Diameter to depth dependence of impact craters

Planet. Space Sci., Vol. 28, pp. 567-573. pergamon Press Ltd., 1980. Printed in Northern Ireland

DIAMETER

TO

DEPTH

DEPENDENCE K. NAGEL*

Max-Planck-Institut

OF IMPACT

CRATERS

and H. FECHTIG

fiir Kernphysik,

Heidelberg,

W. Germany

(Received in final form 27 Nuuember 1979) Abstract-Laboratory impact experiments in the micron to millimeter projectile size range in silicate and metal targets have been performed in order to clarify the still ambigously interpreted velocity dependence of the crater diameter to depth ratios (D/T). The experimental results clearly show the independence of the D/T ratio of velocities above a threshold velocity of 34 km s-i. The D/T ratio is a function of target properties and of projectile density p. For a given target, the resulting approximate relation is D/T-p-” with (Y varying between l/2 and l/5.

undisturbed target surface

1. INTRODUCllON

Lunar microcraters usually exhibit a central glasslined pit surrounded by a more or less concentric spallation zone (Fig. la). This morphology of lunar microcraters is extensively described by various authors (e.g. Horz et al., 1971; Neukum et al., 1972; Fechtig et al., 1975). There also exists a variety of experimental impact data for the simulation of craters seen on lunar rocks (e.g. Bloch et al., 1971; Vedder, 1971; Gault, 1973). But none of the data on silicate targets are as comprehensive as for craters in metal targets. The velocity dependence of diameter and depth of impact craters in metal targets has unambiguously been determined by Rudolph (1969). As an important result, the independence of the diameter to depth ratio (D/T) of the impact velocity was shown, (Fig. lb for typical crater geometry). Nagel et aI. (1976) have confirmed these results and found that the D/T ratio is a function of projectile and target density. Ambiguous results have been reported for craters in silicate targets. Brownlee et al. (1973) first reported on observations of lunar microcraters with various ratios of crater diameter D to crater depth T (D being the crater pit diameter in contrary to the spallation zone diameter D, according to Fig. la). Smith er al. (1974) suggested, based on selected cratering experiments, that the ratio of D to T of craters on a given target material is a function of the projectile density only. Nagel et al. (1976) have quantitatively measured D/T values on lunar samples and compared them with experimental cratering data on feldspar targets. They have shown that different D/T values correspond to

* Present address: Kernforschungszentrum Karlsruhe. 567

k------OS

//

-

undisturbed target

+D---rl

/ surface

~--:--if-FIG.

1. SCHEMATIC

SILICATE: ZONE

D =

DIAMETER:

DISPLAY

CENTRAL

T=

PIT

DEF7’H;

DIAMETER;

T=

OF IMPACT DIAMETER;

(b)

CRATERS:

D, =

IN METAL:

CRATER

(a) r~

SPAILATION

D =

CRATER

DEFIFI.

different projectile densities resp. composition, and that the D/T ratios seem to be independent of the impact velocity. Vedder and Mandeville (1974) however, published results of simulation experiments with the interpretation that the D/T ratios are not independent of the projectile velocity V, but proportional to V1’3. Systematic experiments have been performed to clarify this discrepancy. In the following, we will discuss our laboratory results, and compare them with former experiments and results of others. 2. EXPERIMENTAL

CONJMTIONS AND DATA

Spherical projectiles of various densities resp. composition have been impacted at different velocities onto a variety of target materials. An electrostatic dust accelerator was used to accelerate particles in the micron size range and a light gas gun was used to accelerate mm-sized projectiles. The experimental conditions were largely chosen to

568

K. NAGJZL andH. FECHTIG

complement our previous experiments on impact crater geometry (Rudolph, 1969; Nagel et al., 1976) and in order to facilitate comparison with other data, especially by Vedder and Mandeville (1974). In our experiments, glass-lined central pits have been produced on silicate target materials at projectile velocities greater than 4 km s-l (Fig. 2a, b). This velocity seems to be a lower limit for the formation of glass-lined pits in the millimeter projectile size range for glass targets. The threshold velocity may lie higher in the case of non-glassy silicate targets such as basalt, which would explain the fact that Gault (1973) has not found any glasslined pits in his experiments on basalt and granite targets at velocities up to 7 kms-‘. It should be

pointed out, however, that other factors such as target size and geometry affect the formation of glass-lined central pits. In several cases, glass-lined central pits were obviously formed during impact but then ejected leaving spallation depressions as in Gault’s experiments. This occurred if shock wave propagation in the target with subsequent reflection expelled the central pit when the wave arrived back at the free surface. Crater diameters and depths as defined in Fig. la, b have been measured individually by application of both mechanical and optical methods for the mm-sized craters and electron-optical methods for the micron-sized craters. The electron-optical methods consisted of the direct measurement of the crater diameter on a scanning electron microscope

TABLET. EXPERIMENTALREWLTSFORDITVALUES KJSINGANELECXROSTATICDUSTAWELERATORAM) ALIGHTGASGUN) Target material

glass ,, 7,

2,

>,

1,

,>

,,

7,

quartz glass 7, 1, 7, 7, 7,

feldspar (bytonite) >. stainless steel 3, ,, ., copper ,. ,. ,, aluminum ,, >, goih ,. 11 glass

Projectile diameter material (km) iron ,> ,, 7, ,, ,, >1 9, ,, ,, ,, 7, >, ,, ,> ,, ,, ,, 1, ,, 7, carbon I, 1. plastic aluminum steel bronze plastic aluminum steel bronze plastic aluminum steel >,

2.48 1.84 1.27 1.01 0.69 0.54 0.36 0.50 0.18 2.35 1.69 1.58 1.16 0.74 0.57 0.38 1.3 0.6 0.4 1.2 0.2 0.6 0.3 0.2 2.5. lo3 2.5. lo3 2.0. lo3 2.0. 10s 2.5. lo3 2.5 . lo3 1.6. lo3 2.5. lo3 2.5. lo3 2.5. lo3 1.6. lo3 2.0. 103

velocity -(km/set) 2.6 3.3 4.5 5.6 6.6 7.6 8.4 11.0 14.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 4.8 7.5 10.8 5.2 21.1 7.5 13.1 20.8 4.4 4.8 4.3 3.8 4.3 4.8 4.5 4.5 4.4 4.6 4.1 4.7

Crater diameter D depth T (wm) (pm) 2.50 1.85 1.27 1.16 0.86 0.73 0.50 0.80 0.33 2.40 1.69 1.58 1.33 0.92 0.76 0.54 1.5 0.8 0.6 2.6 1.1 1.4 1.0 0.8 5.8. lo3 7.7. lo3 8.3. lo3 7.4.103 8.5. lo3 8.5 . lo3 6.6. 10s 6.1. lo3 5.0. 103 6.6. 103 6.7 . lo3 3.0. 103

1.12 1.75 1.06 0.96 0.70 0.57 0.40 0.72 0.28 1.15 2.17 2.05 1.77 1.15 1.15 0.77 1.30 0.70 0.54 0.80 0.30 0.40 0.25 0.20 2.3. lo3 3.6. lo3 5.5. 103 5.2. lo3 4.8. lo3 7.8. lo3 6.8 103 7.0. 103 2.4. lo3 3.3. 10s 3.6. lo3 1.1.103

D/T

Fig.

2.23 1.06 1.20 1.21 1.23 1.28 1.25 1.11 1.18 2.09 0.78 0.77 0.75 0.80 0.66 0.70 1.15 1.14 1.11 3.25 3.67 3.50 4.00 4.00 2.52 2.14 1.51 1.42 1.77 1.09 0.97 0.87 2.08 2.00 1.86 2.73

3a ,1 ,, ,, ,, 1. 7. ,> ,, 7, >, ,, ,> 7, .> ., >> ,, 3b 1, ,, 7, >, 5 ,, ., ., .> 3, ,, ,, 1, >, 1, 6

Diameter

FIG. 2.

EXAMPLES

OF

mm-SIZED

CENTI~LPITSURROUNDED

to depth

GLASS-LINED

dependence

CENTRAL

BY ASPALLATION~~NE:

569

of impact craters

PITS: (a) VIEW

OF

(b) A CI~VTRALFTF

THE

WHOLE

CRATER

INMAGNIFICATION.

WITH

Diameter to depth dependence of impact craters image and of the determination of parallaxes between different points (see Rudolph, 1969; Vedder, 1971). The accuracy of the measurements lies around f 15%. Our experimental data are listed in Table 1, together with our former results on the same subject (Nagel et aI., 1975, 1976). 3. DI!XXJ!SSION OF ‘IWE EXPE RIMENTAL, RJXSULTS

1. Dependence of the crater diameter on projectile velocity

to depth ratio

Our results on the velocity dependency of the diameter to depth ratio, D/T, are displayed in Fig. 3a, b for the investigated projectile/target combinations. Additionally, some selected data from

t

O.ll 1

10 20 50 5 projectile vclocity( km/see)

2

571

Rudolph (1969) have been inserted for comparison. It can clearly be seen that the D/T ratio is independent of impact velocity above a target- and/or projectile-dependent threshold velocity of 35 km s-l. This threshold velocity compares well with the finding of the formation of glass-lined pits of the complete destruction and spreading-out of iron projectiles in the same velocity range for impacts on metal targets (Neukum, 1969; Dietzel et al., 1972). Furthermore, Rudolph’s (1969) results for metal targets are confirmed. The independence of the D/T ratio of projectile velocity is valid not only for impacts on metal targets but also for impacts on silicate targets. This result is contrary to Vedder and Mandeville’s (1974) interpretation, who inferred with D/TV 1’3. In order to resolve this discrepancy, we have plotted Vedder and Mandeville’s data in Fig. 4 beside ours (see Fig. 3a). Contrary to us, Vedder and Mandeville measure the penetration, P, of the projectile into the target, i.e. the distance from the bottom of the central pit to the undisturbed target surface. Their central pit diameter is comparable to our D. Since the penetration P is only lo-20% different from depth T and probably nearly proportional, we can directly compare the two sets of data, keeping a slight P versus T off-set in mind. The two sets of data agree rather well. However, we cannot follow their interpretation of a velocity dependence of the D/T rep. D/P ratio. Our highervelocity data clearly show that the ratio is constint

t

. x

Fe-glass

WT):thm

work

Fe-esoda

Lyme glass

(D/P)

Vedder

and Msndevillo

(1974)

i?-Y+d

O;’

Projectile 20 projectile

FIG.

3.

DENCE

50 velocity

FIG. 4. COMPARISON

1km/s-x)

TARGETS

WITH

MANDEVILLE EXPE RIh4ENTAL OF THE

RESULTS

D/T RATIO: (a) FOR METAL

FOR THE vEL0CTl-Y FOR SILICATE

TARGETS

velocity

DEPEN-

TARGETS;

(b)

BOTH

SJXS

(DIAM!ZTER TION)

THE (1974).

OF

DATA

TO DEPTH)

OF OUR

v (kmhec)

D/T RESULTS FOR

PENETRA TION

DATA

THJZ EXP ERIMENTAL ARE AND

ARE COMPARABLE

SIMILAR. OF

D/P

AND

THE

CONDITIONS RATIO

(DIAMETER

AGREE

SILICATE

OF VEDDER OF

TO PEm-

RATHER

WELL.

AND IN

D/T

K. NAGELand H. FECHTIG

572

The dependencies of the D/T ratio as a function of velocity could not be investigated in the mass range of lo-*g, because the maximum velocities achievable in the light gas gun experiments have been limited to above 6 km s-l. 3. Dependence of the D/T ratio on projectile diameters We could show that in a given size class, i.e. micron-size range or m-size range, the constancy of the D/T with velocity and a pY dependence of D/T on projectile density is valid. There is, however, a difference in the absolute values of the D/T ratios going from one size class to another. This can be seen from the data listed in Table 2, where our results for pm-sized craters are compared with projectile density (g/cm31 those for mm-sized craters for Cu, Al, Au, stainless FIG. 5. DEPENDENCE OF THE D/T RATIO ON PROJEXXILE steel, and glass targets. (The data for iron projecDENSlTY RESPECTIVELY COMPOSITION IN THE IllIll-SIZE tiles into gold, aluminium and copper are from RANGE. Rudolph, 1969). It results that the D/T ratios for and that the interpretation of a velocity depencraters in metal targets are comparable for both dence is probably due to the fact that Vedder and size ranges, whereas in the case of glass targets the Mandeville measured too close to the velocity ratio is a factor of 2 higher for mm-sized craters threshold (3-5 km s-l) above which conditions only than for micron sized craters. stabilize and D/T becomes constant. Experimental values in the meter size range come from missile impacts (Moore, 1971; Moore, 1976). The D/T ratios lie between 3 and 5. Unfor2. Dependence of the D/T ratio on projectile density tunately, no information is given on the composiFigure 5 shows our experimental result of ratios tion or density of the projectiles used in these of crater diameter D to crater depth T as a funcexperiments. We assume steel projectiles. The only tion of projectile density p for copper, gold and other terrestrial sources are natural (hypervelocity) aluminium targets for- mm-sized craters. The D/T meteorite impact craters. A fresh, well-investigated ratio dependencies on -projectile density can be crater of this kind is the Meteor Crater, Arizona approximated by the following empirical laws: (e.g. Shoemaker, 1960; Roddy et al. 1975). Reconstruction of the original depth to diameter ratio D/T p-o.2o gold target: using the data of Roddy et al. (1975) gives D/T= 6. D/T- p-o.32 copper target: Neglecting possible target dependencies, this could be the approximate D/T ratio for a big iron aluminium target: D/T- p-0.43 OFD/T VALUES FOR pm- ANDmm-SIZEDCRATERS TABLE2. COMPARISON Target material CU

Ai’ Ai ,> stainless steel

>,

glass

,,

material

Projectile diameter (cLm)

iron steel iron steel iron steel iron

1.3 2.0. 0.9 1.6. 0.9 1.6. 1.2

steel iron steel

2.0. 103 0.54 2.0. lo3

103 lo3

lo3

velocity

diameter D

Crater depth T

km se1

km)

bm)

5.2 4.3 7.6 4.5 5.2 4.1 5.2

3.8 8.3. 3.2 6.6. 3.5 6.7. 2.6

4.1 7.6 4.7

6.2. lo3 0.73 3.0. lo3

lo3

io3 lo3

2.2 5.5. 3.2 6.8 1.5 3.6. 0.8

lo3 103 lo3

3.0 * 103 0.57

1.1. lo3

D/T 1.7zto.3 1.51tzO.2 l.OztO.2

1.0*0.1 2.3*0.4 1.9Zto.3 3.3zko.5

2.1zkO.4 1.3~1~0.2 2.7+0:4

Diameter to depth dependence of impact craters

573

with V = impact velocity hence 5, %

I

‘0

D/T = 1.32 x D0.o8b

T/d - V213 too. The discrepancy with the results of Vedder and Mandeville (1974) is dissolved if one restricts the validity of the constancy of D/T to velocities above 4 km s-l.

1

2

3

4

5

Craterdiemeter

6

7 log

8

9

10

D [win]

FIG. 6. FUNCTIONAL DEPENDENCE OFTWE J3f~wa-10 ON CRATER DIAMETER FROM MICRON- TO KILOMETER-SIZED CRATERS.

meteorite impacting on earth. This cannot be checked any further at the moment. On the basis of the experimental or terrestrial meteorite crater data, it is possible, however, to do some order of magnitude considerations of the functional dependence of the D/T ratio on crater diameter from micron sizes to kilometer sizes. In Fig. 6 the available D/T data are plotted against crater diameter. As indicated already in the micron-to mm-size range, the D/T ratio grows slowly with the crater size. The approximate functional dependence is D/T - ct0.0s4. 4. CONCLUSION

This paper has discussed a set of data investigat-

ing the ratio of the crater diameter to crater depth as a function of projectile data such as its velocity, density and absolute diameter. Although the data are by far not complete, it could be shown that (1) the ratio D/T is constant above a minimum impact velocity of approx. 4 km s-‘; (2) the ratio D/T is inversely proportional to pey of the projectile density, with y ranging from 0.2 to 0.5; (3) the ratio D/T is slowly increasing with increasing projectile diameter. This law seems to be valid also for very large projectiles, even into the km-size range. In an earlier paper Bloch et al. (1971) have found D/d - v2J3, with d =projectile diameter. this paper we know

From the resuIts of

D/T = cont. above V = V,,

= 4 km s-l,

Acknowledgement-Dr. G. Neukum has contributed to this paper by many valuable discussions for which we are gratefut to him. The experiments using mm-sized projectiles have been performed at the Emst-Mach-Institute at Freibnrg, Br.. We like to thank Dr. E. Schneider for his cooperation.

Bloch, M. R., Fechtig, H., Gentner, W., Neukum, G., and Schneider E. (1971). Proc. Lunar Sci. Conf. Znd, 26392652. Brownlee, D. E., HGrz, F., Vedder, J. F., Gault, D. E., and Hartung, H. B. (1973). Proc. Lunar Sci. Conf. 4th, 3197-3212. Dietzel, H., Neukum, G., Rauser, P., (1972). .I. Geophys. Res. 77, 1375-139s. Fechtig, H., Gentner, W., Hartung, J. B., Nagel, K., Neuknm, G., Schneider, E., and Storzer, D., (1975). Proc. Soviet-American Conf. Cosmochemistry of the Moon and Planets &foscow). The Lunar Science Institute, Houston. Gault, D. E., (1973). The Moon, 6, 32-44.

H&z, F., Hartung, J. B., and Gault, D. E., (1971). J. Geophys. Res. 76, 5770-5798. Moore, H. J., (1971). J. Geophys. Res. 76, 5750-5755. Moore, H. J., (1976). Geological Survey Professional Paper 812-B. Nagel, K., Neukum, G., Eichhoin, G., Fechtig, H., Miiller, O., and Schneider, E., (1975). Proc. Lunar Sci. Conf. 6th, 3417-3432. Nagel, K., Neukum, G., Dohnanyi, J. S., Fechtig, H., and Gentner, W., (1976). Proc. Lunar Sci. Conf. 7th, 10211029. Nagef, K., Neukum, G., Fechtig, H.. and Gentner, W., (1976). Earth Planet. Sci. tett., 30. 234-240. N&k&, G., (1969). Master’s thesis; Universitgt Heidelberg. Neukum, G., Schneider, E., Mehl, A., Storzer, D., Wagner, G. A., Fechtig, H., and Bloch, M. R., (1972). Proc. Lunar Sci. Co@. 3rd, 2793-2810. Roddy, D. J., Boyce, J. M., Colton, G. W., and Dial, A. J., (1975). Proc. Lunar Sci. Conf. 6th, 2621-2644. Rudolph, V., (1969). Naturforsch. 24a, 326331. Shoemaker, E. M., (1960). Strucmre of the Earth’s Crust and Deformation of Rocks, 418-434. Intl. Geol. Cong. XXI Session, pt. 18, Copenhagen. Smith, D., Adams, N. G., and Khan, H. A., (1974). Nature Land. 252, 101-106. Vedder, J. E., (1971). Earth Planet. Sci. E&t. 11,291296. Vedder, J. F., and Mandeville, J.-C., (1974). 1. Geophys. Res. 79, 3247-3256.