Crater Data Research Articles

ELCD: Efficient Lunar Crater Detection Based on Attention Mechanisms and Multiscale Feature Fusion Networks from Digital Elevation Models

The detection and counting of lunar impact craters are crucial for the selection of detector landing sites and the estimation of the age of the Moon. However, traditional crater detection methods are based on machine learning and image processing technologies. These are inefficient for situations with different distributions, overlaps, and crater sizes, and most of them mainly focus on the accuracy of detection and ignore the efficiency. In this paper, we propose an efficient lunar crater detection (ELCD) algorithm based on a novel crater edge segmentation network (AFNet) to detect lunar craters from digital elevation model (DEM) data. First, in AFNet, a lightweight attention mechanism module is introduced to enhance the feature extract capabilities of networks, and a new multiscale feature fusion module is designed by fusing different multi-level feature maps to reduce the information loss of the output map. Then, considering the imbalance in the classification and the distributions of the crater data, an efficient crater edge segmentation loss function (CESL) is designed to improve the network optimization performance. Lastly, the crater positions are obtained from the network output map by the crater edge extraction (CEA) algorithm. The experiment was conducted on the PyTorch platform using two lunar crater catalogs to evaluate the ELCD. The experimental results show that ELCD has a superior detection accuracy and inference speed compared with other state-of-the-art crater detection algorithms. As with most crater detection models that use DEM data, some small craters may be considered to be noise that cannot be detected. The proposed algorithm can be used to improve the accuracy and speed of deep space probes in detecting candidate landing sites, and the discovery of new craters can increase the size of the original data set.

The Timing of Alluvial Fan Formation on Mars

Abstract The history of rivers on Mars is an important constraint on Martian climate evolution. The timing of relatively young, alluvial fan-forming rivers is especially important, as Mars’s Amazonian atmosphere is thought to have been too thin to consistently support surface liquid water. Previous regional studies suggested that alluvial fans formed primarily between the Early Hesperian and the Early Amazonian. In this study, we describe how a combination of a global impact crater database, a global geologic map, a global alluvial fan database, and statistical models can be used to estimate the timing of alluvial fan formation across Mars. Using our global approach and improved statistical modeling, we find that alluvial fan formation likely persisted into the last ∼2.5 Gyr, well into the Amazonian period. However, the data we analyzed were insufficient to place constraints on the duration of alluvial fan formation. Going forward, more crater data will enable tighter constraints on the parameters estimated in our models and thus further inform our understanding of Mars’s climate evolution.

An Improved Global Catalog of Lunar Impact Craters (≥1 km) With 3D Morphometric Information and Updates on Global Crater Analysis

AbstractImpact craters are common surface features on planetary surfaces. Their distribution offers important clues regarding geological and temporal processes on the Moon. Numerous endeavors have generated global catalogs of lunar craters; however, most of the existing catalogs only contain large craters (larger than several kilometers in diameter), and none of them offer three‐dimensional (3D) morphometric information. In this study, we first present a machine‐learning approach for automatic crater detection from digital elevation models (DEMs). Our crater detection approach can achieve a detection rate of about 85%. We also present an approach for extracting 3D morphometric information of craters based on the topography. These approaches were applied to producing a global crater data set covering the entire lunar surface that includes approximately 1.32 million craters (≥1 km). Verification was performed against previously published catalogs (Head et al., 2010, https://doi.org/10.1126/science.1195050; Robbins, 2019, https://doi.org/10.1029/2018je005592), with about 23% of our craters transferred from the previous catalogs after a rim‐fitting process. The crater catalog includes 3D morphometric data on the craters such as depths. Global analyses of craters based on this improved catalog indicate that the lunar mare and highlands have distinctive crater density differences of small craters (1–5 km). Craters of 2.5–5 km have reached saturation in several local regions in the highlands. Small craters (1–5 km) on the lunar mare are deeper than those on the highlands. The data in our comprehensive crater catalog can support various other lunar scientific studies.

Studying the Global Spatial Randomness of Impact Craters on Mercury, Venus, and the Moon With Geodesic Neighborhood Relationships

AbstractImpact crater records on planetary surfaces are often analyzed for their spatial randomness. Generalized approaches such as the mean second closest neighbor distance (M2CND) and standard deviation of adjacent area (SDAA) are available via a software tool but do not take the influence of the planetary curvature into account in the current implementation. As a result, the measurements are affected by map distortion effects and can lead to wrong interpretations. This is particularly critical for investigations of global data sets as the level of distortion typically increases with increasing distance from the map projection center. Therefore, we present geodesic solutions to the M2CND and SDAA statistics that can be implemented in future software tools. We apply the improved methods to conduct spatial randomness analyses on global crater data sets on Mercury, Venus, and the Moon and compare the results to known crater population variations and surface evolution scenarios. On Mercury, we find that the emplacement of smooth plain deposits strongly contributed to a global clustering of craters and that a random distribution of Mercury's basins is not rejected. On Venus, the randomness analyses show that craters are largely randomly distributed across all sizes but where local nonrandom distributions due to lower crater densities in regions of recent volcanic activity may appear. On the Moon, the global clustering of craters is more pronounced than on Mercury due to mare volcanism and the Orientale impact event. Furthermore, a random distribution of lunar basins is not rejected.

LUNAR TERRAIN RECONSTRUCTION FROM MULTI-VIEW LROC NAC IMAGES BASED ON SEMI-GLOBAL MATCHING IN OBJECT SPACE

Abstract. Most of the lunar surface area has been observed from different viewing conditions thanks to the on-orbit work of lunar orbiters, a large amount of images are available for photogrammetric three-dimensional mapping, which is an important issue for lunar exploration. Theoretically, multi-view images contain more information than a single stereo pair and can get better 3D mapping results. In this paper, the semi-global matching method is applied to the object space, and the steps of cost calculation, cost aggregation, and elevation calculation are performed to obtain the three-dimensional coordinates directly. Compared with the traditional image-based semi-global matching method, the object-based semi-global method is more easily extended to multi-view images, which is beneficial for applying multi-view image information. In addition, it does not require steps such as stereo rectification and forward intersection, that is, the overall pipeline is more elegant. Using the LRO NAC images covering Apollo 11 landing area as the experimental data, the result shows that the object-based semi-global matching is competent for the multi-view image matching and the multi-view image result achieves higher accuracy and more details than the single stereo pair. Furthermore, the experimental results of Zhinyu crater data show that this method can also alleviate the uncertainty of the lunar orbiter's positioning to some extent.

Giordano Bruno: Small crater populations––Implications for self-secondary cratering

Giordano Bruno is a lunar farside Copernican-age crater. The relatively few superposed impact craters on its floor and ejecta blanket and extensive bright rays indicate its youth. High-resolution Lunar Reconnaissance Orbiter Camera images reveal that the frequency and the characteristics of the cumulative size-frequency distributions of the small-diameter impact craters and their morphology vary across the clastic ejecta and impact melt covered surfaces. Crater frequencies (N(10) defined as ≥10 m km−2) vary by a factor of 10 s–100 s (N(10) 2–700) across the ejecta blanket, and between the ejecta and the melt deposits. Numerous craters on the ejecta blanket are degraded and buried by debris and impact melt, indicating that these partially buried craters formed during the deposition of the ejecta and prior to or during the emplacement of the impact melt. From geologic relations and crater statistics we conclude that a significant fraction of the craters observed on the ejecta blanket and the melt were formed during the cratering process itself and represent "self-secondaries." Further, we conclude that these craters do not represent an extra-lunar primary impact production population. Self-secondary craters are formed by material launched into near-vertical trajectories and having velocities such that their flight time is sufficiently long that the bulk of the clastic ejecta and impact melt are deposited before that material impacts the surface. The presence of a significant number of self-secondary craters on the ejecta makes the determination of relative and absolute age dates problematic. Crater counts would indicate an inappropriately old age. Using data for craters on the melt surfaces and for small-diameter bright ejecta craters, an absolute model age of 1 Ma is estimated. This age is considerably younger than that estimated by other studies and probably represents a maximum age.

Revised recommended methods for analyzing crater size‐frequency distributions

AbstractImpact crater populations help us to understand solar system dynamics, planetary surface histories, and surface modification processes. A single previous effort to standardize how crater data are displayed in graphs, tables, and archives was in a 1978 NASA report by the Crater Analysis Techniques Working Group, published in 1979 in Icarus. The report had a significant lasting effect, but later decades brought major advances in statistical and computer sciences while the crater field has remained fairly stagnant. In this new work, we revisit the fundamental techniques for displaying and analyzing crater population data and demonstrate better statistical methods that can be used. Specifically, we address (1) how crater size‐frequency distributions (SFDs) are constructed, (2) how error bars are assigned to SFDs, and (3) how SFDs are fit to power‐laws and other models. We show how the new methods yield results similar to those of previous techniques in that the SFDs have familiar shapes but better account for multiple sources of uncertainty. We also recommend graphic, display, and archiving methods that reflect computers’ capabilities and fulfill NASA's current requirements for Data Management Plans.

Problem of lunar mascons: An alternative approach

The origin of lunar mascons is discussed on the base of results of the orbital experimental exploration of the Moon by the Gravity Recovery and Interior Laboratory and the Lunar Reconnaissance Orbiter missions. We lead the discussion on the basis of representations of Galactocentric paradigm which links processes in the Solar System and on its planets with the Galaxy influences. The article describes a new approach to the interpretation of the crater data, which takes into account the quasi-periodic bombardments of the Moon by galactic comets. We present a preliminary evaluation of the age of mascons as well as of craters and mares on the Moon based on this approach.

The Moon Zoo citizen science project: Preliminary results for the Apollo 17 landing site

Moon Zoo is a citizen science project that utilises internet crowd-sourcing techniques. Moon Zoo users are asked to review high spatial resolution images from the Lunar Reconnaissance Orbiter Camera (LROC), onboard NASA's LRO spacecraft, and perform characterisation such as measuring impact crater sizes and identify morphological 'features of interest'. The tasks are designed to address issues in lunar science and to aid future exploration of the Moon. We have tested various methodologies and parameters therein to interrogate and reduce the Moon Zoo crater location and size dataset against a validated expert survey. We chose the Apollo 17 region as a test area since it offers a broad range of cratered terrains, including secondary-rich areas, older maria, and uplands. The assessment involved parallel testing in three key areas: (1) filtering of data to remove problematic mark-ups; (2) clustering methods of multiple notations per crater; and (3) derivation of alternative crater degradation indices, based on the statistical variability of multiple notations and the smoothness of local image structures. We compared different combinations of methods and parameters and assessed correlations between resulting crater summaries and the expert census.We derived the optimal data reduction steps and settings of the existing Moon Zoo crater data to agree with the expert census. Further, the regolith depth and crater degradation states derived from the data are also found to be in broad agreement with other estimates for the Apollo 17 region. Our study supports the validity of this citizen science project but also recommends improvements in key elements of the data acquisition planning and production.

Zumba crater, Daedalia Planum, Mars: Geologic investigation of a young, rayed impact crater and its secondary field

Zumba is a ∼2.9km diameter rayed crater on Mars located on extensive lava plains in Daedalia Planum to the southwest of Arsia Mons. It is a well-preserved young crater with large ejecta rays that extend for hundreds of kilometers from the impact site. The rays are thermally distinct from the background lava flows in THEMIS daytime and nighttime thermal infrared data, a unique characteristic among martian rayed craters. Concentrated within the rays are solitary or dense clusters of secondary craters with associated diffuse dark-toned deposits along with fewer secondary craters lacking dark-toned deposits. Using CTX images, we have mapped secondary craters with dark-toned deposits, collectively termed “secondary fields”, to investigate their distribution as a function of distance from the impact site. The mapped secondary field was then used to investigate various aspects of the crater-forming event such as the surface angle and direction of the projectile, the effect of secondary craters on surface age estimates, and the number of secondary craters produced by the impact event. From our mapping, a total of 13,064 secondary fields were documented out to a 200km radial distance beyond a 15km-wide non-secondary zone around Zumba crater. Results show that the highest areal coverage of secondary fields occurs within 100km of Zumba and within its rays, decreasing radially with distance to a background scattering of small secondary fields that are <10km2 in size (∼91.9% of the total population). The strong east–west asymmetry of crater rays and low areal coverage of fields to the south of Zumba correlate well with studies of Zumba impact melt deposits, indicating a moderately oblique impact projectile coming from the south. Using primary craters in a ∼101km2 sample region and all craters (primaries and secondaries) from 43 select secondary fields in two map sectors in the study area, we obtain ages of ∼580±100Ma and ∼650±70Ma, respectively, for the lava flows into which Zumba impacted. These ages are consistent with and intermediate to 0.1–1Ga volcanic flow units within and near Daedalia Planum. For craters within the secondary fields, a log differential plot of the data shows a pronounced downward deflection of the binned points for craters <100m in diameter. This is an indication that possible aeolian erosion and deposition, in combination with emplacement and remobilization of Zumba ejecta, have modified the lava flow surfaces in Daedalia Planum over time. Our crater count results also show that even in the presence of large numbers of secondary craters, the age of the primary crater surface can still be identified from the data for craters >100m. We estimate that ∼352,000 secondary craters were produced by the Zumba impact event.

Issue Information

Cover. Evolving and increasingly hazardous radiation levels in space. (top) ACE dose rates (red) are based on fits to CRIS spectra [O'Neill, 2006]; CRaTER measurements (green) from the zenith‐facing D1/D2 detectors are used as proxies for lens dose rates behind 0.3 g/cm2 Al shielding Schwadron et al. [2012]. The sunspot number predictions (the lower black and blue dashed lines) show two cases based on a Gleissberg‐like and a Dalton‐like minimum, the results of which are similar. The dose predictions (solid blue line and the upper black and blue dashed lines) are from a sunspot‐based model of the heliospheric magnetic field and the correlated variation in modulation of GCRs. The ACE data, CRaTER data, and model results are projected to the lunar surface. (bottom) Same as the top panel, but for a longer time span. See pp. 622–632.

Dark matter as a trigger for periodic comet impacts.

Although statistical evidence is not overwhelming, possible support for an approximately 35×106 yr periodicity in the crater record on Earth could indicate a nonrandom underlying enhancement of meteorite impacts at regular intervals. A proposed explanation in terms of tidal effects on Oort cloud comet perturbations as the Solar System passes through the galactic midplane is hampered by lack of an underlying cause for sufficiently enhanced gravitational effects over a sufficiently short time interval and by the time frame between such possible enhancements. We show that a smooth dark disk in the galactic midplane would address both these issues and create a periodic enhancement of the sort that has potentially been observed. Such a disk is motivated by a novel dark matter component with dissipative cooling that we considered in earlier work. We show how to evaluate the statistical evidence for periodicity by input of appropriate measured priors from the galactic model, justifying or ruling out periodic cratering with more confidence than by evaluating the data without an underlying model. We find that, marginalizing over astrophysical uncertainties, the likelihood ratio for such a model relative to one with a constant cratering rate is 3.0, which moderately favors the dark disk model. Our analysis furthermore yields a posterior distribution that, based on current crater data, singles out a dark matter disk surface density of approximately 10M⊙/pc2. The geological record thereby motivates a particular model of dark matter that will be probed in the near future.

Distribution of Early, Middle, and Late Noachian cratered surfaces in the Martian highlands: Implications for resurfacing events and processes

Most of the geomorphic changes on Mars occurred during the Noachian Period, when the rates of impact crater degradation and valley network incision were highest. Fluvial erosion around the Noachian/Hesperian transition is better constrained than the longer‐term landscape evolution throughout the Noachian Period, when the highland intercrater geomorphic surfaces developed. We interpret highland resurfacing events and processes using a new global geologic map of Mars (at 1:20,000,000 scale), a crater data set that is complete down to 1 km in diameter, and Mars Orbiter Laser Altimeter topography. The Early Noachian highland (eNh) unit is nearly saturated with craters of 32–128 km diameter, the Middle Noachian highland (mNh) unit has a resurfacing age of ~4 Ga, and the Late Noachian highland unit (lNh) includes younger composite surfaces of basin fill and partially buried cratered terrain. These units have statistically distinct ages, and their distribution varies with elevation. The eNh unit is concentrated in the high‐standing Hellas basin annulus and in highland terrain that was thinly mantled by basin ejecta near 180° longitude. The mNh unit includes most of Arabia Terra, the Argyre vicinity, highland plateau areas between eNh outcrops, and the Thaumasia range. The lNh unit mostly occurs within highland basins. Crater depth/diameter ratios do not vary strongly between the eNh and mNh units, although crater losses to Noachian resurfacing appear greater in lower lying areas. Noachian resurfacing was spatially non‐uniform, long‐lived, and gravity‐driven, more consistent with arid‐zone fluvial and aeolian erosion and volcanism than with air fall mantling or mass wasting.

Correlating multispectral imaging and compositional data from the Mars Exploration Rovers and implications for Mars Science Laboratory

In an effort to infer compositional information about distant targets based on multispectral imaging data, we investigated methods of relating Mars Exploration Rover (MER) Pancam multispectral remote sensing observations to in situ alpha particle X-ray spectrometer (APXS)-derived elemental abundances and Mössbauer (MB)-derived abundances of Fe-bearing phases at the MER field sites in Gusev crater and Meridiani Planum. The majority of the partial correlation coefficients between these data sets were not statistically significant. Restricting the targets to those that were abraded by the rock abrasion tool (RAT) led to improved Pearson’s correlations, most notably between the red–blue ratio (673nm/434nm) and Fe3+-bearing phases, but partial correlations were not statistically significant. Partial Least Squares (PLS) calculations relating Pancam 11-color visible to near-IR (VNIR; ∼400–1000nm) “spectra” to APXS and Mössbauer element or mineral abundances showed generally poor performance, although the presence of compositional outliers led to improved PLS results for data from Meridiani. When the Meridiani PLS model for pyroxene was tested by predicting the pyroxene content of Gusev targets, the results were poor, indicating that the PLS models for Meridiani are not applicable to data from other sites. Soft Independent Modeling of Class Analogy (SIMCA) classification of Gusev crater data showed mixed results. Of the 24 Gusev test regions of interest (ROIs) with known classes, 11 had >30% of the pixels in the ROI classified correctly, while others were mis-classified or unclassified. k-Means clustering of APXS and Mössbauer data was used to assign Meridiani targets to compositional classes. The clustering-derived classes corresponded to meaningful geologic and/or color unit differences, and SIMCA classification using these classes was somewhat successful, with >30% of pixels correctly classified in 9 of the 11 ROIs with known classes.This work shows that the relationship between SWIR multispectral imaging data and APXS- and Mössbauer-derived composition/mineralogy is often weak, a perhaps not entirely unexpected result given the different surface sampling depths of SWIR imaging (uppermost few microns) vs. APXS (tens of μm) and MB measurements (hundreds of μm). Results from the upcoming Mars Science Laboratory (MSL) rover’s ChemCam Laser Induced Breakdown Spectroscopy (LIBS) instrument may show a closer relationship to Mastcam SWIR multispectral observations, however, because the initial laser shots onto a target will analyze only the upper few micrometers of the surface. The clustering and classification methods used in this study can be applied to any data set to formalize the definition of classes and identify targets that do not fit in previously defined classes.

A new global database of Mars impact craters ≥1 km: 2. Global crater properties and regional variations of the simple‐to‐complex transition diameter

We have generated a new, 384,343‐entry global crater database of Mars, statistically complete for craters with diameters D ≥ 1 km. In this release, the database contains detailed morphologic and morphometric data for craters D ≥ 3 km (future releases will extend these to smaller diameters). With detailed topographic data for the largest crater database to‐date, we analyzed crater depth‐to‐diameter ratios for simple and complex morphologies across various terrains and for the planet as a whole and investigated the simple‐to‐complex morphology transition. Our results are similar to those in the published literature, but we found a substantial terrain dependence of the simple‐to‐complex transition that occurs at ∼11‐km‐diameter craters at high latitudes. This suggests a model that requires melting of volatiles during high‐latitude crater formation that fill the crater during the modification phase but will still support the simple morphology to larger diameters. We also use this database to reexamine previously observed distributions and patterns to show its fidelity and to further explore other global relationships of fresh craters, those with central peaks, pits, and summit pits. We present the global distribution of craters with different types of ejecta and morphometric properties. Overall, this database is shown to be comparable to previous databases where there is overlap and to be useful in extending prior work into new regimes.

Patterns of accumulation and flow of ice in the mid-latitudes of Mars during the Amazonian

Evidence has accumulated that non-polar portions of Mars have undergone significant periods of glaciation during the Amazonian Period. This evidence includes tropical mountain glacial deposits, lobate debris aprons, lineated valley fill, concentric crater fill, pedestal craters, and related landforms, some of which suggest that ice thicknesses exceeded a kilometer in many places. In some places, several lines of evidence suggest that ice is still preserved today in the form of relict debris-coved glaciers. The vast majority of deposit morphologies are analogous to those seen in cold-based glacial deposits on Earth, suggesting that little melting has taken place. Although these features have been broadly recognized, and their modes of ice accumulation and flow analyzed at several scales, they have not been analyzed and well-characterized globally despite their significance for understanding the evolution of the martian climate. A major outstanding question is the global extent of accumulation and flow of ice during periods of non-polar glaciation: As a mechanism to address this question, we outline two end-member scenarios to provide a framework for further discussion and analysis: (1) ice accumulation was mainly focused within individual craters and valleys and flow was largely local to regional in scale, and (2) ice accumulation was dominated by global latitudinal scale cold-based ice sheets, similar in scale to the Laurentide continental ice sheets on Earth. In order to assess these end members, we conducted a survey of ice-related features seen in Context Camera (CTX) images in each hemisphere and mapped evidence for flow directions within well-preserved craters in an effort to decipher orientation preferences that could help distinguish between these two hypotheses: regional/hemispheric glaciation or local accumulation and flow. These new crater data reveal a latitudinal-dependence on flow direction: at low latitudes in each hemisphere (<40–45°) cold, pole-facing slopes are strongly preferred sites for ice accumulation, while at higher latitudes (>40–45°), slopes of all orientations show signs of ice accumulation and ice-related flow. This latitudinal onset of concentric flow of ice within craters in each hemisphere correlates directly with the lowest latitudes at which typical pedestal craters have been mapped. Taken together, these observations demarcate an important latitudinal boundary that partitions each hemisphere into two zones: (1) poleward of ∼45°, where net accumulation of ice is interpreted to have occurred on all surfaces, and (2) equatorward of ∼45°, where net accumulation of ice occurred predominantly on pole-facing slopes. These results provide important constraints for deciphering the climatic conditions that characterized Mars during periods of extensive Amazonian non-polar glaciation.

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 Cassini ISS 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.

Detection of real periodicity in the terrestrial impact crater record: quantity and quality requirements

Aims. To determine the quantity and quality requirements for the terrestrial impact crater data which would allow reliable detection of real periodicity. Methods. Artificial impact crater data samples of different size and accuracy are simulated. Erosion is considered, as well as the effect of the unknown ratio between periodic and aperiodic impacts. The probabilities for detecting real and false periodicities are solved with the Rayleigh test from these simulated data. Results. Reliable detection of real periodicity is currently impossible – unless all impacts on Earth have been periodic.

The origin of Patom Crater, East Siberia, from geological and geochemical data

A multidisciplinary expedition of geologists‐ geochemists, geophysicists, and astronomers studied Patom Crater in Bodaibo District, north of Irkutsk oblast, in 2006. This paper presents new geological and geochemical data evidencing an endogenous origin of the crater. As was discovered, it represents a central ring structure with a cone of clastic material of limestone and other rocks. The structure appeared to have a zoned pattern created by consequent formation of early stage ring swell, late stage ring swell, ring trench, and central mound. Hence, it took quite some time to form Patom Crater, and it could not have been produced by a single event like meteorite collapse. The whole amount of analyzed stone samples within and around the crater gives no evidence of meteorite substance or any geochemical anomalies that could be related to it. Hypogene fluids and gases played important role in the formation of Patom Crater affecting the rocks of the cone. Along with oxidized fluids (H 2 O and CO 2 ), some reduced gases (CO, H 2 ) were found in the rocks of the crater. This points to a quite deep source of fluids. Patom Crater is not meteoritic, but was formed by endogenous processes, the most important being an outbreak of fluid substance from great depth, which led to the formation of a clastic cone.

The first new application of the Mathematical Theory of Stochastic Processes to lunar and planetary science: Topography-Profile Diagrams of Mars

The Mathematical Statistics Theory (MST) and the Mathematical Theory of Stochastic Processes (MTSP) are different branches of the more general Mathematical Probability Theory (MPT) that can be used to investigate physical processes through mathematics. Each model of a stochastic process, according to MTSP, can provide one or more interpretations in the MST domain. A large body of work on impact crater statistics according to MST exists, showing cumulative crater frequency (N km −2) as a function of age (years) for some particular crater diameter. However, this is only one possible representation in the MST domain of the bombardment of the planetary surface modeled as a stochastic process according to MTSP. The idea that other representations are possible in the MST domain of the same stochastic process from MTSP has been recently presented. The importance of the approach is that each such mathematical-based interpretation can provide a large amount of new information. Coupled with MOLA data, Topography-Profile Diagrams (TPD) are one of the many examples that can provide a large amount of new information regarding the history of Mars. TPD consists of: (1) Topography-Profile Curve (TPC), which is a representation of the planet’s topography, (2) Density-of-Craters Curve (DCC), which represents density of craters, (3) Filtered-DCC (FDCC), which represents DCC filtered by a low-pass filter, included with the purpose of reducing the noise, and (4) Level-of-Substance-Over-Time Curve (LSOTC), which represents interpretation of the influence on the distribution of craters shown by FDCC. TPC uniquely corresponds to the computation of TPD, whereas DCC depends on algorithms for computing the elevation of each crater according to the topography, center coordinates, and radius of impact crater, and FDCC relies on the architecture of the custom designed low-pass filter for filtering DCC. However, all variations of DCC and FDCC, which includes the various impact crater data sets, showed a correlation among the density of craters and elevation over 70–80% of the planet surface. Additionally, if we assume that the ocean primarily caused the noted correlation, LSOTC offers a mathematical approach for estimating topographic change of the ocean’s extent over time. Accordingly, TPD is the first new practical application of MTSP to lunar and planetary sciences, showing correlation of topography to a physical process.