Nonuniform cratering of the Moon and a revised crater chronology of the inner Solar System

We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronology method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analytically, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth-Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Varying depths of this megaregolith between the mare and highlands is a plausible partial explanation for differences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.     

Near-Earth object velocity distributions and consequences for the Chicxulub impactor

An Öpik-based geometric algorithm is used to compute impact probabilities and velocity distributions for various near-Earth object (NEO) populations. The resulting crater size distributions for the Earth and Moon are calculated by combining these distributions with assumed NEO size distributions and a selection of crater scaling laws. This crater probability distribution indicates that the largest craters on both the Earth and the Moon are dominated by comets. However, from a calculation of the fractional probabilities of iridium deposition, and the velocity distributions at impact of each NEO population, the only realistic possibilities for the Chicxulub impactor are a short-period comet (possibly inactive) or a near-Earth asteroid. For these classes of object, sufficiently large impacts have mean intervals of 100 and 300 Myr respectively, slightly favouring the cometary hypothesis.     

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.     

Investigating target versus impactor influences on Martian crater morphology at the simple‐complex transition

Comparing craters of identical diameter on a planet is an empirical method of studying the effects of different target and impactor properties while holding total impact energy nearly constant. We have analyzed the Martian crater population within a narrow diameter range (7 km < crater diameter < 9 km) at the simple‐complex crater transition using three approaches. We looked for correlations of morphology with surface geology using a global crater database and global geologic map. We examined selected regions in detail with high‐resolution images to further understand the relationship between crater morphology and bulk target properties. Finally, we examined craters in close proximity to each other in order to hold target properties constant, so that we could isolate impactor effects on crater morphology. We found a strong correlation between target properties and interior crater morphology, and we found little evidence that impactor properties (other than impact angle) affect crater appearance. Central uplift and wall slumping are enhanced for less consolidated targets. Layered targets affected both the excavation and modification stages of complex crater formation; the resulting craters have pseudoterraces, flat floors, and central pits.     

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.     

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.     

Crater dimensions from apollo data and supplemental sources

A catalog of crater dimensions that were compiled mostly from the new Apollo-based Lunar Topographic Orthophotomaps is presented in its entirety. Values of crater diameter, depth, rim height, flank width, circularity, and floor diameter (where applicable) are tabulated for a sample of 484 craters on the Moon and 22 craters on Earth. Systematic techniques of mensuration are detailed. The lunar craters range in size from 400 m to 300 km across and include primary impact craters of the main sequence, secondary impact craters, craterlets atop domes and cones, and dark-halo craters. The terrestrial craters are between 10 m and 22.5 km in diameter and were formed by meteorite impact.     

Crater size-shape profiles for the moon and mercury: Terrain effects and interplanetary comparisons

New crater size-shape data were compiled for 221 fresh lunar craters and 152 youthful mercurian craters. Terraces and central peaks develop initially in fresh craters on the Moon in the 0–10 km diameter interval. Above a diameter of 65 km all craters are terraced and have central peaks. Swirl floor texture is most common in craters in the size range 20–30 km, but it occurs less frequently as terraces become a dominant feature of crater interiors. For the Moon there is a correlation between crater shape and geomorphic terrain type. For example, craters on the maria are more complex in terms of central peak and terrace detail at any given crater diameter than are craters in the highlands. These crater data suggest that there are significant differences in substrate and/or target properties between maria and highlands. Size-shape profiles for Mercury show that central peak and terrace onset is in the 10–20 km diameter interval; all craters are terraced at 65 km, and all have central peaks at 45 km. The crater data for Mercury show no clear cut terrain correlation. Comparison of lunar and mercurian data indicates that both central peaks and terraces are more abundant in craters in the diameter range 5–75 km on Mercury. Differences in crater shape between Mercury and the Moon may be due to differences in planetary gravitational acceleration (gMercury=2.3gMoon). Also differences between Mercury and the Moon in target and substrate and in modal impact velocity may contribute to affect crater shape.     

Marine‐target craters on Mars? An assessment study

Abstract— Observations of impact craters on Earth show that a water column at the target strongly influences lithology and morphology of the resultant crater. The degree of influence varies with the target water depth and impactor diameter. Morphological features detectable in satellite imagery include a concentric shape with an inner crater inset within a shallower outer crater, which is cut by gullies excavated by the resurge of water. In this study, we show that if oceans, large seas, and lakes existed on Mars for periods of time, marine‐target craters must have formed. We make an assessment of the minimum and maximum amounts of such craters based on published data on water depths, extent, and duration of putative oceans within “contacts 1 and 2,” cratering rate during the different oceanic phases, and computer modeling of minimum impactor diameters required to form long‐lasting craters in the seafloor of the oceans. We also discuss the influence of erosion and sedimentation on the preservation and exposure of the craters. For an ocean within the smaller “contact 2” with a duration of 100,000 yr and the low present crater formation rate, only ?1–2 detectable marine‐target craters would have formed. In a maximum estimate with a duration of 0.8 Gyr, as many as 1400 craters may have formed. An ocean within the larger “contact 1‐Meridiani,” with a duration of 100,000 yr, would not have received any seafloor craters despite the higher crater formation rate estimated before 3.5 Gyr. On the other hand, with a maximum duration of 0.8 Gyr, about 160 seafloor craters may have formed. However, terrestrial examples show that most marine‐target craters may be covered by thick sediments. Ground penetrating radar surveys planned for the ESA Mars Express and NASA 2005 missions may reveal buried craters, though it is uncertain if the resolution will allow the detection of diagnostic features of marine‐target craters. The implications regarding the discovery of marine‐target craters on Mars is not without significance, as such discoveries would help address the ongoing debate of whether large water bodies occupied the northern plains of Mars and would help constrain future paleoclimatic reconstructions.     

Intra-crater glacial processes in central Utopia Planitia, Mars

We describe and interpret a series of previously unidentified glacial-like lobes (34-43°N; 107-125°E) that were discovered as part of a survey of large (D > 5 km) impact craters in Utopia Planitia, one of the great northern plains of Mars. The lobes have characteristics that are consistent with a glacial origin. Evidence includes curvilinearity of form, lineations and ridges, and surface textures that are thought to form by the sublimation of near-surface volatiles. The lobes display morphologies that range from wedge-shaped to near-circular to elongate. The flow directions are towards the northern walls in the case of craters with large single lobes, and in all directions in the case of the largest (D > 30 km) craters. Concentric crater fill is also interspersed within craters of our study region, with such craters having much higher filling rates than those with flow lobes. We suggest that the impact crater population in south-west Utopia Planitia demonstrates a spectrum of glacial modifications, from low levels of filling in the case of craters with elongate lobes at one extreme, to concentric crater fill in highly-filled craters at the other.     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

Differential melt scaling for oblique impacts on terrestrial planets

Analytical estimates of melt volumes produced by a given projectile and contained in a given impact crater are derived as a function of impact velocity, impact angle, planetary gravity, target and projectile densities, and specific internal energy of melting. Applications to impact events and impact craters on the Earth, Moon, and Mars are demonstrated and discussed. The most probable oblique impact (45°) produces ～1.6 times less melt volume than a vertical impact, and ～1.6 and 3.7 times more melt volume than impacts with 30° and 15° trajectories, respectively. The melt volume for a particular crater diameter increases with planetary gravity, so a crater on Earth should have more melt than similar-size craters on Mars and the Moon. The melt volume for a particular projectile diameter does not depend on gravity, but has a strong dependence on impact velocity, so the melt generated by a given projectile on the Moon is significantly larger than on Mars. Higher surface temperatures and geothermal gradients increase melt production, as do lower energies of melting. Collectively, the results imply thinner central melt sheets and a smaller proportion of melt particles in impact breccias on the Moon and Mars than on Earth. These effects are illustrated in a comparison of the Chicxulub crater on Earth, linked to the Cretaceous–Tertiary mass extinction, Gusev crater on Mars, where the Mars Exploration Rover Spirit landed, and Tsiolkovsky crater on the Moon. The results are comparable to those obtained from field and spacecraft observations, other analytical expressions, and hydrocode simulations.     

Micron‐scale hypervelocity impact craters: Dependence of crater ellipticity and rim morphology on impact trajectory,projectile size,velocity, and shape

The interstellar collector on NASA's Stardust mission captured many particles from sources other than the interstellar dust stream. Impact trajectory may provide a means of discriminating between these different sources, and thus identifying/eliminating candidate interstellar particles. The collector's aerogel preserved a clear record of particle impact trajectory from the inclination and direction of the resultant tracks. However, the collector also contained aluminum foils and, although impact crater studies to date suggest only the most inclined impacts (>45° from normal) produce crater morphologies that indicate trajectory (i.e., distinctly elliptical), these studies have been restricted to much larger (mm and above) scales than are relevant for Stardust (μm). It is unknown how oblique impact crater morphology varies as a function of length scale, and therefore how well Stardust craters preserve details of impactor trajectory. Here, we present data from a series of impact experiments, together with complementary hydrocode modeling, that examine how crater morphology changes with impact angles for different‐sized projectiles. We find that, for our smallest spherical projectiles (2 μm diameter), the ellipticity and rim morphology provide evidence of their inclined trajectory from as little as 15° from normal incidence. This is most likely a result of strain rate hardening in the target metal. Further experiments and models find that variation in velocity and impactor shape complicate these trends, but that rim morphology remains useful in determining impact direction (where the angle of impact is >20° from normal) and may help identify candidate interstellar particle craters on the Stardust collector.     

Impact cratering records of the mid-sized, icy saturnian satellites

Resolution of Voyager 1 and 2 images of the mid-sized, icy saturnian satellites was generally not much better than 1 km per line pair, except for a few, isolated higher resolution images. Therefore, analyses of impact crater distributions were generally limited to diameters (D) of tens of kilometers. Even with the limitation, however, these analyses demonstrated that studying impact crater distributions could expand understanding of the geology of the saturnian satellites and impact cratering in the outer Solar System. Thus to gain further insight into Saturn’s mid-sized satellites and impact cratering in the outer Solar System, we have compiled cratering records of these satellites using higher resolution CassiniISS images. Images from Cassini of the satellites range in resolution from tens m/pixel to hundreds m/pixel. These high-resolution images provide a look at the impact cratering records of these satellites never seen before, expanding the observable craters down to diameters of hundreds of meters. The diameters and locations of all observable craters are recorded for regions of Mimas, Tethys, Dione, Rhea, Iapetus, and Phoebe. These impact crater data are then analyzed and compared using cumulative, differential and relative (R) size-frequency distributions. Results indicate that the heavily cratered terrains on Rhea and Iapetus have similar distributions implying one common impactor population bombarded these two satellites. The distributions for Mimas and Dione, however, are different from Rhea and Iapetus, but are similar to one another, possibly implying another impactor population common to those two satellites. The difference between these two populations is a relative increase of craters with diameters between 10 and 30 km and a relative deficiency of craters with diameters between 30 and 80 km for Mimas and Dione compared with Rhea and Iapetus. This may support the result from Voyager images of two distinct impactor populations. One population was suggested to have a greater number of large impactors, most likely heliocentric comets (Saturn Population I in the Voyager literature), and the other a relative deficiency of large impactors and a greater number of small impactors, most likely planetocentric debris (Saturn Population II). Meanwhile, Tethys’ impact crater size-frequency distribution, which has some similarity to the distributions of Mimas, Dione, Rhea, and Iapetus, may be transitional between the two populations. Furthermore, when the impact crater distributions from these older cratered terrains are compared to younger ones like Dione’s smooth plains, the distributions have some similarities and differences. Therefore, it is uncertain whether the size-frequency distribution of the impactor population(s) changed over time. Finally, we find that Phoebe has a unique impact crater distribution. Phoebe appears to be lacking craters in a narrow diameter range around 1 km. The explanation for this confined “dip” at D = 1 km is not yet clear, but may have something to do with the interaction of Saturn’s irregular satellites or the capture of Phoebe.     

The role of arcuate ridges and gullies in the degradation of craters in the Newton Basin region of Mars

A survey of craters in the vicinity of Newton Basin, using high-resolution images from Mars Global Surveyor and Mars Odyssey, was conducted to find and analyze examples of gullies and arcuate ridges and assess their implications for impact crater degradation processes. In the Phaethontis Quadrangle (MC-24), we identified 225 craters that contain these features. Of these, 188 had gullies on some portion of their walls, 118 had arcuate ridges at the bases of the crater walls, and 104 contained both features, typically on the same crater wall. A major result is that the pole-facing or equator-facing orientation of these features is latitude dependent. At latitudes >44° S, equator-facing orientations for both ridges and gullies are prevalent, but at latitudes <44° S, pole-facing orientations are prevalent. The gullies and arcuate ridges typically occupy craters between ∼2 and 30 km in diameter, at elevations between −1 and 3 km. Mars Orbiter Laser Altimeter (MOLA) elevation profiles indicate that most craters with pole-facing arcuate ridges have floors sloping downward from the pole-facing wall, and some of these craters show asymmetry in crater rim heights, with lower pole-facing rims. These patterns suggest viscous flow of ice-rich materials preferentially away from gullied crater walls. Clear associations exist between gullies and arcuate ridges, including (a) geometric congruence between alcoves and sinuous arcs of arcuate ridges and (b) backfilling of arcuate ridges by debris aprons associated with gully systems. Chronologic studies suggest that gullied walls and patterned crater floor deposits have ages corresponding to the last few high obliquity cycles. Our data appear consistent with the hypothesis that these features are associated with periods of ice deposition and subsequent erosion associated with obliquity excursions within the last few tens of millions of years. Arcuate ridges may form from cycles of activity that also involve gully formation, and the ridges may be in part due to mass-wasted, ice-rich material transported downslope from the alcoves, which then interacts with previously emplaced floor deposits. Most observed gullies may be late-stage features in a degradational cycle that may have occurred many times on a given crater wall.     

Shallow and deep fresh impact craters in Hesperia Planum,Mars

The depths of 109 impact craters 2–16 km in diameter, located on the ridged plains materials of Hesperia Planum, Mars, have been measured from their shadow lengths using digital Viking Orbiter images (orbit numbers 417S–419S) and the PICS computer software. On the basis of their pristine morphology (very fresh lobate ejecta blankets, well preserved rim crests, and lack of superposed impact craters), 57 of these craters have been selected for detailed analysis of their spatial distribution and geometry. We find that south of 30°S, craters <6.0 km in diameter are markedly shallower than similar-sized craters equatorward of this latitude. No comparable relationship is observed for morphologically fresh craters >6.0 km diameter. We also find that two populations exist for older craters <6.0 km diameter. When craters that lack ejecta blankets are grouped on the basis of depth/diameter ratio, the deeper craters also typically lie equatorward of 30° S. We interpret the spatial variation in crater depth/diameter ratios as most likely due to a poleward increase in volatiles within the top 400 m of the surface at the times these craters were formed.     

Nonuniform cratering of the terrestrial planets

We estimate the impact flux and cratering rate as a function of latitude on the terrestrial planets using a model distribution of planet crossing asteroids and comets [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433]. After determining the planetary impact probabilities as a function of the relative encounter velocity and encounter inclination, the impact positions are calculated analytically, assuming the projectiles follow hyperbolic paths during the encounter phase. As the source of projectiles is not isotropic, latitudinal variations of the impact flux are predicted: the calculated ratio between the pole and equator is 1.05 for Mercury, 1.00 for Venus, 0.96 for the Earth, 0.90 for the Moon, and 1.14 for Mars over its long-term obliquity variation history. By taking into account the latitudinal dependence of the impact velocity and impact angle, and by using a crater scaling law that depends on the vertical component of the impact velocity, the latitudinal variations of the cratering rate (the number of craters with a given size formed per unit time and unit area) is in general enhanced. With respect to the equator, the polar cratering rate is about 30% larger on Mars and 10% on Mercury, whereas it is 10% less on the Earth and 20% less on the Moon. The cratering rate is found to be uniform on Venus. The relative global impact fluxes on Mercury, Venus, the Earth and Mars are calculated with respect to the Moon, and we find values of 1.9, 1.8, 1.6, and 2.8, respectively. Our results show that the relative shape of the crater size-frequency distribution does not noticeably depend upon latitude for any of the terrestrial bodies in this study. Nevertheless, by neglecting the expected latitudinal variations of the cratering rate, systematic errors of 20-30% in the age of planetary surfaces could exist between equatorial and polar regions when using the crater chronology method.     

Bias-corrected population, size distribution, and impact hazard for the near-Earth objects

Utilizing the largest available data sets for the observed taxonomic (Binzel et al., 2004, Icarus 170, 259-294) and albedo (Delbo et al., 2003, Icarus 166, 116-130) distributions of the near-Earth object population, we model the bias-corrected population. Diameter-limited fractional abundances of the taxonomic complexes are A-0.2%; C-10%, D-17%, O-0.5%, Q-14%, R-0.1%, S-22%, U-0.4%, V-1%, X-34%. In a diameter-limited sample, ∼30% of the NEO population has jovian Tisserand parameter less than 3, where the D-types and X-types dominate. The large contribution from the X-types is surprising and highlights the need to better understand this group with more albedo measurements. Combining the C, D, and X complexes into a “dark” group and the others into a “bright” group yields a debiased dark-to-bright ratio of ∼1.6. Overall, the bias-corrected mean albedo for the NEO population is 0.14±0.02, for which an H magnitude of 17.8±0.1 translates to a diameter of 1 km, in close agreement with Morbidelli et al. (2002, Icarus 158 (2), 329-342). Coupling this bias corrected taxonomic and albedo model with the H magnitude dependent size distribution of (Stuart, 2001, Science 294, 1691-1693) yields a diameter distribution with 1090±180 NEOs with diameters larger than 1 km. As of 2004 June, the Spaceguard Survey has discovered 56% of the NEOs larger than 1 km. Using our size distribution model, and orbital distribution of (Stuart, 2001, Science 294, 1691-1693) we calculate the frequency of impacts into the Earth and the Moon. Globally destructive collisions (∼10²¹ J) of asteroids 1 km or larger strike the Earth once every 0.60±0.1 Myr on average. Regionally destructive collisions with impact energy greater than 4×10¹⁸ J (∼200 m diameter) strike the Earth every 56,000±6000 yr. Collisions in the range of the Tunguska event (4-8×10¹⁶ J) occur every 2000-3000 yr. These values represent the average time between randomly spaced impacts; actual impacts could occur more or less closely spaced solely by chance. As a verification of these impact rates, the crater production function of Shoemaker et al. (1990, Geological Society of American Special Paper 247) has been updated by combining this new population model with a crater formation model to find that the observed crater production function on both the Earth and Moon agrees with the rate of crater production expected from the current population of NEOs.     

SOME MORPHOLOGIC SYSTEMATICS OF COMPLEX IMPACT STRUCTURES

Similarities among impact structures on different planets and satellites suggest that the cratering process transcends variations in both target and impactor. In particular, impact may control the spacing of concentric rings, if not their actual emplacement. In at least four respects the scaled horizontal dimensions of complex meteorite-impact structures on Earth resemble those of multi-ring basins and large craters on the Moon, Mars, Mercury, and some outer satellites: (1) Base diameter of the (topographic) central peak is a constant 20% to 25% of the rim diameter in small complex craters; (2) it averages only half as much in large structures that also have concentric rings; (3) the inner ring of a two-ring crater lacking a central peak is half the diameter of the outer ring; (4) adjacent rings of complex craters that have more than two concentric rings are spaced at a constant interval of about (2.0 ± 0.2)^0.5 D, both inside and outside the main ring. Two minor differences in morphology suggest that uniquely terrestrial conditions may control some horizontal dimensions of meteorite craters: (1) the inner ring of a two-ringed structure that also has a central peak is 0.5X the diameter of the outer, not 0.4X as it is for peak-plus-ring basins on the planets; and (2) two-ring and multi-ring meteorite craters occupy the same size range, whereas on planets most two-ring basins are smaller than multi-ring basins.     

Doublet craters on Venus

Of the impact craters on Earth larger than 20 km in diameter, 10-15% (3 out of 28) are doublets, having been formed by the simultaneous impact of two well-separated projectiles. The most likely scenario for their formation is the impact of well-separated binary asteroids. If a population of binary asteroids is capable of striking the Earth, it should also be able to hit the other terrestrial planets as well. Venus is a promising planet to search for doublet craters because its surface is young, erosion is nearly nonexistent, and its crater population is significantly larger than the Earth's. After a detailed investigation of single craters separated by less than 150 km and “multiple” craters having diameters greater than 10 km, we found that the proportion of doublet craters on Venus is at most 2.2%, significantly smaller than Earth's, although several nearly incontrovertible doublets were recognized. We believe this apparent deficit relative to the Earth's doublet population is a consequence of atmospheric screening of small projectiles on Venus rather than a real difference in the population of impacting bodies. We also examined “splotches,” circular radar reflectance features in the Magellan data. Projectiles that are too small to form craters probably formed these features. After a careful study of these patterns, we believe that the proportion of doublet splotches on Venus (14%) is comparable to the proportion of doublet craters found on Earth (10-15%). Thus, given the uncertainties of interpretation and the statistics of small numbers, it appears that the doublet crater population on Venus is consistent with that of the Earth.