Laboratory Impact Experiments
Our impact experiments support the development of a downrange shift of the outer crater with respect to the nested crater (Fig. 11). In the experiment with a 3 cm thick, unconsolidated, dry sand layer covering a stronger layer of damp, cohesive sand, there is, at the initial stage of the cratering (i.e., maximum depth reached), a rather symmetric bowl-shaped cavity (Fig. 11 A1). However, when this cavity expands outward the material flow is accentuated in the weaker, upper layer, and a stair-shaped, concentric transient cavity forms (Fig. 11 A2). Interestingly, the floor of the excavated outer crater does not follow the surface of the stronger damp sand layer. Instead there is a shallow, inclined surface through the dry sand layer. A similar transitional, outward increase in target stratigraphy is observed in the outer crater at Lockne (Fig. 2). Notice also that with this relatively thick upper layer there is no obvious ejecta layer forming from the inner, nested crater (Fig. 11 A3).
Figure 11. Slightly oblique view of quarter-space geometry impact experiments to illustrate the formation of offset concentricity for impacts into targets with a weaker layer covering a more rigid substrate. The weaker, upper layer is here represented by dry, unconsolidated beach sand (light gray), covering a layer of cohesive, damp beach sand (dark gray). The projectiles were shot obliquely from the right (white arrow with stippled black border). Projectile velocity (v), projectile radius (r), projectile weight and material (w), angle of trajectory above the horizontal (θ), thickness of dry sand layer (H), and lapse time from impact (T) are given in the figure. A) 3 cm thick dry sand layer. B) 2 cm thick dry sand layer. A1 and B1) Maximum depth reached of the transient crater. A2 and B2) Continued concentric development of the transient crater with a downrange wider excavated outer crater in the dry sand layer. A3 and B3) Final fresh crater. Stippled white line indicates the crater's cross section. Note the near-absent inner crater ejecta in A3 and the asymmetrically distributed, darker inner crater ejecta covering the downrange excavated outer crater in B3. Note also the uprange ejecta forbidden zone.
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With a decrease in the thickness of the upper, weaker layer the crater development is somewhat different although still rendering a concentric structure: At the initial stage (i.e., maximum depth reached) the cavity is significantly more concentric than in the experiment with a thicker weak layer (Fig. 11 B1 versus A1). With the continued growth of the cavity a separate ejecta curtain develops from the crater in the damp sand layer (Fig. 11 B2). This results in a crater with a well-developed ejecta layer from the inner crater in the damp sand covering the floor of the outer, dry sand crater as well as the dry sand ejecta layer on the near surroundings of the whole structure (dark-colored damp sand covering light-colored dry sand in Fig. 11 B3). This is consistent with the nested, basement crater excavation process at Lockne, and seemingly also with the development of the nested craters in Martian cases A, B, and C.
Direct comparisons of the lab experiments with Lockne and the Martian case studies are of course complicated by the large difference in size scale. Previous scaling analyses (e.g., Holsapple and Schmidt 1987; Schmidt and Housen 1987; Ormö et al. 2010) have shown that laboratory cratering experiments can replicate larger-scale cratering events as long as certain nondimensional parameters are the same in the experiments and the larger natural events. When this is true, the experiments are said to be similar to the larger impacts in the sense that they are geometric replicas, i.e., scaled-down versions, of the larger events.
Two of those nondimensional parameters are important here. The first, known as π2, is the ratio ga/U2, where g is gravity, a is the projectile radius, and U is the impact speed. The π2 is essentially an inverse Froude number for an impact: if multiplied by the ratio of target density to projectile density it becomes the ratio of gravitational force to inertial force). For our experiments (a = 0.01 m, g = 9.81 m s−2, U = 400 m s−2) π2 = 6 × 10−7. The initial conditions for the Martian Case A, B, and C craters are of course unknown. Rough estimates are derived here by assuming an impact speed in the range of 104–2 × 104 m s−1. Crater scaling relations (Schmidt 1980) then give impactor radii in the range from 25 to 30 m for Case A and 95 to 120 for Case B. Given that the total crater diameter for Case B (2.2 km) is close to that of Case C (2.5 km), the estimated impactor radii would be approximately equal for the two cases. Using these ranges of impactor radii and speeds and g = 3.7 m s−2 for Mars gives π2 = 2.2 × 10−7 to 1.2 × 10−6 for Case A and 8.8 × 10−7 to 4.7 × 10−6 for Cases B and C. The lab experiments have a π2 value that is about in the middle of the range of estimated values for the Case A crater, and about a factor of 1.5–8 lower than those estimated for Cases B and C. Therefore, the π2 values for the lab experiments are not too far off from those of the Martian craters considered here.
The second scaling parameter of importance is the ratio of target strength, Y, to a characteristic lithostatic stress, ρgD, where ρ is the target density, and D is the crater diameter. When this ratio is large, the crater size is determined by target strength and when it is small, gravitational forces determine crater size. For targets with a weak layer over a stronger basement material, such as the present lab experiments and, presumably, the Martian craters, the crater formed in the weak upper layer would be gravity dominated because of the small value of Y/ρgD. This is equivalent to saying that the strength of the upper layer is unimportant in determining the size of the crater in that material for either the lab experiment or for the Martian craters. However, the situation is different for the crater formed in the basement material: In the lab experiments, the craters formed at 1G in the damp sand substrate form in the strength-dominated regime (Schmidt 1983). For the Martian craters we do not know the properties of the rigid substrate, but for a basaltic target the transition between strength and gravity-dominated craters would occur at about 130 m crater diameter. Thus, the inner, nested crater in Case A (about 200 m) is slightly above this transition, and the nested craters in Case B (about 1 km) and Case C (about 600 m) are definitely gravity controlled. Therefore, while the π2 values for the lab experiments are not too different from those of the Martian craters, the strength/gravity ratio Y/ρgD is likely much larger in the lab experiments.
As a result, we cannot say that the lab experiments are similar to the Martian craters because the nested crater in the basement material is strength-dominated in the lab case, but not for the larger Case A, B, and C craters. The implication is that the ratio of the sizes of the craters formed in the upper layer and in the basement probably differs between the lab experiments and the larger craters. On the other hand, it may be that the offset in the crater centers is not sensitive to the strength of the basement layer, cf. the 3-D numerical simulation of the Lockne crater in Fig. 4. It seems likely that the offset is instead dependent more on the thickness of the upper layer and impact angle. If this is the case, then the lab experiments should be reasonable proxies for the outcomes of the much larger, higher speed impacts that produced the Martian craters, as well as the Lockne crater. This possibility could be investigated further in additional lab experiments and numerical simulations.
It should also be noted that the mechanisms for concentric crater formation may differ between the lab experiments and larger-scale planetary craters. In the lab experiments, the nested crater in the basement material is smaller than that in the upper layer because of the higher strength of the basement material following the model by Quaide and Oberbeck (1968). On the other hand, the strength of the basement is unimportant for the Martian craters because, as noted above, they form in the gravity-dominated regime. In this case, the appearance of nested craters must be due to some other mechanism: Even though strength may be unimportant at gravity-dominated craters, there will still be differences in the density and wave speed of the upper layer and the basement. The product of density and wavespeed is the mechanical impedance of a material. It determines how a shock wave reflects when it hits a boundary between materials with different densities and wavespeeds. Possibly, at large scale, the differing impedances of the two layers could result in reflection of the shock, with a reduction in energy deposition in the basement. However, at this stage, we do not know if it is the impedance that is the critical factor. It may be that it is either the wavespeed or the density that has the major effect. An impact into a target with a low-density layer on top of a high-density layer may well show a larger crater in the upper layer. This should also be addressed in future experiments and code calculations.