20 km in diameter at a ballistic range of 1000 km. The
50
strength of naturally occurring materials (not to mention
shockedmaterials) decreaseswith increasedsize owing to the
largenumberof flaws.The survivalof a singlecompetent6-km
0 '
I
,
blockduringejectionat a minimumvelocityof 1.15km/s seems
0
10
highly unlikely if even possible.Even the existenceof a single
DISPERSION (cm)
flawlessblock of the preimpact material is improbable.
Low-velocity excavation/compression. At the relatively Fig. 19. The effect of clusterdispersionon the apex anglesof the
low impact velocities(<1 km/s) typical for lunar secondary herringbonepattern and downrangefan of ejecta.The apex angleis
definedin Figure 17.The apexangledependsnot only on impactangle
cratering, peak shock pressuresare low. Consequently,target (Figure 17) but also on dispersion.Data representclustersof broken
strengthas well as projectile propertiesbecomesvery impor- pyrex impacting at 1-2 km/s at a 45ø angle. At thesevelocities,an
tant. Impacts into low-strength sand targets reasonably uprangezone of avoidanceis not formed for solid body impactors.
\
\
\
\
SCHULTZAND GAULT:CLUSTEREDIMPACTS
3719
Fig.20. Theeffect
ofasymmetry
ina clustered
impactor
onthedirection
oftheherringbone
ridge
pattern.
Theimpact
anglewas45ø directedfrom left to right (horizontalwith respectto the photograph).The herringbonepatternis symmetric
with respectto the sequence
and distributionof craterletsratherthan the directionof impact.High framerate photographs
show,however,that mostof the debrisfrom the crateris ejecteddownrangealongthe directionof impact.The stringof
craterletsand the principalimpactorclusterimpactednearlysimultaneously,within 0.15 ms.
physicalbasisfor consideringclusteredimpactsasa reasonable publishedphotographsof the experimentalcraters except
analogyfor secondarycratering.Section6.2 directlycompares perhapsthe downrangemember of a crater pair. A subdued
the morphology of clustered impact craters with lunar
appearanceof the crater assemblagewas not produced.
secondarycraters.
Secondarycratersaround a primary crater smallerthan 200
km in diametertypicallydisplaya pattern of ridges(seeFigure
23) commonly called the herringbone pattern [see Howard,
6.2. Lunar Secondary Craters and ClusteredImpacts
1974; Oberbeckand Morrison, 1974;Schultz, 1976]. Although
similar structures have been previously produced in the
Clusteredimpactsin the laboratory producefeaturesthat laboratory by the simultaneousimpact of two projectiles
closelyresemblelunar secondaries.Previousexperimentsby [Oberbeck and Morrison, 1974], many lunar secondaries
Oberbeck and Morrison [1974] produced one important
display the herringbone pattern without being double, and
feature, the intercrater ridge, but did not reproduce other
many single secondarieshave numerous ridges. Moreover,
equally important observedstructures.The following discus- Oberbeckand Morrison showedthat two-bodyimpactsrequire
sionhighlightscommonelementsbetweenclusteredimpactand exceedinglylow-angletrajectories(impactanglelessthan 20ø),
secondaries.
relatively large times betweenimpactsor "atypical" eventsto
Figures 24 and 25 illustrate typical secondary craters
match the observedapex anglesof lunar secondaries.Clustered
associatedwith Copernicusand Orientale. Table I compares impactsas shownby the presentexperimentsdemonstratethat
the occurrencesof typical featuresshownin Figures23 and 24
apex angles are controlled by both impact angle and cluster
andproducedin thelaboratorybyclusteredanddoubleimpacts dispersion. Apex angles typical for lunar secondariesare
(Figure 16). Clusteredimpacts were shown (Figure 12) to
producedby clustersat impact angles(45ø) expectedfor ejecta
produceshallowcraterswith a rangeof floor morphologiesand plumesas indicated in laboratory experimentsand theoretical
profilesthat dependon the size of the clusterrelative to its computer models.
velocity. Such cratersalso have a distinctivesubduedappearTwo other featurescommon to clusteredimpactsand lunar
ancewith a ridgelikerim, reflectingthehighlyinteractiveejecta secondaries include the herringbone pattern collaring the
plume. These characteristicstypify many lunar secondaries uprange. rim and the distal ends of the ridges bending
(Figure23). The nearlysimultaneous
impactsby two projectiles downrangeto becomemore radial with respectto the primary
describedby Oberbeckand Morrison [1 974] did not produce crater. Although the downrangecurvingof the distalendsof the
this spectrumof distinctivemorphologies.
Publishedprofiles herringbonepattern wasalsonotedin the two-bodyimpactsby
acrossthe septumseparatingthe twin eventsshow a shallow- Oberbeckand Morrison [1974], the effectis not aspronounced.
Table I also comparesthe distribution of lunar secondary
appearingcrater,but suchprofilesdo not representthe entire
crater complex as easily seen in the photographs of the ejecta with the distribution of ejecta around clusteredand
experiments or many of the observed lunar secondaries. double impacts. The downrangefan and rapid thinning of
Relativelyshallowprofilesfor cratercomponentsare produced ejectacharacteristic
of clusteredimpactorstypifiesmanylunar
for two-body impacts,but they requirevery low impact angles secondaries
[seeSchultz, 1976]and clusteredimpactsbut are
in contrast with clustered impacts. Similarly, the subdued not observedin the available data for two-body impacts.
appearanceand the distinctiverim profile are not visiblein the Clusteredimpactorstypically remain on or near the surfacefor
3720
SCHULTZ AND GAULT: CLUSTERED IMPACTS
Fig. 2 la
Fig. 21b
Fig. 21. Comparisonof ejectadynamicsfor single-bodyand clusteredimpactorsat normal and 45ø impact angles.The
first frame indicatesmomentof impactfollowedby 1, 5, 10, 50, 100, and 150 ms. Figure21a showsa verticalsingle-body
impactby 0.635-cm-diameter
aluminum(0.376g) into compactedpumiceat 1.61km/s, (821120)andcanbe comparedwith
a clusteredpyrex impact (0.298 g) into the sametargetat 1.77 km/s (830526).The single-bodyimpactquicklyestablishes
a conicalplumethat progressively
becomeswiderat the base.In contrast,theclusteredimpact(Figure2lb) resultsin a cloud
that slowlyevolvesinto a conicalplumeat verylatetimeswith progressively
increasinganglesfrom the surface.Largeclumps
of shock-lithifiedejectaare visiblein the originalframesof the movierecordsfor the clusteredimpactexperiments(bottom
photograph,Figure2lb). Obliqueimpacts(Figure21cand21d)by singleandclustered
impactorsaresignificantly
different.
The singleimpactorproduces
a plumethatisinitiallyasymmetric
but becomes
symmetric
at latetimes(0.635-cmpyrex(0.298
g) sphereat 1.55 km/s into compactedpumice;830541).The clusteredimpactor,however,neverproducesa symmetrical
plumeshape;rather,the plumeformsan inclinedcurtainthat movesdownrange(0.2981g clusteredpyrexat 1.62km/s into
compactedpumice;830538).
SCHULTZ
ANDGAULT:
CLUSTERED
IMPACTS
3721
Fig. 21d
Fig. 21c
Fig. 21. (continued)
sand or compactedpumice,whereastwo-body impactorsare
buried beneaththe floor in laboratory experimentsat comparable velocitiesunlessthe impact angleis highly oblique.
The morphology of clusteredimpactscloselyresemblesthe
interior structures of suspectedbasin secondaries.Unusual
subdued
craters
around
the Orientale
and Imbrium
basins
become new plausible candidates for secondary impact
structures.For example,the cratersParrot C, Alpetragius,and
Airy all have a very subduedappearancewith an anomalously
pronouncedcentral mound [see Schultz, 1976, pp. 98-100].
Suchcratersare unlike expecteddegradedremnantsof primary
impacts but could be explained as secondaries.Previously
3722
SCHULTZAND GAULT: CLUSTEREDIMPACTS
lowshock
pressure
events,
therelative
strength
of thetarget
CRATER-CONTAINED
PROJECTILE
MASS FRACTION
1.0
I
I
becomesimportant. Compactedpumicetargetsillustratethis
trend. Single impactorsinto compactedpumicedisplace2.5
timeslessmassthan the sameimpactorsinto sand;however,
I
they displace about 30 times more mass than the same
impactorsinto solid basalt. Thus secondaryimpactson the
0 0.6
•_.
Mo
30g-
•' 0.2--
--
moon may excavate very different amounts of local material
_
dependingon the target.Basaltsurfacesandlooselycompacted
dark mantledepositsillustratetwo possibleextremes.
Oberbecket al. [ 1975]indicatethat theirexperimentalresults
werenotdirectlyusedto estimatecrateringefficiencies
for large
secondarycraters.Rather, the displaced-mass
ratios shownin
Table2 werebasedon shallow-buried
nuclearexplosioncraters
Feprojectiles
AIprojectilesß
•
--
in alluvium.Nevertheless,
the deriveddiameter-energy
scaling
relationin the paperby Oberbecket al. [1975equation(A2)]
IMPACT
ANGLE
is essentially
thesameasthat derivedfor impacteventsin sand
Fig. 22. The fraction of projectilematerialm relativeto total launched quotedby Gault[ 1974].Table2 alsoreveals
thatthedisplacedprojectilemassme containedinsidethe crater for differentimpact massratiospredictedfrom the presentexperiments
reasonably
angles,impactingm•s, andimpactordensity.The clustered
impactors
match
the
results
estimated
from
the
nuclear
explosion
data by
represent0.16-cm-diameteraluminum or iron shotlaunchedwith an air
etal. [ 1975]for impactvelocities
greaterthan0.5km/
gun at velocitiesof about 1• m/s into no. 40 sand.Verticalimpacts Oberbeck
90 ø
75 ø
60 ø
45 ø
30 ø
15 ø
(90ø) retain between75 and 95% of the impactingmasswithin the
crater,whereasobliqueimpactsloseprogressively
incteeing amounts.
At 30ø, nearlyall the aluminumand 75% of the steelimpactorsare
found outside the crater.
s. If this widelyusedscalingrelationis consideredvalid, then
the experimentalresultsreportedherein shouldbe equally
valid.
To place this discussionin better perspective,we first
considerthe emplacementof ejectaat 0.4R from the rim of a
150-km-diameter
proposedsecondarycraterssuchas the Struve L [seeSchultz,
1976, p. 248; Wilhelms, 1976] and large crater chains[Schultz
and Mendenhall, 1979] exhibit many of the same features
producedin the laboratory. Struve L, in particular, exhibits a
downrange fan of debris, large raised rim, and floor profile
typical of obliqueclusteredimpacts.
This and section6.1 have provided a physicaland observational basisfor consideringclusteredimpacts to be important
for secondarycratering. Section6.3 considersthe implication
of suchan analogyfor estimatingthe degreeof mixing between
ejectafrom the primary crater and material excavatedby the
secondaryimpact.
6.3.
Secondary Cratering Efficienciesand Mixing Ratios
The resultsof laboratoryexperiments
involvingsingle-body
impactsinto sandhavebecomethefoundationfor interpreting
the degreeof local versusforeign componentson the lunar
surfaceandfor estimatingthesizesof ejectafragments
from the
sizesof secondary
craters.This sectionconsiders
the implications of both viewingsecondarycrateringas an ensembleof
impactingdebris and consideringthe effectsof impacting
crater on the moon. If we assume that this
crater has undergone plastic deformation and slumping
resultingin 40% enlargement,thenwe canestimatethe ballistic
range(---52 km) and velocityat impact(-294 m/s) for a 45ø
ejection angle. Expressionsfor displaced-mass
ratios from
Oberbecket al. [1975] predictthat a solidblock 500 m across
(density
of 3.0g/cm3,ejection
angleof 45ø) woulddisplace
abouttwiceasmuchlocalmaterialasimpactingprimaryejecta.
Direct extrapolationof laboratoryexperimentsof solid body
impacts into sand predicts a displaced-massratio of 3.0,
whereasextrapolation of impactsinto pumicepredictsa ratio
of 0.56. Becauseclusteredimpacts provide a more realistic
analogyfor secondarycratering,the displacedmassratio must
be reducedby a factor between5 and 10. If the target is more
competent than sand or pumice, then further reduction is
1.o I I 1 1
PROJECTILEMASS
< 20•
targetswith finite strength.
Table 2 showsvaluesof displacedmassratios for different
ballisticrangesandejectamasses.
Theseratiosarecalculatedon
the basisof expressions
for singleimpactorsusedby Oberbeck
ß0
ON CRATER
FLOOR
et al. [1975] and extrapolationsof empiricaldata usedin the
present paper. If the calculated displaced-massratios are
reducedby a factorof 5 owingto clusteredimpactors,thenthe
amount of primary materialpreservedin an ejectadepositor
00, ø1
i
i
90 ø
75 ø
60 ø
45 ø
30 ø
15 ø
secondarycraterincreases
significantly.
IMPACT
ANGLE
A factor of 5 reductionin crateringefficiencyis, however,a
veryconservative
estimate.As discussed
in section6.2, impacts Fig. 23. The fraction of projectile material m relative to the total
I
•0.2i
into sandtargetsareperformedin orderto minimizestrength launchedmassmocontainedon the surfacefor differentimpactangles
and impactor density. Vertical impacts retain only 20-45% on the
effects,therebypermittinganalogieswith large,high-velocity surface(solid circles)with about one half of this on the crater floor
eventswhere strongshockwavespulverizethe target prior to
(open circles). Oblique impacts below 30ø ricochet most of the
excavation.Sincesecondaryimpactsrepresentlow-velocity, projectilesout of the crater and are depositedon top of the surface.
SCHULTZ AND GAULT: CLUSTERED IMPACTS
3723
•::.:..:::::
==============================
:'
Fig. •a
Fig•24b
Fig. 24c
Fig. 24d
...
:.:...:.
Fig.24. Examples
oflunarsecondary
crater•
withfeatures
accountable
byclustered
impactors.
Figure
24ashows
a l-kmwidesecondary
craterassociated
with Aristarchus,whoserim is about55 km to the northeast(arrow indicatesdirection).
Multiple ridgesform a herringbonepatternasymmetricwith respectto the directionof impact(seeFigure20). A ridge
comprises
the craterfloor. LunarorbiterphotogaphV-195M. Figure24billustratesa shallowl-km-widesecondary
crater
complexalsoassociated
with Aristarchus,whichis 115 km to the south-southwest
(arrow indicatesdirection).This crater
is muchshallowerthan the precedingexample.The herringbone
patternappearsto collarthe uprangerim. In thisand the
previousexamplethe distal endsof the V-shapedridgesbend downrange.Lunar orbiter photographV-192-M. The
Aristarchussecondary
in Figure24c has a smallerdiameter-to-depth
ratio than the previousexamplesbut containsa
pronouncedcentralmound. The crater is about 1.2 km in diameter and is 115km from the rim of Aristarchusto the southwest.
The impactexperiments
indicatethat sucha moundcanbeformedby a tightlyclustered
or veryfriablesolidimpactorand
largelyrepresents
targetratherthan projectiledebris.Lunar orbiterphotographV-192-M. Figure 24d showsa large(4.3km diameter)secondary
associated
with, but 225 km from the rim of, Copernicus.
The herringbonepatternwrapsaround
the uprangecraterrim that hasverylittle relief.The subduedshallowappearance,
herringbonepattern,and rim profile
suggestformationby a clusterof ejecta.Lunar orbiter photographIV-126-H3.
necessary.
Thus the displaced-mass
ratio near the rim of a 150km-diameter lunar crater should be 0.1, i.e., 90% primary
material.
Table 2 provides estimatesat greater distancesfrom the
crater rim. At 1R from the rim of a 150-km-diametercrater (as
defined above), the ballistic range is about 100 km. Single
impactorsat velocitiesof producingsecondarycratersfrom 10
m to I km would result in 8 to 35%, respectively,primary
material. Clustered impactors having the same mass would
resultin 71-82% primary material. At 4R from the crater rim
the ballisticrangeis about 300 km with a velocityof 608 m/s
(sphericalmoon). Single impactorsproducing 10 m to I km
secondarycratersat this distancewould resultin depositswith
only 3 to 17%primary material. Clusteredimpactors,however,
could produce ejecta deposits containing from 20 to 62%
primary material. If the target has significant compressive
strength,the primarycomponentevenat 4R from the craterrim
could be greater, i.e., 50-90%. As discussedbelow, however,
suchpercentagesmay not correspondto spectrallyobservedor
sampledpercentagesbecausethe projectile componentis not
necessarilyintimately mixed with the depositsat the point of
impact but are disperseddownrange.
At basin scalesthe near-rim displaced-mass
ratio decreases
further. For example,the Fra Mauro regionis about 1200km
from the centerof the Imbrium basin.If the gravity-controlled
excavationcraterrim had a radiusof 300 km, then the required
3724
SCHULTZ AND GAULT: CLUSTEREDIMPACTS
:
Fig.25a
Fig.25b
...,..... •....,• •..•.•.•...•.•....
..•...•,,
.?7o•-.•.•.
...,..
,.•..•.•?•.•,•,•
•?•,•
ß •
' ...•.• -,•.,.
•.• •-.,• •.....
...•.•. ,.•,,.•
:.,.•.•,•
ß.•
, ..
? .,.•?•
......•..• ,:...,'.,.,...•
.%•... ....•.
......
•.d..•,•.,..•,
. '• .•",
•.•...
•.•-•...
• •.?•'--'•-•?
..........
: ?
.... •:••
•,,,.....
,..'.•-•.•..
•.,.'A
•'•.".
...•.-•?•....•
'•--,.
•'•'"•'•'•"•
•"'•••
, • ß
. .
• •'• ..--
.• •'•,•,.¾.•,,•..•.,•.
•?.•,.•.... '----.•?•
• •.•, .....
.......
'••.,,
•
.....
• ....
...•,.
........, ....•'....
,?•.,,-•.•.:
,•
Fig. 25c
.........
•.
• .•
..
.•.
Fig. 25d
Fig.25. Examples
of largebasin-related
lunarsecondary
cratershavingfeatures
characteristic
of clustered
impactcraters.
Thefine-scale
surfacetextures(e.g.,herringbone
ridges)preserved
aroundsmallerrecentlunarimpacts(Figure24) havebeen
largelydestroyed
sincethemajorimpactbasinswereformed.Neve•heless,
thecraterrim profile,crater•oor profile,and
downrange
scouring
suggest
groupsof impactors.
Figure24ashows
a 16-km-diameter
secondary
associated
withOrientale.
The exaggerated
craterrim anddownrange
fan of ejectaresemble
thecraterin Figure16b.Figure24bshowsan elongate
secondary
crater19km in diameteralsoassociated
withOrientale.Thecrater•oor contains
a mound,perhaps
indicating
a moretightlygroupedimpactingclusterthantheclusterresponsible
for thecraterin Figure25a.Figure25cillustrates
shallowcraters(arrows)with unusu• centralmoundsthat couldbe understood
as Imbriumsecondaries
producedby
clustered
impactors.
An openclustered
impactor
couldhaveprodu•d thehummocky-•oored
andridgelike
rimof thecrater
in Figure24d.Lunarorbiterphotographs
(a) IV-174-H3,(b) 182-H2,(c) 101-M,and(• 96-H2.
times its own mass.Expressionsusedby Oberbecket aL [ 1975]
predict 11 times its own mass.As a cloud of ejectaimpacting
a surfacewith strengthcomparableto compactedpumice, an
equivalentmasswould excavatea factor of 1.2 times its own
mass.Consequently,about 80% of the ejectadepositcould be
primary material in contrast with 15-20% predicted by
Morrison and Oberbeck [1975]. Table 2 permits additional
comparisonsfor different sizeimpactors.
approximately
as Rø'5.To first order,suchconsiderations
The above exercises serve to illustrate that significant
predictteto be about500 m. If teis takento representa single
quantities of primary material can be preserved in ejecta
block(comprising
a solidejecta
curtain
ofthisthickness)d'then
such a block impacting at 45ø would excavate from 2.3 depositseven at basin scales.Large solid blocks of ejecta
(extrapolated from pumice) to 10 (extrapolated from sand) embeddedin an ejecta curtain indeed may produce relatively
ballisticrangeapproaches1000km with an impactvelocityof
1.15km/s. This rangeis about 3 Refrom the excavationcrater
rim (radius of Re) or 0.8 Re from the Apennine scarping.
Geometricscalingof the crateringprocess[Post, 1974;Schultz
and Gault, 1979;Housenet al., 1983]indicatesthat the effective
thickness
teof debrisarrivingballisticallyat sucha distance(i.e.,
mass per unit area divided by the bulk density) scales
SCHULTZ
ANDGAULT:CLUSTERED
IMPACTS
3725
TABLE 1. ComparisonsBetweenSecondaryand ExperimentalCraters
Secondary Clustered Two-Body
Craters
Impacts
Impacts
Profile
Range
inaspect
ratios
(5-30)
Hummocky,
mounded,
concavefloors
High-relief
rim
Subdued
appearence
Herringbonepattern
,/
Single
Multiple
(>2)
Apex angles
180ø
135ø
90ø
x/
x/
x/
90ø*
60ø
45ø
90 ø
<20 ø
b
Asymmetry
Uprange collar
Downrange
curving
c
Ejecta distribution
Downrange
fan
Surficial
projectile
component
Rapidthinning
ofejecta
*Impact anglefrom horizontal.
a. Multiple ridgesoccurbut typicallyasextensionsof primary intercraterridge.
b. Apex angleslessthan 90ø havebeenproducedfor 2-body impactswhen the impact
angleis verysmall(<15ø) and whenthe relativetime betweencomponentimpactsis large.
c. Downrange curving of distal ends of pattern occursbut to a lesserdegreethan in
clusteredimpacts.
largeamountsof local materialmixedwith primaryejecta. Oberbeck, 1978; H6rz et al., 1983]?H6rz et al. [1983] have
Suchblocksshouldbe viewed,however,as end-membersof a
rangeof ejectasizesthat forceusto considerthe implications
of manysmalleraccompanying
objectswithinan ejectacurtain
arrivingovera finite periodof time.
recentlysummarizedtheir resultsfor the relative amount of
ballistically transported Ries crater material and locally
excavated material by secondarycratering. They concluded
that the models of Morrison and Oberbeck [1978] are in
Are theseresultsinconsistentwith the detailedanalysisof the reasonable agreement (factor of 2-4) for ejecta deposits
continuousejectadepositsaroundthe 26 km-diameterRies betweenthe morphologiccrater rim and 1.5R from this rim
impactcrateron the Earth [Oberbeck,1975;Morrisonand where they estimatethat the relative amount of Ries-derived
TABLE 2. Comparisonof ExtrapolatedCrateringEfficiencies
Single
Ballistic
Crater
Impact
Range Diameter Velocity
km
km
50
10-2
10-1
100
10-2
10-1
300
10-2
10-1
1000
10-2
10-1
Impactor
Diameter
a
km/s
m
0.287
2.8
38
1
520
0.403
1
2.2
31
420
0.608
1
1.6
24
290
1.151
1
10
20
1.1
15
208
5 km
11 km
Oberbeck
etal.[1975]
b
5.6
2.2
CrateringEfficiency(M/m)
No. 140-200 Compacted Clustered
Sand
c
30
9.2
0.89
11
4.4
2.8
45
14
1.8
32
13
4.3
84
24
5.0
91
36
14
4.6
3.5
8.0
160
49
15
3.6
2.5
pumicea impactor
½
8.0
2.1
0.71
0.28
0.53
0.11
13
3.3
0.85
26
6.3
1.8
54
14
3.6
0.7
0.46
1.4
0.55
0.22
4.0
1.6
0.62
11
4.5
1.8
0.58
0.44
aDerivedfrom scalingrelationsgivenby Oberbecket al. [1975] for solidimpactor.
bFromTableI of Oberbeck
et al. [ 1975].
CFromrelationgivenin Figure 1 for sand.
aFromrelationgivenin Figure1 for pumice.
½Assumes
efficiencyis reduceda factorof 8 for low-densityclustersfrom valuesgivenby Oberbecket al. [ 1975].
Actualvaluesmay be reducedanotherfactor of 0.2 for targetwith compressive
strength.
3726
SCHULTZ AND GAULT: CLUSTEREDIMPACTS
material should radially decreasefrom about 75 to 15% with
large local variations. Such results contrast with the above
suggestionsthat clusteredimpacts would preservea significantly larger primary component.
Two factors, however, favor the direct application of the
single-bodyimpact scenarioto the Ries. First, the continuous
depositsare best preservedwhere the preimpact surfacewas
largely freshwaterdepositsreachingthicknessesa few tens of
meters.Such depositsare easilyexcavated,evenat low impact
velocities. Second, the presence of an atmosphere can
drastically modify the structure and makeup of the ejecta
curtain. Schultz and Gault [1979] noted that if near ambient
atmosphericconditionsexistedat late times,then ejectaaslarge
as 10m couldhavebeendeceleratedby air dragto nearterminal
velocity. Laboratory experiments illustrate the effective inflight drag sorting of ejecta sizeswhere the larger size ejecta
form an undistortedbut diffusedejectacurtain resemblingthat
formed in vacuum conditions [Schultz and Gault, 1982].
Smaller ejectaare incorporatedin a turbulent ejectacloud. At
scalesapproachingthe Rieseventand under ambientterrestrial
atmospheric conditions, however, only ejecta sizes with
terminal velocitiesapproachingimpact-inducedwinds can be
incorporated in such a cloud, and these ejecta represent
centimeter-sized
debris[Schultzand Gault, 1982].Eventhough
it is estimated that 10-m-sized ejecta arriving at a crater
little or no uprangematerialis depositedand that downrange
debrisleavesthe surfaceat low angles(seesection5). Thesetwo
phenomenawill enhancethe developmentof downrangeejecta
flow within the continuousejecta depositsas describedby
Oberbeck[1975]. Downrangeejectaflow in a vacuum seems
necessary
to accountfor ejectaflow lobes[Howard, 1974]and
departuresof ejectathinning from a simplepower-lawdecay
[Settle and Head, 1977].
6.4.
Origin of Crater Rays
A variety of origins for crater rays has been proposed.
Baldwin [1963] viewed rays as impacts of rock flour ejected
along jets during early crater formation and as downrange
ejectafrom secondarycraters. Oberbeck[ 1971] proposedthat
ray material is largely composedof locally derivedcrystalline
material associatedwith secondarycratering. Schultz [1976]
suggested
that rays have four origins:surfacescouringby lowdensityejectaclusters,laterally transportedprimary material,
locally ejected debris from secondarycraters, and physically
altered local materials. All mechanismscan be supportedby
observations,and the rate of ray disappearancedependson the
particularstyleof formation. The clusteredimpactexperiments
provide new insightfor thesevarious mechanisms.
diameter from the rim of a Ries-sized event will be decelerated
The experimentalresultsdemonstratethat clusteredimpacts
to terminal velocity, this velocity is too high (>500 m/s) to be at oblique anglesin particulate materialsresult in downrange
trapped in a near-rim ejectacloud by air drag alone. Thus large depositionof the projectilematerialon the surface.This process
undeceleratedejecta, and evendeceleratedlarge ejecta,will be is enhancedby a more competenttarget surfaceand provides
separatedfrom the finer ejectafractions,therebyimpactingthe an explanation for the large variations in albedo and spectral
surfacenot as membersof a well-defined ejecta curtain but as signatureof primary ejectaat large distancesfrom the parent
more widelyspacedmissiles.Again suchconditionsfavor direct craters on the moon [Schultz, 1976; Saunders et al., 1976;
application of Oberbeck et al.'s [1975] model of secondary Pieterset al., 1982]and on Ganymede[Poscolieriand Schultz,
crater action to the Ries.
1980]. Certain signatures seem paradoxical if cratering
Cratering efficiencyonly partly controlsthe observedmixing efficiencyvaluesof Oberbecket al. [1975] or if the mechanism
ratio between local and primary materials from secondary proposedby Oberbeck[1971] are used without modification,
cratering,particularlyat largerelativedistancesfrom the crater althoughthis mechanismremainsoperativefor isolatedejecta
rim in a vacuum. The dispersalof the projectilealso must be material.
considered.Low-velocityverticalimpacts(-•500m/s) into sand
At very large distancesfrom the primary crater, clustersof
or pumicetypicallyresultin burial of the projectile.As the angle ejectanaturally disperseowing to interparticlecollisionsand
of impact decreases
below a critical angle,the projectile(or the cumulativevelocity/angledispersionsin the swarmduring
fragments)is ricocheteddownrangeas describedby Gault and ejection.Increaseddispersionand increasedimpact velocities
Wedekind[ 1978].Thiscriticalangledependson thetargetand for large ballistic rangesincreasethe likelihood of individual
projectile,but for illustration, ricochetbecomesimportant for impact eventsof the type consideredby Oberbecket al. [ 1975],
rock targets at anglesbelow 30ø and for particulate targets at therebyincreasingthe crateringefficiencyand the importance
anglesbelow 15ø. Low-velocity vertical impacts by clustered of locally derived material. Very small ejecta, however, may
impactorsinto particulate targetsresult in projectilemateriai simply scour the regolith without excavating subregolith
remaining on top of the crater floor. At very modestoblique materials.This processappliesnot only to highly comminuted
angles (-•60ø), however, the ricochet component increases primary ejecta but also to primary, secondary,and tertiary
dramaticallyand most of the projectilematerialremainson the debris ricocheteddownrange.Consequently,the photometric
surfacedownrange.Consequently,we shouldexpectconsider- signatureof a ray can be pronouncedwithout freshlyexposed
able primary material transported laterally downrange from rock surfaces. The high-resolution Apollo thermal infrared
isolatedsecondarycomplexes.The lateral transportof primary data supportsucha senario[Schultz and Mendell, 1978].
projectilematerial'shouldincreasewith increasedprojectile Thus there probably are severaloriginsfor crater rays that
dispersal(obviously to a limit) and with more competent reflect the physical state of the ejecta ("rock flour" or solid
targets, such as mare basalts.Such a scenarioindicatesthat blocks)and the depth of penetration(regolith versussubregomixing ratios estimated solely from remotely sensed data lith excavation). The studies by Oberbeck et al. [1975]
should be highly variable. Moreover, dilution of a primary addressedthe importance of locally derived material from
ejecta component at large ballistic ranges may result from singleimpactors,i.e., Baldwin'ssolidejectablocks.The results
ricochetand dispersalas well as in situ mixing resultingfrom presentedhere underscorethe importance of the preserved
secondarycratering.
primarysignaturethroughclustersof ejecta,i.e., Baldwin'srock
The dynamicsof ejectafrom clusteredimpactsindicatethat flour.
SCHULTZAND GAULT:CLUSTEREDIMPACTS
7.
CONCLUDING
3727
REMARKS
Clusteredimpactsresultin cratersand processes
that depart
significantly from single-body or two-body impacts. The
observed differences provide new clues for understanding
secondary cratering processesand low-strength/low-density
impacts in general. The following list summarizesthe more
significantexperimentalresultswith applicationsto planetary
processes.
1. Clusteredimpacts displace5-10 times less mass than
does a single impact of the same mass. This reduction in
crateringefficiencyhas important implicationsfor predicting
the relative contribution of local and primary materials from
secondary cratering. It also underscores the difficulty in
estimatingejectasizesfrom observedsecondarycraters.
2. Crater morphologyis stronglydependenton the sizeand
velocity of a clusteras well as the relative densityand strength
betweenthe target and projectile.Crater floors were produced
ranging from "flat" (with an incipient multiring pattern) to
moundedto bowl-shaped.The craterrims are typically high in
reliefrelativeto their diameter,andthe ejectathinsrapidly from
the rim. These morphologiescharacterizelunar and Martian
secondarycraters and certain craterson Enceladus.
3. Oblique impacts of clustered projectiles consistently
produce an ensembleof V-shaped ridges whose apex angle
dependson the clusterdispersionand impact angle. Secondary
craters commonly display V-shaped ridges (the herringbone
pattern) and the experimentalresultsare consistentwith impact
anglescloseto 45ø.
4. Clusteredverticalimpactsproducean amorphouscloud
at early times that evolvesat later times into the well-defined
(classic)single-bodyejectaplume. The ejectaplume becomes
gradually more inclinedfrom the horizontal until at late times
it resembles
the plumeproducedby a singleimpactor.Clustered
obliqueimpactsdevelopan equallydistinctivelow-angleejecta
plume with little uprangedeposits.The evolution of the ejecta
plume shouldenhanceejectaflow around large impact craters.
5. Clusteredoblique impactsdo not form the distinctive
butterfly pattern of a single-bodyimpact but form a fan-shaped
pattern extendingdownrange.This uniquepattern may help in
identifyinglargebasinsecondaries.
It alsocontributes
to the
Fig. A1. Spatial distributionof pits producedby pyrex fragments
impactingan aluminumwitnessplate.Pyrexfragmentswerecreatedas
a 0.635-cmpyrexspherepassedthrougha thin pieceof paperat 5.5 km/
s. Original sizeof pyrex shownat edgeof cluster.
dispersionof the pyrex fragmentsis largelydue to centrifugal
force resultingfrom spin on the projectileduring launch. Two
methods were used to calibrate the lateral dispersion and
overall cluster configuration at impact. The first method
employed aluminum witnessplates placed at the target; the
secondusedhigh frame rate overheadviewsthat recordthe first
contact at the target surface. Figure A1 illustrates a typical
result for hypervelocityfragments impacting an aluminum
witnessplate. Each clusterdisplaysa relatively well-contained
pattern with uniform distribution of fragment sizes.The size
distributionof holesin the witnessplate is shownin FigureA2.
No systematicattempt has been made to translate the size
distributionof the holesto actualfragmentsizeexceptto note
that an unbroken 0.635-cm pyrex sphere at about the same
velocityproducesa 0.85-cmhole in a witnessplate of the same
thickness(0.09 cm). Thusthe sizeof the holeswill approximate
the sizeof the fragmentsfor sufficientlylarge fragments.The
cumulative sizedistribution in Figure A2 indicatesthat about
formation of crater rays.
6. Projectile material from a clustered impact largely
2.5 --
remains on the surface: contained by the crater in vertical
impacts and strewn downrange in oblique impacts. The
combination of projectile disperson, reduced cratering
efficiency,andthedownrangefan-shaped
distributionmayhelp
explain variations in the albedo and spectral signature of
!
i
i
I
,
I
i
1
,
"
.:
1.5-
primary material.
Preliminaryresultsat very high impact velocities(>6 km! s)
revealboth similar and strikinglydifferentphenomena[Schultz
and Gault, 1983]. We strongly suspectthat craters below a
certainsizeon the Earth and Venusmay be very differentfrom
comparablesize craterson the Moon owing to atmospheric
breakup,assuggested
by Melosh[1981].Detailedcomparisons
and discussions
will be forthcomingin a future contribution.
1.0
-
.5
-_
I
0.0
0.0
APPENDIX
.4
LOG
Fig. A2.
.6
.8
i
1.0
D, mm
Cumulative size distribution of holes createdby shattered
For impact velocitieshigher than 1 km/s, clusterswere pyrex as shownin Figure A1. Falloff at sizessmallerthan 1 mm largely
producedby fragmentingpyrexspheres
astheypassedthrough reflectsfragmentsunableto penetrate0.09-cm-thickaluminumwitness
thin aluminum foil (1-2 km/s) or paper (>3 km/s). The lateral plate.
3728
SCHULTZ AND GAULT: CLUSTERED IMPACTS
175holeslargerthan I mm wereproducedin thisexample.The
large numberof surfacepits that did not penetratethe witness
plateindicatesthat the changein slopeat smallsizesin Figure
A2 probablyis not relatedto fragmentsizebut to the thickness
of the witnessplate. Extrapolationof the slopeat largersizes
to 1 mm suggests
over 300 of this sizeand larger. High-speed
framingcamerasabovethetargetrecordedverysimilarpatterns
for impactsinto sandand compactedpumice.
The distributionof the clusteralong the trajectorycan be
framingrate, the exposuretime is about 44 ps. Streaksof
individualfragments
in suchphotographs
aswellasinterframe
spacingof the clusters
demonstrate
that no significant
lossin
velocity(<10%) resultedfrom the aluminumfoil usedto break
up theprojectileat lowervelocities
(<1.5km/s). Measurements
of thesmeared
cluster
imageandlengths
ofindividual
fragment
streaksrelativeto theclustersmearindicatethatthelengthof
theclusteris approximately
thesameasthewidth.At higher
impactvelocities
(2-6 km/s),in-flightimages
arenotpossible
directlymeasuredfrom the highframerate (:>7500frames/s) at the framing ratesused,but there is no reasonto believethat
photographsfor impactvelocitieslowerthan 1.5 km/s. At this therewill be a significant
changein the shapeof the cluster.
TABLE B1. Cratering Efficiency
No.
Projectilea
vp
V•
820554
820555
820556
821215
821216
820502
820503
820504
821119
821120
820546
810510
810511
821222
821223
821236
830211
821210
821122
830546
830548
830549
830203
830608
830603
0.3756-A1
0.3756-A1
0.0453-A1
0.3759-A1
0.3759-A1
0.3755-A1
0.3755-A1
0.0056-A1
0.3759-A1
2.16
0.665
480
800216
800203
800207
800209
830540
830539
830534
830538
830536
830531
830541
800214
800553
800554
800556
800559
800561
800562
800563
800564
800565
0.3759-A1
0.3760-A1
0.3752-A1
0.3752-A1
0.1481-Cd
0.1487-Cd
0.132-Fe
0.298-PX
0.1486-Cd
0.1487-Cd
7.837-SNY
2.566-HNY
2.397-HNY
0.2980-BPX
0.2986-BPX
2.461-HNY
14.8-H2
69.3-A1C
31.8-A1C
21.4-A1C
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-PX
17.7-A1C
30.3-A1C
32.5-A1C
31.6-A1C
96.4-A1C
27.6-A1C
35.6-A1C
35.6-A1C
97.1-A1C
7.71-SNY
:.o6
0.899
1.58
(2.0)
2.01
2.29
0.89
1.61
0.?15
6.09
5.64
4.83
5.08
4.23
3.6?
2.10
1.22
0.204
0.197
0.176
4.35
1.33
0.172
0.173
0.105
O.110
0.104
1.46
1.44
1.45
1.62
1.56
1.90
1.55
0.101
0.072
0.054
0.082
0.059
0.077
0.087
0.080
0.059
0.159
166
67.2
217
353
270
267
7.79
102
167
90
799
834
347
308
222
268
171
22.6
187
46.3
40.4
197
64.3
79.4
426
1120
396
345
80.6
38.4
29.8
18.3
41.4
15.9
139
284
264
179
448
1310
690
467
442
1571
374
•r•
2.15
2.27
1.18
1.24
E-8
E-7
E-8
E-7
1980
685
2300
894
4.01 x E-8
1450
2.48 x E-8
921
2,48 x E-8
910
4.79 x E-9
1.27 x E-7
E-8
E-7
E-9
E-9
E-9
E-9
E-9
E-9
E-8
E-8
E-6
E-5
1780
347
571
308
2730
2840
3000
2650
2150
1150
1480
195
30.6
23.1
E-5
21.6
3.87
1.96
2.50
2.71
2.15
2.42
2.81
7.32
1.14
2.54
7.22
1.52
1.91
x
x
x
x
•r•
x
x
x
x
x
x
x
x
x
x
x
x
x
(6.67 x E-8)
(7.56 x E-7)
2.00 x E-5
(4.64 x E-5)
(1.32 x E-4)
(1.36 x E-4)
(2.01 x E-4)
(1.18 x E-7)
(3.70 x E-7)
(4.13 x E-7)
(4.57 x E-7)
(1,02 x E-6)
(6.95 x E-7)
4.18
2.51
3.16
5.63
2.72
x
x
x
x
x
P
P
0.159
P
0.318
0.159
0.159
0.95
1.87
1.87
S1
S1
S1
P
P
P
P
P
P
P
P
P
P
P
P
P
P
50
S1
S2
S2
49
27.6
21.2
27.4
346
165
128
78.8
178
68.4
2.10 x E-4
23.1
1.22
1.21
1.43
2.63
1.58
25.0
22.3
21.1
27.5
82.5
Figures
0.318
0.318
0.159
0.318
0.318
0.318
0.318
0.0794
0.318
0.318
0.318
0.318
0.318
0.159
0.159
S1
S1
597
27.3
14.8
9.37
24.1
E-4
E4
E-4
E-4
E-5
S1
1020
334
E-8
E-4
E-4
E-4
E-4
x
x
x
x
x
Target
b
S1
$2
S2
P
P
P
P
P
P
P
S2
S2
S2
S2
S2
S2
S2
S2
S2
S2
(4)
(2.•)
1.87
(4.4)
(4.6)
(5.2)
(6.9)
(0.8)
(2.43)
(2.75)
(3.8)
(5.4)
(7.95)
0.318
8.1
5.2
5.2
5.8
2.9
2.3
2.9
2.9
2.9
1.27
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
90 ø
45 ø
45 ø
90 ø
45 ø
60 ø
90 ø
45 ø
90 ø
45 ø
45 ø
45 ø
45 ø
30 ø
30 ø
30 ø
30 ø
30 ø
1,3
1,3
1,3
1,3
1,3,14b
1,2
1,2,14a
1,2
1,2
1,2,21a
1,2
1,2
1,2
2
2
2
2
2
2
2,4,6
2,4,6
2,4,6
3,14b
3
3
3,5,6
3,5,6
3,5,6
3,5,6
4,17b
4,17b
4
4,16,17b,21d
4,17a
4,17a
4,17b,21c
5,6
5
5
5
5
5
5
5
5
5
SCHULTZANDGAULT:CLUSTERED
IMPACTS
3729
TABLE BI. (Continued)
No.
Projectile
a
Vp
VD
71'
2
try
Target
b
r
0
Figures
1.27
1.873
1.873
1.8
1.8
1.8
1.8
5
6
6
6
6
6
6
17a
m-t
800568
830602
830601
3031
4445
5152
3940
_
0.160
0.150
0.136
0.025
0.0282
0.0259
0.0214
175
1060
831
163
209
238
187
830535
7.70-SNY
42.68-PP
51.89-PL
58-RE
61-HBE
60-S1
72-PP
0.2980-BPX
1.47
--
1.56
2.67
3.27
9.09
7.14
8.47
1.24
7.89
x
x
x
x
x
x
x
E-5
E-5
E-5
E-4
E-4
E4
E-3
DLG-530
DLG-533
DLG-125
VGP-645
VGP-640
VGP-713
VGP-771
VGP-896
VGP-898
VGP-721
VGP-723
VGP-724
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
6.46
6.11
5.17
2.83
2.18
1.18
0.872
1.04
0.721
0.440
0.410
0.133
1260
1580
1120
128
83
46.0
35.1
268
190
19.8
103
32.8
2.40 x
2.68 x
3.75 x
6.25 x
1.05 x
3.60 x
6.59 x
9.26 x
1.93 x
2.59 x
5.96 x
5.66 x
--
P
5.4
15 ¸
90 ¸
90 ¸
90 ¸
90 ¸
90 ¸
90 ¸
30 ¸
4890
6140
4350
3980
2580
1430
1090
1040
738
614
400
128
S3
S3
S3
S3
S3
S3
S3
S3
S3
S3
S3
S3
0.318
0.318
0.318
0.318
0.318
0.318
0.318
0.318
0.318
0.318
0.318
0.318
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
1,3
1,3
1,3
1,3
1,3
1,3
1,3
1,3
1,3
1,3
1,3
1,3,5,6
[39-X]
[43-X]
[47-0]
[46-0]
[48-X]
[45-0]
DLG-196
DLG-197
DLG-198
DLG-199
0.454-LX
0.448-LX
0.373-A1
0.464-LX
0.439-LX
0.429-LX
0.376-A1
0.376-A1
0.376-A1
0.376-A1
6.41
6.05
4.40
3.86
2.63
2.56
4.39
5.04
5.92
6.10
1140
1020
693
700
606
435
1665
1953
2414
2323
3.47 x E-9
3.90 x E-9
5.19 x E-9
9.65 x E-9
2.03 x E-9
2.13 x E-9
5.20 x E-9
3.94 x E-9
2.85 x E-9
2.69 x E-9
4520
4110
3350
2730
2360
1830
7100
8330
10,300
9910
S4
S4
S4
S4
S4
S4
glassshot
glassshot
glassshot
glassshot
0.452
0.452
0.318
0.455
0.445
0.442
0.318
0.318
0.318
0.318
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
90¸
1,3
1,3
1,3
1,3
1,3
1,3
2
2
2
2
DLG-200
DLG-203
DLG-204
DLG-380
DLG-381
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.376-A1
6.17
6.07
5.96
5.54
6.00
691
724
706
596
633
2.63 x
2.72 x
2.82 x
3.26 x
2.78 x
11,050
11,600
11,300
9530
10,100
lead shot
lead shot
lead shot
lead shot
lead shot
0.318
0.318
0.318
0.318
0.318
90¸
90¸
90¸
90¸
90¸
2
2
2
2
2
DLG-382
VGP-737
0.376-A1
0.376-A1
5.78
1.87
580
146
3.00 x E-9
2.84 x E-8
9280
2340
lead shot
lead shot
0.318
0.318
90 ¸
90 ¸
2
2
VGP-772
VGP-773
0.376-A1
0.376-A1
1.88
1.94
649
694
2.83 x E-8
2.66 x E-8
2770
2960
glassshot
glassshot
0.318
0.318
90¸
90¸
2
2
VGP-774
VGP-976
VGP-977
VGP-978
VGP-823
VGP-825
0.376-A1
0.376-A1
0.376-A1
0.376-A1
0.2611-A1H
0.2660-A1H
1.93
2.53
2.40
2.41
1.79
1.99
172
244
224
241
299
308
2.69
1.57
1.75
1.73
4.69
3.79
2750
3900
3570
3840
1670
1690
lead shot
lead shot
lead shot
lead shot
S3
S3
0.318
0.318
0.318
0.318
0.476
0.476
90 ¸
90¸
90 ¸
90 ¸
90 ¸
90 ¸
2
2
2
2
3
3
x E-7
x
x
x
x
x
x
E-9
E-9
E-9
E-9
E-8
E-8
E-8
E-8
E-7
E-7
E-7
E-6
E-9
E-9
E-9
E-9
E-9
E-8
E-8
E-8
E-8
E-8
E-8
38.6
31.2
20.4
4.1
5.0
5.8
3.8
S2
P
P
S3
S3
S3
S3
No., experimentnumber(bracketsindicatedata from Schmidt,1980).
m,projectile
mass
(g);t, projectile
type(see
footnote);
Vpimpact
velocity
(km/s);Vadisplaced
volume
oftarget
(cm3);
rr2,gravity-scaled
size
= 3.22gr/v2(Values
in parentheses
indicate
r basedoncluster
radius);
try,cratering
efficiency,
equalto/t Va/m;target,targettype(seefootnote);
r, projectileradius(valuesin parentheses
areclusterradii;valuesin bracketsareequivalentradii);0, impactanglefrom the horizontal.Read
x E-8 as x 10-8.
aA1,aluminum;A1H, hollowaluminum;A1C,aluminumshot;Cd, cadmium;Fe, steel;PX, pyrex;BPX, brokenpyrex;SNY, solidnylon;HNY,
hollownylon;H2, water;PP, plasterof Paris;PL, "Ductseal"puttylikeplastic;RE, low-viscosity
albumenin thin-walledspheroid;HBE, highviscosityalbumenin thin-walledspheroid;S1, no. 140-200sand.
bP,compacted
pumice,
density
= 1.28;S1, no. 140-200
sand,density
= 1.55;S2,no.40 sand,density
= 1.7;S3,no.24 sand,density
= 1.46;
S4, Ottawa Flintshotsand[seeSchmidt,1980],density= 1.80.
3730
SCHULTZ AND GAULT: CLUSTERED IMPACTS
TABLE B2. Crater Aspect Ratios
No.
rn- t
v
r
830526
821231
821225
821226
830531
830534
830608
820503
830203
830548
830549
830602
830211
820546
821210
821222
830601
821120
821215
821216
VGP-823
VGP-825
830606
830603
830203
830608
800206
800205
800207
3031
4445
5152
3940
830546
821227
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2980-BPX
0.2986-BPX
0.3755-A1
0.2980-BPX
2.566-HNY
2.397-HNY
42.68-PP
0.2980-PX
0.3760-A1
0.1486-Cd
0.1481-Cd
51.89-PL
0.3759-A1
0.3759-A1
0.3759-A1
0.2611-HAl
0.2660-HA1
0.2986-BPX
2.4610-HNY
0.2980-BPX
0.2986-BPX
10.0-AIC
31.I-AIC
31.8-AIC
.58-RE
61-HBE
60-S
72-PP
7.837-SNY
0.2980-BPX
1.77
4.83
4.25
4.06
1.90
1.45
0.133
2.01
4.35
0.197
0.176
0.150
3.70
0.715
2.10
4.85
0.136
1.61
0.899
1.58
1.79
1.99
6.1
0.172
4.35
0.133
0.117
0.095
0.110
0.0250
0.0282
0.0259
0.0214
0.204
4.19
830542
0.2980-BPX
1.37
•p
Target
0
Da
P
P
P
P
P
P
S1
P
S1
P
P
P
P
P
P
P
P
P
S1
S1
S3
S3
S1
S1
S1
S1
S2
S2
S2
S3
S3
S3
S3
P
P
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
11.0
14.2
15.6
17.3
18.7
10.4
12.8
15.4
15.9
10.8
9.1
23.2
18.1
10.8
13.4
16.7
24.4
13.9
14.8
16.7
NA
NA
20.9
11.1
15.88
12.75
22.78
26.2
25.7
19.3
18.4
20.3
15.9
14.6
13.3
P
45
NA
(3.52)
1.63x E-3
(4.0)
1.48x E-3
(0.91)
0.126
(0.78)
0.200
(7.95)
1.89x E-4
(2.75)
4.56 x E-3
(4.25)
1.26x E-3
0.318 2.78
(4.0)
1.48 x E-3
1.87
0.093
1.87
0.087
1.87
1.56
0.318 2.2
0.95
2.78
0.159 6.9
0.159 6.9
1.873 1.89
0.318 2.78
0.318 2.78
0.318 2.78
0.476 0.59
0.476 0.59
2.1
0.01
1.87
0.119
4
1.48 x E-3
4.23
1.26x E-3
11.5
0.0021
5.8
0.0507
5.2
0.072
1.8
1.1
1.8
0.35
1.8
0.34
1.8
0.41
0.95
2.18
3.8
(1.29 x E-3)
NA
NA
Davg P
0.22
0.5
1.82
2.29
0.15
0.37
0.77
3.8
1.48
0.34
0.41
6.5
2.29
2.54
2.72
3.43
2.49
3.09
4.16
4.70
NA
NA
4.5
0.75
14.8
0.78
1.19
1.83
1.77
1.2
1.3
1.6
3.5
2.45
0.45
NA
Figures,
flat
flat
mound
mound
flat
flat
mound
pit
mound
mound
mound
pit
pit
pit
pit
pit
mound
pit
pit
pit
NA
NA
bowl
mound
mound
flat
flat
flat
flat
mound
mound
mound
pit
pit
flat
7a,9,10b,lla, 12a,15a,16,21b
8,9,10a,lla, 12a,14a,15b
9,11a,12a,15b
9,11a,12a,15b
9,11a,12a,15a,17a
9,11a,12a,15a
10b
7b,lla, 12a
10a
1la, 12a
11a,12a,13
1la, 12a
11a,12a,15b
1la, 12a
11a,12a
11a,12a
11a,12a,13
11a,12a,15a
1lb,12b
11b,12b
11b,12b
11b,12b
11b,12b
11b,12b
1lb,12b
11b,12b
1lb,12b
11b,12b
1lb,12b
11b,12b
11b,12b
1lb,12b
1lb,12b
1la, 12a,13
11a,12a,15b
--
20
Abbreviations
thesameasin TableB1.m, projectile
mass(g);t, projectile
type(seeTableB1footnote);v, velocity(km!s);r, projectile
radius(valuesin parentheses
indicateclusterradius);•p,densityof projectile;
target(seeTableB1footnote);
0, impactanglefrom
normal;Da,apparent
craterdiameter
(referenced
to originaltargetsurface);
d•vg,
average
craterdepth;P, craterfloorprofile.
TABLE B3. ProjectileDispersal(Aluminum Shot Into No. 40 Sand)
No.
791117
791118
791119
791202
800203
800205
800207
800209
800214
800553
800554
800556
800559
800561
800562
800563
800564
rn- t
59.6-A1
59.6-A1
60.0-AI
60.0-AI
69.3-A1
31.1-AI
31.8-AI
21.4-A1
17.7-A1
30.3-A1
32.5-A1
31.6-A1
96.4-A1
27.7-A1
35.6-A1
35.6-A1
97.1-A1
rc
NA
NA
NA
NA
4.3
5.8
5.2
6.9
8.1
5.2
5.2
5.8
2.9
2.3
2.9
2.9
2.9
N
159
159
160
160
185
83
85
57
47
81
87
84
257
74
95
95
259
vp
NA
0.134
0.106
NA
0.105
0.101
0.110
0.104
0.101
0.072
0.054
0.082
0.066
0.077
0.087
0.080
0.59
0
90
90
90
90
90
90
90
90
90
45
45
45
45
30
30
30
30
m.•
ms_•
m•
mp
mp
mp
NA
NA
NA
NA
0.13
0.30
0.30
0.31
0.27
NA
0.18
0.13
0.004
0.024
0.029
0.027
0.0036
0.23
0.46
0.45
0.29
0.21
0.49
0.34
0.36
0.62
0.82
0.87
0.93
0.49
1.00
0.99
1.00
0.70
0.83
0.86
0.69
0.85
0.92
0.77
0.95
0.95
.78
NA
0.31
0.19
0.51
0.031
0.037
0.031
0.265
Figures
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
23,24
m,projectile
mass
(g);t, projectile
type(seeTableB1);re,cluster
radius;
N, number
ofprojectiles;
vp,impactvelocity
(km! s); 0, impactanglefrom horizontal;rni,projectilemassrecoveredinsidecrater;rnsi,projectilemassrecoveredon
the surfaceinsidecrater;rns,projectilemasson the surface(insideand outsidecrater).
SCHULTZAND GAULT:CLUSTEREDIMPACTS
3731
Morrison, R. H., and V. R. Oberbeck,A compositionand thickness
model for lunar impact crater and basin deposits.Proc. Lunar
Planet. Sci. Conf, 9th, 3763-3785, 1978.
earlystages
ofthestudy,andCarolcontributed
substantially
to thedata
reduction. The techniciansat the Ames Vertical Gun Range deserve Oberbeck,V. R., Laboratorysimulationof impactcrateringwith high
explosives,J. Geophys.Res., 76, 5732-5749, 1971.
specialrecognition
for theirdedicated
services:
Earl Brooks,Wayne
Logsdon,
JoeAstalfa,andRogerKrause.
Thepaperbenefited
fromthe Oberbeck,V. R., The role of ballistic erosion and sedimentationin
criticalreviews
by H.J. MooreandF. Hrrz, andthehelpfuldiscussions lunar stratigraphy,Rev. Geophys.SpacePhys.,13, 337-362, 1975.
with S. Croft, D. Orphal, P.D. Spudis,C. Pieters,and B.R. Hawke. Oberbeck, V. R., and R. H. Morrison, Laboratory simulation of the
herringbonepatternassociated
with lunar secondarycraterchains,
This work wasdone at the Lunar and PlanetaryInstitute, ownedand
Acknowledgements.
We gratefullyacknowledge
the laborsof
Marcus Mendenhalland Carol Polansky.Marcus helpedto hatchthe
operatedby the UniversitiesSpaceResearchAssociationunder
contract NASW-3389 with the National Aeronautics and Space
Administration.Lunar and PlanetaryInstitutecontribution550.
Moon, 9, 415-455, 1974.
Oberbeck, V. R., and R. H. Morrison, Candidate areas for in situ
ancient lunar materials, Proc. Lunar Sci. Conf, 7th, 2983-3005,
1976.
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D. E. Gault, Murphys Centerof Planetology,Box 833, Murphys, CA
95247.
P. H. Schultz, Department of GeologicalSciences,Brown University, Providence,RI 02912.
(ReceivedFebruary 8, 1984;
revisedAugust29, 1984;
acceptedNovember 1, 1984.)