Velocity Impact Craters in Ice and Ice&Hyphen

Home , Henry (Martian crater), Robertson (crater)

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, University of California,Los Angeles,California 90024

S. W. KIEFFER

U.S. GeologicalSurvey, Flagstaff,,Arizona 86001

T. J. AHRENS

Divisionof Geologicaland PlanetarySciences, California Institute of Technology,Pasadena, California 91125

We produced a seriesof decimeter-sizedimpact craters in blocks of ice near 0øC and -70øC and in ice-saturatedsand near -70øC as a preliminary investigationof crateringin materialsanalogous to those found on Mars and the outer solar systemsatellites. The projectilesused were standard0.22 and 0.30 caliber bulletsfired at velocitiesbetween 0.3 and 1.5 km/s, with kineticenergies at impactbetween 109 and 4 x 10•ø ergs. Crater diameters in the ice-saturatedsand were -•2 timeslarger than cratersin the same energy and velocity range in competentblocks of granite, basalt and cement.Craters in ice were -•3 times larger. If this dependenceof crater size on strengthpersists to large hypervelocityimpact craters,then surfacesof geologicunits composedof ice or ice-saturatedsoil would have greatercrater count ages than 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 determining relative interplanetary chronologies.The relative sizesof cratersin ice and ice-saturatedsand imply that the tensile strengthof ice-saturatedsand is a strong inverse function of temperature.If this is true, then Martian impact crater energy versusdiameter scaling may also be a function of latitude.

INTRODUCTION where Eo is the muzzle energy, rn is the bullet mass, p is the densityof air, A is the cross-sectionalarea of the bullet, and Ca Impact cratering is recognized as an important processin is the coefficient of drag. Equation (1) was derived by in- planetary accretionand in shapingthe solid surfacesof plan- tegration of Newton's secondlaw using a low-viscosity,'V- ets 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?CaApestimated for 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 sys- Three types of target blocks were used. They were prepared tem consist of rock materials and their weathered products. and characterized as follows: Consequently,terrestrial small-scale impact and explosionex- 1. 'Ice-saturatedsand' (ISS) blocksconsisted of water-sat- periments 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 un- nance of ice and ice-saturated soils, both at and far below the til the sand was covered by a thin water layer. The mixture melting point of water over large portions of Mars, the aster- was slowly stirred to remove air bubbles.The mixture was fro- oids, and particularly the satellitesof the outer solar system, zen in the container. we performed a seriesof low-velocity impact experimentsin 2. 'Supercooledice' (S-ice) blo,cks consisted of pure water ice and ice-saturated sand. The objective of these impact ex- ice frozen to about -70øC, with the same dimensions as the periments was to provide a preliminary survey of the mor- blocks of ice-saturated sand. To prevent the formation of phology and kinetic energy-dimensionalscaling of cratersin large single crystals or bubbles, these blocks were built up icy media comparedto impactsat similar kinetic energiesand layer by layer, adding first water and then crushed ice until velocities in rock and cohesionless sand. the ice was barely saturated. The water-ice mixture was then EXPERIMENTAL PROCEDURE frozen, producing blocks having a uniform fine grain phane- ritic texture with tiny bubbles(<0.1 mm) thinly distributedin The projectiles used were standard 0.22 and 0.30 caliber the interior. bullets fired at velocities between 0.3 and 1.5 km/s. Table 1 3. 'Temperate ice' (T-ice) blocks consistedof pure water givesthe ballistic data derived from manufacturer'sspecifica- ice near 0øC and were prepared in three ways. The first type tions for the bullets used. Impact kinetic energiesat the mea- of temperate ice blocksused were commercially producedand sured firing ranges(R) of 8-13 yd (7-12 m) were interpolated maintained in a freezer at a temperature of--•28øF (-2.2øC). from the ballistic data using the equation These blocks were --•36 x 20 x 20 cm in size. The commercial method of freezing produced a roughly tabular amorphous R= C•Ap core ('cloudy zone') imbedded in a matrix of elongated rodlike crystals(--•0.5-1 cm long and 0.2-0.3 cm thick) oriented Copyright¸ 1979by the American GeophysicalUnion. perpendicularto the face of the tabular cloudy zone. This pro- Paper number 9B 1305. 8023 0148-0227/79/009B- 1305501.00 8024 CROFTET AL.: SECONDMARS COLLOQUIUM

TABLE 1. Bullet Ballistic Data

Velocity, km/s Energy, ergs Bullet Mass,g Muzzle 100yd* Muzzle 100yd* m/Cap'l, cm 22 Short (22S)•- 1.88 0.334 0.275 1.04E95 7.05E8 5.36E4 22 Long (22L)•- 1.88 0.378 0.294 1.34E9 8.13E8 4.20E4 22 Long Rifle (22LR)•- 2.59 0.383 0.310 1.90E9 1.25E9 5.01E4 22 Hornet (22H)•- 3.24 1.25 NA 2.54E10 NA 4.86E4 (estimated) 30-06SPRG Accelerator 3.56 1.48 NA 3.88E10 NA 4.86E4 (SPRG)•- (estimated) 30-06PSP (PSP)•- 8.10 0.975 0.856 3.85E10 2.97E10 8.11E4

NA is not available. * 1 yd=0.91m. •-Abbreviationused in Table 2. $Read 1.04E9as 1.04x 109.

vided for highly anisotropicmaterial propertieswhose effects 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 ('pressed blocks') were smooth.Bullet name, target type, range,and crater depth and prepared by compressingcrushed ice in a pressurevessel until diameterwere recordedfor each shot.Those data are grouped fusion. This produceda uniform but porphyritic texture with accordingto target compositionand listed by shot number in many millimeter-sizedbubbles. These blocks were cylinders order of increasing 'trapactenergy in Table 2. Crater 5 is with diametersand lengthsof--,20 cm. shown in 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 discardedsamples where the bullet ob- With the notable exception of craters formed in the com- viously hit an air pocket). Theseblocks were cylinders--,25 cm mercialice blocks,the craterswere hemiellipticalcups in 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-di- constant 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 insulated boxes sand craters.Visible fracturing was concentratednear the im- for immediate transport to the firing range. Temperaturesin- pact site and near the rear face of the target block. Shots4 (S- side the insulated containers were monitored. On the basis of ice) and 9 (ISS), which were fired into blocks which each al- (1) the time between removal from the refrigeratorsuntil use ready had a 5-cm crater in them (whosevisible fracture zones at the firing range (a few hours), (2) the air temperaturesin- were small in comparisonto the block size), completelyshat- sidethe insulatedboxes at the time of target use (--•0øCfor the tered the blocks.Identical shots(3 in S-ice and 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 cratersproduced ex- and (4) the parameterizedtemperature history calculationsof tensive, less obvious interior failure beyond the visible frac- Schneider[1974], it is estimatedthat the surfacetemperatures ture systems. of the supercooledice and ice-saturatedsand blockshad risen The upper limit of usable impact energieswas set by the between 5 ø and 10øC, while those of the temperature ice target block sizeand composition.For blocksin the size range blocks had risen a few tenths of a degree. The temperature used,the upper energy limit for ice blocksis --,3 x 10•ø ergs, gradient near the surfaceof the supercooledice and ice-satu- becauseshot 16 at 3.7 x 10•ø ergs completely destroyed the rated sand blocks is estimated to have been --•0.5øC/cm from targetblock, while shot3, at 2.5 x 10•ø ergs, did not. The up- Schneider's [1974] calculations. Edges and corners of the per limit for the ice-saturatedsand blocksappears to be near blocks would 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, craters were producedwith cra- faces,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 possibleeffects on the expectedcrater di- At time of use, target blocks were removed from the in- mensionsdue to the large change of crater size relative to the sulated boxes and the containersin which they were frozen target size. Gehring[1970b] analyzed the depth of penetration and were immediately buried in an embankment of soil with of a projectileof given massand energyas a function of target one exposed vertical face into which the bullet was fired. thicknessin metals. He found very little changein expected Figure 1 shows the 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 blocks used as targets. rowed slightly [Gehring,1970a] and the depth increasedrap- were the 27 x 33 cm bottom faces,which had smooth sur- idly toward penetration.The suddenincrease in crater depth faces.The target facesof the pot and pressedblocks were the is due to spallationand failure of the target'srear face caused CROFT ET AL.: SECOND MARS COLLOQUIUM 8025

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Fig. 1. Crater $ in ice-saturatedsand showing an exampleof the cratersdiscussed in this report and the target arrange- mentof ice-saturatedsand block bunkered by sandwith onevertical face exposed. Note the relativelylarge depth/diameter ratio(-•0.4 compared to typicalhard rock values of-•0.2) andthe system of crackssurrounding the crater to approximately one crater radiusbeyond the slightlyraised rim. White scalebar is ,-•10.5 cm long. 8026 CROFT ET AL.' SECOND MARS COLLOQUIUM

TABLE 2. Crater Data Summary

Range, Energy Diameter Depth Shot Bullet* yd-• Ei, ergs D, cm d, cm Notes

S-Ice I 22S 13.3 1.00E9•: 4.5 +_ 0.5 2.6 2 22L 13.3 1.26E9 7+_3 2.5 double crater, Di = 4 cm, Do = 10cm 3 22H 13.3 2.48E10 ---23 ---13 block split 4 22H 13.3 2.48E10 ...... block destroyed,prefractured by I

Ice-Saturated Sand 5 22S 10 1.01E9 4.25 +_ 0.25 1.8 6 22L 10 1.82E9 4.9 +_ 0.1 2.0 in same block as 5 7 22L 10 1.82E9 5.0 1.8 8 22H 13.3 2.48E10 12 5.0 block split 9 PSP 10 3.69E10 ...... block destroyed,prefractured by 7 l0 SPRG 10 3.70E10 ---16 ---5.6 block split T-Ice (Commercial) 11 22s 10 1.01E9 6 0.8 into cloudy zone 12 22s 10 1.01E9 6.5 2.6 perpendicularto grain axes, square crater 13 22S 10 1.01E9 6.5 3.0 perpendicularto grain axes, square crater 14 22S 10 1.01E9 4.5 10.9 parallel to grain axes, conical crater 15 22LR 10 1.82E9 4.9 +_ 0.5 8.5 parallel to grain axes,conical crater 16 SPRG 10 3.70E10 block destroyed

T-Ice (Pots) 17 22S 9.2 1.01E9 6.5 +_ 0.5 3 pot 6, large singlecrystals in block 18 22LR 10.8 1.81E9 3.8 +_ 0.3 1.5 pot 2, wrong or faulty bullett?? T-Ice (PressedBlocks) 19 22S 8.3 1.02E9 5 3 upper quadrant spalledoff 20 22LR 10.8 1.81E9 ---10 ---5.5 upper right half spalledoff

*See Table I for full designation. •- 1 yd = 0.91 m. $Read1.00E9 as 1.00x 109. by the strongrarefaction generated by reflectionof the pri- foration. However, as seen in Figure 2 and discussedbelow, mary shockoff of the free rear face. By buryingthe targetsin the depth/diameter ratio of crater 3, which would be anoma- a medium with a density comparable to the target density, lously large had near performation occurred,is similar to that shockreflection and spallationare reduced,increasing the ef- of the other ice craters. Thus any effects of varying target fective target thickness.Crater 3, with a crater depth/block thickness relative to crater size are deemed small for these ex- thicknessratio of--.0.7, is the only crater large enoughto have periments. possiblyhad its dimensionssignificantly altered by near per- Burial of the target was also intended to reduce lateral spal- lation. However, as is seen in Figure 1, the loose nature of the sand prevented effective enclosureof the upper forward portions of the target. As a result, large sectionswere spalled off o Ice-Sat Sand 15 •' SupercooledIce of the upper face of the blocks containing craters 19 and 20 ß Temperate Ice (which were otherwisenormal). The three largestcraters (3, 8, 4- Granite (Bauer & Calder,1969) • Basalt(Gault, 197:5) J _ and 10) completely split their respectivetarget blocks owing to ] a Sando(Oberbeck,1971) j insufficient lateral containment. Becausethe energy required to generate fractures beyond the true crater is small in com-

_ parisonto the energyneeded to 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. Crater shapes in the highly anisotropic commercial ice - ••,•+• blocks depended on the orientation of ice crystalsat the face 0 in which the crater was formed. Craters 14 and 15 were 0 5 t0 t5 20 Diameter (cm) 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 shape in comparisonto thosein the polycrystalline for low-velocity impactsin granite and hypervelocityimpacts in sand and basalt. The numbersin this figure refer to crater numbersgiven in anisotropic ice blocks. Ejecta consistedof large rodlike seg- Table 2 and designatefour data points consideredanomalous as dis- ments of individual crystalsand a relatively undamaged 'plug' cussed in the text. thrown several feet in front of the target. The undamaged na- CROFT ET AL.: SECOND MARS COLLOQUIUM 8027

1oo _ i i i i i iii I i i i I i iii I i i i i i i ity to hypervelocityimpacts in sand (Oberbeck[1971], appar- ß Ice-Sat Sand - /x "Super"lce ent crater dimensions),and the mean curve of Gault's [1973] - o "Temperate"lce ß• .•<.•,/sec_ hypervelocityimpacts in basalt and granite. The anomalous • - amSand (Oberbeck,(Stoffler et197,,;75al, ) _• k•y•' a /' T•.•' •/s depthsof craters 14 and 15 in the commerciallyprepared ice E - -•F•"-• '•' .... '• • • blocks are immediately apparent. Crater 11 appears abnormally shallowbecause the 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 well- .- •o•'•o• • - defined 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 experi- {•0 s ' , , , , , ,,••09 , , , , , , ,{0,• •0 , , , , , , '•'0•{ ments, is probably the result of inhomogeneitiesin the target ImpQct Energy (ergs) block. These four craters were ignored in least-squaresfitting of the data. The lines labeled ice and ice-sat. sand are least- Fi 8. 3. •ependence o• cmte• diamete• on impact ene•8• •o• ice (dashed line) and ice-saturatedsand (uppermost solid line) cmte•s square fits to the data. From the figure it is seen that the compared to cmte•s in the same cne•8• and ve]ocit• mnSe in •ock depth/diameter ratios of cratersin rock are ,--0.2,of cratersin (]owe• solid lines) and sand (dot-dashedlines). The numbersb• cer- sand are ,--0.25, of craters in ice-saturated sand are •-0.35, and tain s•mbo]s in this •Su•e •e•e• to the numbe• o• superposedimpacts of cratersin ice are nearly 0.5. Thus at leastsmall-scale craters •ep•esentedb• the sins]e s•mbo], in ice are nearly hemisphericalin shape. Interestingly, this correspondsto the shapesuggested as necessaryby Ostro and ture of the plug is consistentwith observationsand calcu- Pettengill [1978] to account for the unexpectedpolarization lations by Curran et al. [1977] for similar low-velocityimpacts. properties of radar returns from Europe, Ganymede, and Although it is possiblethat vapor formation ejectedthe plug, Callisto, whosecrusts apparently are largely composedof ice. we do not believeit likely at theselow velocitiesand suspect Figure 3 showsthe correspondingplot of crater diameter as that elastic forcesejected 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 grainsoriented perpendicularto [1963] into cementare shown,as well as additional apparent the projectilevelocity, and are roughlyinverted pyramids in sand crater data from Oberbeck [1970] and StOffier et al. shape. Two faces of the 'pyramid' consistof the broken ends [1975].The uppermostsolid line is a least-squaresfit to the of grains,while the other two Sidesare defined by the sidesof ice-saturated sand data. The estimated energy-diameter rela- the 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 re- size and orientationin small-scale,low-velocity impacts. liable fit. Craters 14 and 15 are omitted from this figure be- For all craters, projectile de.formationwas similar to that cause their dimensionswere completely altered by the ani- found 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.Bullets turned '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 disintegrated to 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 hyper- missilecomponents in impactsin alluvium [Moore, 1976]. velocity craters are somewhatlarger in diameter but have Figure 2 showsthe quantitative relation betweendepth and about the same depth as Bauer and Calder's low-velocity cra- diameter for the cratersformed in theseexperiments. Included ters. This could be due to either the different velocities used or for comparisonare steel and tungstencarbide ball bearing im- peculiaritiesof the materialproperties of the targets.The ki- pacts in Disraeli Light granite by Bauer and Calder [1969] in netic energy-diameterrelations of the sand cratershave no- the samevelocity and energyrange as our impacts,1ow-¾eloc- ticeablydifferent logarithmic slopes that are weak functionsof

TABLE 3. Empirical Energy-DiameterRelations (Shown in Figure 3)

Energy Range of Target Material Energy-DiameterRelation* Data, ergs Source

Sand V = 1 km/s D = 0.044 E 0'28 107-1011 Oberbeck [ 1970] V = 2 km/s D = 0.34 E 0'29 107-1011 Oberbeck[ 1970] V = 6 km/s D = 0.021 E 0'29 107-1011 Oberbeck [ 1970] (estimated) Ice (estimated) D--- 1.4 x 10-3 E ø-4 109-3 x 10 lø this paper Ice-saturated sand D = 2.36 x 10-3 E ø-36 109-4 x 10 lø this paper Cement D = 1.6 x 10-3 E ø'37 7 X 106-7 X 109 Vanzant [ 1963] Basalt D = 1.1 X 10-3 E ø-37 101-1012 Gault [1973] Granite D= 1.2X 10-4E ø'46 2X109-5X10 II Bauer and Calder [ 1969] *D is in centimeters,and E is in ergs. 8028 CROFT ET AL..' SECOND MARS COLLOQUIUM

TABLE 4. Rock Tensile Strengths Material Or,bars Type Test Reference

Granite 75 static Maurer and Rinehart [ 1960] Pink 68 static Rinehart [ 1965] 388 dynamic Rinehart[ 1965] Charcoal gray 140 _+8 static Reichmuth [1968] 179 _+35 dynamic Reichmuth[1968] Cheyenne Mt. 88 _+18 static Reichmuth[1968] Bohus 80 _ 10 static Wijk et al. [1978] Westerly 1140 _+110 dynamic Cohnand Ahrens[1979] Basalt Buckboard Mesa 184 dynamic Curranet al. [ 1977] Ralston 1168 _+160 dynamic Cohnand Ahrens [1979] Cement 30-60 static LaLonde and Janes[ 1961] velocity [Oberbeck, 1970]. The energy-diameter relations largement of the crater continuesby tensile failure and spall- shown in Figure 3 are given in numerical form in Table 3. ing until radial tensile stressesfall below o,. Cracks often ex- Two significant observationscan be made from these data. tend far beyond the crater into the target becauseof the strong First, at a given energy, craters in ice-saturated sand are tensile tangential stresses[Kutter and Fairhurst, 1971]. Crush- times larger, and cratersin ice are --,3 times larger in diameter ing early in the impact event and spallingvia tensile failure than craters in rock. The increasein crater diameter at a given late in the event account for both the distribution of ejecta energy from rock to ice-saturatedsand to ice is of the same or- particle sizes and the visual appearance of craters in hard der as the increasein the depth/diameter ratio, implying a de- rock. Both low- [Bauer and Calder, 1969] and high- [Moore et pendence of both size and morphometry on material proper- al., 1962] velocity craters have similar inner zones of highly ties. Second, the logarithmic slopes of the low-velocity and fractured and crushedmaterial surroundedby a larger zone of hypervelocity impacts are similar to the slopefor the ice-satu- radial and spall fractures.The ejecta in both high- and low- rated sand. Because crater dimensions are obtained late in the velocity impacts consistsof fine crushedmaterial from the in- impact event and at relatively low pressures,we believe that net crater zone grading into large spall fragments from the the similarity of slopesimplies that similar mechanismsof ma- outer zone. Crater edges are often irregular. In the ice and terial failure operate in the late stagesof both low-velocity small ice-saturatedsand cratersthe outer spall zone was not as and hypervelocity impacts. obvious, and the largest ejected particle sizeswere relatively It has been postulated that the final size of craters in com- smaller than the largest hard rock fragmentsin comparison to petent media in this diameter range is determined by the dy- the crater diameter. Only the large ice-saturatedsand craters namic tensile strengthof the material [Curran et al., 1977;J. S. exhibited a prominent spall zone and large spall fragments. Rinehart, personal communication, 1978]. Near the point of This implies that crushing and spalling occur in ice and hard impact the peak shock stressgreatly exceedsthe material's dy- rock craters, though perhaps in differing relative importance. namic compressivestrength oc, thus crushing target materials The edgesof the ice craterswere also quite regular. which are subsequentlyejected. At greater distancesthe com- The tensile strengthsof sand (o, = 0), ice, ice-saturated pressivestresses fall below oc, but excavation continuesbe- sand, cement, basalt, and granite show an inverse correlation cause the tensile stresses in the rarefaction still exceed the with the crater size progressionobserved. The tensile strengths much smaller dynamic tensile strengtho, of the material. En- 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 ice-

_ I I I I I I _ saturated sand are functions of temperature as shown in Fig- •"" _ 150 ure 4. For ice, o, showsa slight increasewith decreasingtem- - /%(ICE-SAT SAND) - perature. In accord with the correlation of tensile strength - / - with crater size we would expect cratersin supercooledice to - ß be marginally smaller than craters in temperate ice. There is - / - some indication in Figure 3 that this is the case,but more data 100 _ ß must be obtained to be sure. For ice-saturated sand, o, is ac- / -'- tually smaller than o, for ice near the melting point, but the -. ..-f.- available data imply a strongincrease in o, as the temperature decreases.Comparison with o, for cement and granite implies õ0 - % (ICE) o-.-•.-' - that to obtain craters in ice-saturated sand in the size range observedrequires o, (ISS) near -70øC to be somewherebe- - . . o-T(ICE-SAT. SAND) - tween 20 and 50 bars. Again, more data need to be obtained // to be sure, but the crater data appear to confirm a strong tem- ...... perature dependenceof o, (ISS) on temperature. % -10 -20 -30 -40 -50 -60 -70 A more quantitative treatment is prevented at this time by Temperature (øC) the lack of direct o, measurements of the cratered material, forcing comparisonsto be made betweenstrengths cited in the Fig. 4. Variation of crushingstrength o½ and 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. someinvestigators reporting values similar to static values and CROFT ET AL.: SECOND MARS COLLOQUIUM 8029

others giving dynamic measurementsmuch larger than static at -• 1.5-2 km in sedimentaryrock and at -•4 km in crystalline values. rock, implying the transition to be a function only of energy and target material properties. DISCUSSION These observationssuggest that the diameter range of cra- The validity of scalingresults from typical lab-sizedcraters ters for which strengtheffects are nonnegligiblebut of dimin- tens of centimetersin diameter to craters exceedinghundreds ishing importance in determining crater dimensionsextends of meters in diameter is generally somewhatdubious. In par- from -• 10 m, where gravity effectsfirst become noticeable, to ticular, crater dimensionsin competent targets at the scale of several kilometers. The diameter range of craters typically decimeters are determined by strength properties, whereas used in determining the relative and absoluteages of geologic gravity dominatescratering efficiency at diameterslarger than 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] extends from --,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 effectivetensile strengthof 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: versusimpact energyrelation for missileimpacts in soil inter- 1. The crater count agesof competent icy or ice-saturated sectthe extrapolationsof similar relationsfor cratersin sand soil geologicunits that are not in cratering equilibrium for the [Oberbeck, 1970] and rock [Gault, 1973] at energiesaround range of crater diameters used in age determinations will be 1015-1016ergs, correspondingto diametersof 5-10 m (the greater than the crater count agesof competentrock units ex- trend toward convergenceis apparent in Figure 3). Taken by periencingidentical infall histories.This is bestdemonstrated itself, this implies a disappearanceof strength effects by by relating the flux of impactingobjects, N (number of impac- energiesof---1016 ergs. Gault [1973],in limiting the valid range tors per unit area per unit time in a prescribedimpactor radius of extrapolation of his empirical scalingequations for craters (r) interval), with the primary crater production rate F (num- in basalt, observedthat during surface explosionsin rock at ber of craters formed per unit area per unit time in a pre- energiesof 1015-1016ergs, large spall platesthat 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 popu- before settling,reducing the diameterof the final crater. Cer- lation of impactors is usually expressedin the form [Hart- tainly, Sailor Hat B, a 2 x 1019erg hemisphericalhigh-ex- mann, 1969; Gault, 1970] plosive (HE) surface burst on basalt producing an apparent N = k,r -/• (2) crater diameter of--,48 m [Vortman, 1968], is far smaller than the --•150-m diameter predicted by simple extrapolation of where kl and fl are positive constants.Upon impact at veloc- Gault's relation given in Table 3 (ignoring effectsof depth of ity V an impactor will have kinetic energy E: burst, rock porosity,etc.). This implies that gravity beginsto E • 2/3,rrpV•r 3 (3) affect crater dimensionssignificantly at diameters ar9und 5- 10m. where p is the bulk densityof the impactor. The diameter D of There is evidence, however, that strength properties con- the crater generated by this impact is given by a power law tinu•e to measurably affect crater dimensions at diameters scalingrelation much larger than 10 m. Crater dimensionsand empirical scal- D = k2El/" (4) ing relationsfor surfaceHE burstsgiven by Vortman[1968] indicate that at equal energies,craters in rock continue to be where k2 is a constantfor a given planet and lithology and a is -•25% smaller than craters in dry soil up through the largest the scalingcoefficient with a value [Gault et al., 1975] between energy (-• l017ergs) for which data in both media are avail- 3 (strength dominated) and 4 (gravity dominated). Equations able. Similar strength-induced differences are noted in ex- (2), (3), and (4) may be combined to eliminate E and r and plosioncraters with large scaleddepths-of-burst to energiesof thereby convert the cratering flux into a crater production rate •>1021ergs (D >• 100m), the upperlimit of availabledata [To- as a function of crater diameter: man, 1970; Cooper, 1977]. Thus strength effects persist to F = k V2/3k2"B/3D-"B/3 (5) energiesmuch larger than Moore's [1976] extrapolatedinter- section, implying changes in the empirical scaling laws at where all other constants have been absorbed into k. energiesof •<10Is ergs.Schultz and Spencer[1979] reported 2- Hartmann [1977] calculated correction factors that can be 3 timesas many craters in the 10-to 100-mdiameter range on used to predict the crater production rate Fi on any planet rel- ejectadeposits than 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 differ- Fi- XYZFs (6) ences between the incompetent ejecta and the competent pondedmelt. The diameter-frequencydistributions for craters where X is the ratio of the calculatedflux of a specificfamily on the two surfaceunits convergetoward an extrapolated in- of impactorsonto the planet under investigationto the calcu- tercept near 3 km. Schultz interpretedthis as the size range lated flux of that family on the standardplanet, Y correctsfor wheregravity becomessignificant in relationto strengthin de- the difference in mean impact velocity for the family on the termining crater dimensions.Dence et at. [1977] note that the two planets,and Z correctsfor the differencein surfacegrav- transition from simple to complex craterson the earth occurs ity. Hartmann's values of Y and Z range from --,0.5 to 2 for 8030 CROFT ET AL..' SECOND MARS COLLOQUIUM the terrestrialplanets and somewhathigher for satellitesin the There is also a marked inverse correlation between crater size outer solar system.A strengthcorrection factor S may be de- and impact velocity at a given energysuch that the sand cra- fined analogouslyto Y and Z by noting that comparisonof (4) ters formed by projectilestraveling -•6 km/s [Stbffier et al., with the scalinglaws given in Table 3 indicatesthat the in- 1975] lie near the extrapolation of our approximate low-veloc- creasein craterdiameter with decreasingmaterial strength is ity energy-diameterrelation for ice. The depth/diameter ra- reflected primarily by an increasein k2. Therefore S may be tios of the sand craters are similar to the ratios for craters in definedfrom (5) and (6) holding X, Y, Z, D, and V constant: granite and basalt (Figure 2) and are much smallerthan ex- pectedon the basisof strengthproperties alone. The anoma- (7) lous logarithmic slopes, depth/diameter ratios, and the where k2(/) refers to the surfacebeing investigatedand k:(s) porous,cohesionless nature of sand suggestthat the mecha- refers to a known standard surface.(The values of k: can be nisms dominant in the formation of craters in sand are differ- compared directly only if the values of a are similar. When ent from those that dominate cratering in competent materi- differencesin a are large, k:(i)/k:(s) becomesthe ratio of cra- als. Oberbeck[1970] suggeststhat at low impact velocitiesthe ter diameters in different media within a small energy interval major constrainton crater size is the energyrequired to lift and will be a function of energy.) Hartmann's suggestedstan- material out of the crater against gravity, whereas at higher dard surface is an average of dated lunar maria, which are impact velocitiesthe highershock pressures increase the effec- layered targetswith varying depthsof regolith overlying bed- tive shear strengthof sand, changingthe relative importance rock [Quaide and Oberbeck, 1968]. of strength to gravity in cratering processes.Oberbeck sug- The approximatemass range of objectswith impact veloci- geststhat the changeof relativeimportance between strength ties of 10-30 km/s that producecraters between 0.1 and 10 km and gravity is indicated by the changeof the scalingcoeffi- in diameteri s -• 108-1014g, basedon a scalingrelation given cient from -•3.8 at V = 0.5 km/s to -•3.4 at V = 5 km/s. In by Gault[1974]. If the diameterincrements in (5) are logarith- contrast,the diameter-energyscaling coefficient of high-veloc- mic [Hartmann, 1969],then the value of • for theseparticles is ity missile impacts in sand, colluvium, alluvium, and soil in -•3 [Gault, 1970]. Substitutionof this value of fl into (5) gives the energyrange of 10IS-1016ergs found by Moore [1976] is absolute values between 3 and 4 for the exponentsof k2 and -•2.4, a very different result. Consequently,the size of equal D. Becauseof the decreasein the importance of strengthin energy craters in cohesionlessrock materials relative to com- craters larger than a few meters,the diameter ratio of craters petent icy materialsat energiesabove l0 ll ergsis very difficult in ice-saturatedsoil to thosein rock producedby identical im- to predict on the basisof currently available data. pacts(k:(ISS)/k:(rock)) will probablybe muchsmaller than The presenceof water in both competent[Butkovich, 1971; 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 explosioncraters in different media on the earth, correspondingdry target diameters.Boyce and Roddy [1978] the exponentof k:(ISS)/k2(rock) is so large that the primary have discussedthe possible effects of such enlargementson crater production rate in ice-saturatedsoils at 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 enlargement occursbecause (1) water vapor is essen- erated in rock by the same impact flux. Thus S can be as large tially an uncondensablegas comparedto rock vapor, greatly as Y or Z, with decreasingstrength working in the samedirec- enhancing gas accelerationof particles [Butkovich,1971] and tion as decreasinggravity and increasingimpact velocity. It is (2) material shear strengthdecreases with 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., see discussion 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(estimated by the graphical larger production rate for a given flux on ice-saturated soil impedence-matchtechnique of Gaultand Heitowit [1963] from surfaceswill produce higher 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 expected in 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, becauseshock pres- variations in crater dimensionsdue to differencesin strength suresdecay rapidly with distance.Also, becausethe 50-kbar of competentmaterials of different composition.The magni- limit refers to liquid water, higher shock pressureswould be tude of the effectof contrastingcratering properties of regolith required to vaporize ice, becauseextra energy is required to and bedrock on crater diameter-frequency distributions has bring the temperature of the ice up to 0øC and then to melt been discussedpreviously for 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 incompetent media would always be concludethat our targetsact as dry, competentsubstances and larger than those of equal energy in weak competent media that the large sizes of our craters are due to strength effects becauseincompetent materials representthe limiting case of alone. At the higher impact velocitiescharacteristic of crater- zero tensile strength. However, the logarithmic slopesof the ing on Mars, melting and vaporizationare expectedto occur, energy-diameterrelations for the sand cratersshown in Figure but if ground temperatures at the impact site are far below 3 are significantlysmaller than thoseof the competenttargets. freezing,the actual amount of water and vapor generatednear CROFT ET AL.: SECOND MARS COLLOQUIUM 803 I

the crater periphery that might produce wet crater enlarge- Bauer, A., and P. N. Calder, Projectile penetration in rock, in Proc. ment may be negligible. Can. Rock Mech. Symp.5th, 157-170, 1969. Boyce,J. M., and D. J. Roddy, Martian rampart craters:Crater proc- If the strong extrapolated dependenceof o, (ISS) on tem- essesthat may affect diameter-frequencydistributions (abstract), perature is valid, then latitudinal variationsin the subsurface Reports of Planetary Geology Program, 1977-1978, NASA Tech. temperature structure of the Martian crust of the type sug- Memo., TM-79729, 162-165, 1978. gested by Fanale [1976] would give rise to latitudinal varia- Burton, D. E., C. M. Snell, and J. B. Bryan, Computer designof high tions in the energy-diameter scaling relations as well. This explosiveexperiments to simulate subsurfacenuclear detonations, Nucl. Technol., 26, 65-87, 1975. would causeice-saturated soil surfacesnear the equator to ap- Butkovich, T. R., Mechanical properties of ice, Quart. Colo. Sch. pear older than similar surfacesnear the poles. Johansen Mines, 54, 349-360, 1959. [1979], using the distribution of Martian impact crater ejecta Butkovich, T. R. Influence of water and rocks on effects of under- blanket morphologies,has presentedevidence favoring just groundnuclear explosions, J. GeophysRes., 76, 1993-201l, 1971. Chapman,C. R., J. A. Mosher,and G. Simmons,Lunar crateringand such a substantialsubsurface temperature variation: Martian erosion from Orbiter 5 photographs, J. Geophys.Res., 75, 1445- rampart craters, which occur preferentially at low latitudes, 1466, 1970. have ejecta blanket morphologiesthat can be approximated Cintala, M. J., E. M. Parmentier, and J. W. Head, Characteristicsof by impactsinto soupy mud [Gault and Greeley,1978]. Other crateringprocesses on icy bodies:Implications for outer planet sat- craters,which have ejecta blanket morphologiesmore like dry ellites, Reports of the Planetary Geology Program, NASA Tech. Memo., TM-80339, 179-181, 1979. lunar craters, occur preferentially at high latitudes. If these Cohn, S. N., and T. J. Ahrens,Dynamic tensilestrength of analogsto ejecta morphologiesare valid indicatorsof the amount of liq- lunar rocks (abstract),in Lunar and Planetary ScienceX, pp. 224- uid groundwaterpresent at the crater locality at the time of 226, Lunar and Planetary ScienceInstitute, Houston, Tex., 1979. impact, then any enlargement that did occur in craters with Cooper, H. F., Jr., A summary of explosion cratering phenomena diametersof a few kilometers or lessmay be attributed to the relevant to meteor impact events,in Impact and Explosion Crater- ing, edited by D. J. Roddy, R. O. Pepin, and R. B. Merrill, pp. 11- wet mechanismsin equatorial areas and to our dry, low- 44, Pergamon,New York, 1977. strengthmechanism in the colderpolar regions.Alternatively, Culp, F. L., and H. L. Hooper, Study of impact crateringin sand,J. the lunarlike craterscould be impactswhich occurredin dry, Appl. Phys.,32, 2480-2484, 1961. rocky surfaces,in which case, rampart craters would be im- Curran, D. R., D. A. Shockey,L. Seaman,and M. Austin, Mechanics and models of cratering in earth media, in Impact and Explosion pactsin groundcontaining significant ice or water. If this were Cratering, edited by D. J. Roddy, R. O. Pepin, and R. B. Merrill, the case, then the dry, low-strength mechanismwould prob- pp. 1057-1087,Pergamon, New York, 1977. ably not be significantbecause rampart crater ejecta morphol- Dence, M. R., R. A. F. Grieve, and P. B. Robertson, Terrestrial im- ogieswould then imply significantmelting at large distances pact structures:Principal characteristics and energyconsiderations, from the impact point due to the passageof the shock, and in Impact and ExplosionCratering, edited by D. J. Roddy, R. O. Pe- pin and R. B. Merrill, pp. 247-275,Pergamon, New York, 1977. any crater enlargementwould be dominated by effectsdue to Fanale, F. P., Martian volatiles: Their degassinghistory and geo- the melted water. chemical fate, Icarus 28, 179-202, 1976. In conclusion,consideration of target strengthbroadens the Gaffney, E. S., Equation of state of ice and frozen soils(abstract), in already large uncertainty limits on current estimatesof the ab- Lunar and Planetary ScienceX, pp. 416-418, Lunar and Planetary Science Institute, Houston, Tex., 1979. soluteages of Martian features.If someMartian surfaceswere Gault, D. E., Saturationand equilibrium conditionsfor impact crater- essentiallyice-free during cratering, while others were satu- ing on the lunar surface:Criteria & implications,Radio Sci., 5, 273- rated with ice or liquid water, strength considerationscould 29 l, 1970. possibly alter the currently accepted sequenceof geologic Gault, D. E., Displacedmass, depth, diameter, and effectsof oblique events between different regions on Mars and between Mars trajectoriesfor impact craters formed in dense crystalline rocks, Moon, 6, 32-44, 1973. and other planets in the solar system.Because these low-ve- Gault, D. E., Impact cratering, A Primer in Lunar Geology, NASA locity experiments suggest trends and scaling differences Tech. Memo., TM-62395, 137-173, 1974. which might affect our interpretation of Martian and icy Gault, D. E., and R. Greeley, Exploratory experimentsof impact cra- planet agesand crater forms, and becauseof the indicationsof ters formed in viscous-liquidtargets: Analogs for Martian rampart craters?,Icarus, 34, 486-495, 1978. crater size dependenceon material strength,we feel it highly Gault, D. E., and E. D. Heitowit, The partition of energy for hyper- desirable to extend cratering experiments and simultaneous velocity impact cratersformed in rock, Proc. Symp. Hypervelocity material property measurements to lower temperatures, Impact 6th, 2(2), 419-456, 1963. higher energies,and higher pressuresand strain ratesin order Gault, D. E., J. E. Guest, J. B. Murray, D. Dzurisin, and M. C. Malin, to provide a proper foundation for studying craters on Mars Some comparisonsof impact craterson Mercury and the moon, J. Geophys.Res., 80, 2444-2460, 1975. and beyond. Gehring,J. W., Jr., Theory of impacton thin targetsand shieldsand correlationwith experiment,in High VelocityImpact Phenomena, Acknowledgments. We thank Henry Moore and JosephBoyce for editedby R. Kinslow, p. 105,Academic, New York, 1970a. critical reviews and Eloise Luera and Gayle Croft for assistancein Gehring, J. W., Jr., Engineeringconsiderations in hypervelocityim- preparationof the manuscript.We are also grateful to G. Hager, 31st pact,in High VelocityImpact Phenomena, edited by R. Kinslow,p. 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 fragmen- ments,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 Tech- Hartung, J. B., F. 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