Laboratory impacts into dry and wet sandstone with and without an overlying water layer: Implications for scaling laws and projectile survivability

Abstract— Scaling laws describing crater dimensions are defined in terms of projectile velocity and mass, densities of the materials involved, strength of the target, and the local gravity. Here, the additional importance of target porosity and saturation, and an overlying water layer, are considered through 15 laboratory impacts of 1 mm diameter stainless steel projectiles at 5 km s^?1 into a) an initially uncharacterized sandstone (porosity ?17%) and b) Coconino Sandstone (porosity ?23%). The higher‐porosity dry sandstone allows a crater to form with a larger diameter but smaller depth than in the lower‐porosity dry sandstone. Furthermore, for both porosities, a greater volume of material is excavated from a wet target than a dry target (by 27–30%). Comparison of our results with Pi‐scaling (dimensionless ratios of key parameters characterizing cratering data over a range of scales) suggests that porosity is important for scaling laws given that the new data lie significantly beneath the current fit for ice and rock targets on a π_v versus π₃ plot (π_v gives cratering efficiency and π₃ the influence of target strength). An overlying water layer results in a reduction of crater dimensions, with larger craters produced in the saturated targets compared to unsaturated targets. A water depth of approximately 12 times the projectile diameter is required before craters are no longer observed in the targets. Previous experimental studies have shown that this ratio varies between 10 and 20 (Gault and Sonett 1982). In our experiments ?25% of the original projectile mass survives the impact.     

Time-resolved studies of hypervelocity vertical impacts into porous particulate targets: Effects of projectile density on early-time coupling and crater growth

The depth and duration of energy and momentum coupling in an impact shapes the formation of the crater. The earliest stages of crater growth (when the projectile transfers its energy and momentum to the target) are unrecoverable when the event is described by late stage parameters, which collapse the initial conditions of the impact into a singular point in time and space. During the coupling phase, the details of the impact are mapped into the ejecta flow field. In this experimental study, we present new experimental and computational measurements of the ejecta distribution and crater growth extending from early times into main-stage ballistic flow for hypervelocity impacts over a range of projectile densities. Specifically, we assess the effect of projectile density on coupling depth and location in porous particulate (sand) targets. A non-invasive high-speed imaging technique is employed to capture the velocity of individual ejecta particles very early in the cratering event as a function of both time and launch position. These data reveal that the effects of early-stage coupling, such as non-constant ejection angles, manifest not only in early-time behavior but also extend to main-stage crater growth. Time-resolved comparisons with hydrocode calculations provide both benchmarking and insight into the parameters controlling the ejection process. Measurements of the launch position and metrics for the transient diameter to depth ratio as a function of time demonstrate non-proportional crater growth throughout much of excavation. Low-density projectiles couple closer to the surface, thereby leading to lower ejection angles and larger effective diameter to depth ratios. These results have implications for the ballistic emplacement of ejecta on planetary surfaces, and are essential to interpreting temporally resolved data from impact missions.     

The MEMIN research unit: Scaling impact cratering experiments in porous sandstones

Abstract– The MEMIN research unit (Multidisciplinary Experimental and Modeling Impact research Network) is focused on analyzing experimental impact craters and experimental cratering processes in geological materials. MEMIN is interested in understanding how porosity and pore space saturation influence the cratering process. Here, we present results of a series of impact experiments into porous wet and dry sandstone targets. Steel, iron meteorite, and aluminum projectiles ranging in size from 2.5 to 12 mm were accelerated to velocities of 2.5–7.8 km s^?1, yielding craters with diameters between 3.9 and 40 cm. Results show that the target’s porosity reduces crater volumes and cratering efficiency relative to nonporous rocks. Saturation of pore space with water to 50% and 90% increasingly counteracts the effects of porosity, leading to larger but flatter craters. Spallation becomes more dominant in larger‐scale experiments and leads to an increase in cratering efficiency with increasing projectile size for constant impact velocities. The volume of spalled material is estimated using parabolic fits to the crater morphology, yielding approximations of the transient crater volume. For impacts at the same velocity these transient craters show a constant cratering efficiency that is not affected by projectile size.     

Crater morphology in sandstone targets: The MEMIN impact parameter study

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.     

Hypervelocity impacts into ice‐topped layered targets: Investigating the effects of ice crust thickness and subsurface density on crater morphology

Many bodies in the outer solar system are theorized to have an ice shell with a different subsurface material below, be it chondritic, regolith, or a subsurface ocean. This layering can have a significant influence on the morphology of impact craters. Accordingly, we have undertaken laboratory hypervelocity impact experiments on a range of multilayered targets, with interiors of water, sand, and basalt. Impact experiments were undertaken using impact speeds in the range of 0.8–5.3 km s^?1, a 1.5 mm Al ball bearing projectile, and an impact incidence of 45°. The surface ice crust had a thickness between 5 and 50 mm, i.e., some 3–30 times the projectile diameter. The thickness of the ice crust as well as the nature of the subsurface layer (liquid, well consolidated, etc.) have a marked effect on the morphology of the resulting impact crater, with thicker ice producing a larger crater diameter (at a given impact velocity), and the crater diameter scaling with impact speed to the power 0.72 for semi‐infinite ice, but with 0.37 for thin ice. The density of the subsurface material changes the structure of the crater, with flat crater floors if there is a dense, well‐consolidated subsurface layer (basalt) or steep, narrow craters if there is a less cohesive subsurface (sand). The associated faulting in the ice surface is also dependent on ice thickness and the substrate material. We find that the ice layer (in impacts at 5 km s^?1) is effectively semi‐infinite if its thickness is more than 15.5 times the projectile diameter. Below this, the crater diameter is reduced by 4% for each reduction in ice layer thickness equal to the impactor diameter. Crater depth is also affected. In the ice thickness region, 7–15.5 times the projectile diameter, the crater shape in the ice is modified even when the subsurface layer is not penetrated. For ice thicknesses, <7 times the projectile diameter, the ice layer is breached, but the nature of the resulting crater depends heavily on the subsurface material. If the subsurface is noncohesive (loose) material, a crater forms in it. If it is dense, well‐consolidated basalt, no crater forms in the exposed subsurface layer.     

Non-intrusive measurements of crater growth

An experimental technique to measure crater growth is presented whereby a high speed video captures profiles of a crater forming after impact obtained using a vertical laser sheet centered on the impact point. Unlike previous so called “quarter-space experiments,” where projectiles were launched along a transparent Plexiglas sheet so that growth of half a crater could be viewed, the use of the laser sheet permits viewing changes in crater shape without any physical interference to the cratering process. This technique indicates that for low velocity impacts (<300 m/s) into 220 μm glass beads that are without cohesion and where the projectile is not disrupted, craters initially grow somewhat proportionally, but that later their depths remain essentially constant while their diameters continue to expand. In addition, these experiments indicate that as the impact velocity increases, the rate of growth and the transient depth to diameter ratio at the end of ejecta excavation decreases. These last two observations are probably due to the large time of penetration of the projectile, which becomes a significant fraction of the time of crater formation. This is contrary to the expectations for the scaling rules, which assumes a point source. Very high curtain angles (>45°) are also seen, and could be due to the low friction angle of the target. Significant crater modification, which is rarely seen in “quarter-space experiments,” is also observed and appears to be controlled by the dynamic angle of repose of the target. These latter observations indicate that differences in target friction angles may need to be considered when determining near rim ejecta-mass distributions and large-scale crater modification processes on the planets.     

Hypervelocity impact craters in ammonia rich ice

Research on the impact cratering process on icy bodies has been largely based on the most abundant ice, water. However little is known about the influence of other relatively abundant ices such as ammonia. Accordingly, data are presented studying the influence on cratering in ammonia rich ice using spherical 1 mm diameter stainless steel projectiles at velocities of 4.8±0.5 km s⁻¹. The ice target composition ranged from pure water ice, to solutions containing 50% ammonia and 50% water by weight. Results for crater depth, diameter, volume and depth/diameter ratio are given. The results showed that the presence of ammonia in the ice had a very strong influence on crater diameter and morphology. It was found that with only a 10% concentration of ammonia, crater diameter significantly decreased, and then at greater concentrations became independent of ammonia content. Crater depth was independent of the presence of ammonia in the ice, and the crater volume appeared to decrease as ammonia concentration increased. Between ammonia concentrations of 10 and 20% crater morphology visibly changed from wide shallow craters with a deeper central pit to craters with a smoothly increasing depth from the crater rim to centre. Thus, a small amount of ammonia within a water ice surface may have a major effect on crater morphology.     

Impacts onto H2O ice: Scaling laws for melting, vaporization, excavation, and final crater size

Shock-induced melting and vaporization of H₂O ice during planetary impact events are widespread phenomena. Here, we investigate the mass of shock-produced liquid water remaining within impact craters for the wide range of impact conditions and target properties encountered in the Solar System. Using the CTH shock physics code and the new 5-phase model equation of state for H₂O, we calculate the shock pressure field generated by an impact and fit scaling laws for melting and vaporization as a function of projectile mass, impact velocity, impact angle, initial temperature, and porosity. Melt production nearly scales with impact energy, and natural variations in impact parameters result in only a factor of two change in the predicted mass of melt. A fit to the π-scaling law for the transient cavity and transient-to-final crater diameter scaling are determined from recent simulations of the entire cratering process in ice. Combining melt production with π-scaling and the modified Maxwell Z-model for excavation, less than half of the melt is ejected during formation of the transient crater. For impact energies less than about 2 × 10²⁰ J and impact velocities less than about 5 km s⁻¹, the remaining melt lines the final crater floor. However, for larger impact energies and higher impact velocities, the phenomenon of discontinuous excavation in H₂O ice concentrates the impact melt into a small plug in the center of the crater floor.     

Modeling the 2.7?km in Diameter, Shallow Marine Ritland Impact Structure

The newly discovered Ritland impact structure (2.7?km in diameter) has been modeled by numerical simulation, based on detailed field information input. The numerical model applies the SOVA multi-material hydrocode, which uses the ANEOS equation of state for granite, describing thermodynamical properties of target and projectile material. The model displays crater formation and possible ejecta distribution that strongly supports a 100?m or less water depth at the time of impact. According to the simulations resurge processes and basinal syn- and postimpact sedimentation are highly dependent on water depth; in more than 100?m of water depth, much more powerful resurge processes are generated than at water depths shallower than 100?m (the Ritland case). In Ritland the 100?m high (modeled) crater rim formed a barrier and severely reduced the resurge processes. In the case of deeper water, powerful resurge processes, tsunami wave generations and related currents could have triggered even more violent crater fill sedimentation. The presented model demonstrates the importance of understanding the interactions between water layer and both syn-impact crater fill and ejecta distribution. According to the presented simulations ejecta blocks up to 10?m in diameter could be transported up to about 5?km outside the crater rim.     

Numerical modeling of asteroid survivability and possible scenarios for the Morokweng crater‐forming impact

The fate of the impactor is an important aspect of the impact‐cratering process. Defining impactor material as surviving if it remains solid (i.e., does not melt or vaporize) during crater formation, previous numerical modeling and experiments have shown that survivability decreases with increasing impact velocity, impact angle (with respect to the horizontal), and target density. Here, we show that in addition to these, impactor survivability depends on the porosity and shape of the impactor. Increasing impactor porosity decreases impactor survivability, while prolate‐shaped (polar axis > equatorial axis) impactors survive impact more so than spherical and oblate‐shaped (polar axis < equatorial axis) impactors. These results are used to produce a relatively simple equation, which can be used to estimate the impactor fraction shocked to a given pressure as a function of these parameters. By applying our findings to the Morokweng crater‐forming impact, we suggest impact scenarios that explain the high meteoritic content and presence of unmolten fossil meteorites within the Morokweng crater. In addition to previous suggestions of a low‐velocity and/or high‐angled impact, this work suggests that an elongated and/or low porosity impactor may also help explain the anomalously high survivability of the Morokweng impactor.     

Impact crater formation in icy layered terrains on Mars

Abstract— We present numerical simulations of crater formation under Martian conditions with a single near‐surface icy layer to investigate changes in crater morphology between glacial and interglacial periods. The ice fraction, thickness, and depth to the icy layer are varied to understand the systematic effects on observable crater features. To accurately model impact cratering into ice, a new equation of state table and strength model parameters for H₂O are fitted to laboratory data. The presence of an icy layer significantly modifies the cratering mechanics. Observable features demonstrated by the modeling include variations in crater morphometry (depth and rim height) and icy infill of the crater floor during the late stages of crater formation. In addition, an icy layer modifies the velocities, angles, and volumes of ejecta, leading to deviations of ejecta blanket thickness from the predicted power law. The dramatic changes in crater excavation are a result of both the shock impedance and the strength mismatch between layers of icy and rocky materials. Our simulations suggest that many of the unusual features of Martian craters may be explained by the presence of icy layers, including shallow craters with well‐preserved ejecta blankets, icy flow related features, some layered ejecta structures, and crater lakes. Therefore, the cratering record implies that near‐surface icy layers are widespread on Mars.     

Numerical modelling of the impact crater depth-diameter dependence in an acoustically fluidized target

2D numerical modelling of impact cratering has been utilized to quantify an important depth-diameter relationship for different crater morphologies, simple and complex. It is generally accepted that the final crater shape is the result of a gravity-driven collapse of the transient crater, which is formed immediately after the impact. Numerical models allow a quantification of the formation of simple craters, which are bowl-shaped depressions with a lens of rock debris inside, and complex craters, which are characterized by a structural uplift. The computation of the cratering process starts with the first contact of the impactor and the planetary surface and ends with the morphology of the final crater. Using different rheological models for the sub-crater rocks, we quantify the influence on crater mechanics. To explain the formation of complex craters in accordance to the threshold diameter between simple and complex craters, we utilize the Acoustic Fluidization model. We carried out a series of simulations over a broad parameter range with the goal to fit the observed depth/diameter relationships as well as the observed threshold diameters on the Moon, Earth and Venus.     

Constraints on the size of the Vredefort impact crater from numerical modeling

Abstract— The Vredefort structure in South Africa was created by a meteorite impact about two billion years ago. Since that time, the crater has been deeply eroded; so to estimate its original size, researchers have had to rely heavily upon comparison to other terrestrial impact structures. Recent estimates of the original crater diameter range from 160 km to as much as 400 km. In this study, we combined the capabilities of both hydrocode and finite-element modeling, using the former to predict where the pressure of an impact-generated shock wave would have been high enough to form planar deformation features (PDFs) and shatter cones and the latter to follow the subsequent displacement of these shock isobars during the collapse of the crater. We established constraints on the sizes of the projectile and the transient crater (and, thus, on the size of the final crater) by comparing the observed locations of PDFs around Vredefort to the results of our simulations of impacts by projectiles of various sizes. These simulations indicate that a rocky projectile with a diameter of ～10 km, impacting vertically at a velocity of 20 km/s generates shock pressures that are consistent with the distribution of PDFs around Vredefort. These projectile parameters correspond to a transient crater ～80 km in diameter or a final crater ～120–160 km in diameter. Allowing for uncertainties in our modeling procedures, we consider final craters 120 to 200 km in diameter to be consistent with the observed locations of PDFs at Vredefort. The shock pressure contour corresponding to the formation of shatter cones is almost horizontal near the surface, making the locations of these features less useful constraints on the crater size. However, they may provide a constraint on the amount of erosion that has occurred since the impact.     

Scaling of oblique impacts in frictional targets: Implications for crater size and formation mechanisms

Almost every meteorite impact occurs at an oblique angle of incidence, yet the effect of impact angle on crater size or formation mechanism is only poorly understood. This is, in large part, due to the difficulty of inferring impactor properties, such as size, velocity and trajectory, from observations of natural craters, and the expense and complexity of simulating oblique impacts using numerical models. Laboratory oblique impact experiments and previous numerical models have shown that the portion of the projectile’s kinetic energy that is involved in crater excavation decreases significantly with impact angle. However, a thorough quantification of planetary-scale oblique impact cratering does not exist and the effect of impact angle on crater size is not considered by current scaling laws. To address this gap in understanding, we developed iSALE-3D, a three-dimensional multi-rheology hydrocode, which is efficient enough to perform a large number of well-resolved oblique impact simulations within a reasonable time. Here we present the results of a comprehensive numerical study containing more than 200 three-dimensional hydrocode-simulations covering a broad range of projectile sizes, impact angles and friction coefficients. We show that existing scaling laws in principle describe oblique planetary-scale impact events at angles greater than 30° measured from horizontal. The displaced mass of a crater decreases with impact angle in a sinusoidal manner. However, our results indicate that the assumption that crater size scales with the vertical component of the impact velocity does not hold for materials with a friction coefficient significantly lower than 0.7 (sand). We found that increasing coefficients of friction result in smaller craters and a formation process more controlled by impactor momentum than by energy.     

Impact cratering of granular mixture targets made of H2O Ice–CO2 Ice–pyrophylite

Experiments related to impacts onto three-component targets which could simulate cometary nucleus or planetary regolith cemented by ices are presented here. The impact velocities are from 133 to 632 m s⁻¹. The components are powdered mineral (pyrophylite), H₂O ice, and CO₂ ice mixed 1:1:0.74 by mass. The porosity of fresh samples is about 0.48. Two types of the samples were studied: nonheated samples and samples heated by thermal radiation. Within the samples a layered structure was formed. The cratering pattern strongly depended on the history of the samples. The craters formed in nonheated targets had regular shapes. The volume was easy to be determined and it was proportional to impact energy E. The crater depth scales as E^0.5. Impacts on the thermally stratified target led to ejection of a large amount of material from the loose sub-crustal layer. For some particular interval of impact velocity a cratering pattern can demonstrate unusual properties: small hole through the rigid crust and considerable mass transfer (radially, outward of the impact point) within sub-crustal layer.     

The structural inventory of a small complex impact crater: Jebel Waqf as Suwwan,Jordan

The investigation of terrestrial impact structures is crucial to gain an in‐depth understanding of impact cratering processes in the solar system. Here, we use the impact structure Jebel Waqf as Suwwan, Jordan, as a representative for crater formation into a layered sedimentary target with contrasting rheology. The complex crater is moderately eroded (300–420 m) with an apparent diameter of 6.1 km and an original rim fault diameter of 7 km. Based on extensive field work, IKONOS imagery, and geophysical surveying we present a novel geological map of the entire crater structure that provides the basis for structural analysis. Parametric scaling indicates that the structural uplift (250–350 m) and the depth of the ring syncline (<200 m) are anomalously low. The very shallow relief of the crater along with a NE vergence of the asymmetric central uplift and the enhanced deformations in the up‐range and down‐range sectors of the annular moat and crater rim suggest that the impact was most likely a very oblique one (~20°). One of the major consequences of the presence of the rheologically anisotropic target was that extensive strata buckling occurred during impact cratering both on the decameter as well as on the hundred‐meter scale. The crater rim is defined by a circumferential normal fault dipping mostly toward the crater. Footwall strata beneath the rim fault are bent‐up in the down‐range sector but appear unaffected in the up‐range sector. The hanging wall displays various synthetic and antithetic rotations in the down‐range sector but always shows antithetic block rotation in the up‐range sector. At greater depth reverse faulting or folding is indicated at the rim indicating that the rim fault was already formed during the excavation stage.     

Characteristics of oceanic impact‐induced large water waves—Re‐evaluation of the tsunami hazard

Abstract— The potential hazard of a meteorite impact in the ocean is controversial with respect to the destructive power of generated large ocean waves (tsunamis). We used numerical modeling of hypervelocity impact to investigate the generation mechanism and the characteristics of the resulting waves up to a distance of 100–150 projectile radii. The wave signal is primarily controlled by the ratio between projectile diameter and water depth, and can be roughly classified into deep‐water and shallow‐water impacts. In the latter, the collapse of the crater rim results in a wave signal similar to solitary waves, which propagate and decay in agreement with shallow‐water wave theory. The much more likely scenario for an asteroid impact on Earth is a relatively small body (much smaller than the water depth) striking the deep sea. In this case, the collapse of the transient crater results in a significantly different and much more complex wave signal that is characterized by strong nonlinear behavior. We found that such waves decay much more rapidly than previously assumed and cannot be treated as long waves. For this reason, the shallow‐water theory is not applicable for the computation of wave propagation, and more complex models (full solution of the Boussinesq equations) are required.     

SMART‐1 end of life shallow regolith impact simulations

The SMART‐1 end‐of‐life impact with the lunar surface was simulated with impacts in a two stage light‐gas gun onto inclined basalt targets with a shallow surface layer of sand. This simulated the probable impact site, where a loose regolith will have overlaid a well consolidated basaltic layer of rock. The impact angles used were at 5° and 10° from the horizontal. The impact speed was ~2 km s^?1 and the projectiles were 2.03 mm diameter aluminum spheres. The sand depth was between approximately 0.8 and 1.8 times the projectile diameter, implying a loose lunar surface regolith of similar dimensions to the SMART‐1 spacecraft. A crater in the basement rock itself was only observed in the impact at 10° incidence, and where the depth of loose surface material was less than the projectile diameter, in which case the basement rock also contained a small pit‐like crater. In all cases, the projectile ricocheted away from the impact site at a shallow angle. This implies that at the SMART‐1 impact site the crater will have a complicated structure, with exposed basement rock and some excavated rock displaced nearby, and the main spacecraft body itself will not be present at the main crater.     

On the explosive formation of macroscopic hypervelocity projectiles for use in the study of planetary cratering

In this paper we show that by modifying a conventional lined hollow charge, such that the explosive is asymmetrically distributed, it is possible to form projectiles of controllable mass (up to ～1 g) moving in the forward direction with speeds of the order of 10 km s^?1. Measurements of the projectile speed and estimates of its mass are found to agree well with the predictions of the one dimensional theory of Carleone and Chou (1974). A comparison is made of the crater formation obtained by firing both modified and unmodified lined hollow charges at basalt. We indicate how it should be possible to increase the velocity of the projectile up to ～14 km s^?1 and the application that such a technique would have to problems in both cratering physics and planetary studies.     

The effect of the oceans on the terrestrial crater size‐frequency distribution: Insight from numerical modeling

Abstract— On Earth, oceanic impacts are twice as likely to occur as continental impacts, yet the effect of the oceans has not been previously considered when estimating the terrestrial crater size‐frequency distribution. Despite recent progress in understanding the qualitative and quantitative effect of a water layer on the impact process through novel laboratory experiments, detailed numerical modeling, and interpretation of geological and geophysical data, no definitive relationship between impactor properties, water depth, and final crater diameter exists. In this paper, we determine the relationship between final (and transient) crater diameter and the ratio of water depth to impactor diameter using the results of numerical impact models. This relationship applies for normal incidence impacts of stoney asteroids into water‐covered, crystalline oceanic crust at a velocity of 15 km s^?1. We use these relationships to construct the first estimates of terrestrial crater size‐frequency distributions (over the last 100 million years) that take into account the depth‐area distribution of oceans on Earth. We find that the oceans reduce the number of craters smaller than 1 km in diameter by about two‐thirds, the number of craters ?30 km in diameter by about one‐third, and that for craters larger than ?100 km in diameter, the oceans have little effect. Above a diameter of ?12 km, more craters occur on the ocean floor than on land; below this diameter more craters form on land than in the oceans. We also estimate that there have been in the region of 150 impact events in the last 100 million years that formed an impact‐related resurge feature, or disturbance on the seafloor, instead of a crater.