Most impacts occur at an angle with respect to the horizontal plane. This is primarily reflected in the ejecta distribution, but at very low angle structural asymmetries such as elongation of the crater and nonradial development of the central peak become apparent. Unfortunately, impact craters with pristine ejecta layers are rare on Earth and also in areas with strong past or ongoing surface erosion on other planetary bodies, and the structural analysis of central peaks requires good exposures or even on-site access to outcrop. However, target properties are known to greatly influence the shape of the crater, especially the relatively common target configuration of a weaker layer covering a more rigid basement. One such effect is the formation of concentric craters, i.e., a nested, deeper, inner crater surrounded by a shallow, outer crater. Here, we show that with decreasing impact angle there is a downrange shift of the outer crater with respect to the nested crater. We use a combination of (1) field observation and published 3-D numerical simulation of one of the best examples of a terrestrial, concentric impact crater formed in a layered target with preserved ejecta layer: the Lockne crater, Sweden; (2) remote sensing data for three pristine, concentric impact craters on Mars with preserved ejecta layers further constraining the direction of impact; as well as (3) laboratory impact experiments, to develop the offset in crater concentricity into a complementary method to determine the direction of impact for layered-target craters with poorly preserved ejecta layers.
A fundamental problem in the interpretation of field studies of terrestrial craters as well as observations of craters on other bodies is that the conditions of the impact, e.g., the projectile mass, speed, impact angle, etc., are generally unknown. Furthermore, many observable features of an impact crater, such as its size, cannot be used to infer the impact conditions. This is a result of the point-source nature of impact cratering in which the outcome of an impact depends on a power-law combination of the projectile properties (e.g., Holsapple and Schmidt 1987). Therefore, the observed size of a crater cannot separately determine, say, both the projectile mass and speed; only the power-law combination can be inferred.
The obliquity of the impact, which is the subject of this article, has also been difficult to estimate reliably for an existing crater. Highly oblique impacts do leave some clues in that the crater has an elongated, rather than circular, shape. In addition, the ejecta blanket exhibits uprange and downrange so-called forbidden zones that are devoid of ejected material (Gault and Wedekind 1978). A brief summary of these effects is given below.
In this article, we introduce a new method that can be used to estimate impact obliquity and direction for craters formed in layered targets. A common configuration of such targets is that of a weaker layer (e.g., water and sediments, regolith) covering a more rigid basement (e.g., Quaide and Oberbeck 1968; Ormö and Lindström 2000). The basic idea is that an impact that punches through the upper layer generates a concentric set of two craters; one in the upper, generally weaker layer, and one in the more competent basement material (e.g., Quaide and Oberbeck 1968). A similar effect is seen also for multilayered targets with downward increasing strength (see fig. 6 in Shuvalov 2002). We here show that oblique impacts leave a signature in that the centers of the two craters are offset, which can be used to estimate the obliquity and direction of the impact. This method could be especially useful in cases of absent or poorly preserved ejecta. This article is a starting point in the development of the method.
The remainder of this section briefly summarizes how impact obliquity affects the shape of the crater and its ejecta blanket, and then describes the formation of nested craters in layered targets, using the marine-target Lockne crater, Sweden, as an example.
Effects of Impact Obliquity on the Resulting Crater and Ejecta Blanket
Most natural impacts of cosmic bodies in our solar system occur with an oblique trajectory of the impacting body, most commonly 45° (Shoemaker 1962). However, the impact angle, measured from the impact velocity vector to the target plane, has a normal distribution around this mean value; both higher and lower impact angles may occur, although with decreasing probability. In their comprehensive review of what was known to date on the effects of impact angle on the cratering process Pierazzo and Melosh (2000) stress that all impacts occurring at an angle are by definition oblique, but that the term has frequently become synonymous with low-angle impacts. We concur with Pierazzo and Melosh (2000) although we here focus on the range of oblique impacts that leave a visually detectable imprint on the crater morphology.
Fresh, tectonically undeformed impact craters are most commonly considered as circular in planform. Even so, calculations by Collins et al. (2011) show that about 2–4% of craters in the size range 5–100 km on the terrestrial planets and the Moon are elongated, although the rate becomes significantly higher for craters larger than 100 km. Sources of the noncircularity include the influence from pre-existing target structures, resulting in the formation of polygonal craters (Öhman et al. 2008), projectile shapes, and simultaneous impacts by clustered projectiles (Oberbeck 1972).
The impact angle also affects the elongation of the crater, but only if the impact is sufficiently oblique (Pierazzo and Melosh 2000 and references therein). For impacts above a certain angle, the propagation of the shock is similar to that from a vertical impact (with the same normal component of velocity), and the resulting crater has a nearly circular shape (Melosh 1989).
The transition impact angle below which craters are distinctly noncircular depends on the conditions of the impact (e.g., Collins et al. 2011). Laboratory experiments in particulate, unconsolidated targets exhibit circular craters down to impact angles as low as 5–10° (Gault and Wedekind 1978), although case studies from the Moon, Mars, and Venus (Glotch et al. 1999; Bottke et al. 2000) show that the threshold angles in natural craters are a few degrees higher (i.e., 12–15°). Impact experiments in both metal and rock targets show the angle may be as high as 30–40° (Christiansen et al. 1993; Burchell and Mackay 1998). The cross section of simple craters in the strength-dominated regime also changes with impact angle from being basically bowl-shaped at 45° to having a steep uprange, and shallow downrange crater wall for angles less than 30° (Gault and Wedekind 1978).
It has also been suggested that the central peak or peak rings of complex craters may become shifted uprange and even breached along the trajectory (Schultz and Anderson 1996), but studies of natural Venusian craters do not support any correlation between central peak and peak ring location and impact angle (Ekholm and Melosh 2001; McDonald et al. 2008). Numerical simulation shows that although there is skewed development of the central peak generation during the early stages of crater modification with a downrange migration from an initial uprange position, continued crater modification leads to a central position of the peak in the final crater (Shuvalov and Dypvik 2004). However, despite its final central position, the development of the central peak is not axially symmetric (Scherler et al. 2006; Kenkmann and Poelchau 2009; Wulf et al. 2012), the extreme case being the elongated central ridge seen in some elliptical craters from highly oblique impacts (e.g., Bottke et al. 2000).
The distribution of ejecta is also affected by impact angle. While the ejecta are distributed symmetrically around the crater for impact angles above 45°, the distribution is nearly perpendicular to the projectile trajectory at impact angles below 5–10°, forming the so-called butterfly pattern (Gault and Wedekind 1978). Examples of asymmetrical ejecta patterns for two Martian craters are given in Fig. 1. For such low impact angles the propagation of the shock wave differs significantly from that of a vertical impact, and instead it obtains an elongated canoe-shape with a mainly sidewise expansion throwing the ejecta away from the projectile's line of advance (Melosh 1989). Herrick and Hessen (2006) showed for Martian craters that at impact angles below 20° there is a drastic decrease in ejecta distributed uprange from the crater. A forbidden zone (Gault and Wedekind 1978) develops, which often has the shape of an outward curving “V” with the apex at the crater rim. At angles less than 15° there is also a less curved, V-shaped forbidden zone that appears downrange of the crater. The combined effect of the two forbidden zones leads to the butterfly pattern of the ejecta field. Recent numerical studies show, however, that the threshold angle at which the forbidden zone forms increases with the size of the impact, with a well-developed uprange forbidden zone already at 60° for the impact of a 10 km diameter stony asteroid (Collins et al. 2011; Shuvalov 2011).
Notwithstanding the recently suggested method of using structural asymmetry of central peaks (Wulf et al. 2012), the various ejecta distribution patterns around oblique impact craters have, so far, offered the most convenient tool to estimate the impact angle for craters on planetary bodies with relatively low erosion rate, such as Mars and the Moon. However, the situation is more complicated for terrestrial impact craters due to the combination of strongly erosive surface processes and the friability of the ejecta fields.
Concentric Craters from Impacts into Layered Targets Exemplified by the Lockne Crater, Sweden
Concentric craters in layered targets have been suggested to form from (1) an airblast (Melosh 1989), (2) target layer strength-induced variations in the excavation flow (i.e., Quaide and Oberbeck 1968), (3) extensive slumping of a poorly consolidated upper layer (e.g., Horton et al. 2006 and references therein), or (4) a combination of the two latter (Ormö and Lindström 2000). Melosh (1989) uses the term inverted sombrero when describing the morphology of certain complex craters surrounded by a shallow excavated shelf (e.g., the Red Wing crater). He proposes the brim of the inverted sombrero to be caused by the forceful airblast from the impact. The best known example of a concentric crater with an outer crater formed by the collapse and slumping of an upper sedimentary layer is the Chesapeake Bay impact structure (CBIS), on the east coast of the USA (e.g., Poag et al. 2004; Horton et al. 2006). However, here we are interested in the concentricity as a primary feature formed during crater excavation but also independent of potential influences from an atmosphere.
A common feature among well-preserved marine-target craters such as Flynn Creek in Tennessee (Roddy 1977; Melosh 1989), Kärdla in Estonia (Puura and Suuroja 1992), and the Lockne crater, Sweden (Lindström et al. 1996, 2005a) is that the apparent basement crater is surrounded by a shallow excavated shelf that may extend far beyond the crater rim, thus giving the crater a concentric shape (Ormö and Lindström 2000). We have chosen to use the Lockne crater in our analysis of concentric craters as it is one of the few impact structures on Earth that maintains an ejecta layer that still displays the direction of impact (Lindström et al. 2005) (Fig. 2). The impact occurred about 458 Ma in a relatively deep epicontinental sea (Ormö et al. 2002; Lindström et al. 2005b; Shuvalov et al. 2005). Despite the high age, the crater is today relatively well preserved because it was covered by postimpact sediments and subsequent overthrust nappes of the Caledonian orogeny shortly after its formation. The crater has since been re-exposed and is now easily accessible on land with good exposure.
The concentric structure consists of a shallow outer crater developed in the target sedimentary sequence surrounding a 7.5 km wide, deeper, nested crater in the basement. Geophysical modeling indicates a central uplift in the nested crater (Sturkell and Ormö 1998; Sturkell et al. 1998), and the formation of a central uplift is supported by 3-D numerical simulation (Lindström et al. 2005b). The outer crater is partially covered by basement crater ejecta resting on progressively higher stratigraphic levels outward from the crater. This has been observed up to 12 km from the crater center (Sturkell 1998), but even as far as 45 km SW from the crater center there is indication for erosion of the sedimentary strata in connection with crystalline ejecta deposition from Lockne (Sturkell et al. 2000). Sturkell (1998) interpreted the disconformity surface as a result of erosion by the water resurge. However, the existence of a coherent, basement crater ejecta layer over parts of the surface led to the reinterpretation of the surface as a result of the excavation flow during cratering (Ormö et al. 2002; Lindström et al. 2005a).
Dalwigk and Ormö (2001) and other work on the Lockne crater from that time (e.g., Ormö and Miyamoto 2002) give a centro-symmetrical position of the outer and inner craters. However, the subsequent revelation that the crystalline breccia outside the basement crater is indeed the preserved ejecta and not the brecciated floor of the outer crater, and the discovery of impact-related rocks outside the eastern rim of the basement led Lindström et al. (2005a) to make a complete reassessment of the geology and structure of the Lockne crater. It became evident that the crater had an asymmetric development between the downrange and uprange sides. In addition, 3-D numerical simulations from the same time showed that an outward-directed shallow excavation flow can only account for the inner few kilometers of the observed outer crater (Lindström et al. 2005b; Shuvalov et al. 2005). Further geological observation of the main extent of coherent basement crater ejecta and the distribution of a characteristic autochthonous sediment breccia (the Ynntjärnen breccia), interpreted to have formed in the zone of shallow excavation flow in the water and sediment layer surrounding the nested crater, caused Lindström et al. (2008) to place the outer crater wall approximately where we have located the circle indicating the position of the outer crater in Fig. 2. The outward continuation of the disconformity surface, i.e., to the distance given by Sturkell (1998), is possibly explained by a combination of strong outward water movements during the crater excavation even beyond the water cavity wall and by its subsequent both inward and outward collapse. The relatively pristine distribution of the basement crater ejecta layer is constrained by the water resurge deposits that came to cover the seafloor crater during the crater modification stage (Fig. 2). The basement crater ejecta express an asymmetrical distribution interpreted by Lindström et al. (2005a) to be a primary feature indicative of an approximately east-west trajectory of the bolide. In addition to the basement crater ejecta distribution, the direction of impact for the Lockne crater is also expressed in its concentric morphology.
The Mechanism of Concentric Crater Formation
The concentric shape of the Lockne crater is a consequence of the target composed of >500 m of seawater and 80 m of sediments of various degree of consolidation forming a relatively weak layer on top of the crystalline basement. Figure 3 shows a 2-D numerical simulation of the development of a concentric crater in a layered target with seawater acting as the weaker layer over a granitic basement. Quaide and Oberbeck (1968) (see also Oberbeck and Quaide 1967, 1968) describe the mechanism of concentric crater formation in a comparison between laboratory experiments of impacts into layered targets and remote sensing studies of lunar craters with diameters less than a few hundred meters to estimate the regolith thickness from craters in regolith-covered rock. They divided the experimental and observed lunar craters into four morphological groups depending on the combination between impact size and decreasing relative thickness of the weak layer: (1) simple bowl-shaped “normal geometry” with no apparent influence from the more rigid substrate for sufficiently thick upper layers, (2) “central mound geometry,” (3) “flat-bottomed geometry,” and finally (4) “concentric geometry” where cratering also occurs in the substrate.
Quaide and Oberbeck (1968) describe the formation of each of the morphologies in terms of the downward component of the radial material flow beneath the crater. The downward flow is inhibited when a substrate is present at shallow depths. With a relative decrease in the thickness of the weaker surface layer the crater floor becomes flattened. The occurrence of a central mound and whether it is made up of residual uncratered surface layer material or crushed substrate depend on how the shock wave is transmitted from the overlying layer into the substrate, which in turn depends on the relative differences in dynamic yield strength of the materials. With continued thinning of the weak surface layer, central mounds no longer appear and the crater becomes flat bottomed. The pressure (and the accompanying pressure release) from the shock wave at the interface between the weak layer and the substrate is now sufficient to lead to the acceleration of all material in the weaker layer in the central part of the crater, thus preventing the formation of a central mound. If the dynamic yield strength of the substrate exceeds the pressure of the shock wave transferred to the substrate then cratering will only occur in the upper layer causing a relatively wide, flat-bottomed crater. When the surface layer is so thin that the energy transmitted to the substrate overcomes its dynamic yield strength a concentric crater develops. Both the crater in the weak layer and the nested crater in the substrate grow simultaneously but the crater in the weaker surface layer grows to a greater size. While much of the kinetic energy of the projectile is released in the upper weak layer, this layer also requires relatively less energy to be cratered, i.e., less energy is consumed by the crushing and melting of rock. Therefore, the crater in the weak layer (e.g., regolith on the Moon, water and sediments at Lockne) gets relatively wider than a corresponding crater in a homogeneous basement (Ormö et al. 2002). However, the Quaide and Oberbeck model is possibly applicable only to strength-dominated cratering. For craters as large as the Lockne and the Martian craters dealt with in this study there may be other, yet poorly known, effects of the layering. We elaborate more on this in the section comparing our impact experiments with the natural craters.
Water is a target material that avoids the strength-related scaling problems. Gault and Sonett (1982) noticed how experimental impacts into a layered target of water over quartz sand generate water cavities that get progressively wider with increased projectile kinetic energy until finally, cratering is initiated also in the substrate. In this way, a small, nested crater develops in the substrate surrounded by a wide, cylindrical outer crater in the water layer. Gault and Sonett (1982) refer to the delayed initiation of cratering of the substrate as “the protective effect of water.” During the expansion of the water cavity a shallow excavation flow develops along the interface with the more resistant substrate. Shuvalov et al. (2005) notice the same shallow excavation flow in their 3-D numerical simulations of the formation of the Lockne crater. Furthermore, they show how the outer crater becomes wider on the downrange side than on the uprange side of the nested crater (Fig. 4). The same asymmetry is also observed in 3-D simulations of marine impacts by Artemieva and Shuvalov (2002), and by Ormö et al. (2010) in low-velocity impact experiments into a target with water over wet sand in their study on how the offset of the water cavity influences the water resurge. Thus, as the concentricity of the crater is initiated already during the expansion of the transient cavity the development may occur for both simple and complex craters (as exemplified by Lockne).
During the decades that have passed since the above cited work by Quaide and Oberbeck, concentric craters have received rather little attention until recently: Dohi et al. (2012) use a two-stage light-gas gun launching nylon projectiles at 2 and 4 km s−1 into basalt blocks covered with mortar layers of varied thickness to include the effects of a layered structure in existing strength regime scaling laws (Holsapple 1993, 1994). Despite some problems with spallation of the weaker layer hampering the interpretation of the size and morphology of the outer crater they could use the relation between weaker layer thickness and the dimensions of the nested crater in the basalt to revise the scaling laws. With the application of the Quaide-Oberbeck crater morphology method Bart et al. (2011) performed a remote sensing global mapping of the lunar regolith thickness. In 143 Lunar Reconnaissance Orbiter Camera images they observed a total of 10,663 individual craters in the size range from 5.2 to 271.6 m in diameter that showed enough influence from the weaker, upper regolith layer to be used in determination of its thickness.
Remote Sensing and Field Observation of Concentric Craters
Layered targets are frequent on the Earth, Moon, and Mars, but possibly also elsewhere in the solar system such as on some of the natural satellites of the outer planets, and on certain asteroids. Here, we focus on comparisons of three selected craters on Mars (for location see Fig. 5), with results from impact experiments, published numerical simulations for layered-target impacts, as well as our own and published observational data for the terrestrial Lockne crater. However, the evaluation of the influence of the impact angle on the morphology of the resulting crater requires a set of craters that exhibit both an offset concentric structure as well as a well-preserved ejecta layer that indicates the likely direction and obliquity of the projectile trajectory. Until recently the areal coverage of images with sufficient resolution has been too limited to allow detailed studies of a sufficient number of Martian craters in layered targets with preserved ejecta layers. However, the situation has improved greatly with the recent Mars Reconnaissance Orbiter (MRO) and Mars Odyssey (MO) missions.
For this study, we used MRO Context (CTX) Camera images (5 m/pixel resolution) (Malin et al. 2007) to methodically search areas on Mars where layered deposits have been suggested, either as volatile rich sediments, e.g., Arcadia Planitia (e.g., Kadish et al. 2009, 2010), or consolidated sedimentary rock, e.g., Meridiani Planum (e.g., Edgett and Parker 1997; Edgett and Malin 2002) and Utopia Planitia (Tanaka et al. 2005) (Fig. 5). Inspecting approximately 20 images we found several examples (see Fig. 6; Table 1) of concentric craters of different sizes and with ejecta and distinct rims that indicate that they are not too deeply eroded. The craters in frames A–C seem to have some offset in the concentricity as well as a corresponding irregularity in the ejecta distribution. However, lack of image data with sufficient resolution over these craters prevents us from analyzing the cause for any potential offset in their concentricity (compare case studies A–C in Figs. 8–10). From the observed concentric craters in layered targets we selected three impact structures as case studies due to their (1) good coverage of images obtained through the MRO High-Resolution Imaging Science Experiment (HiRISE) (McEwen et al. 2007) and the CTX (Malin et al. 2007) camera allowing detailed morphological analysis; (2) pristine ejecta distribution as, in one of the three cases, further revealed by the MO Thermal Emission Imaging System (THEMIS) (Christensen et al. 2004) near-infrared imagery; (3) a low amount of slumping indicating that the concentricity is a primary feature formed during excavation (Lockne type) and not by extensive postimpact slumping (CBIS type; see Horton et al. 2006); and (4) their relatively well-known target setting. From the HiRISE images we created a digital terrain model (DTM) for one of the craters. It was produced using the NASA Stereo Pipeline stereogrammetry package (e.g., Moratto et al. 2010). Both images of the stereo pair (P01_001348_1769_XI_03S003W and P02_001678_1772_XI_02S003W) were processed from CTX experiment data records (EDR) products available from the NASA planetary data systems (PDS) geosciences node.
Table 1. Image data for images in Fig. 6 showing examples of concentric craters in Arcadia Planitia, Mars
Crater diameter (m)
In addition, impact experiments were performed at the Experimental Projectile Impact Chamber (EPIC) of the Laboratory for Experimental Impact Cratering, Centro de Astrobiología, Spain. The EPIC consists of a 7 m wide, funnel-shaped test bed, and a 20.5 mm caliber compressed N2 gas gun of our own design (Fig. 7). The test bed can be filled with any type of target material, but is specifically designed for wet target experiments. The shape and size of the test bed diminish disturbances from reflected surface waves in wet targets with a water layer (i.e., “marine impact”). Experiments are done under ambient pressure. The gas gun can launch projectiles of any material and dimensions <20 mm (smaller diameters using sabots), and at varied angles from vertical to near horizontal. The projectile velocities are of the order of a few hundreds of meters per second depending mainly on the gas pressure, as well as projectile diameter and density. For dry sand targets, the transient crater diameter is typically about 30 cm.
The present experiments used 200 bar pressure and a spherical, 20 mm diameter Delrin projectile with a mass of 5.7 g. The impact angle was 53° over the horizontal plane. The experiments were done in a quarter-space geometry using a specially designed camera tank with a 45 mm thick, bullet-proof glass window to allow the high-speed recording of the cross sectional development of the crater, as well as using the weight of the glass to minimize any vibrations that may affect the growth of the crater. The high-speed camera is a Photron Fastcam 1280PCI. The projectile velocity was estimated with a combination of tracking software and a Shooting Chrony Alpha M-1 chronograph to be 400 ± 5 m s−1. The velocity is about a factor of two above the speed of sound in dry sand, i.e., usually around 200 m s−1 (e.g., Piekutowski 1980; Oelze et al. 2002).
The experiments were prepared with layered targets of dry sand covering damp sand. The damp sand layer was flattened and compacted with a broad metal stamp. Dry sand was distributed over the flat damp sand surface and a flat, horizontal top surface was created with a broad scraper. Two experiments were carried out for varied thickness of the dry sand layer. In the first experiment the dry sand layer is 3 cm thick and in the second the thickness of the layer was reduced to 2 cm to obtain more cratering of the lower, more cohesive, damp sand substrate. The properties of the sand are given in Ormö et al. (2010), but the strength of the damp sand is unknown. However, this is considered irrelevant for the experiments as we here are only concerned about relative differences.
Comparison between Natural Impact Craters and Laboratory Experiments
Martian Case Studies
The three selected Martian case studies, Cases A, B, and C, all show an offset in their concentricity, i.e., the outer crater has a downrange shift with respect to the nested crater. In addition, the ejecta distribution around the craters is pristine, but asymmetrical, which is a prerequisite for determining the direction of the impact (Figs. 8-10). The current lack of THEMIS data with enough resolution for Cases A and C compared with the better data set available for Case B forced us to use only a contrast stretch of the original HiRISE frames of the former to highlight their ejecta layers (Figs. 8B and 10C). The ejecta distribution can then be compared with the asymmetric development of the concentric crater morphology.
In Case A the concentric structure is formed by a set of two outer craters surrounding a much smaller, deeper nested crater (Figs. 8A and 8C). This morphology is expected if there is more than one weak layer over a more resistant substrate (See fig. 6 in Shuvalov 2002). The total crater is about 700 m wide and located in Arcadia Planitia (194.847° E 46.582° N) in layered deposits, likely ground ice-rich sediments as indicated by polygons (Fig. 8C) over a rocky basement. The absence of polygons within the nested crater gives further indication that it is developed in a lower, more rigid (i.e., less porous) substrate than the shallow, concentric outer craters. The existence of even a thinner, uppermost weaker layer is supported by the smaller concentric craters to the NE and SE of the Case A crater (inset figs. A1 and A2 in Fig. 8A). The nested crater has a raised rim apparently formed by a separate ejecta development in analogy with the observed basement crater rim of Lockne and numerical simulations of the Lockne and other impacts into layered targets (cf. Artemieva and Shuvalov 2002; Shuvalov 2002; Lindström et al. 2005).
The ejecta extend rather symmetrically in most directions except for a roughly V-shaped sector on the uprange side and possibly also a slight weakening on the downrange side (Fig. 8A). The coherent ejecta layer shows a more prominent distribution perpendicular to the proposed direction of the projectile trajectory, noticeably with a slight arching in downrange direction (Fig. 8B). As the uprange forbidden zone is not as well developed as would be expected for an impact at an impact angle of <20° (cf. Herrick and Hessen 2006) we assume the impact angle may have been somewhat higher. However, the additional weakening observed on the downrange side would support a rather low angle although still not expressing the butterfly appearance known for highly oblique impacts. Hence, we estimate that the impact angle falls within the range of about 20–30°. In any case, the ejecta distribution gives the direction of impact with good certainty (gray arrows in Figs. 8A and 8B). Along this assumed trajectory there is also an obvious downrange offset of the wider, outer craters with respect to the nested, inner crater.
An alternative for a multilayer concentric crater would be that a smaller impact, by coincidence, would have hit in the center of an already existing crater. We think this can be excluded due to the slightly elongated morphology and asymmetrical ejecta distribution of the nested crater indicating a trajectory identical to that of the concentric host crater. In addition, the chance for a bull's-eye hit with the same trajectory is considered much smaller than for the formation of a concentric crater in this area of Mars where, in fact, such craters are relatively common as shown in Fig. 6.
The analysis of the approximately 2.2 km wide Case B crater (i.e., Ada crater, Fig. 9) enjoys the additional information provided by the THEMIS. The HiRISE image shows a very fresh appearance of the crater (i.e., no superimposed smaller craters). The crater is located in a part of Meridiani Planum (356.8 °E, 3.1 °S) expressing a rather smooth, hummocky surface with few impact craters, except for a cluster of small depressions just to the East of the studied crater (Fig. 9A). The smooth surface material seems to drape an older cratered, rougher surface. The direction of impact is indicated by the ejecta distribution more clearly visible in a THEMIS night-time thermal emission image (Fig. 9C). The rayed ejecta are mainly distributed perpendicular, and slightly less downrange with respect to the inferred projectile trajectory (black arrow in Fig. 9C). On the uprange side there is an indication for a V-shaped forbidden zone although the near-field continuous ejecta layer still reaches a distance almost one crater diameter beyond the crater rim in this direction. From the ejecta distribution we estimate that the impact angle above the horizontal plane may not have been as low as the 20° needed for a fully developed uprange forbidden zone, making 30° a plausible approximation.
This part of Meridiani Planum is suggested to have layered deposits that include evaporites, mainly as sulfates (Hynek et al. 2002; Herkenhoff et al. 2004). Possible sulfate deposits are visible as light-toned material on the wall of the outer crater (Fig. 9B), but the absence of similarly bright material at the rim of the inner, nested crater favors an interpretation as a concentric crater formed in a target with a weaker, upper layer, rather than the morphology being the result of terracing (Figs. 9B, 9D, and 9E). We also argue that the nested crater is surrounded by a rather homogeneous, but asymmetric ejecta deposit resembling the relatively wide, homogeneous, and asymmetric ejecta flap on the brim of the Lockne basement crater (Fig. 2) and the model in the 3-D numerical simulation by Shuvalov et al. (2005) (Fig. 4). A stereo-derived digital elevation model (DEM) shows the near-horizontal configuration and uniform thickness of the upper target layer (Figs. 9D and 9E). There is a low hill at the central part of the floor of the nested crater (Fig. 9B). The crater is too small to be a complex crater with a central peak (cf. Pike 1980). Instead, we suggest the central rise to be an additional effect of the layering, most likely indicating a more resistant layer at some depth below the floor of the nested crater in analogy with the crater morphology model by Quaide and Oberbeck (1968). An alternative is a slump deposit from the crater wall as the floor of the nested crater shows some subcircular depressions that may be pitted melt as suggested for certain Martian craters by Tornabene et al. (2012).
This approximately 2.5 km wide crater is located in the central part of Utopia Planitia at 125 °E, 40.1 °N (Fig. 5). The target is relatively smooth, fluvial, and volcaniclastic deposits that cover rougher deposits originating from the Elysium volcanic area (Tanaka et al. 2005). The materials constitute but a part of the several km thick sedimentary and volcanic deposits that fill the approximately 3300 km wide Utopia impact basin (McGill 1989; Smith et al. 1999). A smooth, hummocky appearance of the area around the Case C crater (Fig. 10A) indicates that the area may be covered by the tens of meters thick, ice-rich mantle deposits described by Morgenstern et al. (2007) from an area farther to the west. The detailed HiRISE image in Fig. 10B shows a fresh appearance of the Case C with no obvious indication of any mantling to have occurred since the emplacement of the ejecta. Rayed ejecta extend in all directions to a distance of several crater diameters. Closer to the crater a more coherent ejecta layer is visible (Fig. 10B). After applying a similar contrast stretch as done for the HiRISE image of Case A the outline of this near-field ejecta layer becomes more evident. It extends to about one crater radius on the NW side while to about twice that distance on the other sides of the crater (Fig. 10C). The rather well-preserved rayed ejecta surrounding the coherent ejecta layer show that the asymmetry in the ejecta distribution is primary and not a result of later erosion. Likewise, the ejecta distribution around the nested crater is more confined on its NW side and more spread out on the opposite, SE, side (Fig. 10B). Together with the distribution of the main coherent ejecta layer around the whole concentric crater this suggests a direction of impact from the NW. The absence of a well-developed uprange forbidden zone implies that the impact angle was not as low as the required 20°. Instead the ejecta distribution more resembles that obtained in numerical simulations of the Lockne crater (Lindström et al. 2005b; Shuvalov et al. 2005), which showed that 45° was low enough to obtain a similar ejecta asymmetry.
Laboratory Impact Experiments
Our impact experiments support the development of a downrange shift of the outer crater with respect to the nested crater (Fig. 11). In the experiment with a 3 cm thick, unconsolidated, dry sand layer covering a stronger layer of damp, cohesive sand, there is, at the initial stage of the cratering (i.e., maximum depth reached), a rather symmetric bowl-shaped cavity (Fig. 11 A1). However, when this cavity expands outward the material flow is accentuated in the weaker, upper layer, and a stair-shaped, concentric transient cavity forms (Fig. 11 A2). Interestingly, the floor of the excavated outer crater does not follow the surface of the stronger damp sand layer. Instead there is a shallow, inclined surface through the dry sand layer. A similar transitional, outward increase in target stratigraphy is observed in the outer crater at Lockne (Fig. 2). Notice also that with this relatively thick upper layer there is no obvious ejecta layer forming from the inner, nested crater (Fig. 11 A3).
With a decrease in the thickness of the upper, weaker layer the crater development is somewhat different although still rendering a concentric structure: At the initial stage (i.e., maximum depth reached) the cavity is significantly more concentric than in the experiment with a thicker weak layer (Fig. 11 B1 versus A1). With the continued growth of the cavity a separate ejecta curtain develops from the crater in the damp sand layer (Fig. 11 B2). This results in a crater with a well-developed ejecta layer from the inner crater in the damp sand covering the floor of the outer, dry sand crater as well as the dry sand ejecta layer on the near surroundings of the whole structure (dark-colored damp sand covering light-colored dry sand in Fig. 11 B3). This is consistent with the nested, basement crater excavation process at Lockne, and seemingly also with the development of the nested craters in Martian cases A, B, and C.
Direct comparisons of the lab experiments with Lockne and the Martian case studies are of course complicated by the large difference in size scale. Previous scaling analyses (e.g., Holsapple and Schmidt 1987; Schmidt and Housen 1987; Ormö et al. 2010) have shown that laboratory cratering experiments can replicate larger-scale cratering events as long as certain nondimensional parameters are the same in the experiments and the larger natural events. When this is true, the experiments are said to be similar to the larger impacts in the sense that they are geometric replicas, i.e., scaled-down versions, of the larger events.
Two of those nondimensional parameters are important here. The first, known as π2, is the ratio ga/U2, where g is gravity, a is the projectile radius, and U is the impact speed. The π2 is essentially an inverse Froude number for an impact: if multiplied by the ratio of target density to projectile density it becomes the ratio of gravitational force to inertial force). For our experiments (a = 0.01 m, g = 9.81 m s−2, U = 400 m s−2) π2 = 6 × 10−7. The initial conditions for the Martian Case A, B, and C craters are of course unknown. Rough estimates are derived here by assuming an impact speed in the range of 104–2 × 104 m s−1. Crater scaling relations (Schmidt 1980) then give impactor radii in the range from 25 to 30 m for Case A and 95 to 120 for Case B. Given that the total crater diameter for Case B (2.2 km) is close to that of Case C (2.5 km), the estimated impactor radii would be approximately equal for the two cases. Using these ranges of impactor radii and speeds and g = 3.7 m s−2 for Mars gives π2 = 2.2 × 10−7 to 1.2 × 10−6 for Case A and 8.8 × 10−7 to 4.7 × 10−6 for Cases B and C. The lab experiments have a π2 value that is about in the middle of the range of estimated values for the Case A crater, and about a factor of 1.5–8 lower than those estimated for Cases B and C. Therefore, the π2 values for the lab experiments are not too far off from those of the Martian craters considered here.
The second scaling parameter of importance is the ratio of target strength, Y, to a characteristic lithostatic stress, ρgD, where ρ is the target density, and D is the crater diameter. When this ratio is large, the crater size is determined by target strength and when it is small, gravitational forces determine crater size. For targets with a weak layer over a stronger basement material, such as the present lab experiments and, presumably, the Martian craters, the crater formed in the weak upper layer would be gravity dominated because of the small value of Y/ρgD. This is equivalent to saying that the strength of the upper layer is unimportant in determining the size of the crater in that material for either the lab experiment or for the Martian craters. However, the situation is different for the crater formed in the basement material: In the lab experiments, the craters formed at 1G in the damp sand substrate form in the strength-dominated regime (Schmidt 1983). For the Martian craters we do not know the properties of the rigid substrate, but for a basaltic target the transition between strength and gravity-dominated craters would occur at about 130 m crater diameter. Thus, the inner, nested crater in Case A (about 200 m) is slightly above this transition, and the nested craters in Case B (about 1 km) and Case C (about 600 m) are definitely gravity controlled. Therefore, while the π2 values for the lab experiments are not too different from those of the Martian craters, the strength/gravity ratio Y/ρgD is likely much larger in the lab experiments.
As a result, we cannot say that the lab experiments are similar to the Martian craters because the nested crater in the basement material is strength-dominated in the lab case, but not for the larger Case A, B, and C craters. The implication is that the ratio of the sizes of the craters formed in the upper layer and in the basement probably differs between the lab experiments and the larger craters. On the other hand, it may be that the offset in the crater centers is not sensitive to the strength of the basement layer, cf. the 3-D numerical simulation of the Lockne crater in Fig. 4. It seems likely that the offset is instead dependent more on the thickness of the upper layer and impact angle. If this is the case, then the lab experiments should be reasonable proxies for the outcomes of the much larger, higher speed impacts that produced the Martian craters, as well as the Lockne crater. This possibility could be investigated further in additional lab experiments and numerical simulations.
It should also be noted that the mechanisms for concentric crater formation may differ between the lab experiments and larger-scale planetary craters. In the lab experiments, the nested crater in the basement material is smaller than that in the upper layer because of the higher strength of the basement material following the model by Quaide and Oberbeck (1968). On the other hand, the strength of the basement is unimportant for the Martian craters because, as noted above, they form in the gravity-dominated regime. In this case, the appearance of nested craters must be due to some other mechanism: Even though strength may be unimportant at gravity-dominated craters, there will still be differences in the density and wave speed of the upper layer and the basement. The product of density and wavespeed is the mechanical impedance of a material. It determines how a shock wave reflects when it hits a boundary between materials with different densities and wavespeeds. Possibly, at large scale, the differing impedances of the two layers could result in reflection of the shock, with a reduction in energy deposition in the basement. However, at this stage, we do not know if it is the impedance that is the critical factor. It may be that it is either the wavespeed or the density that has the major effect. An impact into a target with a low-density layer on top of a high-density layer may well show a larger crater in the upper layer. This should also be addressed in future experiments and code calculations.
Our analysis of natural craters such as Lockne and the three selected Martian examples, our oblique impact experiments, and published numerical simulations show that the previously well-known concentricity of craters from impacts into layered targets is affected by the impact angle. For highly oblique impacts into targets with a weaker surface layer covering a stronger substrate (e.g., sediments over a basement) the outer crater formed in the weak layer has an accentuated development on the downrange side. This creates a downrange offset of the outer crater with respect to the nested crater in the substrate. In this way the direction of impact can be determined for these craters even in the absence of a pristine ejecta layer.
The currently most frequently used method for estimating the direction and obliquity of impact is based on the observed pattern of crater ejecta. Unfortunately, the preservation of often friable ejecta deposits is very poor, especially in areas on planetary bodies with relatively active surface-shaping processes, e.g., Earth and Mars (for periods in the planet's geological history). The recent application of asymmetry of the internal structure of central peaks of Martian oblique impact structures has offered an alternative to the ejecta distribution (Wulf et al. 2012) method of estimating impact angle. We here suggest an additional method for identifying direction and obliquity of impact based on the offset between the outer and nested craters in concentric impact structures. In addition to indicating the impact direction, the offset is likely a function of the impact angle over the horizon, as well as layer thickness relative to the projectile size. The reason for the offset can possibly be found in the variation between the downrange and the uprange flow-field, the same effect known to generate lower downrange than uprange ejection angles (e.g., Anderson et al. 2003, 2004).
We have here merely begun this investigation. Based on the recent development in the studies of oblique impacts (see the Introduction) we anticipate that this will require not only small-scale impact experiments but also advanced 3-D numerical simulation of events of varied magnitude.
The planned continuation of the project includes continued laboratory experiments and 3-D numerical simulations to study the mechanisms for the offset of the outer crater, and quantitative mapping of Martian and lunar concentric craters with preserved ejecta layers to determine the relations between craters with offset in concentricity relative to centro-symmetrical concentricity to search the threshold angle for which the offset occurs.
The work by J. Ormö is supported by grants AYA2008-03467⁄ESP and AYA2011-24780/ESP from the Spanish Ministry of Economy and Competitiveness, and project 90449201 “Concentric Impact Structures in the Palaeozoic (CISP)” from the Swedish Research Council (Vetenskapsrådet). HiRISE image credit: NASA/JPL-Caltech/Univ. of Arizona, and CTX image credit: NASA/JPL-Caltech/MSSS. The authors are grateful to Livio Tornabene and Michael Poelchau for constructive criticism on an earlier version of the paper.