VOL. 84, NO. B14
JOURNAL
OF GEOPHYSICAL
RESEARCH
DECEMBER
30, 1979
Low-Velocity Impact Craters in Ice and Ice-Saturated Sand With
Implications for Martian Crater Count Ages
S. K.
CROFT
Departmentof Earth and SpaceSciences,Universityof California,Los Angeles,California90024
S. W.
KIEFFER
U.S. GeologicalSurvey,Flagstaff,,Arizona 86001
T.
J. AHRENS
Divisionof Geologicaland PlanetarySciences,CaliforniaInstituteof Technology,
Pasadena,California91125
We produced a seriesof decimeter-sizedimpact craters in blocks of ice near 0øC and -70øC and in
ice-saturatedsandnear -70øC as a preliminary investigationof crateringin materialsanalogousto those
found on Mars and the outer solarsystemsatellites.The projectilesusedwere standard0.22 and 0.30 caliber bulletsfired at velocitiesbetween0.3 and 1.5km/s, with kineticenergiesat impactbetween109and
4 x 10•øergs.Craterdiameters
in the ice-saturated
sandwere-•2 timeslargerthancratersin the same
energy and velocity range in competentblocksof granite, basalt and cement.Craters in ice were -•3 times
larger. If this dependenceof crater size on strengthpersiststo large hypervelocityimpact craters,then
surfacesof geologicunitscomposedof ice or ice-saturatedsoil would havegreatercratercountagesthan
rocky surfaceswith identical influx histories.The magnitudeof the correctionto crater countsrequired
by this strengtheffect is comparableto the magnitudesof correctionsrequired by variations in impact
velocity and surfacegravity usedin determiningrelative interplanetarychronologies.The relative sizesof
cratersin ice and ice-saturatedsandimply that the tensilestrengthof ice-saturatedsand is a strong inversefunction of temperature.If this is true, then Martian impact crater energyversusdiameter scaling
may also be a function of latitude.
where Eo is the muzzle energy, rn is the bullet mass, p is the
densityof air, A is the cross-sectional
area of the bullet, and Ca
Impact cratering is recognized as an important processin is the coefficient of drag. Equation (1) was derived by inplanetary accretionand in shapingthe solid surfacesof plan- tegration of Newton's secondlaw using a low-viscosity,'Vets and satellites in the solar system. Crater counting is fre- squared'drag force appropriatefor bullets [Albertsonet al.,
quently used,and is often the only techniqueavailable,for es- 1960]. The quantity rn?CaApestimatedfor each bullet is also
timating both the relative and absolute ages of geologic given in Table 1.
featureson other planets. Most surfacesin the inner solar sysThree types of target blocks were used. They were prepared
tem consistof rock materials and their weathered products. and characterized as follows:
Consequently,terrestrialsmall-scaleimpact and explosionex1. 'Ice-saturatedsand' (ISS) blocksconsistedof water-satperiments have been performed primarily in rock or soil. urated sand frozen to approximately -70øC. Containers --•27
However, becauseof the recognition of the probable domi- x 33 x 16 cm in size were filled with sand and then water unINTRODUCTION
nance of ice and ice-saturated soils, both at and far below the
melting point of water over large portionsof Mars, the asteroids, and particularly the satellitesof the outer solar system,
we performed a seriesof low-velocity impact experimentsin
ice and ice-saturatedsand. The objective of these impact experiments was to provide a preliminary survey of the morphology and kinetic energy-dimensionalscalingof cratersin
icy media comparedto impactsat similar kinetic energiesand
velocities
in rock and cohesionless
EXPERIMENTAL
sand.
PROCEDURE
The projectiles used were standard 0.22 and 0.30 caliber
bullets fired at velocities between 0.3 and 1.5 km/s. Table 1
givesthe ballistic data derived from manufacturer'sspecifications for the bullets used. Impact kinetic energiesat the measured firing ranges(R) of 8-13 yd (7-12 m) were interpolated
from the ballistic data using the equation
Copyright¸ 1979by the AmericanGeophysicalUnion.
Paper number 9B 1305.
1305501.00
zen in the container.
2. 'Supercooledice' (S-ice) blo,cksconsistedof pure water
ice frozen to about -70øC, with the same dimensions as the
blocks of ice-saturated sand. To prevent the formation of
large single crystals or bubbles, these blocks were built up
layer by layer, adding first water and then crushedice until
the ice was barely saturated.The water-ice mixture was then
frozen, producing blocks having a uniform fine grain phaneritic texturewith tiny bubbles(<0.1 mm) thinly distributedin
the interior.
3. 'Temperate ice' (T-ice) blocks consistedof pure water
ice near 0øC and were prepared in three ways. The first type
of temperate ice blocksusedwere commerciallyproducedand
maintained in a freezer at a temperature of--•28øF (-2.2øC).
These blocks were --•36 x 20 x 20 cm in size. The commercial
method of freezing produced a roughly tabular amorphous
core ('cloudy zone') imbedded in a matrix of elongatedrodlike crystals(--•0.5-1 cm long and 0.2-0.3 cm thick) oriented
perpendicularto the face of the tabular cloudyzone. This pro-
R= C•Ap
0148-0227/79/009B-
til the sand was covered by a thin water layer. The mixture
was slowly stirred to remove air bubbles.The mixture was fro-
8023
8024
CROFTET AL.: SECONDMARSCOLLOQUIUM
TABLE
1.
Bullet Ballistic Data
Velocity, km/s
Bullet
Mass,g Muzzle 100yd*
Energy, ergs
Muzzle
100yd*
m/Cap'l, cm
22 Short (22S)•22 Long (22L)•22 Long Rifle (22LR)•22 Hornet (22H)•-
1.88
0.334
0.275
1.04E95
1.88
2.59
3.24
0.378
0.383
1.25
0.294
0.310
NA
1.34E9
1.90E9
2.54E10
7.05E8
8.13E8
1.25E9
NA
5.36E4
4.20E4
5.01E4
4.86E4
30-06SPRG
3.56
1.48
NA
3.88E10
NA
4.86E4
8.10
0.975
0.856
3.85E10
2.97E10
8.11E4
(estimated)
Accelerator
(SPRG)•30-06PSP(PSP)•-
(estimated)
NA is not available.
* 1 yd=0.91m.
•-Abbreviationusedin Table 2.
$Read 1.04E9as 1.04x 109.
vided for highly anisotropicmaterial propertieswhoseeffects flat end faces,which had vertical relief of <•3mm.All facesof
on the craters are noted below.
the commercial ice blocks were used; these surfaceswere also
The second temperate ice blocks ('pressedblocks') were smooth.Bullet name, target type, range,and crater depth and
prepared by compressingcrushedice in a pressurevesseluntil diameterwere recordedfor eachshot.Thosedata are grouped
fusion. This produceda uniform but porphyritic texture with accordingto target compositionand listed by shotnumber in
many millimeter-sizedbubbles.These blocks were cylinders order of increasing 'trapactenergy in Table 2. Crater 5 is
with diametersand lengthsof--,20 cm.
shownin Figure 1. Depths were measuredfrom the original
The third temperateice ('pot') blockswere preparedby sat- target surface. Diameters are averages of the largest and
urating a container filled with crushedice and then freezing. smallest diameters of each crater.
This method produced nonuniform porphyritic textureswith
RESULTS
occasionallarge air pockets(which did not affect the results
reported below, as we discardedsampleswhere the bullet obWith the notable exception of craters formed in the comviouslyhit an air pocket).Theseblockswere cylinders--,25cm mercialice blocks,the craterswere hemiellipticalcupsin cross
in diameter and --•15 cm long.
section.The subsurfacefracture systemswere both concentric
The internal temperaturesof the blockswere made initially and radial in pattern similar to thosefound around --•5-cm-diconstant by prolonged residencein monitored refrigerators. ameter impact cratersin ArkansasNovaculite by Curran et al.
The volumesof the refrigeratorsavailable severelylimited the [1977]. Radial fractureswere dominant in cratersin ice, while
maximum practical size of the target blocks. The blocks re- fine concentric fractures predominated in the ice-saturated
mained in the refrigeratorsuntil transferredto insulatedboxes sand craters.Visible fracturing was concentratednear the imfor immediate transportto the firing range. Temperaturesin- pact site and near the rear face of the targetblock. Shots4 (Sside the insulated containers were monitored. On the basis of
ice) and 9 (ISS), which were fired into blockswhich each al(1) the time between removal from the refrigeratorsuntil use ready had a 5-cm crater in them (whosevisiblefracture zones
at the firing range (a few hours), (2) the air temperaturesin- were small in comparisonto the block size),completelyshatsidethe insulatedboxesat the time of targetuse(--•0øCfor the tered the blocks.Identical shots(3 in S-iceand 10 in ISS) into
temperate ice blocks and -14øC for the ice-saturatedsand undamaged blocks produced measurablecraters and only
and supercooledice blocks),(3) the thermal propertiesof ice, split the blocks.It is concludedthat the cratersproducedexand (4) the parameterizedtemperaturehistory calculationsof tensive,less obvious interior failure beyond the visible fracSchneider[1974], it is estimatedthat the surfacetemperatures ture systems.
of the supercooledice and ice-saturatedsandblockshad risen
The upper limit of usable impact energieswas set by the
between 5ø and 10øC, while those of the temperature ice targetblock sizeand composition.For blocksin the sizerange
blocks had risen a few tenths of a degree.The temperature used,the upper energylimit for ice blocksis --,3 x 10•øergs,
gradient near the surfaceof the supercooledice and ice-satu- becauseshot 16 at 3.7 x 10•øergscompletelydestroyedthe
rated sand blocks is estimated to have been --•0.5øC/cm from
targetblock,while shot3, at 2.5 x 10•øergs,did not. The up-
Schneider's [1974] calculations. Edges and corners of the per limit for the ice-saturatedsandblocksappearsto be near
blockswould have been a few degreeswarmer, but as the cra- 5 X 10iø ergs.In order to gain as large a rangein energyas
ters were formed in the approximate centers of the block possiblefor scalinganalysis,craterswere producedwith crafaces,the influence of temperatureedge effectson crater for- ter/target block dimension ratios ranging from --,0.1 to 0.7.
mation was deemednegligible.
There are several possibleeffectson the expectedcrater diAt time of use, target blocks were removed from the in- mensionsdue to the large changeof crater size relative to the
sulated boxes and the containersin which they were frozen target size. Gehring[1970b]analyzedthe depth of penetration
and were immediately buried in an embankment of soil with of a projectileof given massand energyas a functionof target
one exposed vertical face into which the bullet was fired. thicknessin metals.He found very little changein expected
Figure 1 showsthe placement and orientation of a block of crater dimensionsuntil the depth of the expectedcrater was
ice-saturated sand in a sand embankment. The faces of the su>•0.5 the target thickness, beyond which the diameter nar-
percooledice and ice-saturatedsand blocksused as targets. rowed slightly [Gehring,1970a]and the depth increasedrapwere the 27 x 33 cm bottom faces,which had smooth sur- idly toward penetration.The suddenincreasein crater depth
faces.The target facesof the pot and pressedblockswere the is due to spallationand failure of the target'srear face caused
CROFT ET AL.: SECOND MARS COLLOQUIUM
8025
...
.:
:.
....
.?.
•..•i
•:
.
..-....
,..
:..:,.
''•.:.,.*•:,- -//
•
.
/-
.:.
. -.•
ß
-•
,...
•:½•".,
'•;•
...*•a.
a*•*
.?•.-.•;,•:
.:
.....•:..,..}•--
:.•... - ..
...-::...;...-½•.e**
.... .
ß
'::;'•:½•
.•..,
.....
•. -.... . •
ß:-.
........
;.:
...,;..**
. -•
'*'"•.
4"**
....
, .
.;:i;•:•:.
**:'•':'
"
.........:.
::.
.
..
..
.,..
-•.,.•.-.-::.
....
....:.:•;::,...:..,.:,;.::.:.....:-'t:
' ......,&;-½...:.'*-"
.½7½:
.**'
.....
.•..........
.'•.... -•
'.c.....
:• ...,
-½•..,::
,,,....½
. .:--.,:,.:.,•....•
.......
:.&.'•...-.,
....
.....
, . •..
... ?--•:x
:•{;;...?-*':';
...•...
•,....;:.•,
'
...•.;:•;:
?.'.Zq•
..,....' :•'•*•½•:•:•:.:'"
:";* :•;":'"*:'
ß
.•:.;
•......
..............
:........
•,:..
ß.
:•::::"•,
_
......
,'"":.. '*'•::..':•,:.'?:::..:C::•:;;.;-•*
....
'":
•'•'•'•'••,
.....
.•••-•••••4:•;,,.::.•.:
...
,..
• .. .....,:-.:....
?:...
.*'• :•½:,•...:
...';'•. ......-.....a.-..::,...y..***,:,::::.,•.
, .:-.:..•.:.,.:...:,.....,,&.,:.,,•
•.:,.,
..- ..:•,.:,•,
::.•.•::,.
• ,.:
..:..,?,.:..
**;•,.•..•.,.
.... ½•...-..:,,:,:,•..•,:;,:r.,...:..*-**
...........
ß............
.....
,, .........
, .......
.....,
.............
,........
..•,,.½a•,.:•.'"•')•,....•,
..............................
.........
a.._.•.•...••..•.••.•••..
.•,•.:.:;"•:..•';:.:;:•'
......
,::
...... •..
.............
........
..**.,
.....
......
. ...
.:..;
...........
,:..,...............
:e..........
..:.•
.:...
. ........
.......
........
•'•:..:
ß
•... .
. •'.
..:',•;.• .............
•'
.,.* •*...•:•'
.....',;:•;'•-,'
•..'e'-?'•<•.
'•;:• :;.
•' ';....•:
.. .....:,.:.
• '.•
•
.;,: ..-.-::,•
.... .4::: '..' .•.'**•,½'*
.. *
.
..,.
.....
ß
,
.,•-•;:.
.• •;•,:*-•:,
ß.......;."*:::•;.'."
'.,..:'•'-"'"..'•'•.::*':'
.•::'
*
:;• •
............
.:'•.½-,.:.
'""
'•"•-•:•-•:•
".
ß•-'......ß½';;,.C:
ß
',..";½
.•,,:,
.....
•..•,,
.
•
... •.
.
--• .. :-..
....,;..'•'•'..¾'
' ........:...½½}..:.......
,..,-.......,.....,:;:::
.....
-';:'
%::.-.:-':." "".:'..':,.'*"
.%.•.. "-
•-
........
./
......
,
...
½ .•
. ,
..,*.:,-7,''"
;....:.:'-.C•-;..'•
.,.
.--.-:.
Fig. 1. Crater $ in ice-saturatedsandshowingan exampleof the cratersdiscussed
in this reportand the target arrangementof ice-saturated
sandblockbunkeredby sandwith oneverticalfaceexposed.Note the relativelylargedepth/diameter
ratio(-•0.4compared
to typicalhardrockvaluesof-•0.2) andthesystem
of crackssurrounding
thecraterto approximately
one crater radiusbeyondthe slightlyraisedrim. White scalebar is ,-•10.5cm long.
8026
CROFT ET AL.' SECOND MARS COLLOQUIUM
TABLE 2.
Shot
Bullet*
Range,
yd-•
Energy
Ei, ergs
Crater Data Summary
Diameter
Depth
D, cm
d, cm
I
22S
13.3
1.00E9•:
S-Ice
4.5 +_ 0.5
2
22L
13.3
1.26E9
7+_3
2.48E10
2.48E10
---23
2.6
2.5
---13
Notes
double crater, Di = 4 cm,
Do = 10cm
block split
block destroyed,prefracturedby I
3
22H
13.3
4
22H
13.3
5
6
7
8
9
22S
22L
22L
22H
PSP
10
10
10
13.3
10
l0
SPRG
10
3.70E10
11
12
22s
22s
10
10
1.01E9
6
0.8
1.01E9
6.5
2.6
into cloudy zone
perpendicularto grain axes,
13
22S
10
1.01E9
6.5
3.0
perpendicularto grain axes,
14
22S
10
1.01E9
4.5
10.9
15
22LR
10
1.82E9
4.9 +_ 0.5
16
SPRG
10
3.70E10
17
22S
18
19
20
......
Ice-Saturated
Sand
4.25 +_ 0.25
1.8
4.9 +_ 0.1
2.0
5.0
1.8
1.01E9
1.82E9
1.82E9
2.48E10
12
5.0
3.69E10
......
---16
---5.6
in same block as 5
block split
block destroyed,prefracturedby 7
block split
T-Ice (Commercial)
square crater
square crater
parallel to grain axes,
conical crater
8.5
parallel to grain axes,conical
crater
block destroyed
T-Ice (Pots)
9.2
1.01E9
6.5 +_ 0.5
3
pot 6, large singlecrystals
22LR
10.8
1.81E9
3.8 +_ 0.3
1.5
pot 2, wrong or faulty bullett??
22S
22LR
8.3
10.8
1.02E9
5
1.81E9
---10
in block
T-Ice (PressedBlocks)
3
---5.5
upper quadrant spalledoff
upper right half spalledoff
*See Table I for full designation.
•- 1 yd = 0.91 m.
$Read1.00E9as 1.00x 109.
by the strongrarefactiongeneratedby reflectionof the primary shockoff of the free rear face.By buryingthe targetsin
a medium with a density comparableto the target density,
shockreflectionand spallationare reduced,increasingthe effective target thickness.Crater 3, with a crater depth/block
thicknessratio of--.0.7, is the only crater large enoughto have
possiblyhad its dimensionssignificantlyaltered by near per-
15
o
Ice-Sat
Sand
•' Supercooled
Ice
ß Temperate Ice
4- Granite (Bauer & Calder,1969)
• Basalt
(Gault,
197:5)
J
] a Sando(Oberbeck,
1971
)
_
j
_
foration. However, as seen in Figure 2 and discussedbelow,
the depth/diameter ratio of crater 3, which would be anomalously large had near performation occurred,is similar to that
of the other ice craters. Thus any effects of varying target
thickness relative
to crater size are deemed small for these ex-
periments.
Burial of the target was also intended to reduce lateral spallation. However, as is seenin Figure 1, the loosenature of the
sand prevented effective enclosureof the upper forward portions of the target. As a result, large sectionswere spalled off
of the upper face of the blocks containing craters 19 and 20
(which were otherwisenormal). The three largestcraters(3, 8,
and 10) completelysplit their respectivetarget blocksowing to
insufficient lateral containment. Becausethe energy required
to generate fractures beyond the true crater is small in com-
parisonto the energyneededto crushand eject material from
the crater [Gault et al., 1975; Kutter and Fairhurst, 1971], the
effectsof large-scaletarget splitting on crater dimensionsare
also considered Small.
0
-
••,•+•
0
5
Crater shapes in the highly anisotropic commercial ice
blocks depended on the orientation of ice crystalsat the face
t0
t5
20
in which
the
crater
was formed.
Craters
14 and
15 were
formed in the face with the long axesof the ice grains parallel
to the projectile velocity. The cratersare abnormally deep and
Fig. 2. Depth/diameter relation for the cratersin this study and conical in shapein comparisonto thosein the polycrystalline
for low-velocity impactsin granite and hypervelocityimpactsin sand
and basalt. The numbersin this figure refer to crater numbersgiven in anisotropic ice blocks. Ejecta consistedof large rodlike segTable 2 and designatefour data points consideredanomalousas dis- ments of individual crystalsand a relatively undamaged 'plug'
cussed in the text.
thrown several feet in front of the target. The undamaged naDiameter
(cm)
CROFT ET AL.: SECOND MARS COLLOQUIUM
1oo
_
i
ß Ice-Sat
i
i
i i iii
I
i
i
i
I i iii
I
i
i
i
i
i i
Sand
- /x "Super"lce
- o "Temperate"lce
•
E
ß•
aSand
Sand
(Oberbeck,
- m
(Stoffler
et197,,;75
al, )
_•
-•F•"-•
.-
{•0s
•o•'•o•
' , , , , , ,,•
•09
.•<.•,/sec
_
k•y•' a/'
T•.•' •/s
'•'
.... '• • •
•
, , , , , , ,{0,••0
-
, , , , , ,'•'0•
{
ImpQct Energy (ergs)
8027
ity to hypervelocityimpactsin sand(Oberbeck[1971], apparent crater dimensions),and the mean curve of Gault's [1973]
hypervelocityimpactsin basalt and granite. The anomalous
depthsof craters 14 and 15 in the commerciallypreparedice
blocks are immediately apparent. Crater 11 appears abnormally shallowbecausethe depth measuredwas to the top of
debris left in the crater rather than to the bottom of the debris
layer as was done for the other craters.Crater 2 had a welldefined depth but consistedof a double crater with an inner
deep portion ,--4 cm acrossand an outer shallow spall zone
,--10 cm across.This crater shape,unique in this set of experiments, is probably the result of inhomogeneitiesin the target
block. These four craterswere ignored in least-squaresfitting
of the data. The lines labeled
Fi 8. 3. •ependence o• cmte• diamete• on impact ene•8• •o• ice
(dashed line) and ice-saturatedsand (uppermostsolid line) cmte•s
compared to cmte•s in the same cne•8• and ve]ocit• mnSe in •ock
(]owe• solidlines)and sand(dot-dashedlines).The numbersb• certain s•mbo]s in this •Su•e •e•e• to the numbe• o• superposedimpacts
•ep•esentedb• the sins]e s•mbo],
ice and ice-sat. sand are least-
square fits to the data. From the figure it is seen that the
depth/diameter ratiosof cratersin rock are ,--0.2,of cratersin
sand are ,--0.25, of craters in ice-saturated sand are •-0.35, and
of cratersin ice are nearly 0.5. Thus at leastsmall-scalecraters
in ice are nearly hemisphericalin shape. Interestingly, this
correspondsto the shapesuggestedas necessaryby Ostro and
ture of the plug is consistentwith observationsand calcu- Pettengill [1978] to account for the unexpectedpolarization
lationsby Curranet al. [1977]for similar low-velocityimpacts. properties of radar returns from Europe, Ganymede, and
Although it is possiblethat vapor formation ejectedthe plug, Callisto, whosecrustsapparentlyare largely composedof ice.
we do not believeit likely at theselow velocitiesand suspect
Figure 3 showsthe corresponding
plot of craterdiameteras
that elasticforcesejected the plug. At higher velocities,both a function of impact energy. In addition to the data of Gault
plug and individual crystalsare fragmented.
[1973] and Bauer and Calder [1969] an energy-diametercurve
Craters 12 and 13 were formed in commercial block faces derived from the low-velocity steel bullet impactsof Vanzant
with the long axesof the ice grainsorientedperpendicularto [1963] into cementare shown,as well as additional apparent
the projectilevelocity,and are roughlyinvertedpyramidsin sand crater data from Oberbeck [1970] and StOffier et al.
shape. Two facesof the 'pyramid' consistof the broken ends [1975].The uppermost
solidline is a least-squares
fit to the
of grains,while the other two Sidesare definedby the sidesof ice-saturatedsand data. The estimated energy-diameterrelathe ice grains.Crater 11 was formed in the amorphouscloudy tion for the ice craters (dashed line in Figure 3) appears to
zone and has a typical hemisphericalprofile. These cratersin have a logarithmic slope equal to or slightly larger than the
the commercial ice blocks illustrate the importance of grain ice-saturatedsand slope,but the data are insufficientfor a resizeand orientationin small-scale,low-velocityimpacts.
liable fit. Craters 14 and 15 are omitted from this figure beFor all craters,projectile de.formationwas similar to that cause their dimensionswere completely altered by the anifound in other studies.In the low-velocity permafrost craters sotropy of the commercialice block face in which they were
the bullet was recovered in the bottom of the crater or in front
formed. Crater 18 has a normal depth/diameter ratio but is
of the target.Bulletsturned 'insideout' at velocitiesof -•300 lessthan half its expecteddiameter in Figure 3. The small size
m/s, in accordwith observationsby Culœand Hooper [1961]. could be the result of a faulty bullet. Comparison of the
At velocities of •1 km/s the bullets disintegratedto a fine curves of Gault [1973] and Bauer and Calder [1969] between
gray powder in accordwith observationsof end productsof Figures2 and 3 showsthat at a given energy,Gault's hypervelocity craters are somewhatlarger in diameter but have
missilecomponentsin impactsin alluvium [Moore, 1976].
Figure 2 showsthe quantitative relation betweendepth and about the same depth as Bauer and Calder's low-velocity cradiameter for the cratersformed in theseexperiments.Included ters. This could be due to either the different velocities used or
for comparisonare steeland tungstencarbide ball bearing im- peculiaritiesof the materialpropertiesof the targets.The kipactsin Disraeli Light granite by Bauer and Calder [1969] in netic energy-diameterrelationsof the sand cratershave nothe samevelocityand energyrangeas our impacts,1ow-¾eloc- ticeablydifferentlogarithmicslopesthat are weak functionsof
TABLE 3. Empirical Energy-DiameterRelations(Shownin Figure 3)
Target Material
Energy-DiameterRelation*
Energy Range of
Data, ergs
Source
Sand
V = 1 km/s
V = 2 km/s
V = 6 km/s
(estimated)
Ice (estimated)
Ice-saturated
Cement
Basalt
Granite
sand
D = 0.044 E 0'28
107-1011
D = 0.34 E 0'29
107-1011
D = 0.021 E 0'29
107-1011
Oberbeck[ 1970]
Oberbeck[ 1970]
Oberbeck[ 1970]
D--D =
D =
D =
1.4 x 10-3 E ø-4
2.36 x 10-3 E ø-36
1.6 x 10-3 E ø'37
1.1 X 10-3 E ø-37
109-3 x 10 lø
109-4 x 10lø
7 X 106-7 X 109
101-1012
D=
1.2X 10-4E ø'46
2X109-5X10
*D is in centimeters,
and E is in ergs.
II
this paper
this paper
Vanzant [ 1963]
Gault [1973]
Bauer and Calder [ 1969]
8028
CROFT ET AL..' SECONDMARS COLLOQUIUM
TABLE 4.
Material
Or,bars
Granite
Pink
Charcoal gray
Cheyenne Mt.
Bohus
Westerly
Basalt
Buckboard
Ralston
Cement
Rock Tensile Strengths
Mesa
Maurer and Rinehart [ 1960]
Rinehart [ 1965]
Rinehart[ 1965]
Reichmuth [1968]
Reichmuth[1968]
Reichmuth[1968]
Wijk et al. [1978]
CohnandAhrens[1979]
184
1168_+160
30-60
dynamic
dynamic
static
Curranet al. [ 1977]
CohnandAhrens[1979]
LaLonde and Janes[ 1961]
are obtained
late in the
impact event and at relatively low pressures,we believe that
the similarity of slopesimplies that similar mechanismsof material failure operate in the late stagesof both low-velocity
and hypervelocity impacts.
It has been postulated that the final size of craters in competent media in this diameter range is determinedby the dynamic tensile strengthof the material [Curran et al., 1977;J. S.
Rinehart, personal communication, 1978]. Near the point of
impact the peak shockstressgreatly exceedsthe material's dynamic compressivestrength oc,thus crushing target materials
which are subsequentlyejected.At greater distancesthe compressivestressesfall below oc, but excavation continuesbecause the tensile
stresses in the rarefaction
still exceed the
much smaller dynamic tensile strengtho, of the material. En_
150
I
I
I
I
I
I
_
•""
-
_
/%(ICE-SAT
SAND) -
-
/
-
-
ß
- /
100
_
-
ß
/
-'-
-.
õ0
-
-.
%
..-f.% (ICE) o-.-•.-'
//
-
. oT(ICE-SAT.
SAND) -
.......
-10 -20 -30 -40 -50 -60 -70
Temperature (øC)
Reference
static
static
dynamic
static
dynamic
static
static
dynamic
velocity [Oberbeck, 1970]. The energy-diameter relations
shown in Figure 3 are given in numerical form in Table 3.
Two significant observationscan be made from these data.
First, at a given energy, craters in ice-saturated sand are
times larger, and cratersin ice are --,3 times larger in diameter
than cratersin rock. The increasein crater diameter at a given
energy from rock to ice-saturatedsandto ice is of the same order as the increasein the depth/diameter ratio, implying a dependenceof both size and morphometry on material properties. Second, the logarithmic slopes of the low-velocity and
hypervelocityimpactsare similar to the slopefor the ice-saturated sand. Because crater dimensions
Type Test
75
68
388
140 _+8
179 _+35
88 _+18
80 _ 10
1140_+110
largement of the crater continuesby tensile failure and spalling until radial tensile stressesfall below o,. Cracks often extend far beyond the crater into the target becauseof the strong
tensile tangential stresses[Kutter and Fairhurst, 1971]. Crushing early in the impact event and spallingvia tensile failure
late in the event account for both the distribution of ejecta
particle sizes and the visual appearanceof craters in hard
rock. Both low- [Bauer and Calder, 1969] and high- [Moore et
al., 1962] velocity craters have similar inner zones of highly
fractured and crushedmaterial surroundedby a larger zone of
radial and spall fractures.The ejecta in both high- and lowvelocity impacts consistsof fine crushedmaterial from the innet crater zone grading into large spall fragments from the
outer zone. Crater edges are often irregular. In the ice and
small ice-saturatedsand cratersthe outer spall zone was not as
obvious, and the largest ejected particle sizeswere relatively
smaller than the largest hard rock fragmentsin comparisonto
the crater diameter. Only the large ice-saturatedsand craters
exhibited a prominent spall zone and large spall fragments.
This implies that crushingand spalling occur in ice and hard
rock craters, though perhaps in differing relative importance.
The edgesof the ice craterswere alsoquite regular.
The tensile strengthsof sand (o, = 0), ice, ice-saturated
sand, cement, basalt, and granite show an inverse correlation
with the crater size progressionobserved.The tensile strengths
of the rocks are given in Table 4. They range from a few tens
to a few hundreds of bars. The tensile strengthsof ice and icesaturated sand are functions of temperature as shown in Figure 4. For ice, o, showsa slight increasewith decreasingtemperature. In accord with the correlation of tensile strength
with crater size we would expect cratersin supercooledice to
be marginally smaller than craters in temperate ice. There is
someindication in Figure 3 that this is the case,but more data
must be obtained to be sure. For ice-saturated sand, o, is actually smaller than o, for ice near the melting point, but the
available data imply a strongincreasein o, as the temperature
decreases.Comparison with o, for cement and granite implies
that to obtain craters in ice-saturated sand in the size range
observedrequires o, (ISS) near -70øC to be somewherebetween 20 and 50 bars. Again, more data need to be obtained
to be sure, but the crater data appear to confirm a strong temperaturedependenceof o, (ISS) on temperature.
A more quantitative treatment is prevented at this time by
the lack of direct o, measurements of the cratered material,
forcing comparisonsto be made betweenstrengthscited in the
Fig. 4. Variation of crushingstrengtho½and tensile strengthot of
literature that may or may not be appropriate. There are also
ice [from Butkovich, 1959] and ice-saturatedsand [from Tsytovich,
1975] with temperature. Dashed lines are extrapolations.Data for ot inconsistenciesin the measured values of dynamic o,, with
(ice-sat.sand) are particularly restrictedin temperaturerange.
someinvestigatorsreporting values similar to staticvalues and
CROFT ET AL.: SECOND MARS COLLOQUIUM
8029
othersgiving dynamic measurementsmuch larger than static at -• 1.5-2 km in sedimentaryrock and at -•4 km in crystalline
rock, implying the transition to be a function only of energy
and target material properties.
DISCUSSION
These observationssuggestthat the diameter range of craThe validity of scalingresultsfrom typical lab-sizedcraters ters for which strengtheffectsare nonnegligiblebut of dimintens of centimetersin diameter to cratersexceedinghundreds ishing importance in determining crater dimensionsextends
of meters in diameter is generally somewhatdubious. In par- from -• 10 m, where gravity effectsfirst becomenoticeable, to
ticular, crater dimensionsin competenttargetsat the scale of several kilometers. The diameter range of craters typically
decimeters are determined by strength properties, whereas used in determining the relative and absoluteagesof geologic
gravitydominatescrateringefficiencyat diameterslargerthan units on the moon [e.g., Young, 1975; Neukum and Kb'nig,
a few kilometers, with an ill-defined transition in between 1976] and Mars [e.g., Masursky et al., 1977] extendsfrom --,l0
[Gault et at., 1975]. The extent of the influence of strength m to -• 10 km. These two rangesoverlap. Further, it has been
propertiesin crateringat large scalesis brought into further postulatedthat Mars is or was totally or partially coveredby a
questionby the recognitionthat most natural rock and soil thick layer of ice-saturatedsoil. Consequently,the differences
units have faults, joints, and impact or weathering fractures in crater diameter between equal energy impacts in icy and
that decreasethe effectivetensilestrengthof the unit with in- rocky media presentedin this report may have implications
creasingcrater size.Moore [1976] noted that the ejectedmass for Martian crater count analyses:
1. The crater count agesof competent icy or ice-saturated
versusimpact energyrelation for missileimpactsin soil intersoil
geologicunits that are not in cratering equilibrium for the
sectthe extrapolationsof similar relationsfor cratersin sand
[Oberbeck, 1970] and rock [Gault, 1973] at energiesaround range of crater diameters used in age determinationswill be
1015-1016
ergs, correspondingto diametersof 5-10 m (the greater than the crater count agesof competentrock units extrend toward convergenceis apparent in Figure 3). Taken by periencingidenticalinfall histories.This is bestdemonstrated
itself, this implies a disappearanceof strength effects by by relating the flux of impactingobjects,N (number of impacenergiesof---1016ergs.Gault[1973],in limiting the valid range tors per unit area per unit time in a prescribedimpactor radius
of extrapolationof his empirical scalingequationsfor craters (r) interval), with the primary crater productionrate F (numin basalt, observedthat during surface explosionsin rock at ber of craters formed per unit area per unit time in a preenergiesof 1015-1016
ergs,large spallplatesthat would have scribedcrater diameter interval) in a manner similar to that of
been ejected at smaller diameterswere only slightly moved Gault [1970]. The cumulative radius-flux relation of a popubefore settling,reducingthe diameterof the final crater.Cer- lation of impactors is usually expressedin the form [Hartmann, 1969; Gault, 1970]
values.
tainly, Sailor Hat B, a 2 x 1019erg hemispherical
high-explosive (HE) surface burst on basalt producing an apparent
crater diameter of--,48 m [Vortman, 1968], is far smaller than
the --•150-m diameter predicted by simple extrapolation of
Gault's relation given in Table 3 (ignoring effectsof depth of
burst, rock porosity,etc.). This implies that gravity beginsto
affect crater dimensionssignificantly at diameters ar9und 510m.
There is evidence, however, that strength properties continu•e to measurably affect crater dimensions at diameters
much largerthan 10 m. Crater dimensionsand empiricalscaling relationsfor surfaceHE burstsgiven by Vortman[1968]
indicate that at equal energies,cratersin rock continue to be
-•25% smaller than craters in dry soil up through the largest
energy(-• l017ergs)for which data in both media are available. Similar strength-induceddifferences are noted in explosioncraterswith large scaleddepths-of-burstto energiesof
•>1021ergs(D >• 100m), the upperlimit of availabledata [Toman, 1970; Cooper, 1977]. Thus strength effects persist to
energiesmuch larger than Moore's [1976] extrapolatedintersection, implying changes in the empirical scaling laws at
energiesof •<10Is ergs.Schultzand Spencer[1979]reported2-
N = k,r -/•
(2)
where kl and fl are positive constants.Upon impact at velocity V an impactor will have kinetic energy E:
E • 2/3,rrpV•r3
(3)
where p is the bulk densityof the impactor. The diameter D of
the crater generated by this impact is given by a power law
scalingrelation
D = k2El/"
(4)
where k2 is a constantfor a given planet and lithologyand a is
the scalingcoefficientwith a value [Gault et al., 1975] between
3 (strengthdominated) and 4 (gravity dominated). Equations
(2), (3), and (4) may be combined to eliminate E and r and
thereby convert the cratering flux into a crater production rate
as a function
of crater diameter:
F = k V2/3k2"B/3D
-"B/3
(5)
where all other constants have been absorbed into k.
Hartmann [1977] calculated correction factors that can be
3 timesasmanycraters
in the 10-to 100-mdiameter
rangeon usedto predict the crater production rate Fi on any planet relejectadepositsthan on presumablycontemporaneous
smooth ative to a standard rate Fs:
pondedmelt at King Crater. Schultzsuggested
that the difference in crater density may be attributable to strength differences between the incompetent ejecta and the competent
pondedmelt. The diameter-frequencydistributionsfor craters
on the two surfaceunits convergetoward an extrapolated intercept near 3 km. Schultz interpretedthis as the size range
wheregravitybecomessignificantin relationto strengthin determining crater dimensions.Dence et at. [1977] note that the
transition from simple to complex craterson the earth occurs
Fi-
XYZFs
(6)
where X is the ratio of the calculatedflux of a specificfamily
of impactorsonto the planetunder investigationto the calculated flux of that family on the standardplanet, Y correctsfor
the differencein mean impact velocity for the family on the
two planets,and Z correctsfor the differencein surfacegravity. Hartmann's values of Y and Z range from --,0.5 to 2 for
8030
CROFT ET AL..' SECONDMARS COLLOQUIUM
the terrestrialplanetsand somewhathigherfor satellitesin the
There is also a marked inverse correlation
outer solar system.A strengthcorrectionfactor S may be defined analogouslyto Y and Z by noting that comparisonof (4)
with the scalinglaws given in Table 3 indicatesthat the in-
and impact velocity at a given energysuchthat the sand craters formed by projectilestraveling -•6 km/s [Stbffier et al.,
1975] lie near the extrapolationof our approximatelow-velocity energy-diameterrelation for ice. The depth/diameter ra-
creasein craterdiameterwith decreasing
materialstrengthis
reflectedprimarily by an increasein k2. Therefore S may be
definedfrom (5) and (6) holdingX, Y, Z, D, and V constant:
(7)
where k2(/) refersto the surfacebeing investigatedand k:(s)
refers to a known standardsurface.(The values of k: can be
compared directly only if the values of a are similar. When
differencesin a are large, k:(i)/k:(s) becomesthe ratio of crater diametersin different media within a small energy interval
and will be a function of energy.) Hartmann's suggestedstandard surface is an average of dated lunar maria, which are
layered targetswith varying depthsof regolith overlyingbedrock [Quaideand Oberbeck,1968].
The approximatemassrange of objectswith impact velocities of 10-30 km/s that producecratersbetween0.1 and 10 km
between crater size
tios of the sand craters are similar to the ratios for craters in
granite and basalt(Figure 2) and are much smallerthan expectedon the basisof strengthpropertiesalone.The anomalous logarithmic slopes, depth/diameter ratios, and the
porous,cohesionless
nature of sand suggestthat the mechanisms dominant
in the formation
of craters in sand are differ-
ent from those that dominate cratering in competentmaterials. Oberbeck[1970] suggests
that at low impact velocitiesthe
major constrainton crater size is the energyrequired to lift
material out of the crater against gravity, whereasat higher
impactvelocitiesthe highershockpressures
increasethe effective shear strengthof sand, changingthe relative importance
of strength to gravity in cratering processes.Oberbeck suggeststhat the changeof relativeimportancebetweenstrength
and gravity is indicated by the changeof the scalingcoeffi-
in diameteris -• 108-1014
g, basedon a scalingrelationgiven cient from -•3.8 at V = 0.5 km/s to -•3.4 at V = 5 km/s. In
by Gault[1974].If the diameterincrementsin (5) are logarith- contrast,the diameter-energy
scalingcoefficientof high-velocity missile impacts in sand, colluvium, alluvium, and soil in
the energyrangeof 10IS-1016
ergsfound by Moore [1976]is
-•2.4, a very different result. Consequently,the size of equal
energy cratersin cohesionless
rock materials relative to competenticy materialsat energiesabove l0 ll ergsis very difficult
to predict on the basisof currentlyavailabledata.
The presenceof water in both competent[Butkovich,1971;
pacts(k:(ISS)/k:(rock))will probablybe muchsmallerthan
the factor of 2 implied by Figure 3. However, even if the in- Burton et al., 1975] and incompetent [Moore, 1976] target
creasein diameter (and thus in k:) were only 25%, the typical materials can enlarge crater diameters 2-4 times over the
variation for explosioncratersin different media on the earth, correspondingdry target diameters.Boyceand Roddy [1978]
the exponentof k:(ISS)/k2(rock) is so large that the primary have discussedthe possibleeffectsof such enlargementson
crater production rate in ice-saturatedsoilsat a given diame- Martian crater count ages, with conclusionssimilar to ours.
ter would be -• 1.7-2 times larger than the production rate gen- Crater enlargementoccursbecause(1) water vapor is essenerated in rock by the sameimpact flux. Thus S can be as large tially an uncondensablegas comparedto rock vapor, greatly
as Y or Z, with decreasingstrengthworking in the samedirec- enhancinggas accelerationof particles[Butkovich,1971] and
tion as decreasinggravity and increasingimpact velocity. It is (2) material shear strengthdecreaseswith increasingwater
beyond the scopeof this report to detail the correspondence content [Burton et al., 1975]. The minimum shock pressure
between the production rate and observed crater densities that causeswater to begin vaporization upon release is -•50
(which can be quite complex;e.g.,seediscussion
by Schultzet kbar [Butkovich, 1971]. However, the maximum pressuresat
al. [1977]), but it is probably reasonableto conclude that the the point of impactfor our craters(estimatedby the graphical
larger production rate for a given flux on ice-saturated soil impedence-match
techniqueof GaultandHeitowit[1963]from
surfaceswill producehigher crater frequenciesand larger cra- the Hugoniots of ice, ice-saturatedsand [Gaffney, 1979], and
ter count agesthan found for rock surfacesof the same abso- lead [van Thiel, 1966]) range from -•5 kbar in ice and -•9 kbar
lute age and subjectedto the sameflux.
in ice-saturatedsand for the slowestbullet (V = 0.33 km/s) to
Most of the examplesof differing crater diametersfor equal -•40 kbar in ice and -•90 kbar in ice-saturated sand for our
energy impacts or explosionscited so far have been the result fastest bullet (V = 1.5 km/s). Consequently,vaporization
of the contrastingcratering propertiesof competent and in- would only be expectedin craters 8 and 10 in ice-saturated
competent geologic units of similar rocky composition. Our sand. Even for these craters, vaporization would be minimal
cratering experiments indicate the possibility of significant and confinedto ice near the impact point, becauseshockpresvariations in crater dimensionsdue to differencesin strength suresdecay rapidly with distance.Also, becausethe 50-kbar
of competentmaterialsof different composition.The magni- limit refers to liquid water, higher shockpressureswould be
tude of the effectof contrastingcrateringpropertiesof regolith required to vaporize ice, becauseextra energyis required to
and bedrock on crater diameter-frequency distributions has bring the temperature of the ice up to 0øC and then to melt
been discussedpreviouslyfor the lunar case[e.g., Chapmanet the ice. The amount of melting at the low velocities of our
al., 1970; Young, 1975; Schultz et al., 1977]. It might be ex- projectiles is also very small [Cintala et al., 1979]. Thus we
pected that craters in incompetentmedia would always be concludethat our targetsact as dry, competentsubstancesand
larger than those of equal energy in weak competentmedia that the large sizesof our craters are due to strength effects
becauseincompetentmaterials representthe limiting caseof alone. At the higher impact velocitiescharacteristicof craterzero tensile strength. However, the logarithmic slopesof the ing on Mars, melting and vaporizationare expectedto occur,
energy-diameterrelationsfor the sand cratersshownin Figure but if ground temperaturesat the impact site are far below
3 are significantlysmallerthan thoseof the competenttargets. freezing,the actual amount of water and vapor generatednear
mic [Hartmann, 1969],then the value of • for theseparticlesis
-•3 [Gault, 1970].Substitutionof this value of fl into (5) gives
absolute values between 3 and 4 for the exponentsof k2 and
D. Becauseof the decreasein the importance of strengthin
craterslarger than a few meters,the diameter ratio of craters
in ice-saturatedsoil to thosein rock producedby identical im-
CROFT ET AL.: SECOND MARS COLLOQUIUM
the crater periphery that might produce wet crater enlargement may be negligible.
If the strong extrapolated dependenceof o, (ISS) on temperatureis valid, then latitudinal variationsin the subsurface
temperature structure of the Martian crust of the type suggested by Fanale [1976] would give rise to latitudinal variations in the energy-diameter scaling relations as well. This
would causeice-saturatedsoil surfacesnear the equator to appear older than similar surfacesnear the poles. Johansen
[1979], using the distribution of Martian impact crater ejecta
blanket morphologies,has presentedevidence favoring just
such a substantialsubsurfacetemperature variation: Martian
rampart craters, which occur preferentially at low latitudes,
have ejecta blanket morphologiesthat can be approximated
by impactsinto soupy mud [Gault and Greeley,1978]. Other
craters,which have ejecta blanket morphologiesmore like dry
lunar craters, occur preferentially at high latitudes. If these
ejectamorphologiesare valid indicatorsof the amount of liquid groundwaterpresent at the crater locality at the time of
impact, then any enlargementthat did occur in craters with
diametersof a few kilometers or lessmay be attributed to the
wet mechanismsin equatorial areas and to our dry, lowstrengthmechanismin the colderpolar regions.Alternatively,
the lunarlike craterscould be impactswhich occurredin dry,
rocky surfaces,in which case, rampart craterswould be impactsin groundcontainingsignificantice or water. If this were
the case,then the dry, low-strength mechanismwould probably not be significantbecauserampart crater ejectamorphologieswould then imply significantmelting at large distances
from the impact point due to the passageof the shock, and
any crater enlargementwould be dominatedby effectsdue to
the melted water.
In conclusion,considerationof target strengthbroadensthe
already large uncertainty limits on current estimatesof the absoluteagesof Martian features.If someMartian surfaceswere
essentiallyice-free during cratering, while others were saturated with ice or liquid water, strength considerationscould
possibly alter the currently accepted sequenceof geologic
events between different regionson Mars and between Mars
and other planets in the solar system.Becausethese low-velocity experiments suggest trends and scaling differences
which might affect our interpretation of Martian and icy
planet agesand crater forms, and becauseof the indicationsof
crater size dependenceon material strength,we feel it highly
desirable to extend cratering experiments and simultaneous
material property measurements to lower temperatures,
higher energies,and higher pressuresand strain ratesin order
to provide a proper foundation for studying craters on Mars
and beyond.
803 I
Bauer, A., and P. N. Calder, Projectile penetration in rock, in Proc.
Can. Rock Mech. Symp.5th, 157-170, 1969.
Boyce,J. M., and D. J. Roddy, Martian rampart craters:Crater processesthat may affect diameter-frequencydistributions (abstract),
Reports of Planetary Geology Program, 1977-1978, NASA Tech.
Memo., TM-79729, 162-165, 1978.
Burton, D. E., C. M. Snell, and J. B. Bryan, Computer designof high
explosiveexperimentsto simulate subsurfacenuclear detonations,
Nucl. Technol., 26, 65-87, 1975.
Butkovich, T. R., Mechanical properties of ice, Quart. Colo. Sch.
Mines, 54, 349-360, 1959.
Butkovich, T. R. Influence of water and rocks on effects of under-
groundnuclearexplosions,
J. Geophys
Res.,76, 1993-201l, 1971.
Chapman,C. R., J. A. Mosher,and G. Simmons,Lunar crateringand
erosion from Orbiter 5 photographs, J. Geophys.Res., 75, 14451466, 1970.
Cintala, M. J., E. M. Parmentier, and J. W. Head, Characteristicsof
crateringprocesses
on icy bodies:Implicationsfor outer planet sat-
ellites, Reports of the Planetary Geology Program, NASA Tech.
Memo., TM-80339, 179-181, 1979.
Cohn, S. N., and T. J. Ahrens,Dynamic tensilestrengthof analogsto
lunar rocks (abstract),in Lunar and Planetary ScienceX, pp. 224226, Lunar and Planetary ScienceInstitute, Houston,Tex., 1979.
Cooper, H. F., Jr., A summary of explosion cratering phenomena
relevant to meteor impact events,in Impact and ExplosionCratering, editedby D. J. Roddy, R. O. Pepin, and R. B. Merrill, pp. 1144, Pergamon,New York, 1977.
Culp, F. L., and H. L. Hooper, Study of impact crateringin sand,J.
Appl. Phys.,32, 2480-2484, 1961.
Curran, D. R., D. A. Shockey,L. Seaman,and M. Austin, Mechanics
and models of cratering in earth media, in Impact and Explosion
Cratering, edited by D. J. Roddy, R. O. Pepin, and R. B. Merrill,
pp. 1057-1087,Pergamon,New York, 1977.
Dence, M. R., R. A. F. Grieve, and P. B. Robertson, Terrestrial im-
pact structures:
Principalcharacteristics
and energyconsiderations,
in Impact and ExplosionCratering,editedby D. J. Roddy, R. O. Pepin andR. B. Merrill, pp. 247-275,Pergamon,New York, 1977.
Fanale, F. P., Martian volatiles: Their degassinghistory and geochemical fate, Icarus 28, 179-202, 1976.
Gaffney, E. S., Equation of stateof ice and frozen soils(abstract),in
Lunar and Planetary ScienceX, pp. 416-418, Lunar and Planetary
Science Institute, Houston, Tex., 1979.
Gault, D. E., Saturationand equilibrium conditionsfor impact cratering on the lunar surface:Criteria & implications,Radio Sci.,5, 27329 l, 1970.
Gault, D. E., Displacedmass,depth, diameter,and effectsof oblique
trajectoriesfor impact craters formed in dense crystalline rocks,
Moon, 6, 32-44, 1973.
Gault, D. E., Impact cratering, A Primer in Lunar Geology, NASA
Tech. Memo., TM-62395, 137-173, 1974.
Gault, D. E., and R. Greeley, Exploratory experimentsof impact craters formed in viscous-liquidtargets:Analogs for Martian rampart
craters?,Icarus, 34, 486-495, 1978.
Gault, D. E., and E. D. Heitowit, The partition of energyfor hypervelocity impact cratersformed in rock, Proc. Symp. Hypervelocity
Impact 6th, 2(2), 419-456, 1963.
Gault, D. E., J. E. Guest, J. B. Murray, D. Dzurisin, and M. C. Malin,
Some comparisonsof impact craterson Mercury and the moon, J.
Geophys.
Res.,80, 2444-2460, 1975.
Gehring,J. W., Jr., Theory of impacton thin targetsand shieldsand
correlationwith experiment,in High VelocityImpact Phenomena,
editedby R. Kinslow,p. 105,Academic,New York, 1970a.
Gehring, J. W., Jr., Engineeringconsiderations
in hypervelocityimpact,in High VelocityImpactPhenomena,
editedby R. Kinslow,p.
Acknowledgments. We thank Henry Moore and JosephBoyce for
critical reviews and Eloise Luera and Gayle Croft for assistancein
preparationof the manuscript.We are also grateful to G. Hager, 31st
Naval ConstructionRegiment, for permissionto use the Sea Bee C
463, Academic, New York, 1970b.
Rifle Range at Port Hueneme, California, to perform these experi- Hartmann, W. K., Terrestrial,lunar and interplanetaryrock fragmenments,and to David F. Wismen for courteousand helpful assistance
tation, Icarus, 10, 201-213, 1969.
in logisticsat the rifle range. This work was partially supportedby Hartmann, W. K., Relative crater production rates on planets, Icarus,
NASA grants NGL 05-007-002, NSG 7052 (University of California,
31, 260-276, 1977.
Los Angeles) and NGL 05-002-105 (California Institute of TechHartung, J. B., F. H6rz, F. K. Aitken, D. E. Gault, and D. E. Brownnology). Contribution 3292, Division of Geological and Planetary
lee, The developmentof microcraterpopulationson lunar rocks,
Sciences,California Institute of Technology, Pasadena,California
Proc. Lunar Sci. Conf 4th, 3213-3234, 1973.
91125.
Johansen,L. A., The latitude dependenceof Martian sploshcratering
and its relationshipto water, Reports of Planetary Geology ProREFERENCES
Albertson, M. L., J. R. Barton, and D. B. Simons,Fluid Mechanicsfor
Engineers,pp. 231-247, Prentice-Hall,EnglewoodCliffs, N.J., 1960.
gram,NASA Tech.Memo., TM-80339, 123-125, 1979.
Kutter, H. K., and C. Fairhurst, On the fracture processin blasting,
Int. J. Rock Mech. Mining Sci., 8, 181-202, 1971.
8032
CROFTET AL.'.SECONDMARSCOLLOQUIUM
LaLonde,W. S. Jr., and M. F. Janes,Co.ncrete
Engineering
Handbook,
Schultz,P. H., R. Greeley, and D. E. Gault, Interpretingstatisticsof
small lunar craters,Proc. Lunar Sci. Conf. 8th, 3539-3564, 1977.
Masursky,H., J. M., Boyce,A. L. Dial, G. G. Schaber,and M. E. Schultz, P. H., and J. Spencer,Effectsof substratestrengthon crater
Strobell, Classification and time of formation of Martian channels
statistics:Implications for surface ages and gravity scaling (abbasedon Viking data, J. Geophys.Res.,82, 4016-4038, 1977.
stract), in Lunar and Planetary ScienceX, pp. 1081-1083, Lunar
Maurer, W. C., and J. S. Rinehart, Impact craterformationin rock, J.
and Planetary Science Institute, Houston, Tex., 1979.
Appl. Phys.,31, 1247-1252, 1960.
St6ffler,D., D. E. Gault, J. Wedekind, and G. Polkowski,ExperimenMoore, H. J., Missile impactcraters(White SandsMissile Range,
tal hypervelocity impact into quartz sand: Distribution and shock
NM) and applicationsto lunar research,U.S. Geol. Surv. Prof.
metamorphismof ejecta,J. Geophys.Res.,80, 4062-4077, 1975.
Pap., 812-B, 47 pp., 1976.
Toman, J., Resultsof crateringexperiments,in PeacefulNuclear ExMoore,H. J., R. V. Lugn,and D. E. Gault, Experimental
hyperplosions, pp. 345-375, International Atomic Energy Agency,
pp. 1-4.6, McGraw-Hill, New York, 1961.
velocityimpactcratersin rock,Proc.Hypervelocity
Impact Syrup.
5th, •(2), 625-643, 1962.
Neukum G., and B. K6nig, Dating of individual lunar craters,Proc.
Lunar Sci. Conf. 7th, 2876-2881, 1976.
Oberbeck,V. R., Laboratorysimulationof impactcrateringwith high
explosives,NASA Tech.Memo., TM X-62010, 56 pp., 1970.
Oberbeck,V. R., Laboratorysimulation
of impactcrateringwith high
explosives,J. Geophys.Res., 76, 5732-5749, 1971.
Ostro, S. J., and G. H. Pettengill, Icy craterson the Galilean satellites?,Icarus, 34, 268-279, 1978.
Quaide, W. L., and V. R. Oberbeck, Thicknessdeterminationsof the
lunar surfacelayer from lunar impactcraters,J. GeophysRes., 73,
5247-5270, 1968.
Reichmuth, D. R., Point load testingof brittle materialsto determine
Vienna, Austria, 1970.
Tsytovich,N. A., The Mechanicsof Frozen Ground,426 pp., Scripta
Book Co., Washington, D.C., 1975.
van Thiel, M. (Ed.), Compendiumof shockwave data, Rep. UCRL50108, vol. 1, sects. A-I and A-2, Lawrence Radiat. Lab., Livermore, Calif., 1966.
Vanzant, B. W., Dynamic rock penetrationtestsat atmosphericpressure,in Rock Mechanics:Proceedings
of the5th Symposium
on Rock
Mechanics, edited by C. Fairhurst, pp. 61-91, Pergamon, New
York, 1963.
Vortman, L. J., Craters from surfaceexplosionsand scalinglaws, J.
Geophys.Res., 73, 4621-4636, 1968.
Wijk, G., G. Rehbinder, and G. L6gdstr6m, The relation between the
uniaxial tensile strength and the sample size for Bohus granite,
tensilestrengthand relativebrittleness,
in Statusof PracticalRock
Rock Mech., 10, 201-219, 1978.
Mechanics,
editedby N. E. Grosvenorand B. W. Paulding,Jr., pp. Young, R. A., Mare crater size-frequencydistributions:Implications
134-159,AmericanInstituteof Mining, Metallurgy,and Petrology
for relative surfaceagesand regolithdevelopment,Proc.Lunar Sci.
Engineering,New York, 1968.
Conf. 6th, 2645-2662, 1975.
Rinehart,J. S., Dynamicfracturestrengths
of rocks,Proc.RockMech.
Syrup. 7th, 205-208, 1965.
Schneider,P. J. ConductionHeat Transfer,pp. 263-267, AddisonWesley,Reading,Mass., 1974.
(ReceivedApril 2, 1979;
revisedJuly 19, 1979;
acceptedAugust31, 1979.)