Crater Model Research Articles

Thorium distribution on the Moon: new insights from Chang’E-2 gamma-ray spectrometer**A contributed paper from the International Symposium on Lunar and Planetary Science (ISLPS) held on 2018 June 12–15 at Macau University of Science and Technology.

We present the thorium distribution on the lunar surface derived from observations by the Chang’E-2 gamma-ray spectrometer (CE-2 GRS). This new map shows a similar thorium distribution to previous observations. In combination with this new thorium map and impact cratering model, we investigate the origination of thorium on the Moon’s highlands, which was previously thought to be contributed from Imbrium ejecta. We found that the Imbrium ejecta has a small contribution (∼20%–30%) to the thorium on the lunar highlands but most thorium is likely to be indigenous before the deposition of the Imbrium ejecta. This new thorium map also confirms that the eastern highlands have a relatively higher thorium concentration than the western highlands. We propose that the thin crust and large basins on the eastern highlands are responsible for this difference in thorium.

Simulation and inversion of harmonic infrasound from open-vent volcanoes using an efficient quasi-1D crater model

Volcanic activity excites low frequency acoustic waves, termed infrasound, in the atmosphere. Infrasound observations can be used to provide constraints on eruption properties, such as crater geometry and volume flux. At open-vent volcanoes, such as Erebus (Antarctica) and Villarrica (Chile), the infrasound signal is modulated by the crater properties. Eruptive activity at the bottom of the crater, such as unsteady degassing or explosions, can excite the air mass within the crater into resonance leading to infrasound generation with signals possessing clear spectral peaks, termed harmonics. Therefore, the effect of the crater on the infrasound signal, or crater acoustic response, must be accounted for when inverting harmonic infrasound observations for eruption properties at open-vent volcanoes. Here we develop a linearized model of quasi-one-dimensional (1D) wave propagation inside volcanic crater coupled with 3D axisymmetric radiation into the atmosphere from the crater, with waves generated by a volumetric flow rate source at the bottom of the crater. We perform simulations for a range of volcanic crater geometries, temperature profiles, gas compositions, and source descriptions to explore the influence of these properties on the infrasound signal. The observed infrasound signal depends on the flow rate source-time function, but interference of up- and down-going waves within the crater selectively amplifies the signal at the resonant frequencies of the crater. The crater resonance model presented here is verified by comparison with an established three-dimensional (3D) infrasound code and is shown to be appropriate for realistic crater geometries when the crater radius is less than approximately one quarter of the acoustic wavelength. The model presented here is more computationally efficient and can be used to invert infrasound observations for a range of properties, such as crater geometry or volumetric flow rate associated with eruptions. We demonstrate the utility of our efficient modeling framework by inverting harmonic infrasound observations for the crater geometry and position of the lava lake at Villarrica volcano. This technique may be used at other open-vent volcanoes to constrain dynamic crater geometry and provide insights about lava lake motions and infrasound producing eruption sources.

Numerical simulation of effective solar irradiance and temperatures at simple crater of lunar dayside

Solar radiation plays an important part in lunar surface thermal environment. The topographic effect was usually ignored in previous work, which might cause great uncertainties in surface temperature simulation. To better understand the surface temperatures of the craters at any time and on any location of the Moon, we simulated the effective solar irradiance and temperatures of the Banting crater as an example. In this work, we firstly constructed a three-dimensional Banting crater (16.4$^\circ$E, 26.6$^\circ$N) model based on the elevation data obtained from the Lunar Orbiter Laser Altimeter onboard Lunar Reconnaissance Orbiter (LRO), and then calculated the distribution of the effective solar irradiance at different local times. In addition, we calculated the distribution of percentage of illuminated area of the Banting-like craters at any day time and on all locations of the Moon. These results show that the craters located within 48.2$^\circ$N/S and at the time of 08:48–15:12 are illuminated without any self-shading, while that located at high latitudes or near to dawn/dusk endure different degrees of the self-shading effect. Finally, we simulated the temperatures of the Banting crater at different local times based on the surface radiation balance. Compared to the temperatures measured by Diviner aboard LRO, the results show that the simulated temperatures are well consistent with the Diviner observations, which verified our models and simulation results.

In search of historical roots of the meteorite impact theory: Franz von Paula Gruithuisen as the first proponent of an impact cratering model for the Moon in the 1820s

AbstractFranz von Paula Gruithuisen (1774–1852), the Bavarian medic, physician, and astronomer, enfant terrible of German science, is known for his insightful observations and many extravagant conceptions. However, since the seminal monograph of Baldwin (1949), he is also referenced for early contributions to the meteoritic origin concept of lunar craters. His most commonly cited paper of 1828 is analyzed here for the first time in some detail. For Gruithuisen, impact phenomena were only an outcome of a more general cosmogenic theory, which assumed planet and satellite growth by concentric shell‐like coalescence of the cosmic bodies. The aggregation theory thus defined was initiated in 1794 by Chladni, developed by the Bierberstein brothers and Anton Zach. Gruithuisen was notably the first person to formulate a nascent concept of lunar crater mechanics. This cratering process, as he thought, is based on an uneven gravitational subsidence of concentrically layered spherical impactors (=the solid core of comet) into the plastic sediments. Only the more resistant and heavy central portion of the body was submerging deeper, and therefore, the circular terrace‐like rim of the ring mountains was formed. Gruithuisen tried also to recognize terrestrial equivalents of large‐scale crater‐like mountains on the Moon, and speculated on other impact consequences, such as a catastrophic influence on the history of the biosphere and a cometary source of the terrestrial hydrosphere. These ideas found several conceptual followers in the vital German science of the last decades of 19th century. Thus, despite principal errors in the gravitationally penetrative cratering model, we confirm the claim of recognition of Gruithuisen as one of the founders of the impact hypothesis.

Malvinas (Falkland) Plateau structure versus Mjølnir crater: Geophysical workflow template for proposed marine impact craters

AbstractA diagnostic geophysical‐based template, supported by modelling, is suggested to be used prior to, or in combination with geological/drilling data, when proposing a marine impact crater. The latter refers to impacts occurring in a marine setting and resulting in structures that are currently partially or totally underwater. The methodology is based on the well‐documented Mjølnir crater in the Barents Sea. The template has been developed in conjunction with the recently proposed and debated impact crater on the Malvinas (Falkland) Plateau in the South Atlantic. Despite their different sizes, their comparison adds to the ambiguous nature of the Malvinas structure and shows that the integrated analysis of seismic and potential field data and modelling is crucial for any interpretation of a marine impact crater without relevant geological information. The proposed workflow template utilizes all available geophysical data and is composed of a series of iterative steps, including a range of alternative nonimpact interpretations that must be discussed and accounted for. Subsequently, further iterative geophysical modelling is required to support and decipher the impact related processes. A more complex impact crater model and additional impact crater features can be resolved by physical property modelling. In all cases, a close spatial correspondence of the defined impact structure with potential field anomalies is a necessity to establish a causal relationship. We suggest that the diagnostic workflow template provides a methodology to be applied to future studies of the Malvinas structure, as well as to proposed marine (and, with minor adaptions, to nonmarine) impact craters in general.

Single crater-aided inertial navigation for autonomous asteroid landing

In this paper, a novel crater-aided inertial navigation approach for autonomous asteroid landing mission is developed. It overcomes the major deficiencies of existing approaches in the literature, which mainly focuses on the case where craters are abundant in the camera field of view. As a result, traditional crater based methods require at least three craters to achieve crater matching, which limits their application in final landing phase where craters are scarce in the camera’s field of view. In contrast, the proposed algorithm enables single crater based crater matching based on a novel 2D-3D crater re-projection model. The re-projection model adopts inertial measurements as a reference, and re-projects the 3D crater model onto descent images to achieve the matching to its counterpart. An asteroid landing simulation toolbox is developed to validate the performance of the proposed approach. Through comparison with the state-of-the-art local image feature and crater based navigation algorithms, the proposed approach is validated to achieve a competitive performance in terms of feature matching and pose estimation accuracy with a much lighter computational cost.

A novel crater recognition based visual navigation approach for asteroid precise pin-point landing

This paper proposes a novel terrain-relative navigation (TRN) approach for the asteroid pin-point landing mission. The key concept is encapsulating efficient crater matching with active LiDAR ranging. Importantly, a novel crater to 3D crater model matching approach is proposed. Then, the line-of-sight from lander to crater is employed to guide the LiDAR ranging, and parameters of the matched 3D crater model is efficiently fused with LiDAR ranging to compensate its measurement, resulting in the robustness against the variation of terrain relief. In addition, a crater selection mechanism is proposed to reduce the estimation uncertainty. Monte Carlo simulation results show that the proposed approach is able to provide an adequate navigation performance under a high terrain relief, which is an evident improvement over the traditional methods.

On critical observations that constrain models of terrestrial hypervelocity impact craters

AbstractImpact structures in the crystalline rocks of the Canadian Shield range over two orders of magnitude in size and display morphologies recognized elsewhere in the solar system. This contribution draws upon new examinations of drill core from Canadian craters to reaffirm some relationships, modify others, and refine the transitions from simple to complex with central peak to peak‐ring structures. These include recognizing the hyperbolic form of transient craters, sharpening the allochthon–parautochthon distinction, and proposing new formulae for key relationships. It emphasizes the role of dynamic tensile strength and the attenuation of tensile rarefaction waves in determining the size of both transient and final crater dimensions. On Earth, depth (d) to diameter (D) ratios are not invariant at about 1:10 but change smoothly with size from 1:3 at Brent through 1:5 to 1:10 in the largest; that is, d = 0.4 D0.75. In craters in crystalline rocks, the central peak grows at about uplift = 0.175 D until, at D about 28 km, the uplift rises above the original surface then collapses to form a peak‐ring structure. These relationships demonstrate the dominant role of gravity in attenuating tensile rarefaction waves and controlling transient crater depth and overall size relative to the volume shocked.

Underground parallel pipelines domino effect: An analysis based on pipeline crater models and historical accidents

This paper focuses on the analysis of the possibility of domino effect in underground parallel pipelines relying on historical accident data and pipeline crater models. An underground pipeline can be considered as safe following an accident with an adjacent gas or liquefied pipeline when it remains outside the ground crater generated. In order to prevent the domino effect in these cases, the design of parallel pipelines has to consider adequate pipeline separations based on the crater width, which is one of the widely used methods in engineering applications. The objective of this work is the analysis of underground petroleum product pipelines ruptures with the formation of a ground crater as well as the evaluation of possible domino effects in these cases. A detailed literature survey has been carried out to review existing crater models along with a historical analysis of past accidents. A FORTRAN code has been implemented to assess the performance of the Gasunie, the Batelle and the Advantica crater models. In addition to this, a novel Accident-Based crater model has been presented, which allows the prediction of the crater width as a function of the relevant design pipeline parameters as well as the soil density. Modifications have also been made to the Batelle and Accident-Based models in order to overcome the underestimation of the crater width. The calculated crater widths have been compared with real accident data and the performance evaluation showed that the proposed Accident-Based model has a better performance compared to other models studied in this work. The analysis of forty-eight past accidents indicated a major potential of underground parallel pipelines domino effect which is proven by two real cases taken from the literature. Relying on the investigated accidents, the crater width was smaller than or equal to 20 m in most cases indicating that the definition of underground pipeline separations at around 10 m would be sufficient to ensure a small probability of the domino effect.

Planetary surface dating from crater size-frequency distribution measurements: Poisson timing analysis

The predictions of crater chronology models have customarily been evaluated by dividing a crater population into discrete diameter intervals, plotting the crater density for each, and finding a best-fit model isochron, with the uncertainty in the procedure being assessed using 1/√n estimates, where n is the number of craters in an interval. This approach yields an approximate evaluation of the model predictions. The approximation is good until n becomes small, hence the often-posed question: what is the minimum number of craters for an adequate prediction? This work introduces an approach for exact evaluation of a crater chronology model using Poisson statistics and Bayesian inference, expressing the result as a likelihood function with an intrinsic uncertainty. We demonstrate that even in the case of no craters at all, a meaningful likelihood function can be obtained. Thus there is no required minimum count: there is only varying uncertainty, which can be well described. We recommend that the Poisson timing analysis should be preferred over binning/best-fit approaches. Additionally, we introduce a new notation to make it consistently clear that crater chronology model calibration errors are inseparable from stated crater model ages and their associated statistical errors.

Characterization and geometric modeling of single and overlapping craters in micro-EDM

ABSTRACTIn the micro-electro discharge machining (micro-EDM) process the machined surface consists of tiny overlapping craters. The shape of the crater has significant influence on the characteristics of the machined surface. However, existing models on crater shapes generally do not represent characteristic features of the craters, such as the bulging rim around the crater and the asymmetrical bowl-shape. In this study, experiments were conducted to examine three-dimensional (3D) geometrical features of craters in micro-EDM. Based on the experimental data, a geometric model of craters is proposed to better represent and understand the 3D shapes of single craters. A uniform model and a more realistic nonuniform model of crater geometry are developed, taking into account the bulging rim and the asymmetrical shape in craters. Furthermore, a method of constructing overlapping craters using nonuniform models of single craters is proposed and presented. This method is capable of representing major geometrical features of actual crater clusters.

Estimating the energy repartition in micro electrical discharge machining

This paper presents a new approach for the recording of the total quantity of energy exchanged during the micro electrical discharge machining (EDM) process. In particular, this approach allows for the estimation of the percentage of energy absorbed by the two electrodes (tool and workpiece) using a combination of theoretical models and experimental results, thanks to an advanced discharges measuring approach. An experimental campaign was executed on a Sarix SX200 micro-EDM machine with a tungsten carbide tool electrode. In particular, the process was analyzed for two different electrode shapes, a triangular and a rectangular based parallelepipeds, and two sets of machining parameters. After the execution of the experimental campaign it estimate the total amount of energy that occurred during the entire die sinking process. The energy effectively lost into the tool, into the workpiece and into the dielectric was estimated from the measurement of the volume of material actually removed both from the tool and from the workpiece. The preliminary results appears to fit those presented in the literature and the validity of several theoretical crater models was then assessed. The validation of the presented acquisition method could enable the use of information related to energy repartition in the simulation of the micro-EDM process.

Impact-driven planetary desiccation: The origin of the dry Venus

The fate of surface water on Venus is one of the most important outstanding problems in comparative planetology. Although Venus should have had a large amount of surface water (like the Earth) during its formation, the current water content on the Venusian surface is only 1 part in 100 000 of that of the mass of Earth's oceans. Here a new concept is proposed to explain water removal on a steam-covered proto Venus, referred to as “impact-driven planetary desiccation”. Since a steam atmosphere is photochemically unstable, water vapor dissociates into hydrogen and oxygen. Then, hydrogen escapes easily into space through hydrodynamic escape driven by strong extreme ultraviolet radiation from the young Sun. The focus is on the intense impact bombardment during the terminal stage of planetary accretion as generators of a significant amount of reducing agent. The fine-grained ejecta remove the residual oxygen, the counter part of escaped hydrogen, via the oxidation of iron-bearing rocks in a hot atmosphere. Thus, hypervelocity impacts cause net desiccation of the planetary surface. I constructed a stochastic cratering model using a Monte Carlo approach to investigate the cumulative mass of nonoxidized, ejected rocks due to the intense impact bombardment. The ejecta mass after each impact was calculated using the π-group scaling laws and a modified Maxwell's Z model. The effect of projectile penetration into the ground on the ejecta mass was also included. Next, an upper limit on the total amount of removed water was calculated using the stoichiometric limit of the oxidation of basaltic rocks, taking into account the effect of fast H2 escape. It is shown that a thick steam atmosphere with a mass equivalent to that of the terrestrial oceans would be removed. The cumulative mass of rocky ejecta released into the atmosphere reaches 1 wt% of the host planet, which is 10 000 times of the current mass of the Earth's atmosphere. These results strongly suggest that chemical reactions between such large amounts of ejecta and planetary atmospheres are among the key factors required to understand atmospheric mass and its composition, not only in the Solar System but also in extrasolar systems.

月面巡视区域地形与巡视器通过性统计分析

Based on the reviews of foreign and domestic research results on lunar topography and the exploration results by Chang'e-3 lunar rover, the distribution of lunar rocks and craters were statistically analyzed and the mathematical models of lunar rocks and craters were also built. The trafficability of Chang'e-3 lunar rover was studied and used for the computation of mean free paths for the Chang'e-3 lunar rover. The results of mean free paths can be used for the path planning and motion modes of planetary rover and can be reference to the models of terrain feature for the mission of soft landing in the future.

Modeling cratered surfaces with real and synthetic terrain for testing planetary landers

The autonomous guidance of a spacecraft lander requires extensive testing to develop and prove the technology. Methods such as machine vision for navigation and both vision and LIDAR for hazard avoidance are being studied and developed to provide precise, robust lander guidance systems. A virtual test environment that can simulate these instruments is a vital tool to aid this work. When available, terrain elevation models can provide a base for simulation but they frequently contain artifacts, gaps, or may not have the required resolution. We propose novel techniques to model heavily cratered surfaces for testing planetary landers by combining crater models and fractal terrain to create a multiresolution mesh for simulating a spacecraft descent and landing. The synthetically enhanced models are evaluated by comparing enhanced terrain based on Clementine/RADAR data with higher resolution terrain models from the Selene and the Lunar Reconnaissance Orbiter (LRO) to show that the artificial models are suitable for testing planetary lander systems.

Cosmic ray exposure and pre-atmospheric size of the Gebel Kamil iron meteorite

Cosmogenic He, Ne, and Ar as well as the radionuclides 10Be, 26Al, 36Cl, 41Ca, 53Mn, and 60Fe have been determined on samples from the Gebel Kamil ungrouped Ni-rich iron meteorite by noble gas mass spectrometry and accelerator mass spectrometry (AMS), respectively. The meteorite is associated with the Kamil crater in southern Egypt, which is about 45 m in diameter. Samples originate from an individual large fragment (“Individual”) as well as from shrapnel. Concentrations of all cosmogenic nuclides—stable and radioactive—are lower by a factor 3–4 in the shrapnel samples than in the Individual. Assuming negligible 36Cl decay during terrestrial residence (indicated by the young crater age <5000 years; Folco et al. 2011), data are consistent with a simple exposure history and a 36Cl-36Ar cosmic ray exposure age (CRE) of approximately (366 ± 18) Ma (systematic errors not included). Both noble gases and radionuclides point to a pre-atmospheric radius >85 cm, i.e., a pre-atmospheric mass >20 tons, with a preferred radius of 115–120 cm (50–60 tons). The analyzed samples came from a depth of approximately 20 cm (Individual) and approximately 50–80 cm (shrapnel). The size of the Gebel Kamil meteoroid determined in this work is close to estimates based on impact cratering models combined with expectations for ablation during passage through the atmosphere (Folco et al. 2010, 2011).

Brightness Temperature Calculation of Lunar Crater: Interpretation of Topographic Effect on Microwave Data From Chang'E

In order to quantitatively interpret topographic effect on Chang'E (CE) microwave data, a detailed method to compute brightness temperature (TB) over a lunar crater is proposed, which incorporated the effect of surface tilts. The method improves the effective solar irradiance model of the lunar surface to obtain the temperature profile of the lunar crater. The calculated TB at 37 GHz with the proposed computation method, which is based on three digital elevation models (DEMs) from different sources, are consistent with the observed TB from the CE-2 microwave radiometer. The simulated behavior of TB across crater Hercules reproduces the TB undulation observed by CE in a single swath. TB is significantly affected by the lunar dust of a lunar crater and affected by albedo and emissivity in a lesser degree. Based on the explanation with simplified models, the TB variation over a crater is proved to be significantly affected, through physical temperature, by the crater shape described by DEMs. With the simplified crater model, the amplitude of the TB oscillatory curves is proved to depend on the crater shape.

Asteroid modeling for testing spacecraft approach and landing.

Spacecraft exploration of asteroids presents autonomous-navigation challenges that can be aided by virtual models to test and develop guidance and hazard-avoidance systems. Researchers have extended and applied graphics techniques to create high-resolution asteroid models to simulate cameras and other spacecraft sensors approaching and descending toward asteroids. A scalable model structure with evenly spaced vertices simplifies terrain modeling, avoids distortion at the poles, and enables triangle-strip definition for efficient rendering. To create the base asteroid models, this approach uses two-phase Poisson faulting and Perlin noise. It creates realistic asteroid surfaces by adding both crater models adapted from lunar terrain simulation and multiresolution boulders. The researchers evaluated the virtual asteroids by comparing them with real asteroid images, examining the slope distributions, and applying a surface-relative feature-tracking algorithm to the models.

Variation of the lunar highland surface roughness at baseline 0.15–100 km and the relationship to relative age

AbstractWe report the surface roughness analysis of the lunar highlands for the baseline range 0.15–100 km. We use the Median Differential Slope αm to investigate the scale dependency of the roughness and derive the global αm distribution from SELENE Laser Altimeter and Terrain Camera data. While αm(l) versus baseline l (km) plots vary among different highland types, all highlands commonly show a peak at 3–30 km. The Pre‐Nectarian surface shows a relatively large αm(20–30 km). Our analysis is supported by the simulation of synthetic surface cratering models and crater statistics. In our simulation, a peak of αm(30 km) is successfully reproduced. The actual crater density shows good correlation with an empirical roughness indicator. However, a large part of the Nectarian surface shows a peak at 6–9 km baseline. This peak may be caused by secondary craters and ejecta deposit textures from the Nectarian system basins.

Contribution of in situ geophysical methods for the definition of the São Sebastião crater model (Azores)

Abstract The area located inside the Sao Sebastiao volcanic crater, at the southeast end of Terceira Island (Azores), is characterized by an important amplification of ground motion with respect to the surrounding area, as clearly demonstrated by the spatial distribution of the damage that occurred during the Terceira earthquake (the strongest earthquake felt in the Island during the recent decades — 01/01/1980 — M = 7.2). Geological and geophysical studies have been conducted, to characterize the volcanic crater and understand the different site effects that occurred in the village of Sao Sebastiao. The complexity of the subsurface geology, with intercalations of compact basalt and soft pyroclastic deposits, is associated to extreme vertical and lateral velocity contrasts, and poses a serious challenge to different geophysical characterization methods. The available qualitative model did not allow a complete understanding of the site effects. A new seismic campaign has been designed and acquired, and a single, geologically consistent geophysical model has been generated integrating the existing and new data. The new campaign included two cross-line P-wave seismic refraction profiles, four short SH-wave seismic reflection profiles, and seven multichannel surface wave acquisitions. The integration and joint interpretation of geophysical and geological data allowed mutual validation and confirmation of data processing steps. In particular, the use of refraction, reflection and surface wave techniques allowed facing the complexity of a geology that can pose different challenges to all the methods when used individually: velocity inversions, limited reflectivity, and lateral variations. It is shown how the integration of seismic data from different methods, in the framework of a geological model, allowed the geometrical and dynamic characterization of the site. Correlation with further borehole information, then allowed the definition of a subsoil model for the crater, providing information that allowed a better understanding of the earthquake site effects in the Sao Sebastiao village. The new near-surface geological model includes a lava layer within the soft infill materials of the crater. This new model matches closely with the damage distribution map, and explains the spatial variation of building stock performance in the 1980 earthquake.