Distribution Of Craters Research Articles

Geology: Craters

We investigate the spatial distributions of boulders ejected from 18 lunar impact craters that are hundreds of meters in diameter. To accomplish this goal, we measured the diameters of 13,955 ejected boulders and the distance of each boulder from the crater center. Using the boulder distances, we calculated ejection velocities for the boulders. We compare these data with previously published data on larger craters and use this information to determine how boulder ejection velocity scales with crater diameter. We also measured regolith depths in the areas surrounding many of the craters, for comparison with the boulder distributions. These results contribute to understanding boulder ejection velocities, to determining whether there is a relationship between the quantity of ejected boulders and lunar regolith depths, and to understanding the distributions of secondary craters in the Solar System. Understanding distributions of blocky ejecta is an important consideration for landing site selection on both the Moon and Mars.

Physical Characteristics of the Lunar Regolith Determined From Surveyor Television Observations

The new data on the physical characteristics of the lunar surface derived from the Surveyor pictures can be fitted to a simple ballistic model for the origin and development of the lunar regolith. At a given locality, the size‐frequency distributions of craters on the lunar surface can be represented by two functions: Small craters follow a steady‐state distribution of the form F = ΦCμ, where F is the cumulative number of craters with a diameter ≥ c, c is the diameter of the craters, Φ and μ have the steady‐state values Φ = 1010·9, and μ = −2.00 at all five Surveyor landing sites. Larger craters are represented by the function F = χcλ, where λ < μ, and χ varies from one landing site to another. The solution for c at the intersection of F = χcλ with F = Φcμ, designated as cs, is the upper limiting crater diameter for the steady‐state distribution. The value of cs is a function of the age of the surface on which the regolith has formed. The thickness of the lunar regolith may be estimated from a variety of observational data. The estimated thickness of the regolith at a given Surveyor landing site is bracketed by the original depths of (1) the smallest blocky‐rimmed craters that cut through the regolith and excavate coherent material beneath, and (2) the largest, sharp, raised‐rim craters without blocks that have been excavated wholly within the slightly cohesive material that forms the regolith. Other direct estimates of the thickness of the regolith are the inferred original depth of the largest craters believed to have been formed by drainage of the regolith material into subregolith fissures and, at the Surveyor‐7 site, the depth at which the surface sampler instrument encountered coherent material. The thickest regolith was found at the Surveyor‐6 site, where it is estimated to be more than 10 meters thick, and the thinnest was found at the Surveyor‐7 site, where it is estimated to be 2 to 15 cm thick. Particle counts from sample areas at each of the Surveyor landing sites show an approximately linear relationship between the log of the cumulative particle counts and the log of the particle size. A power function of the form N = KDλ (where N is the cumulative number of particles with diameter equal to or larger than D, and D is the diameter of particles) can be fitted to the data at each site. The size‐frequency distribution of resolvable fragments at the Surveyor 3, 5, and 6 landing sites was found to be the same, within errors of estimation, but at the Surveyor 1 and 7 sites coarse fragments are more numerous. Considering all five sites, we found a strong inverse correlation between the abundance of coarse blocks and the thickness of the regolith. The coarsest fragments are most abundant at the sites with the thinnest regolith.

Lunar Regolith at Tranquillity Base

The regolith at Tranquillity Base is a layer of fragmental debris that ranges in thickness from about 3 to 6 meters. The thickness of the regolith and the exposure histories of its constituent fragments can be related, by means of a relatively simple model, to the observed crater distribution.

Observations of the lunar regolith and the Earth from the television camera on Surveyor 7

Surveyor 7, the last spacecraft of the Surveyor series, landed about 30 km north of the rim crest of Tycho, one of the most prominent and well-known features in the southern part of the moon. About 21,000 pictures were transmitted during two lunar days of operation. At the Surveyor 7 site, the cumulative size-frequency distribution of craters 13 cm to 3 meters in diameter follows closely the distribution of craters observed at the other Surveyor sites in the lunar maria. This distribution of small craters is believed to be a steady-state distribution.

Meteoroid environment near the ecliptic.

A new model of the distribution of solid particles near the ecliptic is developed. The particle-distribution function / is expressed as the product of three distribution functions in the form/ = fvfsfm where /»,/s, and fm give the particle distribution with respect to speed, distance from the sun, and mass. /„' is evaluated from meteor data, /s is evaluated from Mariner IV micrometeoroidflux data and the observed distribution of the asteroids, and fm is evaluated by combining zodiacal-light data, meteoroid-penetration-detector data, optical-meteor data, and the size distribution of meteorites and lunar craters. Nomenclat ure A = cross-section area of particle B = mass-distribution constant C = weak-wave speed CD = drag coefficient D = diameter of impact crater

The Computer Simulation of Lunar Craters

A KDF 9 computer and a micro-film recorder have been used to generate and plot out random crater distributions, and to make 16-mm film of the developing patterns. These studies have shown: (1) that continuing generation of random craters with an inverse square law size distribution produces a mean crater density equal to that observed on the Moon, together with local variations analogous to the Lunar Highlands and Mare. (2) that overlapping and obliteration do not change the size distribution exponent of the remaining craters significantly from –2, although the exponent relating to craters with unbroken rims is affected, (3) that the virtual absence on the Moon of smaller craters overlapped by larger ones arises because of their burial under the outer slopes of the larger crater walls; (4) that crater counts on fixed areas do lead to systematic error, caused by exclusion of large craters from the sample. Further simulations might include the effects of erosion, flooding, and secondary cratering mechanisms, and might also be used for statistical studies.

On the distribution of large lunar craters

The size distribution and location of all the craters of Classes 1, 2 and 3 larger than 25 km in diameter on the front face of the Moon were studied. The diameter distribution of the craters follows approximately the distribution that would be expected from meteoritic impact. Lateral variations in cratering over the lunar surface were determined by dividing the lunar disk into 172 equi-areal zones, each of approximately 76.9 × 10 3 km 2. The number of craters, their average diameter, and the sum of their diameters were measured in each zone. When these parameters are contoured on the lunar surface, they outline not only the maria but also areas on the terrae otherwise indistinguishable. On the terrae the amount of cratering is not random; highly cratered areas occur clustered together with a correlation coefficient of 0.776. Lateral variations in size distribution were studied by dividing the front face of the Moon into 9 zones, each of which has at least 60 large craters abd follows approximately the physiography. The main variations are due to the maria and terrae distribution; however, differences in the terrae are also indicated. It is concluded that meteoritic impact can not offer all the answers to the origin of lunar craters. Either the craters are predominantly volcanic, or some endogenic control on the size of an impact crater exists.

Statistics of impact crater accumulation on the lunar surface exposed to a distribution of impacting bodies

The considerable amount of lunar crater statistics available contains much information about the origin and age of the Moon's features. In addition, these statistics can provide information concerning the relative importance of various erosion mechanisms. In this paper we have derived the statistical distribution of craters as a function of size and of the time of exposure of the surface to impacting bodies. As the time of exposure increases, the crater distribution which initially corresponds to the distribution of impacting bodies, approaches saturation, which does not reflect the distribution of impacting bodies for most cases. An equation has been derived for the distribution of secondary craters resulting from the formation of a primary crater. This allows us to take into account the effects of secondaries on the distribution of craters on the Moon. We find that secondaries do not contribute significantly to the “Moon-wide” statistics for craters larger than 100 meters. The distribution in the lunar highlands is found to be that of a crater-saturated surface. On the other hand, Mare Cognitum is not saturated. The distribution of craters appearing in the Ranger 7 photographs suggests an age of about 1.5 × 10 9 years which would make the maria younger than usually supposed. For the Martian surface we feel crater saturation may have occurred, indicating that meteoric impact is the most important erosion process operating on large-scale features. It has been suggested that the Martian craters indicate that the surface of Mars is old and little water or atmospheric erosion has occurred. Others have suggested that more craters should have been observed, which would indicate a young age and extensive water and/or atmospheric erosion. We feel the age of the surface is difficult to estimate in the case of crater saturation and little can be deduced concerning the importance of water or atmospheric erosion.

Distribution of Lunar craters according to morphology from Ranger VIII and IX photographs

A classification of the craters photographed by the Ranger VIII and IX missions into four categories according to relative sharpness shows that at diameters of 100 meters, the predominant craters have broad rims and low depth-diameter ratios and are partly covered with smaller craters which generally have sharper rims and higher depth-diameter ratios but include all classes. If competing processes of crater formation and destruction are responsible for the mix of crater types observed, an abrupt increase in the proportion of sharp craters suggests an intense episode of crater destruction to produce a smoothed surface that was subsequently recratered. Data comparable to those presented can readily be obtained from Lunar Orbiter photographs to determine if an increase in the proportion of sharp craters is present over more extensive areas and to test various cratering histories that may account for it.

Comments on 'Distribution of Craters on the Lunar Surface'

In a recent study of the distribution of centres of lunar craters, Fielder found two apparent anomalies which he used as arguments against the meteoroidal impact hypothesis for the origin of lunar craters. First of all, the Poisson distribution gave a very bad fit to the number of crater centres in equiareal sectors of the continents and the maria, especially among craters smaller than 40 kilometres in diameter. The second difficulty was a systematic excess in the number density of small craters in the western (trailing) half of the Moon. We will show that these observations could also have been expected even under the impact hypothesis, since the numbers of small and of large craters in a finite region are negatively correlated. Available crater statistics therefore neither preclude nor establish the impact or volcanic hypothesis for the origin or craters.

Origin of the Lunar Maria

THE hypothesis proposed by Kopal1 concerning the origin of the lunar maria is very interesting. However, it is important to note that the distribution of lunar craters on the Earth-turned hemisphere is far from uniform. There are significant, well-marked chains approximately aligned with the central meridian as seen from Earth; in the west (classical sense) the chain to which Vendelinus and Langrenus belong; near the centre, the Walter and the Ptolemaeus chains; in the east, the Grimaldi chain, and so on. The suggestion by Baldwin2, according to which the alignments are not real and are due to lighting effects, does not fit the facts. I have discussed this matter elsewhere3,4. Particularly important, however, is the conclusion that the well-formed maria fit in to the general pattern; it is difficult to avoid the conclusion that, for example, the Mare Crisium is simply a large member of the Vendelinus chain. To introduce a separate origin for the maria presupposes that they are of a nature basically different from that of the craters.

Tests for Randomness in the Distribution of Lunar Craters

Tests for Randomness in the Distribution of Lunar Craters

A stochastic model of the formation and survival of lunar craters: V. Approximate diameter distribution of primary and secondary craters

Approximate upper and lower bounds are obtained for the expected number density of lunar craters by means of a model which takes into account the formation of primary and secondary craters and the destruction of craters by obliteration and filling. Some numerical examples considered are relevant to primary and secondary craters formed by meteoroidal impacts. Predicted number densities are compared with crater-diameter distributions from photographs taken by the Ranger 7 spacecraft. The shape of the observed distribution is the same as that of the predicted distribution, but the observed density of small craters is about 15 times larger than that predicted by analogy with terrestrial explosion craters. If the observed excess in real, then either some primary craters produce an unusually large number of secondaries, or else many of the smaller lunar craters are of internal origin. The excess may be explained in part by incompleteness of secondary crater counts for terrestrial explosion craters upon which the model functions are based.

A stochastic model of the formation and survival of lunar craters: IV. On the nonrandomness of crater centers

It is shown that even if the underlying distribution of craters is completely random, the distribution of centers of observable craters is not. In particular, in finite regions in which a very large crater is found, we would expect to find a dearth of small craters, since the large crater would have obliterated older small craters in its neighborhood. The resulting distribution of the number of crater centers in equiareal regions of the lunar surface is then a mixture of Poisson distributions, and tests of randomness based on goodness of fit of this distribution to the Poisson distribution will not be accurate. Under the meteoroidal impact hypothesis, with disappearance of craters due to filling as well as obliteration, the coefficient of variation of density of small craters in regions of small size can be as large as 30%. This shows that large deviations from the Poisson distribution can be expected, even in homogeneous regions. Another source of variation in crater counts is the grouping together of inhomogeneous regions, for example, maria whose crater densities differ by a factor of 2 or 3. The resulting distribution of numbers of crater centers in equiareal sectors will again be a mixture of Poisson distributions. Empirical crater counts clearly show the negative correlation between density of small craters and the presence of large craters. Simulated plots of randomly formed craters are used to study the probability levels to be expected on applying the test of goodness to fit of the Poisson distribution. It is concluded that there is no reason to reject the hypothesis of randomness of formation of craters of large and moderate size.

Lunar crater distribution from the Ranger 7 photographs

In a recent letter, Miller [1965] presented a size-frequency distribution obtained from one of the Ranger 7 photographs. He found that N=35,800D−1.856 where N is the cumulative number of craters per 10 km2 having diameter greater than D meters. He explained that this represents a higher density than had been predicted earlier by McGillem and Miller [1962], who extrapolated over two or three orders of magnitude from earth-bound telescopic data, and he also suggested that the higher density was due to the formation of secondary craters on the moon. This letter is an attempt to extend his results.

Distribution of Craters on the Lunar Surface

Distribution of Craters on the Lunar Surface

Distribution of small lunar craters based on Ranger 7 photographs

A statistical study of lunar crater diameters was conducted by McGillem and Miller [1962]. Briefly, the study consisted of fitting a straight line of the form log N = log A + B log D to crater size-frequency data based on telescopically observable craters. In this expression N is the cumulative number of craters per unit area having diameter greater than D, and A and B are parameters determined by least squares regression. It was found that the value of B was in the vicinity of −;1.6 for both the maria and the highlands, whereas the value of A depended on the units used and the region considered. When N is the cumulative number of craters per 10 km2 having diameter greater than D meters, the distribution was found to be

Discussion of a paper by C. D. McGillem and B. P. Miller, ‘Lunar surface roughness from crater statistics’

In a recent paper McGillem and Miller [1962] arrive at crater frequencies on a scale of 1 to 100 meters by extrapolating statistical data compiled on the size distribution of craters in the range of sizes visible on lunar maps and photographs. They show that cumulative crater size distribution in the visible range of sizes may be approximated by the law N = AD−B where N is the number of craters having diameter greater than D, and A and B are constants. The coefficient A depends upon the total number of craters per unit area, varying from about 1400 for the maria to 30,000 for the highland regions when D is measured in kilometers and N is in craters per 106 km2. It is found, however, that the exponent B is reasonably independent of location on the lunar surface, having a value of 1.6.

Distribution and Origin of Lunar Craters

THE communication by McCall1 leads me to make some further comments. It is certainly true that the non-random distribution of the large craters is a serious and probably fatal objection to the impact hypothesis so far as the major formations are concerned, though no doubt many small meteoric craters exist. The Mare Crisium seems to be nothing more than an exceptionally large crater-like formation, and is a member of the great western chain which also includes Petavius and Langrenus, in which case it seems that the other circular-type maria are basically similar. Moreover, in the case where one crater breaks into another, the wall of the broken formaation is perfectly preserved up to the point of junction; Thebit is a good case. This could not be so were the second, younger crater produced by a violent impact. I directed attention to this in 19562, and the same point has since been made independently by Kopal and others.

Distribution and Origin of Lunar Craters

I HAVE elsewhere1 expressed agreement with Mr. Moore's view that the lack of shaking-down effects provides an important clue to the origin of lunar craters, and at the same time expressed my own view that the structure of the crater Porter is inexplicable in terms of explosive evisceration, a process which I have never favoured, though simple dish-craters in maria could be produced by a bubble-burst through a thin plastic veneer. The fact that craters appear to have been the product of slow and gentle processes does not, in my view, invalidate my hypothesis. Certainly the large craters stem from subsidence, and, as on Earth, the initiating upwards push may not necessarily have been explosive in every case. The blisters seen in some craters probably reflect gentle pressures without break-out. It remains possible that many of the large cirques were initiated by point-focus explosion, forming axial vents and confocal fractures, not craters. This seems most likely in the case of early structures, since, once fractured, the retaining crust would allow slow gas leakage rather than explosive discharge. It is interesting to note that at least one carbonatite complex reveals some evidence of a recessive stage involving cauldron subsidence2. Moore's suggestion of gentle uplift and subsidence, repeated several times, fits in well with patterns of history in terrestrial volcanic foci, but, as on Earth, one must expect no uniformity of detailed history, and I do not think point-focus explosion can be ruled out, entirely, because of the objection made.