Styles of ejecta emplacement under atmospheric conditions

Laboratory experiments provide essential first-order constraints on processes affecting ballistic ejecta and styles of ejecta emplacement under different atmospheric environments at planetary scales. The NASA-Ames Vertical Gun allows impacting different fine-grained particulate targets under varying atmospheric pressure and density, thereby helping to isolate controlling variables. Further analysis now permits characterizing distinct modes of emplacement that reflect the degree of ejecta entrainment within a turbidity flow created by ejecta curtain movement through the atmosphere

Atmospheric effects on crater growth on Venus

Laboratory experiments allow examining the consequences of complex processes operating over a wide range of scales (both temporal and spatial) and frequently reveal effects that are obvious only in hindsight. Even though all processes may not scale directly, isolation of the controlling variables allows assessing first-order effects through analytical approximations. This approach can be illustrated by the systematic sequence of ballistic ejection, the response of an atmosphere to a strong energy source, the scaling of ejecta thickness, and the role of secondary cratering. Here it is proposed that the effects of atmospheric pressure and density on crater growth (hence, scaling) observed in laboratory experiments has particular relevance for craters on Venus

The role of impact cratering for Mars sample return

The preserved cratering record of Mars indicates that impacts play an important role in deciphering Martian geologic history, whether as a mechanism to modify the lithosphere and atmosphere or as a tool to sample the planet. The various roles of impact cratering in adding a broader understanding of Mars through returned samples are examined. Five broad roles include impact craters as: (1) a process in response to a different planetary localizer environment; (2) a probe for excavating crustal/mantle materials; (3) a possible localizer of magmatic and hydrothermal processes; (4) a chronicle of changes in the volcanic, sedimentary, atmospheric, and cosmic flux history; and (5) a chronometer for extending the geologic time scale to unsampled regions. The evidence for Earth-like processes and very nonlunar styles of volcanism and tectonism may shift the emphasis of a sampling strategy away from equally fundamental issues including crustal composition, unit ages, and climate history. Impact cratering not only played an important active role in the early Martian geologic history, it also provides an important tool for addressing such issues

Effect of impact angle on central-peak/peak-ring formation and crater collapse on Venus

Although asymmetry in ejecta patterns and craters shape-in-plan are commonly cited as diagnostic features of impact angle, the early-time transfer of energy from impactor to target also creates distinctive asymmetries in crater profile with the greatest depth uprange. In order to simulate gravity-controlled crater-growth, laboratory experiments use loose particulate targets as analogs for low-strength material properties following passage of the shock. As a result, impact crater diameter D in laboratory experiments generally is many times greater than the impactor diameter 2r (factor of 40), and early-time asymmetries in energy transfer from oblique impacts are consumed by subsequent symmetrical crater growth, except at the lowest angles (less than 25 deg). Such asymmetry is evident for oblique (less than 60 deg from horizontal) impacts into aluminum where D/2r is only 2 to 4. Because cratering efficiency decreases with increasing crater size and decreasing impact angle, large scale planetary craters (4080 km) should have transient excavation diameters only 6-10 times larger than the impactor. At basin scales, D/2r is predicted to be only 3-5, i.e., approaching values for impacts into aluminum in laboratory experiments. As a result, evidence for early-time asymmetry in impactor energy transfer should become evident on planetary surfaces, yet craters generally retain a circular outline for all but the lowest impact angles

Atmospheric effects on oblique impacts

Laboratory experiments and theoretical calculations often use vertical impact angles (90 deg) in order to avoid the complicating effect of asymmetry. Nevertheless, oblique impacts represent the most likely starting condition for planetary cratering. Changing both impact angles and atmospheric pressure not only allows testing previous results for vertical impacts but also reveals phenomena whose signatures would otherwise be masked in the planetary cratering record. The laboratory studies were performed for investigating impact cratering processes. Impact angles can be increased from 0 to 90 deg in 15 deg increments while maintaining a flat target surface. Different atmospheres (nitrogen, argon, and helium) characterized the effects of both gas density and Mach number. Targets varied according to purpose. Because of the complexities in atmosphere-impactor-ejecta interactions, no single combination allows direct simulation of a planetary-scale (10-100 km) event. Nevertheless, fundamental processes and observed phenomena allow formulating first-order models at such broad scales

Non-random cratering flux in recent time

Proposed periodic cycles of mass mortality have been linked to periodic changes in the impact flux on Earth. Such changes in the impact flux, however, also should be recorded on the Moon. Previous studies have concluded that the impact flux on the Moon over the last 1 to 2 billion years has been reasonably constant, but sudden changes in the impact flux over time intervals as short as 30 my could not be detected in these studies unless the added crater population greatly exceeded the cumulative cratering record. Consequently this study focuses only on bright-rayed craters larger than 1 km thereby not only limiting the study to recent craters but also largely eliminating contamination by secondary craters. Preservation of ray patterns and other fine-scale surface textures in the ejecta provides first-order culling of craters younger than Tycho, i.e., about 100 my. Although a periodic change in the impact flux in the Earth-Moon system cannot yet be confirmed from the data, a non-random component appears to exist with an increased flux around 7 and 15 my. The concentrations in different quadrants of the lunar hemisphere would be consistent with a shower of debris generally smaller than 0.5 km

Early changes in gradation styles and rates on Mars

The wide annulus of massifs and knobs of Isidis and Argyre provided sufficiently large areas for meaningful crater statistics of large craters. Counts were made over adjacent and nested areas in order to test consistency and to derive relative age of each basin. Within the Isidis annulus, charateristic terrains provided counting areas for dating contrasting surface process: channeled hummocky terrain, etched terrains, and intermassif channeled plains. The channeled hummocky terrain contains a high channel density of narrow valley networks cutting both primary Isidis features and old craters. The etched terrains represent a broad region outside the inner high relief massifs of southwestern Isidis where numerous irregular plateaus, mesas, and relict craters indicate a different style of erosion. The intermassif channeled plains occur along the inner mountainous ring. Shallow meandering channels form a large integrated drainage system that is linked to numerous smaller intermountainous basins. These ponds and interconnected tributaries extend beyond the primary inner massif ring through broad canyons

Timing of ancient extensional tectonic features on Mars

Although numerous studies have delineated the Tharsis and post-Tharsis volcanic/tectonic history on Mars, only a few attempts have examined the earlier epochs. This is not an easy task since unambiguous crater ages for pre-Tharsis and early Tharsis units are difficult to determine owing to a variety of active surface processes. Ancient tectonic features, however, have a sufficiently large superposed crater population that should permit relative dating. A technique for crater counting along linear features analagous to areal crater density is proposed. A modification of this approach has been tested and applied to a variety of ancient tectonic features

Floor-fractured crater models of the Sudbury structure, Canada

The Sudbury structure in Ontario, Canada, is one of the oldest and largest impact structures recognized in the geological record. It is also one of the most extensively deformed and volcanically modified impact structures on Earth. Although few other terrestrial craters are recognized as volcanically modified, numerous impact craters on the Moon have been volcanically and tectonically modified and provide possible analogs for the observed pattern of modification at Sudbury. We correlate the pattern of early deformation at Sudbury to fracture patterns in two alternative lunar analogs and then use these analogs both to estimate the initial size of the Sudbury structure and to model the nature of early crater modification at Sudbury

Approximation Theory of Multivariate Spline Functions in Sobolev Spaces

In this paper we study some approximation theory questions which arise from the analysis of the discretization error associated with the use of the Rayleigh-Ritz-Galerkin method for approximating the solutions to various types of boundary value problems, cf. [13, [2], [33, [43, [7], [8], [93, [12], [143, [18], [19], [20] and [22]. In particular, we consider upper and lower bounds for the error in approximation of certain families of functions in Sobolev spaces, cf. [15], by functions in finite-dimensional "polynomial spline types" subspaces, cf. [16]. In doing this, we directly generalize, improve, and extend the corresponding results of[1], [17], [18], [19], [20], and [21]. Throughout this paper, the symbol K will be used repeatedly to denote a positive constant, not necessarily the same at each occurrence and the symbol μ will be used repeatedly to denote a nonnegative, continuous function on [0,∞], not necessarily the same at each occurrence