Crater morphology in sandstone targets: The MEMIN impact parameter study

Authors


Corresponding author. E-mail: anja.dufresne@geologie.uni-freiburg.de

Abstract

Abstract– Hypervelocity (2.5–7.8 km s−1) impact experiments into sandstone were carried out to investigate the influence of projectile velocity and mass, target pore space saturation, target-projectile density contrast, and target layer orientation on crater size and shape. Crater size increases with increasing projectile velocity and mass as well as with increasing target pore space saturation. Craters in water-saturated porous targets are generally shallower and larger in volume and in diameter than craters from equivalent impacts into dry porous sandstone. Morphometric analyses of the resultant craters, 5–40 cm in diameter, reveal features that are characteristic of all of our experimental craters regardless of impact conditions (I) a large central depression within a fragile, light-colored central part, and (II) an outer spallation zone with areas of incipient spallation. Two different mechanical processes, grain fragmentation and intergranular tensile fracturing, are recorded within these crater morphologies. Zone (I) approximates the shape of the transient crater formed by material compression, displacement, comminution, and excavation flow, whereas (II) is the result of intergranular tensile fracturing and spallation. The transient crater dimensions are reconstructed by fitting quadric parabolas to crater profiles from digital elevation models. The dimensions of this transient and of the final crater show the same trends: both increase in volume with increasing impact energy, and with increasing water saturation of the target pore space. The relative size of the transient crater (in percent of the final crater volume) decreases with increasing projectile mass and velocity, signifying a greater contribution of spallation on the final crater size when projectile mass and velocity are increased.

Introduction

Understanding the dynamics of a hypervelocity body impacting onto a planetary surface can give numerous insights into the processes that formed the solar system. After the contact and compression stage of an impact, the expanding shock wave excavates an initially roughly hemispherical cavity in the target, known as the transient crater (Gault et al. 1968; Melosh 1989). However, for almost all craters on solid bodies in our solar system, the final crater morphologies are affected by gravity, yielding the so-called modified final crater (e.g., Melosh 1977; O’Keefe and Ahrens 1993; Melosh and Ivanov 1999). Although gravity-induced modifications do not occur in small-scale, strength-dominated experimental impacts, spallation modifies the crater shape and leads to a substantial increase in total crater volume; i.e., spall fragments can account for over 50% of the total ejected mass (this study; Moore et al. 1962; Lange et al. 1984). Such experimental craters into brittle rocks are generally characterized by a central depression formed during the excavation stage, and an outer spallation zone, which is the result of brittle tensile fracturing and spall fragment ejection. These general features have been described for experiments into gabbro (Lange et al. 1984; Polanskey and Ahrens 1990), basalt (Moore et al. 1962; Gault et al. 1966), granite (Hörz 1969), sandstone (Baldwin et al. 2007; Kenkmann et al. 2011), water ice (Lange and Ahrens 1987; Grey et al. 2001; Grey and Burchell 2003), CO2 ice (Burchell et al. 1998), and artificial materials such as sintered aggregated glass (Love et al. 1993).

In shock wave terminology, spallation is defined as “separation of fragments of material along a plane parallel to the shock wave front, and resulting from the development of dynamic tensile stress components perpendicular to this plane” (Barbee et al. 1972; Johnson 1981; cited in Gilath et al. 1988). The development of spall surfaces in impact experiments, i.e., tensile failure planes, occurs during interaction of the shock wave and the rarefaction wave with the target surface (e.g., Melosh 1984; Polanskey and Ahrens 1990), but ejection of spall fragments from the target surface is not observed until late in the experimental cratering process due to their very low ejection velocity (on the order of m s−1; e.g., Polanskey and Ahrens 1990). Such modification of experimental impact craters by spallation does not occur in nonbrittle materials such as metals (Hörz 1969). In granular media, spallation likewise plays a less prominent role (Melosh 1984; Schultz et al. 2005).

Reconstruction of the transient crater dimensions in experiments can yield a better understanding of the physical parameters that affect crater formation, and provides essential data for numerical modeling (e.g., Wünnemann et al. 2006) and scaling calculations (e.g., Holsapple and Schmidt 1982; Holsapple 1993; Poelchau et al. 2013). For impacts into granular media, “quarter-space” experiments (e.g., Schmidt and Housen 1987; Schultz et al. 2005; Yamamoto et al. 2006), in which the projectile impacts along a transparent Plexiglass sheet, have been performed not only to determine the transient crater size but also to monitor its evolution through time. To avoid the effects on the excavation flow by the Plexiglass window used in quarter-space cratering experiments, Barnouin-Jha et al. (2007) used a nonintrusive laser-sheet technique to define the growth and dimension of the transient crater. They found that the transient crater does not grow in a self-similar manner as suggested by scaling rules (Holsapple 1993), but that its growth and dimensions seem to be a function of projectile velocity, projectile-target interaction time span, and target material friction.

The current study is part of the MEMIN (Multidisciplinary Experimental and Modeling Impact Research Network) program, which focuses on impact experiments into solid geological materials (Kenkmann et al. 2011). Sediments and sedimentary rocks are by far the most frequent target lithology for impact cratering on the Earth’s surface. Examples for impacts into sandstone include Aorounga, Chad (Koeberl et al. 2005); Kamil, Egypt (Folco et al. 2010); Barringer, Arizona, USA (e.g., Shoemaker and Kieffer 1974); Spider, Australia (Abels 2005); Wolfe Creek, Australia (Shoemaker et al. 2005); to name a few. Porosity, interstitial water, and strata layering are typical characteristics of sedimentary rocks on Earth and contribute to the large variety of crater structures. At the planetary perspective, these three parameters are likewise important factors (e.g., porous regoliths). Impact experiments allow the parameters that affect the cratering process to be chosen and controlled individually, and hence provide the unique opportunity to study the influence of each parameter in situ, in real time, and in postimpact analyses. By choosing the Seeberger Sandstone, good control of the target properties is provided due to its homogeneous small grain size and fine layering. At the same time, the use of a geological material narrows the wide gap between experimental/theoretical data and observations at terrestrial impact craters (morphology, subsurface, etc.). Results of the experiments furthermore provide important constraints and input data for numerical simulations. With the detailed morphological investigations presented herein, we aim at (1) correlating variations in experimental impact crater morphology to projectile velocity, target pore space saturation with water, target-projectile density contrast, and target layer orientation, and (2) establishing a method to estimate the transient crater in impact experiments (thereby eliminating the effect of spallation on final crater dimensions) using morphological constraints. The data set generated here is intended to be used for a comparison of the material behaviors that lead to the final crater morphology in experimental craters and strength-dominated craters on a planetary scale.

Methods

Experimental Setup

To date, 18 impact cratering experiments (Poelchau et al. 2013) were conducted at the two-stage light-gas gun facilities of the Ernst Mach Institute (EMI) (Schäfer et al. 2006; Kenkmann et al. 2011) using blocks of Seeberger Sandstein as targets. This sandstone, quarried by the TRACO company, is of uppermost Triassic age (209–200 Ma; Stück et al. 2011) and was deposited as a fluvial sediment within the Thuringian basin, Germany. While the entire stratigraphic sequence is quite heterogeneous, it contains several meter-thick layers of uniform composition. We chose “layer three” because of its high quartz content (containing minor constituent clay minerals and limonite); a homogeneous, small grain size (mean 100 ± 25 μm); a well-sorted texture with a porosity of 23±1% (Poelchau et al. 2013); and 1–5 mm thick layers with few cross-beddings. Blocks were cut with the bedding surfaces (sub)parallel (up to 5° deviation) to the target surface. Two pilot-study impacts into one dry and one water-saturated sandstone block (100 × 100 × 50 cm, Seeberger Sandstein layer five) using steel projectiles with diameters of 10 mm, impact velocities of 5.3 km s−1, and energies of 57–58 kJ (Kenkmann et al. 2011) preceded the described experiments.

In nine of the experiments presented herein (Table 1), cubic sandstone targets with 20 cm side lengths (target identifier “A,” block weight = 16 kg) were used at the 8.5 mm caliber two-stage light-gas gun (Space Light-Gas Gun-SLGG). For these low-energy experiments, steel projectiles (diameter Dp 2.5 mm) with a velocity of around 5 km s−1 and aluminum projectiles (Dp 2.5 and 5 mm) accelerated to 7.0 and 7.8 km s−1 were used. Four high-energy experiments were performed at impact energies between 12.8 and 41.5 kJ, using cubic sandstone targets (identifier “D”; w = 265 kg) with 50 cm side lengths at the 39 mm caliber two-stage light-gas gun (Extra Large Light-Gas Gun—XLLGG). Spheres with Dp of 10 mm of the Campo del Cielo IAB iron meteorite were accelerated to 2.5, 3.5, 4.4, and 4.6 km s−1. Three further experiments with spherical (Dp: 12 mm) steel and Campo del Cielo IAB iron meteorite projectiles at high impact energies (76 kJ) and varying target pore space saturation into 80 × 80 × 50 cm blocks were conducted. All experiments were filmed with high-speed video cameras (50–100 kfps; see Hoerth et al. 2012), and a new custom-built ejecta catcher system was installed (Sommer et al. 2012).

Table 1. Basic parameters and results of all MEMIN impact experiments into sandstone to date.
ExperimentPore space saturation vi (km s−1) E (J)Projectile Dp (mm) mp (g) V (cm3) D (mm) d (mm) d/D
  1. a290-1 BAM steel.

  2. b55X G23J1 aluminum

  3. cCampo del Cielo IAB iron meteorite (CDC).

  4. vi = projectile velocity, E = impact energy, Dp = projectile diameter, mp = projectile mass, = crater volume, = crater diameter, = crater depth, d/D = depth?diameter ratio.

A3-51245.0838steela2.50.0678.363.611.50.18
A5-51255.1873steel2.50.0678.862.411.70.19
A6-51264.8773steel2.50.0677.657.611.00.19
A8-51285.1874steel2.50.0676.450.69.50.19
A13-518250%5.3919steel2.50.06713.474.814.00.19
A11-518190%5.3941steel2.50.06731.1101.614.50.14
A12-518290%5.3932steel2.50.06734.294.118.00.19
A16-51867.8637alb2.50.0222.639.26.40.16
A15-51857.04353al5.00.17942.9104.514.30.14
D5-33002.512813CDCc10.04.1243184.837.30.20
D4-32993.524113CDC10.04.1309183.644.00.24
D2-32964.439688steel10.04.1629242.251.50.21
D3-32984.641513CDC10.04.1614241.455.00.23
P1-28085.358413steel10.04.1715243.456.00.23
P2-280944%5.356913steel10.04.11099286.845.00.16
E1-33824.676032steel12.07.31393365.770.50.19
E2-338350%4.676805steel12.07.31180337.959.60.18
E3-338450%4.674655CDC12.07.32108399.854.70.14

3-D Laser Scans and Digital Terrain Models

Crater topography was investigated visually and with the aid of digital elevation models (DEMs). These models were created based on 3-D laser scanning data. Using the Escan laser scanner (3d digital corporation, USA; spatial resolution of 0.1 mm), scans of the craters were captured from four to six different angles depending on morphological complexities such as overhangs or steeply dipping surfaces, and postprocessed using the accompanying software. Crater diameters were measured along 18 individual transects for each crater (refer to the Appendix) through the DEMs, from which depths were taken and volumes calculated. The DEMs were created within overall errors of approximately 0.75–1.0 vol% for the large craters (D-Series) and approximately 3.7 vol% for the small craters (A-Series). Detailed descriptions of the individual processing steps are provided in the Appendix.

Results

General Crater Morphology

Common morphological features of all craters, independent of the experimental parameters, are (1) a large central depression within highly fragmented target material and (2) an outer spallation zone with areas of incipient spallation along the crater rim (Fig. 1).

Figure 1.

 Morphological characteristics of a typical crater (A5-5125, see Table 1) in a dry sandstone target. a) Photograph showing the central depression with light-colored, highly fragmented target material (white dashed circle, zone I in Fig. 3), and the outer spallation area (zone II in Fig. 3) with incipient spallation (white arrow). b) Slope angle distribution illustrating the outer spallation surface dipping at 10–20° toward the crater center (orange outer areas), the large central depression and pit (dashed black circles).

1. The large central depression (zone I in Figs. 2a and 2b) consists of light-colored, crushed, and unsolidified material. Slope angles of this central depression are between 45 and 72° to the target surface. These depressions have radii amounting to between 19% and 36% of the average radius of their respective host (“final”) crater (Fig. 1a). At higher impact energies (>10 kJ), this area is relatively larger (27–32%) than in lower impact energy (<1 kJ) experiments (19–22%) in dry craters. In targets with partial or full water saturation of the pore spaces (wet targets in the following), they fall uniformly between 24% and 27%, regardless of impact energy. Differences are observed in the aluminum-projectile impacts (27% and 36%). In many craters, a small steep-sided central pit, roughly 2–3 times the projectile diameter, is nested within the large central depression (Fig. 1b).

Figure 2.

 Characteristic profiles of a crater in a (a) dry (A6-5126) and (b) pore space-saturated (A12-5183) sandstone target. Each profile shows the lines for 18 individual crater transects at two times vertical exaggeration, with one profile each highlighted as a black line; scale is in mm. Profile lines that extend to above the original target surface (z = 0) are due to uplifted incipient spallation fragments. Zone (I) is a central depression feature with highly fractured rock. Zone (II) is the outer spallation zone, which is subdivided in the wet crater into a convex-shaped zone (IIa) and a zone with stepped spall (IIb).

2. Dry targets are characterized by spallation zone surfaces sloping at 10–20° (Fig. 2b; zone II in Fig. 2a). In targets with partial or full water saturation, this area consists of two zones, namely, one adjacent to the inner depression with slightly convex slopes (zone IIa in Fig. 2b), and an outer zone with stepped surfaces (zone IIb). These steps consist of sub-parallel and steep surfaces oriented at 70–90° to the target surface. Large spall fragments can be refitted like jigsaw-puzzle pieces into spallation zones in both dry and wet targets. Localized areas of incipient spallation are common where fracturing was incomplete and the fragments remained within the target (Fig. 1a). Often, surfaces of these incipient spall fragments are raised up to 2 mm above the original target surface.

Influence of Experimental Parameters on Crater Morphology

Against the backdrop of features common to all craters, a range of morphometric distinctions can be made with respect to the following specific experimental impact parameters: (1) impact velocity, (2) projectile mass and diameter, (3) pore space water saturation, (4) target-projectile density contrast, and (5) target layer orientation. To establish the relevance of our results, we first discuss the reproducibility and data variation of replicate experiments.

Reproducibility

Experiments performed at roughly equal impact conditions yield a good reproducibility of crater dimensions in the dry sandstone targets (Figs. 3b–d). The dry craters A3-5184 and A5-5125 (Figs. 3b and 3c) compare very closely in volume, whereas A6-5126 is 9% smaller than A3-5124 and 13% smaller than A5-5125 due to one large incipient spall fragment (Fig. 3d). All craters are, however, identical in depth–diameter ratio d/D. At higher impact energy and larger projectiles, the experiments D2-3296 and D3-3298, also in dry targets, show excellent reproducibility, differing in depth by less than 5%. Craters in 90% water-saturated targets (A11-5181 and A12-5183), however, show significant variations in the depth–diameter ratio (d/D; Fig. 3e) due to significant depth-differences of 14.5 and 18.0 mm, respectively. The only difference in impact conditions between the two targets was that A11-5181 was sealed with an approximately 100 μm coat of resin to assure water retention, whereas A12-5183 was unsealed (and, hence, at the surface probably not water-saturated to the identical degree). The volume of the A11-5181 crater is smaller by 10%. Likewise, the higher impact energy experiments (E2-3383 and E3-3384; both blocks unsealed) also show distinct differences in d/D due to significant differences in the amount of incipient spallation; E2-3383 contains unusually large number of incipient spall fragments.

Figure 3.

 a) Reproducibility results in experiments with similar impact conditions; b–d) Craters of the reproducibility study in the small, dry A-Series targets. The influence of incipient spallation on crater shape can be seen in (d). Scale bar is 10 cm. e) Depth–diameter ratios show good agreements in the dry targets (open symbols), but significant difference in the water-bearing ones (closed symbols). f) An increase in crater volume with increasing water content of the target at similar impact energies is observed, which demonstrates a higher cratering efficiency when water is present in the sandstone pore spaces.

Impact Velocity

In this first parameter study with dry sandstone targets (Fig. 4a), 10 mm spherical steel projectiles were accelerated to velocities (vi) between 2.5 and 5.3 km s−1 (Fig. 4a). A higher vi results in a larger crater volume V following the function = 53.1 vi1.582 for the sandstone targets (for V in units of [cm3] and vi in units of [km s−1]). Crater depth d increases with increasing vi at a higher rate (= 21.0 vi0.598) than diameter D (= 117.6 vi0.449, with d and D in units of [mm]). Furthermore, crater shape becomes increasingly more irregular, the spall zone morphology more complex, and the overall target block damaging (radial, vertical, and side spallation fractures) more pervasive. In the low-velocity experiments D5-3300 and D4-3299, additional large circular spall fractures surround the craters at 5–10 cm distance from the rim (Figs. 4b and 4c), which was not observed in the other experiments.

Figure 4.

 a) Experimental results of impacts at varying velocities. b–d) Photos of the D-Series and (e) the pilot-study craters (same scale as (b–d). f) Plot demonstrating the increase in crater volume with increasing projectile velocity. g) Profiles of the D-Series craters, units in [mm]. The black line is a representative profile.

Projectile Diameter and Mass

Projectile mass (mp) was varied from 0.067 g (A5-5125 at the SLGG) to 4.1 and 7.3 g (D3-3298 and E1-3382, respectively, at the XLLGG) through increasing the steel projectile diameter from 2.5 to 10.0 and 12.0 mm. This naturally resulted in higher impact energies (E). Impact velocity was kept approximately equal (4.5–5.1 km s−1). A 90-fold increase in E from A5-5125 to E1-3382 resulted in an approximately 160-fold increase in crater volume (V). Likewise, from A5-5125 to D3-3298, an approximately 50-fold increase in E resulted in 70× the volume. For the two shots (D3-3298 and E1-3382) at the XLLGG, E and V both increase by a factor of approximately 2.

Pore Space Water Saturation

Craters in sandstone blocks containing water in the pore spaces are larger in diameter (Figs. 5c and 5d) and in volume (Fig. 5f) than their dry equivalents (Fig. 5b). At similar impact energies, craters in targets with 44–50% water saturation have a 1.6 times larger volume than those in dry targets, and an approximately 4 times larger volume at 90% water saturation (Fig. 5a). Crater diameters increase by approximately 150% and depth by approximately 124% from zero to 90% water saturation. This unequal growth in depth and diameter leads to consistently smaller d/D for craters in water-saturated targets compared with dry targets. For the sandstone, this transition lies at d/D of approximately 0.19, whereby the degree of water saturation does not define any trend (Fig. 5e) and the ratios consistently fall within the same range (d/D of 0.14–0.19) in wet targets (0.18–0.26 in dry targets) regardless of impact velocity, energy, or projectile size.

Figure 5.

 a) Experimental results of impacts into targets with varying pore space saturation; b–d) contour maps of craters in dry and water-saturated targets of the A-Series at comparable impact energies and selected profiles from each crater. All contours are at 0.1 mm intervals. e) d/D ratios of the respective experiments showing dry (open symbols), 50% saturated (gray symbols), and 90% saturated (black symbols) of the respective parameter studies. f) An increase in crater volume occurs with increasing pore space saturation.

Pore space water saturation changes the spallation behavior as documented by the very pronounced, concentric topographic steps in the outer spallation zone of the 90% saturated targets (IIb in Fig. 2b). In these craters, zone IIa (Fig. 2b) slopes evenly toward the crater center or has convex surfaces before transiting to the inner depression via another pronounced topographic step (Fig. 5d). In the 44–50% water-saturated targets, the spallation zone shows slopes of craters in both dry and fully saturated targets. Incipient spall fragments are fewer and less prominent in craters in the 90% saturated targets compared with experiments with 0–50% saturation.

In addition to differences in the spallation zone, the geometry of the central depression of craters in saturated targets differs from those in dry targets. Those in 90% saturated targets are more pronounced, flatter, and wider, and occasionally bordered by very distinct topographic steps or flat areas (see transition areas I to IIa, Fig. 2), whereas in dry targets, they are typically more conical. In P2-2809 (44% saturation) and E3-3384 (50% saturation), the central depression is very flat, whereas E2-3383 and in A13-5182 (both 50% saturation) have deep, conical central depressions.

Target-Projectile Density Contrast

Impacts at velocities of 7.0 and 7.8 km s−1 with aluminum projectiles (density ρp: 2.7 g cm-3) into dry targets yielded craters with flatter, terraced topographies in the spallation zones (Fig. 6) than impacts of similar energy using steel or meteoritic iron projectiles (ρp: 8.1 and 7.8 g cm−3, respectively) into dry targets (compare experiment A5-5125 in Fig. 4b with A16-5186 in Fig. 6d). Consequently, these craters have lower d/D than craters in dry targets formed by higher density projectiles (Fig. 6a). Using aluminum as projectile material allowed for higher impact velocities to be attained at the light-gas gun. Additionally, two different projectile masses (mp 0.022, Dp 2.5, vi 7.8 km s−1, E 0.6 kJ; mp 0.179 g, Dp 5.0 mm, vi 7.0 km s−1, E 4.4 kJ) were used to reach different impact energies. Compared with the 2.5 mm projectile, the 5 mm projectile with 8 times the mass at 6.5 times the impact energy yielded a crater 16.5 times in volume (compare Figs. 6b and 6d). A central “dome,” not observed in other experiments, was found in the center of the crater produced by the 5 mm diameter aluminum projectile (Fig. 6c). This dome is composed of highly fragmented target rock and shows tensile fractures at its base.

Figure 6.

 a) Experimental results of impacts with aluminum projectiles; b) crater in A15-5185 (7.0 km s−1; 4353 J; 5 mm projectile diameter). c) Close-up of central “dome” showing tensile fractures at its “base,” indicating that tensile stresses were not strong enough to remove the feature from the crater. d) Crater in A16-5186 (7.8 km s−1; 673 J; 2.5 mm projectile diameter). All contours are at 0.1 mm interval.

Target Layer Orientation

In all impact experiments, bedding was oriented more or less parallel to the target surface (deviation of up to 5°), and thus the impact occurred perpendicular to layering. For comparison, one dry cubic sandstone target (A8-5128; Fig. 7b) was oriented with layering perpendicular to the target surface, i.e., parallel to the trajectory of the steel projectile. This resulted in an approximately 25% smaller crater volume compared with an experiment at the same energy with sandstone layering parallel to the target surface (A3-5124, Fig. 7c). The spallation zone of crater A8-5128 is smaller and has surfaces dipping more steeply at 25° compared with crater A3-5124 with spallation surfaces dipping at 10–20°. Also, the central depression is less well defined in A8-5128 and has a flat bottom (Fig. 7d).

Figure 7.

 a) Experimental results of impacts into targets with different layer orientation. b–c) A comparison of craters formed in targets with layering (b) parallel, and (c) perpendicular to impact direction shows a smaller crater volume and diameter for layering parallel to the impact direction. d) Profiles through the respective craters, dashed lines indicate layering, units in [mm].

Spallation

In the MEMIN experiments, up to 80% of the total ejected mass is composed of large “jigsaw”-spall fragments, which are arbitrarily defined as fragments >20 mm long-axis for the large craters (D- and E-Series) and >5 mm for the small A-Series craters. In dry target experiments, the large spall fragments are wedge-shaped with the spall fracture angled at 10–20° degrees to the surface (Fig. 8a). In contrast, those from water-saturated targets are of flat, tabloid, or rhombic shape (see also Sommer et al. 2012). Not all spall fragments fit seamlessly to the crater surface and considerable amounts of fine material adhere to their undersides. By refitting large spall fragments into their original position, their inner rim always forms a circular shape, even if the actual crater has a highly irregular outline (Fig. 8a). This rim encloses the central depression in very good approximation. The two dominant processes of experimental impact cratering, i.e., excavation flow and spallation that these morphological remnants represent are also clearly seen on high-speed video captures (Fig. 8b).

Figure 8.

 a) Spall fragments refitted into the crater enclose the central depression. b) Detachment of spall fragments is observed late in the cratering process on high-speed videos.

Maximum Spallation Zone Extent

Each crater has large radial segments in the spallation zone where no incipient spallation fragments remain in the crater, thus “maximum spallation” has been achieved in that segment. These segments coincide with the maximum crater radius and typically have smooth, planar surfaces compared with the more uneven surface areas where incipient spall fragments remain. This area is herein called the maximum spallation surface. Figure 9 shows as an example the DEM and profile of crater A6-5126: the left-hand side corresponds to the maximum spallation surface, whereas the right-hand side shows topographic variations caused by incipient spallation. This results in a locally smaller crater radius. Fractures outlining the incipient spall fragments are well identified on the target surface (Fig. 9) and within the subsurface (Buhl et al. 2012). Their orientations clearly mirror the maximum spallation surface on the left-hand side, dipping at the same angle (15°) toward the crater center (Fig. 9b).

Figure 9.

 a) Plan view and b) profile of crater A6-5126 showing the maximum spallation surface and maximum crater radius (black circle) on the left-hand side. The dark-gray shaded area in the crater profile was used to calculate the rotational volume for a theoretical crater with complete spallation, i.e., the maximum potential crater volume VMS. Subsurface spallation fractures on the right-hand side of the profile mirror the typical spallation surface dip of 15° and their surface expression (dashed line in [a]) approximate the maximum crater radius.

The rotational volume of the area above the maximum spallation surface is used to estimate the crater volume without incipient spall fragments, referred to here as VMS. It provides the theoretical maximum volume that could have been achieved had spallation been complete and spatially homogeneous with a circular symmetry. Interestingly, despite large variations in experimental parameters, the ratio of the actually observed final crater volume V to VMS lies within a narrow range of 0.60–0.68 for all dry targets, whereas in water-saturated targets, V/VMS is consistently higher at approximately 0.75. The experiment where target layering was parallel to the projectile trajectory resulted in a V/VMS ratio of 0.91, indicating significantly less incipient spallation.

Determining Morphological Remnants of the Transient Crater

To compare experimental with natural impact craters and with numerical models, it is fundamental to define the size and volume of the transient crater. In the pilot study preceding the experimental campaigns, a method of fitting parabolas (Fig. 10a) to the central depression of the crater was applied by Kenkmann et al. (2011), and this method is adopted herein. To verify the parabola fits (a), the following data (b, c) were collected and compared with the parabolas:

Figure 10.

 Methods of fitting parabolas to the central depression: a) the extent of the central depression is determined by the inflexion points at the transition from depression to spall zone, and a 2nd order polynomial fit is applied to this segment (black line). Digitally refitted spall fragments and the central depression extent on contour maps and on photos are also used to define the fitting segment. b–c) Additional methods for cross-checking the fitting results. The diameter Dtc and theoretical ejection angle αtc of the transient crater are determined from parabola fits to the crater morphology. The approximated transient crater diameter Dv and the ejection angle αv are taken from high-speed videos.

b) approximated transient crater diameters on high-speed videos,

c) ejecta cone angles on high-speed videos.

(a) Quadric parabolas were fitted to the central depression on profiles taken from the spatial data of 3-D crater scans (Fig. 10a). The outer limits of the central depression were defined based on the central depression diameter determined by the change in slope in contour maps (e.g., Fig. 4b), and the point of inflexion in digital profiles (Fig. 10a). At this point of inflexion, the concave-shaped central depression changes into a convex or straight slope, corresponding to the transition from the central depression to the spallation zone. Spall fragments were digitally refitted to the profiles and used as a maximum limit for the parabola diameter Dtc (Fig. 10a).

This fitting process had to be adjusted for the aluminum projectile experiments (A15-5185 and A16-5186) because both the respective central depressions have a generally flatter morphology. Fitting parabolas to these craters resulted in transient crater dimensions larger than the refitted spall fragments allowed for. Furthermore, in the crater of A15-5185, a central dome complicates the morphology of the central depression (Fig. 5c). In this case, the parabolas were fitted using only the refitted spall fragments to constrain the parabola diameter Dtc, and the crater depth without the dome was estimated from extension fractures below this feature as seen in cross-sections through the target (Buhl et al. 2012). For crater A16-5186, very few profiles provided a central depression morphology that could be analyzed; these results should therefore be used with caution.

(b), (c) In situ crater growth was analyzed on high-speed videos (Figs. 10b and 10c). During the initial stage of cratering, the transient crater diameter in the videos (herein referred to as Dv; Fig. 10b) grows steadily until it reaches a maximum value, while the ejecta cone simultaneously reaches a relatively constant angle αv (Fig. 11c) (Hoerth et al. 2012). At this point in the cratering process, we assume that the transient crater has reached its maximum size (Hoerth et al. 2012). Using the respective image in the high-speed video (Fig. 10c), Dv and αv are measured. From these data, transient crater volumes were calculated by fitting a parabola to the crater depth d (minus the central pit where necessary) and the ejecta cone angle αv from the videos, and compared with parabola fits to the digital profiles alone.

Figure 11.

 Comparison between video data (circles) and parabola fits (crosses); no video data are available for A8 and A3 and D2, and the video of P2 cannot be fully analyzed due to shadows in the crucial frames. TC = transient crater.

Measured transient crater diameters and ejecta cone angles from video data and those calculated from parabolas are shown in Fig. 11. Given a certain transient crater depth in the calculation of the transient crater volume (i.e., the volume of revolution of the parabola), it is the diameter that is more important than the opening angle. Good agreement between the diameters from parabola fits and from video data is achieved (Fig. 11a), with some discrepancies in the experiments with the highest impact energy (E-Series, >70 kJ). Measurements of the ejecta cone angles are based on the outer perimeter of the ejecta cone in shadowgraphs (Fig. 10c; Hoerth et al. 2012) rather than on trajectories of individual particles. Future work will address the dynamic behavior and the influence particle trajectory angles might have on the results presented here. At the moment, we see the largest discrepancies between these two methods in the water-saturated targets, where ejection behavior might additionally be influenced by development and violent expansion of a vapor phase. A11-5181 might have been additionally affected by the coat of resin on the target block.

A higher cratering efficiency in pore space-saturated targets is also seen in transient crater dimensions (Table 2). From dry (A5-5125) to 90% water saturation (A11-5181, A12-5183), the transient crater volume increases by a factor of 2.0–2.7. Between the craters in dry and in the 50% water-saturated target (A13-5182), no significant difference in transient crater volume was observed.

Table 2. Transient crater dimensions.
ExperimentsParameter Vtc
(cm3)
vol% n Dtc
(mm)
Dv
(mm)
αtc
(°)
αv
(°)
  1. Nd = no data, n = number of digital crater profiles analyzed.

  2. *Target layering parallel to impact direction, vol% refers to the transient crater volume percentage of the final crater volume. Dtc = transient crater diameter from parabola fits, Dv = transient crater diameter from video analyses, αtc and αv are the ejection angles from parabola fits and video analyses, respectively.

D5-33002.5 km s−1128 ± 1252.4 ± 5.11897.8 ± 4.380 ± 454.1 ± 1.055 ± 1
D4-32993.5 km s−1130 ± 1440.5 ± 6.01085.3 ± 5.074 ± 464.8 ± 1.558 ± 2
D2-32964.4 km s−1269 ± 1142.2 ± 0.89115.9 ± 2.4nd60.4 ± 0.5nd
D3-32984.6 km s−1209 ± 3234.2 ± 5.216105.0 ± 9.493 ± 561.4 ± 2.859 ± 1
P1-28085.3 km s−1229 ± 1232.0 ± 1.61482.0 ± 5.094 ± 1065.2 ± 0.258 ± 4
E1-33824.6 km s−1248 ± 4917.8 ± 3.51395.2 ± 9.9130 ± 471.0 ± 2.059 ± 5
P2-280944% sat.404 ± 2736.8 ± 2.56112.0 ± 18nd48.6 ± 1.160 ± 5
E2-338350% sat.312 ± 5226.5 ± 4.416115.9 ± 9.9144 ± 463.8 ± 2.268 ± 5
E3-338450% sat.550 ± 7126.1 ± 3.45159.8 ± 10.1144 ± 453.9 ± 1.768 ± 5
A13-518250% sat.4.1 ± 0.730.5 ± 5.21828.5 ± 2.629 ± 360.9 ± 2.463 ± 2
A11-518190% sat.10.1 ± 2.332.1 ± 8.6443.4 ± 6.050 ± 350.9 ± 4.168 ± 2
A12-518390% sat.13.1 ± 1.038.2 ± 2.91543.3 ± 1.650 ± 358.6 ± 0.966 ± 2
A6-5126773 J3.4 ± 0.444.9 ± 5.41228.4 ± 1.734 ± 256.7 ± 1.654 ± 1
A5-5125874 J4.8 ± 0.454.5 ± 4.11032.9 ± 1.432 ± 254.0 ± 1.456 ± 3
A3-5124839 J4.4 ± 0.252.9 ± 2.21531.6 ± 0.7nd54.9 ± 0.7nd
A8-5128*839 J4.7 ± 0.274.1 ± 3.01035.4 ± 0.7nd47.8 ± 0.7nd
A15-51857.0 km s−113.2 ± 0.930.8 ± 2.1347.6 ± 1.850 ± 351.3 ± 1.150 ± 3
A16-51867.8 km s−11.3 ± 0.0650.6 ± 2.3623.4 ± 0.628 ± 246.7 ± 0.949 ± 4

Target Block Damaging

Experiments in which the impact energy per total upper target block surface area exceeded 10 J cm−2, macroscopically visible damage of the target block surface outside of the crater was induced. In these cases, radial fractures within the crater spallation zone are present and typically extend to outside the crater margin on the target surface. Lateral block damage (Fig. 12), defined as side spallation fractures by Fujiwara (1980), occurs due to reflection of the shock wave from the sides of the target block (Fujiwara et al. 1977; Fujiwara 1980; Ai and Ahrens 2004). Above approximately 15 J cm−2, these features become pervasive. In only two experiments (D2-3396 and D3-3398; Fig. 12) did we find radial fractures in all spall zone segments, side spallation fractures interlinked with each other and with the radial fractures, and pieces of material spalled from the target sides (Fig. 13). Interestingly, the targets suffering the highest block damaging have very similar crater-to-target surface area ratios as the fully water-saturated targets (A11-5181 and A12-5183) and the experiment with the large aluminum projectile (A15-5185). These target blocks, however, did not suffer any or only moderate block damaging (i.e., radial fractures only in few spall zone segments, side spallation fractures visible, but not incisive; Fig. 13).

Figure 12.

 Highest target block damage was observed in block D3-3298, which shows extensive radial and side spallation fractures.

Figure 13.

 Empirical relationship between impact energy normalized to target surface area, the relative crater surface area, and degree of target block disruption outside the impact crater.

Higher damaging occurred in the larger target blocks of the D-Series. In these experiments, 10 mm projectiles were used and higher cratering efficiencies were observed than for those using 2.5 mm projectiles on smaller target blocks (Poelchau et al. 2013). Larger projectiles mean longer shock pulse duration, which, as has been shown in several planar shock wave experiments (Ahrens and Rubin 1993; Meyers 1994), causes the onset of microcracking and spallation at lower tensile stresses. Furthermore, shock wave pressure decreases radially with distance and, therefore, shock wave reflection will occur at higher tensile stresses in smaller blocks for the same impact parameters (compare P1-2808 and D2-3296, D3-3298; Fig. 13). This might explain the higher damage in the blocks with a 50 × 50 cm target surface (D-Series) compared with those with a 80 × 80 cm surface (E- and P-Series) at comparable impact energies. The damaging thresholds are lower for impacts into gabbro, where radial and side spallation fractures are already observed above 5 J cm−2 (using data in Polanskey and Ahrens 1990) compared with moderate damage between 10 and 15 J cm−2 in our experiments.

Discussion

The experimental craters were formed in the strength regime, i.e., the shape of the final crater is governed by rock strength and not by gravity, thereby eliminating gravity-induced crater modification. In this regime, portions of the transient crater are preserved in experiments with brittle target materials (this study; Kenkmann et al. 2011) and metals (where it equals the final crater; Hörz et al. 1995), whereas in experiments using loose granular materials as targets (Barnouin-Jha et al. 2007) and in almost all terrestrial craters (e.g., Grieve 1987), the transient crater is modified by gravity-induced processes such as slumping. We assume that the parabolas fitted into the central depression of our experimental craters approximate the transient crater size quite well. The extent of the central depression equals or is enclosed by the zone of grain crushing (i.e., the light-colored, fragile central part), confirming crushing and excavation as the mechanisms that produced this morphology.

The detailed examination of final crater morphology in the Results section compares craters formed under varying experimental conditions, in which either projectile or target parameters were changed. The kinetic energy (= 0.5 m vi2) of the impacting projectile was altered in three ways: (1) The velocity was increased while keeping the mass of the projectile constant, or (2) the mass was altered while keeping the velocity constant, or (3) the projectile density was reduced by using aluminum instead of steel. In the third case, for shot A16-5186, the kinetic energy was kept approximately equal to shots A3-5124 to A8-5128 by increasing impact velocity, whereas for shot A15-5185, projectile diameter and velocity were both increased, resulting in higher kinetic energy.

The target properties were altered in two ways. (1) Adding water to the sandstone’s pore space reduced empty porosity and weakened the sandstone’s compressive and tensile strength. (2) Changing the orientation of bedding to the impact trajectory made use of inherent petrophysical anisotropies caused by sedimentary layering.

For cratering in the strength regime, scaling rules theoretically predict that crater volume scales with impact energy for impacts in hard, brittle materials (e.g., Holsapple 1993). Experimental results generally confirm this behavior (e.g., Gault 1973; Holsapple and Schmidt 1982; Lange and Ahrens 1987; Shrine et al. 2002) and indicate that combinations of projectile mass and velocity should result in the same crater volumes as long as the impact energy and projectile material remain the same, i.e., VE1.

Scaling of MEMIN final crater volume data is discussed in Poelchau et al. (2013). There they show that for all steel and iron impacts into dry sandstone targets over a range of two orders of magnitude in energy, VE1.12, and for all 50% saturated targets VE1.07. Crater diameters should theoretically scale with the cube root of energy, i.e., DE1/3. An analysis of MEMIN data shows DE0.37 for dry targets and DE0.35 for 50% saturated targets.

Contribution of the Transient Crater and of Spallation to the Final Crater Volume

The fact that the exponents are larger than 1 for the volumes and larger than 1/3 for the diameters shows that craters grow larger with increasing energy than energy scaling theoretically allows. This is caused by increasing the amount of spallation in larger craters (see Fig. 14). Several factors apparently affect the percentage of spallation relative to the transient and final crater volume: (1) projectile diameter, (2) projectile velocity (3), the orientation of target layering, and (4) target pore space saturation with water.

Figure 14.

 Crater volume in relation to impact parameters a) projectile velocity (at high impact energies, i.e., >10 kJ), b) target pore space saturation, c) the reproducibility study including impact trajectory parallel to bedding (A8-5128) at low impact energies (<1 kJ), and d) target-projectile density contrast (i.e., impacts with aluminum projectiles). On the left side, the volume of the final crater (black diamonds) and that of the transient crater as derived from parabola fits (open diamonds) is shown. On the right side, the respective transient crater volume percentages from parabola fits (white) and spall volume percentage (light and dark gray) are shown. Large and jigsaw-spall volume values are from Sommer et al. (2013), whereas small or unspecified spall is calculated by subtracting transient crater and large spall volumes from the final crater volume (large/jigsaw-spall data are not available for all experiments).

The volume of spalled material relative to the volume of the transient crater is increased for cases (1) and (2), i.e., when either projectile diameter or velocity is increased. Case (1) is best explained by the increase in the duration of the shock pulse with larger projectiles. Longer shock pulses can effectively increase spallation, as is observed e.g., in experiments by Ahrens and Rubin (1993), where they showed that spallation occurred at lower tensile strengths in planar shock experiments when the pulse duration was increased. For MEMIN data (Fig. 14), this is visible when comparing impacts with small projectiles (Dp 2.5 mm), which have relative transient crater volumes of approximately 50% of the final crater volume, with impacts with larger 10 mm projectiles, which only attain approximately 30% at the same velocity (approximately 5 km s−1). For case (2), the velocity study shows clear transient crater trends where relative transient crater volumes decrease from 52% at 2.5 km s−1 to 32% at 5.3 km s−1 for the same projectile size. Additionally, experiment E1-3382 (dry) at 4.5 km s−1, larger Dp (12 mm) and mp (7.3 g) and higher impact energy (76 kJ) continues this trend down to 18% transient crater. This may be correlated with the increase in shock pressure with increasing impact velocity. An interesting case can also be seen in Fig. 14c, where the two experiments with an aluminum projectile are compared. The 2.5 mm projectile produced a smaller relative transient crater volume, comparable to the relative transient crater volume of lower velocity impacts with 2.5 mm steel projectiles. This might suggest that either projectile size plays a more dominant role than impact velocity or that projectile density also affects the ratio of transient crater and spall volume.

The volume of spalled material relative to the volume of the transient crater is decreased for case (3), i.e., when target properties are altered by changing the target layer orientation. Figure 14d shows that in experiment A8-5128, the transient crater comprises almost 75% of the final crater volume compared to 50% for other impacts of the A-Series, whereas the actual volume of the transient crater is identical. Thus, transient crater excavation, i.e., direct shock wave interaction and grain crushing, is independent of target layer orientation, whereas tensile fracturing is. This is an effect of higher tensile strength parallel to the target layering, which then reduces spallation. One may assume smaller tensile strength perpendicular to layering due to potentially weaker bonds between layers, particularly if clay minerals preferentially form these layers. Poelchau et al. (2013) measured a slightly lower tensile strength for the target sandstone of 4.1 ± 0.7 MPa perpendicular to the layering compared with 4.7 ± 0.8 MPa parallel to the layering. On the other hand, spallation in impact experiments into rocks without prominent layering reached volumes of spallation similar to our experiments: 60–80% (Lange et al. 1984), and 39–67% of the total crater volume (Polanskey and Ahrens 1990) in gabbro targets. Also, in these experiments, the dip angles for the outer spall surfaces are in a range of values identical to ours. Furthermore, preliminary results of experimental impacts into homogeneous (i.e., nonlayered) quartzite and tuff show comparable ranges of spallation volume percentages (unpublished MEMIN data).

In case (4), where water saturation of the pore space was increased, the relative transient crater volume was reduced for both 50% and 90% saturation in the A-Series, but increased for the E-Series, while no difference is visible for the pilot shots. It is not clear how saturation would cause an increase in spallation for smaller projectile diameters and a decrease in spallation for larger projectile diameters. In any case, more work is required to understand the mechanisms of tensile failure during spallation.

Effects of Saturation on Crater Morphology

Depth, diameter, and general crater shape are influenced by a change in target and projectile parameters. The dominant effects of water saturation of the pore space in our crater experiments are an increase in final crater volume and a decrease in d/D ratios. In comparison, Baldwin et al. (2007) performed wet and dry cratering experiments into two different sandstones, i.e., Coconino Sandstone and an unnamed “test” sandstone. For the test sandstone, which had a porosity of 17% and a large grain size of 0.4 mm, they arrived at d/D-values of 0.22 for the dry as well as the wet experiments. For the Coconino Sandstone, which is comparable to the Seeberger Sandstein in porosity and grain size (Table 3), d/D of 0.15 for the dry and 0.11 for the wet sandstone were measured. However, morphological features common in wet MEMIN craters, e.g., “stepped” spallation zones, were not reported in the wet Coconino sandstone. The main difference in experimental parameters is that Baldwin et al. (2007) used projectiles only seven times the grain size of the target sandstones (compared to 25–120 times in our experiments) and much lower impact energies (approximately 0.05 kJ compared to approximately 0.9 kJ). Normalized to projectile diameter, however, the Coconino shows similar crater diameters at slightly smaller depths (Table 3). It stands to reason that in the Coconino experiments of Baldwin et al. (2007), either the impact energy was insufficient to induce large spall volumes and the characteristic topography of craters in wet targets, or, due to the small projectile size, the material properties of single quartz grains played a more dominant role than petrophysical properties of the sandstone itself.

Table 3. A comparison of MEMIN experiments with Coconino Sandstone experiments from Baldwin et al. (2007).
  Seeberger dryCoconino drySeeberger wetCoconino wet
Porosity (%)23 ± 122.7∼2–3∼0
Pore space saturation (%)90100
Grain size (mm)0.100.150.100.15
E (J)8735394249
Dp (mm)2.51.02.51.0
V (cm3)8.81.231.11.5
D/Dp 25.023.940.640.0
d/Dp 4.53.75.84.5

The degree of pore space saturation shows notable transitions of crater morphologies between dry and full saturation. That is, the morphology of the 50% saturated target compares in some areas to craters in 90% saturated targets in spallation behavior (i.e., transient crater volume percent and topographic steps in zone II), but in other areas, it compares to dry craters in transient crater diameter (normalized to Dp) and in absolute transient crater volume. Furthermore, this crater has a strongly developed small central pit, a large amount of fine material remaining in the central zone, and shows characteristics of both dry and wet morphologies in the spallation zone. Ejecta grain size distribution analyses by Sommer et al. (2013) support these observations, in that the deeper craters of the 90% saturated targets have the largest amount of ejected fine (1–100 μm) material, and in that, in the 50% saturated case, less fine material was ejected than even for the dry craters at identical impact conditions. We attribute the peculiar “dry” as well as “wet behavior” of A13-5182 to inhomogeneous pore water distribution, leaving some volumes of the impact site unsaturated while other areas might have been more than 50% saturated.

Water in the pore spaces of the target lithology lowers the uniaxial compressive strength (Dyke and Dobereiner 1991) and the dynamic tensile strength of the material. Wiid (1970), as cited in Dyke and Dobereiner (1991), showed that water-saturated sandstones only have approximately 50–60% the uniaxial compressive strength of dry sandstones, and Ogata et al. (2004) measured a decrease in dynamic tensile strength of Kimachi Sandstone by approximately 51% in the saturated state. In our MEMIN experiments, enhanced permeability along the bedding planes might have locally led to a higher degree of water saturation, hence facilitating tensile failure by lowering the tensile strength along these planes. Our craters in water-saturated targets have spallation zone surfaces (spall fractures) subparallel to the target surface and to the bedding planes. Compressional stresses in the shock pulse dominated in zone I (Fig. 2), whereas interaction of the shock and rarefaction wave with the target surface occurs in zone II. Near-surface failure due to strength reduction in water-bearing targets or layer-controlled accumulation of water and hence weaker, target surface-parallel horizons could explain the morphology of region II, particularly IIb (Fig. 2).

Projectile Density Effects on Crater Morphology

The density contrast between target and projectile is a very important parameter in cratering, and in general, low-density projectiles (e.g., aluminum) yield flatter and less deep craters than high-density projectiles. Accordingly, d/D for the two experiments with aluminum projectiles are lower (0.14 and 0.16) than the consistently greater than approximately 0.19 ratios with steel projectiles into dry targets. For a projectile diameter of 2.5 mm, we have two experiments with a similar impact energy, namely, A6-5126 (steel projectile at a velocity of 4.8 km s−1) with 773 J, and A16-5186 (Al, 7.8 km s−1) with 673 J. The resultant craters, however, differ significantly in volume (A6-5126: 7.6; A16-5186: 5.4 cm3), depth (A6-5126: 11.0; A16-5186: 6.4 mm), and d/D (A6-5126: 0.19; A16-5186: 0.16). This compares well with data by Love et al. (1993) and Hörz et al. (1993) who showed that penetration depth (normalized to projectile radius) decreases with decreasing target-projectile density contrast. Holsapple (1980) showed that for a higher target-projectile density ratio, the equivalent depth of burst (DOB) in loose sand impacts/explosions is lower than for a smaller target-projectile density ratio. Using DOB = 2·rp·(ρp/ρt)0.5 (where rp is the projectile radius, ρp projectile density, and ρt target density; Birkhoff et al. 1948), we arrive at a DOB of 4.9 mm for A6-5126, and at 2.9 mm for A16-5186. Moreover, these results indicate a relationship between DOB and d/D.

Raising the impact energy by a factor of 6.5 from 673 J (A16-5186) to 4353 J (A15-5185) by using a larger projectile yields a crater 16.5 times in volume and 2.7 times in diameter, and resulted in a central dome not observed elsewhere. Moreover, these Al-projectile cratering experiments caused peculiar terraces in the outer spall zone. Overall, even though the targets were dry, these craters resemble those of steel projectiles into water-saturated targets in spallation zone morphology and in d/D ratios. So far, we have no plausible explanation for this observation.

Application to Impact Craters on Earth and the Planets

The MEMIN program is aimed to better understand natural impact craters on Earth and other planetary bodies. This goal requires scaling of experimental results over several orders of magnitude, which is known to be a very complicated task due to several factors. The effect of target strength anisotropies becomes increasingly more important at larger scales where multitudes of joints, faults and fractures, and compositional variations change rock properties. This has long been recognized in the engineering community where a distinction is made between rock (e.g., lab sample size) and rock mass (outcrop scale); however, methods have been developed to account for these differences (e.g., Hoek and Brown 1997). It is well known that strength anisotropies of the target influence the modes of crater excavation and collapse, and thereby the geometry of impact structures. The strength contrast of lithologies in the target, and the arrangement of zones of weakness determine how intensely such heterogeneities affect stress and strain distribution, and the cratering flow field. Horizontal layering with weak interbeds alternating with competent beds, for instance, results in a preferred localization of deformation along the weak beds and this behavior can influence the cratering process (Kenkmann et al. 2000; Collins et al. 2008).

In natural craters, the quantity of spall material is considered to be on the order of a few projectile masses (Melosh 1984), but not many studies have addressed this issue. In our experiments, spall amounts to up to approximately 80% (with the majority between 46% and 68%) of the total excavated mass, or between 44 and 478 times the projectile mass, underlining the size effect of target strength, and thus material response to high stresses. Large jigsaw-spall fragments, when refitted back into the experimental crater, always outline a circular hollow with an inner spall radius that encloses the calculated transient crater diameter. The rim of the final crater is located at about 1.5–2 inner spall radii. Extrapolating these geometric relationships to craters on Earth and the planets might provide an approximate scale on where to look for spallation fractures. Indications for spallation in nature are preserved, for example, in subhorizontal shear planes in the periphery of the Ries impact crater, Germany (Kenkmann and Ivanov 2006). These detachments occur at 0.8–1.8 crater radii and increasingly shallower levels with increasing distance from the crater center. Thrust faults (Shoemaker 1960; Shoemaker and Kieffer 1974) or interthrust wedges (Poelchau et al. 2009) at Meteor Crater, Arizona (USA) are thought to have formed through the delamination of horizontal areas by spallation and injection of a wedge of bedrock into these gaps during excavation flow (Poelchau et al. 2009). More detailed field work is necessary for these observations to be quantified further.

All MEMIN experiments yield craters in the strength-dominated regime, in stark contrast to almost all natural craters whose final dimensions are governed by gravity-driven processes. Our strategy for a proper scaling to nature includes two complementary approaches: (1) The MEMIN experiments yielded a full data set that can be used to test and compare numerical models against the observed crater morphology using codes such as iSALE or Autodyn. The determination of new material models and Hugoniot Equations-of-State for the target rocks will improve the accuracy of simulations. As numerical models can simulate impact processes of any size, this is the most important approach to scale the experimental results. (2) Dimensionless analysis (e.g., Holsapple 1993) is a tool to extrapolate our data for mesoscale impact experiments to larger crater sizes (see Poelchau et al. 2013).

Inferring projectile velocity and mass or target properties, such as the presence of water in a particular region on Mars, for example, from crater morphology, is as of yet not feasible with the present data set because of the severe differences in the crater modification processes between the strength- and the gravity-dominated cratering regime. In addition, the MEMIN experiments illustrate that similar topographic features can develop under quite different impact conditions: compare the spallation zone morphologies in wet targets (steel projectile) with those produced in impacts with aluminum projectiles at higher velocities into dry targets. Hence, the observed effects on crater morphology are used to understand the material behavior that leads to the final crater morphology in natural impacts, but the morphologies themselves are not directly comparable due to the differences in some processes as stated above.

Conclusions

Within the MEMIN program, we have produced experimental impact craters in sandstone ranging in diameter from 5 to 40 cm. Size and morphometry of these craters have been evaluated under the aspects of variations in impact velocity, impact energy, water saturation of the pore spaces, and projectile/target density contrast. The main results are

  • 1 Replicate experiments under the same conditions generally confirm the reproducibility of crater dimensions.
  • 2 Larger craters are formed in impacts with higher kinetic energy or with higher velocity for the same projectile mass.
  • 3 Increasing water saturation of the pore space also results in larger craters. The final craters are wider and shallower compared with those in dry targets, and the transient crater form is also wider and shallower than for craters in dry targets.
  • 4 Parabola fits to the central depression of the experimental craters give good approximations of the transient crater dimensions.
  • 5 Spallation contributes up to 80% of the final crater volume with the majority for dry sandstones between 46% and 68%. These values are comparable to those in rocks without prominent layering, indicating that target layering perpendicular to impact direction does not substantially influence the amount of spall produced. Impacts into sandstones with water-saturated pore spaces, on the other hand, yield a spall contribution in a generally higher range (62–74%), suggesting that water plays a greater role in spallation than layering.
  • 6 The volume of the transient crater becomes relatively smaller in experiments at higher impact velocity (approximately 50 down to approximately 20%) as well as for larger Dp at the same velocity.
  • 7 The spall zone morphologies differ significantly for craters in dry and water-saturated targets: in the former, it slopes evenly at 10–20° toward the crater center; in the latter, we found a convex slope near the center and a terraced morphology toward the crater rim. Identification of “dry” versus “wet” target materials in natural cases based upon spallation zone morphology is precluded by the fact that high-velocity, low-density projectiles produce the same terraced spall zone morphology as low-velocity, high-density projectiles in targets with water-saturated pore space.

Acknowledgments— This project is funded by the German Research Foundation (DFG), grant KE 732/16-1 in the framework of the DFG research unit FOR-887 “Experimental Impact Cratering—The MEMIN Program.” Many thanks to the reviewers Jens Ormö and Olivier Barnouin, and the special edition editor Natalia Artemieva for careful reviews and insightful comments, which greatly improved this manuscript. We thank the technicians at the EMI and Herbert Ickler (ALU) for their indispensable work and support, and Michael Rudolf for assisting in laser scanner data compilation.

Editorial Handling— Dr. Natalia Artemieva

Appendix

Scanning and Three-Dimensional Model Details

Data Acquisition

A scanner-to-crater distance of 300–400 mm from 4–6 different angles was used, depending on morphological complexities. Quartz crystals and fracture surfaces have a relatively high reflectivity, which can lead to diffusion of the laser beam, thereby jeopardizing the scanner’s innate accuracy. To minimize overall surface reflectivity and to reduce large difference in surface light reflection properties (e.g., pristine, highly reflective crystal surfaces versus crater areas covered with dark, dull, light-absorbing residue from the blast), ambient light conditions were optimized by controlling the amount of natural sunlight entering the scanning room and by using diffuse (semi-transparent paper as filters) fiber-optic point light sources. In some cases, a thin coat of talcum powder (generic pharmacy grade) was applied to some areas of the crater and surrounding target surface where no geochemical survey was planned.

Data Processing

All scans were postprocessed using the accompanying RealScan-USB scan wizard program to eliminate spikes at the scan margins, and to create high-precision (0.1 mm accuracy) 3-D models by merging the individual scans using a minimum of four reference points on each of the paired scans. The output point-cloud raw data is referenced in the scanner-internal coordinate system, which was then translated into a zero-referenced xyz-system (using the software Surfer to identify the respective coordinates and Excel to execute the calculations), and converting the target surface into z = 0 etc. for further processing. After exporting the point-cloud dataset as xyz-files and (re-)converting those into Surfer and ArcGIS compatible formats, a topography was created by the triangularity method kriging. Crater volumes, depths, and surface slope angles were calculated. Traverses across the crater center were generated by using the crater center and its maximum radius extracted from the initial node grid (Surfer) as coordinate points to calculate crater profiles (Fig. A1) in 10° steps in an algorithm that was formulated for this task.

  • image(A1)

[  DEM with profile transect overlay for the crater in target block D3-3298. The conventional notation (000) used in geological mapping is used herein to record the target block orientation: e.g., “north” (000) in our case is “up” of the target impact surface. #01 indicates the profile numbers successively increasing clockwise. ]

Variability and Error in Crater Volume Determination

The processing in three-dimensional model construction is done in several consecutive steps: (1) initial individual scans, (2) merging the scans into one three-dimensional object, (3) rotating the raw model from the scanner-internal reference coordinate system into the horizontal, (4) transferring xyz files from the scanner software into Surfer, and (5) processing data in Surfer and Excel. The whole procedure proves to be highly accurate and reproducible. Repeat scanning and processing of the same crater yielded variations in computed crater volume of up to 2.9% for both large and small craters. These variations are mainly due to different light conditions on the individual scanning days, and additionally from the accuracy of rotation of the merged crater model into the horizontal position. A potential variation in crater depth of ±0.1 mm based on the scanner resolution translates into 0.75–1.0% variation in crater volume for the large craters (D-Series) and an expectedly higher value of about 3.7% for the small craters (A-Series).

Ancillary