Scaling impact melting and crater dimensions: Implications for the lunar cratering record

Abstract— The dimensions of large craters formed by impact are controlled to a large extent by gravity, whereas the volume of impact melt created during the same event is essentially independent of gravity. This “differential scaling” fosters size-dependent changes in the dynamics of impact-crater and basin formation as well as in the final morphologies of the resulting structures. A variety of such effects can be observed in the lunar cratering record, and some predictions can be made on the basis of calculations of impact melting and crater dimensions. Among them are the following: (1) as event magnitude increases, the volume of melt created relative to that of the crater will grow, and more will be retained inside the rim of the crater or basin. (2) The depth of melting will exceed the depth of excavation at diameters that essentially coincide with both the inflection in the depth-diameter trend and the simple-to-complex transition. (3) The volume of melt will exceed that of the transient cavity at a cavity diameter on the order of the diameter of the Moon; this would arguably correspond to a Moon-melting event. (4) Small lunar craters only rarely display exterior flows of impact melt because the relatively small volumes of melt created can become choked with clasts, increasing the melt's viscosity and chilling it rapidly. Larger craters and basins should suffer little from such a process. (5) Deep melting near the projectile's axis of penetration during larger events will yield a progression in central-structure morphology; with growing event magnitude, this sequence should range from single peaks through multiple peaks to peak rings. (6) The minimum depth of origin of central-peak material should coincide with the maximum depth of melting; the main central peak in a crater the size of Tycho should have had a preimpact depth of close to 15 km.     

The terrestrial cratering record: II. The crater production rate

The terrestrial cratering record for the Phanerozoic has a size-frequency distribution of NαD^?2.05 for D > 22.6 km and NαD^?0.24 for D < 11.3 km. This shallowing of the distribution slope at D > 22.6 km reflects the removal of small terrestrial craters by erosion. The number of large craters on the North American and East European cratons provide estimated terrestrial crater production rates for D > 20 km of 0.36 ± 0.1 and 0.33 ± 0.2 × 10^?14 km^?2 year^?1, respectively. These rates are in good agreement with previous estimates and astronomical observations on Apollo bodies. Comparisons with the lunar rate, taking account of the effects of variations in impact velocity, surface gravity, and gravitational cross section, indicate that the lunar and terrestrial rates overlap, if the cratering flux has been constant during the last 3.4 by. If the early (pre 4.0 by) high-flux rate did not decay to a constant value until 3.0 to 2.5 by then the rates differ by a factor of 2 and the Phanerozoic can be interpreted as a period of higher than normal cratering.     

The impact cratering record of Fennoscandia

The current database of craterform structures in Fennoscandia contains 22 structures of impact origin and about fifty other structures which lack sufficient evidence for impact. The discovery rate of new structures has been one or two per year during the past ten years. The proven impact structures are located in southern Fennoscandia and the majority have been found in Proterozoic target rocks. The age of the structures varies from prehistoric to ≤ 1000 Ma and their diameters (D) from 0.04 km to 55 km. Nine of the structures contain impact melt. A characteristic feature of the Fennoscandian impact record is a relatively large number of small (≤ 5 km) but old (> 200 Ma) structures: this is a result of success of geophysical methods to discover small but old impact structures in an eroded shield covered with relatively thin overburden. Some of the large circular structures in satellite images and/or in geophysical maps may represent deeply eroded scars of very old impacts, but due to the lack of shock metamorphic features, impact-generated rocks or identified ejecta layers, they cannot yet be classified as impact sites. Two huge structures are proposed here as possible impact sites on the basis of circular satellite images and distinct geophysical anomalies: the Lycksele structure in northern Sweden (D ~ 120 km, see also Witschard, 1984) and the Valga structure in Latvia/Estonia (D ~ 180 km). However, endogeneous explanations, like buried granites, basement domings, or fault-bounded blocks are also possible for these structures. Hints, such as distal ejecta layers or impact produced breccia dykes, of an Archaean or Early Proterozoic impact structure have not been found in Fennoscandia so far. New ways of searching for these structures are proposed with particular emphasis on high-resolution integrated geophysical methods. The impact cratering rate in Fennoscandia is ~ 2.0 · 10^?14 km^?2 a^?1 (for craters with D > 3 km) corresponding to about two events per every 100 Ma for the last 700 Ma. Due to erosion, this is a minimal estimate but is higher than the global rate probably due to strong research activity for finding impact structures in Fennoscandia.     

The impact cratering record of Fennoscandia

The current database of craterform structures in Fennoscandia contains 22 structures of impact origin and about fifty other structures which lack sufficient evidence for impact. The discovery rate of new structures has been one or two per year during the past ten years. The proven impact structures are located in southern Fennoscandia and the majority have been found in Proterozoic target rocks. The age of the structures varies from prehistoric to 1000 Ma and their diameters (D) from 0.04 km to 55 km. Nine of the structures contain impact melt. A characteristic feature of the Fennoscandian impact record is a relatively large number of small ( 5 km) but old (> 200 Ma) structures: this is a result of success of geophysical methods to discover small but old impact structures in an eroded shield covered with relatively thin overburden. Some of the large circular structures in satellite images and/or in geophysical maps may represent deeply eroded scars of very old impacts, but due to the lack of shock metamorphic features, impact-generated rocks or identified ejecta layers, they cannot yet be classified as impact sites. Two huge structures are proposed here as possible impact sites on the basis of circular satellite images and distinct geophysical anomalies: the Lycksele structure in northern Sweden (D ~ 120 km, see also Witschard, 1984) and the Valga structure in Latvia/Estonia (D ~ 180 km). However, endogeneous explanations, like buried granites, basement domings, or fault-bounded blocks are also possible for these structures. Hints, such as distal ejecta layers or impact produced breccia dykes, of an Archaean or Early Proterozoic impact structure have not been found in Fennoscandia so far. New ways of searching for these structures are proposed with particular emphasis on high-resolution integrated geophysical methods. The impact cratering rate in Fennoscandia is ~ 2.0 · 10^–14 km^–2 a^–1 (for craters with D > 3 km) corresponding to about two events per every 100 Ma for the last 700 Ma. Due to erosion, this is a minimal estimate but is higher than the global rate probably due to strong research activity for finding impact structures in Fennoscandia.     

Impact cratering - a review,with special reference to the economic importance of impact structures and the Southern African impact crater record

Only since several decades has impact cratering been recognized as an important surface process on all planetary bodies in the Solar System. However, as the process has not yet been effectively introduced into geological curricula, it is necessary to inform a wider public about its importance for (i) planetary formation and (ii) evolution, (iii) the understanding of this process as a geological process, (iv) the terrestrial impact crater record and its limitations, and (v) the recognition criteria for terrestrial impact structures, as well as (vi) the need of improvement of the impact cratering record in the light of the potential danger of an impact catastrophe on this planet. It is, particularly for developing countries, of interest to examine the economic and educational-environmental potential of impact structures. That it is possible to carry out an effective, low-budget geological investigation of impact structures within a Second World environment is demonstrated by the discussion of the progress that has been made in recent years with regard to the Southern African impact crater record. Several recommendations on how to improve, on the one hand, the terrestrial impact crater record and, on the other, their general working situation by activation of workers in Developing Countries are discussed.     

A study of lunar impact crater size-distributions

Discrepancies in published crater frequency data prompted this study of lunar crater distributions. Effects modifying production size distributions of impact craters such as surface lava flows, blanketing by ejecta, superposition, infilling, and abrasion of craters, mass wasting, and the contribution of secondary and volcanic craters are discussed. The resulting criteria have been applied in the determination of the size distributions of unmodified impact crater populations in selected lunar regions of different ages. The measured cumulative crater frequencies are used to obtain a general calibration size distribution curve by a normalization procedure. It is found that the lunar impact crater size distribution is largely constant in the size range 0.3 km ?D ? 20 km for regions with formation ages between ≈ 3 × 10⁹ yr and ? 4 × 10⁹ yr. A polynomial of 4th degree, valid in the size range 0.8 km ?D ? 20 km, and a polynomial of 7th degree, valid in the size range 0.3 km ?D ? ? 20 km, have been approximated to the logarithm of the cumulative crater frequencyN as a function of the logarithm of crater diameterD. The resulting relationship can be expressed asN ～D ^α(D) where α is a function depending onD. This relationship allows the comparison of crater frequencies in different size ranges. Exponential relationships with constant α, commonly used in the literature, are shown to inadequately approximate the lunar impact crater size distribution. Deviations of measured size distributions from the calibration distribution are strongly suggestive of the existence of processes having modified the primary impact crater population.     

A comparison between terrestrial, Cytherean and lunar impact cratering records

A comparison between the terrestrial, Cytherean and lunar cratering records indicates that the large craters (diameters   D > D ₀)  on these surfaces all have cumulative numbers that are proportional to   D ^-2.59±0.05  . Atmospheres have a negligible effect on the formation of   D > D ₀  craters. It is shown that this limiting diameter is  45±3 km  in the case of Venus, and  21.0±1.5 km  in the case of Earth. In this large-diameter range, there are about  1.51±0.34  times more craters, per unit area, on Venus than on the Earth, and about  1350±310  times more craters, per unit area, on the Moon than on the Earth.     

Itokawa's cratering record as observed by Hayabusa: Implications for its age and collisional history

In this paper, we study cratering and crater erasure processes and provide an age estimate for the near-Earth Asteroid (25143) Itokawa, the target of the mission Hayabusa, based on its crater history since the time when it was formed in the main belt by catastrophic disruption or experienced a global resetting event. Using a model which was applied to the study of the crater history of Gaspra, Ida, Mathilde and Eros [O'Brien, D.P., Greenberg, R., Richardson, J.E., 2006. Icarus 183, 79–92], we calculate the time needed to accumulate the craters on Itokawa's surface, taking into account several processes which can affect crater formation and crater erasure on such a low-gravity object, such as seismic shaking. We use two models of the projectile population and two scaling laws to relate crater diameter to projectile size. Both models of the projectile population provide similar results, and depending on the scaling law used, we find that the time necessary to accumulate Itokawa's craters was at least ∼75 Myr, and maybe as long as 1 Gyr. Moreover, using the same model and similar parameters (scaled accordingly), we provide a good match not only to Itokawa's craters, but also to those of Eros, which has also been imaged at high enough resolution to give crater counts in a similar size range to those on Itokawa. We show that, as for Eros, the lack of small craters on Itokawa is consistent with erasure by seismic shaking, although for Itokawa, the pronounced deficiency of the smallest craters (<10 m in diameter) requires another process or event in addition to just seismic shaking. A small body such as Itokawa is highly sensitive to specific events that may occur during its history. For example, the two parts of Itokawa, called head and body, may well have joined each other by a low-velocity impact within the last hundred thousand years [Scheeres, D.J., Abe, M., Yoshikawa, M., Nakamura, R., Gaskell, R.W., Abell, P.A., 2007. Icarus 188, 425–429]. In addition to providing an erasure mechanism for small craters, the proposed timescale of that event is consistent with the timescale necessary in our model to form the current, depleted population of just a few small (<10 m) craters on Itokawa, suggesting that it may be the explanation for the discrepancy between Itokawa's cratering record and that obtained from our equilibrium seismic shaking model. Other explanations for the depletion of the smallest craters on Itokawa, such as armoring by boulders lying on the surface, cannot be ruled out.     

Neptune's satellites: Implications from impact crater morphology

The presence of central peak craters and the absence of central pit craters on Triton implies a surface rigidity similar to the Saturnian and Uranian satellites and stronger than that of the Jupiter satellites Ganymede and Callisto. Tectonically degraded terrain may exist at the antipode of the large impact structure on 1989N1. Dome craters on Triton may represent a form of solid state volcanism.     

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.     

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.     

Influence of the asymmetrical cratering rate on the lunar cratering chronology

The lunar cratering rate studied over the past 1.1 Gyr, which is a foundation of the lunar cratering chronology, is a decreasing function of the angular distance from the apex of the orbital motion due to the synchronous rotation of the Moon. We here evaluate an influence of the asymmetrical rate upon the age determination.     

Earth/Moon impact rate comparison: Searching constraints for lunar secondary/primary cratering proportion

Published data for global impact rate of bolides are compared with the cratering rate on the Moon in the past 100 Ma (assumed to be constant). The comparison shows, that in the limits of used models accuracy, the current meteoroid flux in the Earth-Moon system is approximately the same as in the last 100 Ma, provided most of the small (D<200 m) craters counted on the young (?100 Ma) lunar surface are primary, not secondary craters.     

Hydrothermal alteration at the Lonar Lake impact structure,India: Implications for impact cratering on Mars

Abstract— The 50,000 year old, 1.8 km diameter Lonar crater is one of only two known terrestrial craters to be emplaced in basaltic target rock (the 65 million year old Deccan Traps). The composition of the Lonar basalts is similar to martian basaltic meteorites, which establishes Lonar as an excellent analogue for similarly sized craters on the surface of Mars. Samples from cores drilled into the Lonar crater floor show that there are basaltic impact breccias that have been altered by post‐impact hydrothermal processes to produce an assemblage of secondary alteration minerals. Microprobe data and X‐ray diffraction analyses show that the alteration mineral assemblage consists primarily of saponite, with minor celadonite, and carbonate. Thermodynamic modeling and terrestrial volcanic analogues were used to demonstrate that these clay minerals formed at temperatures between 130°C and 200°C. By comparing the Lonar alteration assemblage with alteration at other terrestrial craters, we conclude that the Lonar crater represents a lower size limit for impact‐induced hydrothermal activity. Based on these results, we suggest that similarly sized craters on Mars have the potential to form hydrothermal systems, as long as liquid water was present on or near the martian surface. Furthermore, the Fe‐rich alteration minerals produced by post‐impact hydrothermal processes could contribute to the minor iron enrichment associated with the formation of the martian soil.     

Spinel assemblages in lunar meteorites Graves Nunataks 06157 and Dhofar 1528: Implications for impact melting and equilibration in the Moon's upper mantle

Magnesium‐rich spinel assemblages occur in the two lunar vitric breccia meteorites—Dhofar (Dho) 1528 and Graves Nunataks (GRA) 06157. Dho 1528 contains up to ~0.7 mm cumulate Mg‐rich spinel crystals associated with Mg‐rich olivine, Mg‐ and Al‐rich pyroxene, plagioclase, and rare cordierite. Using thermodynamic calculations of these mineral assemblages, we constrain equilibration depths and discuss an origin of these lithologies in the upper mantle of the Moon. In contrast, small, 10 to 20 μm spinel phenocryst assemblages in glassy melt rock clasts in Dho 1528 and GRA 06157 formed from the impact melting of Mg‐rich rocks. Some of these spinel phenocrysts match compositional constraints for spinel associated with “pink spinel anorthosites” inferred from remote sensing data. However, such spinel phenocrysts in meteorites and Apollo samples are typically associated with significant amounts of olivine ± pyroxene that exceed the compositional constraints for pink spinel anorthosites. We conclude that the remotely sensed “pink spinel anorthosites” have not been observed in the collections of lunar rocks. Moreover, we discuss impact‐excavation scenarios for the spinel‐bearing assemblages in Dhofar 1528 and compare the bulk rock composition of Dho 1528 to strikingly similar compositions of Luna 20 samples that contain ejecta from the Crisium impact basin.     

Tectonic influences on the morphometry of the Sudbury impact structure: Implications for terrestrial cratering and modeling

Abstract— Impact structures developed on active terrestrial planets (Earth and Venus) are susceptible to pre‐impact tectonic influences on their formation. This means that we cannot expect them to conform to ideal cratering models, which are commonly based on the response of a homogeneous target devoid of pre‐existing flaws. In the case of the 1.85 Ga Sudbury impact structure of Ontario, Canada, considerable influence has been exerted on modification stage processes by late Archean to early Proterozoic basement faults. Two trends are dominant: 1) the NNW‐striking Onaping Fault System, which is parallel to the 2.47 Ga Matachewan dyke swarm, and 2) the ENE‐striking Murray Fault System, which acted as a major Paleoproterozoic suture zone that contributed to the development of the Huronian sedimentary basin between 2.45–2.2 Ga. Sudbury has also been affected by syn‐ to post‐impact regional deformation and metamorphism: the 1.9–1.8 Ga Penokean orogeny, which involved NNW‐directed reverse faulting, uplift, and transpression at mainly greenschist facies grade, and the 1.16–0.99 Ga Grenville orogeny, which overprinted the SE sector of the impact structure to yield a polydeformed upper amphibolite facies terrain. The pre‐, syn‐, and post‐impact tectonics of the region have rendered the Sudbury structure a complicated feature. Careful reconstruction is required before its original morphometry can be established. This is likely to be true for many impact structures developed on active terrestrial planets. Based on extensive field work, combined with remote sensing and geophysical data, four ring systems have been identified at Sudbury. The inner three rings broadly correlate with pseudotachylyte (friction melt) ‐rich fault systems. The first ring has a diameter of ?90 km and defines what is interpreted to be the remains of the central uplift. The second ring delimits the collapsed transient cavity diameter at ?130 km and broadly corresponds to the original melt sheet diameter. The third ring has a diameter of ?180 km. The fourth ring defines the suggested apparent crater diameter at ?260 km. This approximates the final rim diameter, given that erosion in the North Range is <6 km and the ring faults are steeply dipping. Impact damage beyond Ring 4 may occur, but has not yet been identified in the field. One or more rings within the central uplift (Ring 1) may also exist. This form and concentric structure indicates that Sudbury is a peak ring or, more probably, a multi‐ring basin. These parameters provide the foundation for modeling the formation of this relatively large terrestrial impact structure.     

Polygonal impact craters in Argyre region,Mars: Implications for geology and cratering mechanics

Abstract— Impact craters are not always circular; sometimes their rims are composed of several straight segments. Such polygonal impact craters (PICs) are controlled by pre‐existing target structures, mainly faults or other similar planes of weakness. In the Argyre region, Mars, PICs comprise ? 17% of the total impact crater population (>7 km in diameter), and PICs are relatively more common in older geologic units. Their formation is mainly controlled by radial fractures induced by the Argyre and Ladon impact basins, and to a lesser extent by the basin‐concentric fractures. Also basin‐induced conjugate shear fractures may play a role. Unlike the PICs, ridges and graben in the Argyre region are mostly controlled by Tharsis‐induced tectonism, with the ridges being concentric and graben radial to Tharsis. Therefore, the PICs primarily reflect an old impact basin‐centered tectonic pattern, whereas Tharsis‐centered tectonism responsible for the graben and the ridges has only minor influence on the PIC rim orientations. According to current models of PIC formation, complex PICs should form through a different mechanism than simple PICs, leading to different orientations of straight rim segments. However, when simple and complex PICs from same areas are studied, no statistically significant difference can be observed. Hence, in addition to enhanced excavation parallel to the strike of fractures (simple craters) and slumping along the fracture planes (complex craters), we propose a third mechanism involving thrusting along the fracture planes. This model is applicable to both simple and small complex craters in targets with some dominating orientations of structural weakness.     

A mechanism for the production of lunar crater rays

Observations of high resolution photographs of part of one of the prominent rays of the lunar crater Copernicus show that there is a concentration of small bright rayed and haloed craters within the ray. These craters contribute to the overall ray brightness; they have been measured and their surface distribution has been mapped. Sixty-two percent of the bright craters can be identified from study of high resolution photographs as concentric impact craters. These craters contain in their ejecta blankets, rocks from the lunar substrate that are brighter than the adjacent mare surface. It is concluded that the brightness of the large ray from the crater Copernicus is due to the composite effect of many small concentric impact craters with rocky ejecta blankets. If this is the dominant mechanism for the production of other rays from Copernicus and other large lunar craters, then rays may not contain significant amounts of ejecta from the central crater or from large secondary craters. They may in fact only reflect local excavation of mare substrate material by myriads of small secondary or tertiary impact craters.     

Floor-fractured crater models of the Sudbury Structure,Canada: Implications for initial crater size and crater modification

Abstract The pattern of radial and concentric offset dikes at Sudbury strongly resembles fracture patterns in certain volcanically modified craters on the Moon. Since the Sudbury dikes apparently formed shortly after the impact event, this resemblance suggests that early endogenic modification at Sudbury was comparable to deformation in lunar floor-fractured craters. Although regional deformation has obscured many details of the Sudbury Structure, such a comparison of Sudbury with lunar floor-fractured craters provides two alternative models for the original size and surface structures of the Sudbury basin. First, the Sudbury date pattern can be correlated with fractures in the central peak crater Haldane (36 km in diameter). This comparison indicates an initial Sudbury diameter of between 100 and 140 km but requires loss of a central peak complex for which there is little evidence. Alternatively, comparison of the Sudbury dikes with fractures in the two-ring basin Schrödinger indicates an initial Sudbury diameter of at least ～ 180 km, which is in agreement with other recent estimates for the size of the Sudbury Structure. In addition to constraining the size and structure of the original Sudbury crater, these comparisons also suggest that crater modification may reflect different deformation mechanisms at different sizes. Most lunar floor-fractured craters are attributed to deformation over a shallow, crater-centered intrusion; however, there is no evidence for such an intrusion at Sudbury. Instead, melts from the evolving impact melt sheet probably entered fractures formed by isostatically-induced flexure of the crater floor. Since most of the lunar floor-fractured craters are too small (<100-km diameter) to induce significant isostatic adjustment, crater modification by isostatic uplift apparently is limited to only the largest of craters, whereas deformation over igneous intrusions dominates the modification of smaller craters.