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Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to describe these scaling laws and determine their coefficients by linear regression, minimizing the error between our model and SPH simulations. The input parameters are the impact angle $\theta$ ($0^{\circ}, 30^{\circ}, 60^{\circ}$, and $90^{\circ}$), total mass $M_T$ ($1M_{\rm Mars}-53M_{\rm Mars}$, where $M_{\rm Mars}$ is the mass of Mars), impact velocity $v_{\rm imp}$ ($v_{\rm esc} - 2v_{\rm esc}$, where $v_{\rm esc}$ is the mutual escape velocity), and impactor-to-total mass ratio $\gamma$ ($0.03-0.5$). We find that the equilibrium pressure at the base of a melt pool can be higher (up to $\approx 80 \%$) than those of radially-uniform global magma ocean models. This could have a significant impact on element partitioning. These melt scaling laws are publicly available on GitHub ($\href{https://github.com/mikinakajima/MeltScalingLaw}{https://github.com/mikinakajima/MeltScalingLaw}$)., Comment: Published in Earth and Planetary Science Letters

Multiring basins dominate the crustal structure, tectonics, and stratigraphy of the Moon. Understanding how these basins form is crucial for understanding the evolution of ancient planetary crusts. To understand how preimpact thermal structure and crustal thickness affect the formation of multiring basins, we simulate the formation of lunar basins and their rings under a range of target and impactor conditions. We find that ring locations, spacing, and offsets are sensitive to lunar thermal gradient (strength of the lithosphere), temperature of the deep lunar mantle (strength of the asthenosphere), and preimpact crustal thickness. We also explore the effect of impactor size on the formation of basin rings and reproduce the observed transition from peak‐ring basins to multiring basins and reproduced many observed aspects of ring spacing and location. Our results are in broad agreement with the ring tectonic theory for the formation of basin rings and also suggest that ring tectonic theory applies to the rim scarp of smaller peak‐ring basins.

Impact cratering is likely a primary agent of regolith generation on airless bodies. Regolith production via impact cratering has long been a key topic of study since the Apollo era. The evolution of regolith due to impact cratering, however, is not well understood. A better formulation is needed to help quantify the formation mechanism and timescale of regolith evolution. Here, we propose an analytically derived stochastic model that describes the evolution of regolith generated by small, simple craters. We account for ejecta blanketing as well as regolith infilling of the transient crater cavity. Our results show that the regolith infilling plays a key role in producing regolith. Our model demonstrates that, because of the stochastic nature of impact cratering, the regolith thickness varies laterally, which is consistent with earlier work. We apply this analytical model to the regolith evolution at the Apollo 15 site. The regolith thickness is computed considering the observed crater size-frequency distribution of small, simple lunar craters (< 381 m in radius for ejecta blanketing and < 100 m in radius for the regolith infilling). Allowing for some amount of regolith coming from the outside of the area, our result is consistent with an empirical result from the Apollo 15 seismic experiment. Finally, we find that the timescale of regolith growth is longer than that of crater equilibrium, implying that even if crater equilibrium is observed on a cratered surface, it is likely the regolith thickness is still evolving due to additional impact craters., 32 pages, 13 figures, 2 tables, and accepted for publication in JGR-Planets

The abundance of moderately siderophile elements (“iron-loving”; e.g. Co, Ni) in the Earth's mantle is 10 to 100 times larger than predicted by chemical equilibrium between silicate melt and iron at low pressure, but it does match expectation for equilibrium at high pressure and temperature. Recent studies of differentiated planetesimal impacts assume that planetesimal cores survive the impact intact as concentrated masses that passively settle from a zero initial velocity and undergo turbulent entrainment in a global magma ocean; under these conditions, cores greater than 10 km in diameter do not fully mix without a sufficiently deep magma ocean. We have performed hydrocode simulations that revise this assumption and yield a clearer picture of the impact process for differentiated planetesimals possessing iron cores with radius = 100 km that impact into magma oceans. The impact process strips away the silicate mantle of the planetesimal and then stretches the iron core, dispersing the liquid iron into a much larger volume of the underlying liquid silicate mantle. Lagrangian tracer particles track the initially intact iron core as the impact stretches and disperses the core. The final displacement distance of initially closest tracer pairs gives a metric of core stretching. The statistics of stretching imply mixing that separates the iron core into sheets, ligaments, and smaller fragments, on a scale of 10 km or less. The impact dispersed core fragments undergo further mixing through turbulent entrainment as the molten iron fragments rain through the magma ocean and settle deeper into the planet. Our results thus support the idea that iron in the cores of even large differentiated planetesimals can chemically equilibrate deep in a terrestrial magma ocean.

Positive free-air gravity anomalies associated with large lunar impact basins represent a superisostatic mass concentration or “mascon.” High-resolution lunar gravity data from the Gravity Recovery and Interior Laboratory spacecraft reveal that these mascons are part of a bulls-eye pattern in which the central positive anomaly is surrounded by an annulus of negative anomalies, which in turn is surrounded by an outer annulus of positive anomalies. To understand the origin of this gravity pattern, we modeled numerically the entire evolution of basin formation from impact to contemporary form. With a hydrocode, we simulated impact excavation and collapse and show that during the major basin-forming era, the preimpact crust and mantle were sufficiently weak to enable a crustal cap to flow back over and cover the mantle exposed by the impact within hours. With hydrocode results as initial conditions, we simulated subsequent cooling and viscoelastic relaxation of topography using a finite element model, focusing on the mare-free Freundlich-Sharonov and mare-infilled Humorum basins. By constraining these models with measured free-air and Bouguer gravity anomalies as well as surface topography, we show that lunar basins evolve by isostatic adjustment from an initially subisostatic state following the collapse stage. The key to the development of a superisostatic inner basin center is its mechanical coupling to the outer basin that rises in response to subisostatic stresses, enabling the inner basin to rise above isostatic equilibrium. Our calculations relate basin size to impactor diameter and velocity, and they constrain the preimpact lunar thermal structure, crustal thickness, viscoelastic rheology, and, for the Humorum basin, the thickness of its postimpact mare fill.

The Lunar Orbiter Laser Altimeter (LOLA) measures the backscattered energy of the returning altimetric laser pulse at its wavelength of 1064 nm, and these data are used to map the reflectivity of the Moon at zero-phase angle with a photometrically uniform data set. Global maps have been produced at 4 pixels per degree (about 8 kilometers at the equator) and 2 kilometers resolution within 20 deg latitude of each pole. The zero-phase geometry is insensitive to lunar topography, so these data enable characterization of subtle variations in lunar albedo, even at high latitudes where such measurements are not possible with the Sun as the illumination source. The geometric albedo of the Moon at 1064 nm was estimated from these data with absolute calibration derived from the Kaguya Multiband Imager and extrapolated to visual wavelengths. The LOLA estimates are within 2 sigma of historical measurements of geometric albedo. No consistent latitude-dependent variations in reflectance are observed, suggesting that solar wind does not dominate space weathering processes that modify lunar reflectance. The average normal albedo of the Moon is found to be much higher than that of Mercury consistent with prior measurements, but the normal albedo of the lunar maria is similar to that of Mercury suggesting a similar abundance of space weathering products. Regions within permanent shadow in the polar regions are found to be more reflective than polar surfaces that are sometimes illuminated. Limiting analysis to data with slopes less than 10 deg eliminates variations in reflectance due to mass wasting and shows a similar increased reflectivity within permanent polar shadow. Steep slopes within permanent shadow are also more reflective than similar slopes that experience at least some illumination. Water frost and a reduction in effectiveness of space weathering are offered as possible explanations for the increased reflectivity of permanent shadow; porosity is largely ruled out as the sole explanation. The south polar crater Shackleton is found to be among the most reflective craters in its size range globally but is not the most reflective, so mass wasting cannot be ruled out as a cause for the crater's anomalous reflectance. Models of the abundance of ice needed to account for the reflectance anomaly range from 3 to 14% by weight or area depending on assumptions regarding the effects of porosity on reflectance and whether ice is present as patches or is well mixed in the regolith. If differences in nanophase iron abundances are responsible for the anomaly, the permanently shadowed regions have between 50 and 80% the abundance of nanophase iron in mature lunar soil.

[1] The Rheasilvia impact on asteroid 4 Vesta may have been sufficiently large to create disrupted terrains at the impact antipode. This paper investigates the amount of deformation expected at the Rheasilvia antipode using numerical models of sufficient resolution to directly observe terrain modification and material displacements following the arrival of impact stresses. We find that the magnitude and mode of deformation expected at the impact antipode is strongly dependent on both the sound speed and porosity of Vesta's mantle, as well as the strength of the Vestan core. In the case of low mantle porosities and high core strengths, we predict the existence of a topographic high (a peak) caused by the collection of spalled and uplifted material at the antipode. Observations by NASA's Dawn spacecraft cannot provide definite evidence that large amounts of deformation occurred at the Rheasilvia antipode, largely due to the presence of younger large impact craters in the region. However, a deficiency of small craters near the antipodal point suggests that some degree of deformation did occur.

[1] We numerically modeled the formation of Rheasilvia crater, an enormous impact basin centered on asteroid 4 Vesta's south pole. Using a trial and error method, our models were adjusted to produce the best possible fit to Rheasilvia's size and shape, as observed during the Vesta orbital stage of the Dawn mission. The final model yields estimates of the shock wave decay, escaped material volume, depth of excavation, and other relevant characteristics, to the extent allowed by the two-dimensional (axially symmetric) approximation of the Simplified Arbitrary Lagrangian Eulerian hydrocode. Our model results permit interpretation of the Dawn data on Vesta's shape, topographic crater profiles, and the origin of the Vestoid asteroid family as escaped ejecta from the Rheasilvia crater.

In this paper we present a new model for the formation of shatter cones. The model follows earlier suggestions that shatter cones are initiated by heterogeneities in the rock, but does not require the participation of an elastic precursor wave: the conical fractures are initiated after the passage of the main plastic compression pulse, not before. Numerical simulations using the hydrocode SALE 2D, enhanced by the Grady–Kipp–Melosh fragmentation model, support the model. The conditions required for the formation of shatter cones are explored numerically and are found to be consistent with the pressure range derived from both explosion experiments and the analysis of shock metamorphic features in impact structures. This model permits us to deduce quantitative information about the shape of the shock wave from the shape and size of the observed shatter cones. Indeed, the occurrence of shatter cones is correlated with the ratio between the width of the compressive pulse and the size of the heterogeneity that initiates the conical fracture. The apical angles of the shatter cones are controlled by the shape of the rarefaction wave.

It has been proposed that the high concentrations of moderately siderophile elements (e.g. Ni and Co) in the Earth’s mantle are the result of metal–silicate equilibration at the base of a deep magma ocean that formed during Earth’s accretion. According to this model, liquid metal ponds at the base of the magma ocean and, after equilibrating chemically with the overlying silicate liquid at high pressure (e.g. 25–30 GPa), descends further as large diapirs to form the core. Here we investigate the kinetics of metal–silicate equilibration in order to test this model and place new constraints on processes of core formation. We investigate two models: (1) Reaction between a layer of segregated liquid metal and overlying silicate liquid at the base of a convecting magma ocean, as described above. (2) Reaction between dispersed metal droplets and silicate liquid in a magma ocean. In the liquid-metal layer model, the convection velocity of the magma ocean controls both the equilibration rate and the rate at which the magma ocean cools. Results indicate that time scales of chemical equilibration are two to three orders of magnitude longer than the time scales of cooling and crystallization of the magma ocean. In the falling metal droplet model, the droplet size and settling velocity are critical parameters that we determine from fluid dynamics. For likely silicate liquid viscosities, the stable droplet diameter is estimated to be ∼1 cm and the settling velocity ∼0.5 m/s. Using such parameters, liquid metal droplets are predicted to equilibrate chemically after falling a distance of

We studied the effect of extreme acceleration and change in acceleration, or jerk, on bacteria to determine if they could survive impact ejection from a planet. Computer simulations based on the spallation model [H.J. Melosh, Icarus 59 (1984) 234–260; H.J. Melosh, Nature 363 (1993) 498–499] for ejecting material from planetary surfaces provided estimates for acceleration, rise time, and jerk for material accelerated to escape velocity. For ejection from Mars, the maximum acceleration predicted was 3×106 m/s2, or 3×105×g, with a rise time of 0.5 ms, and a corresponding jerk of 6×109 m/s3. We tested the resistance of Bacillus subtilis spores and Deinococcus radiodurans cells to high acceleration and jerk by (1) subjecting B. subtilis spores to the forces of an ultracentrifuge and (2) firing both bacteria from a rifle into a plasticene target. We measured the survival of B. subtilis spores at extreme acceleration in an ultracentrifuge operated at its highest speed, 100 000 rpm, corresponding to an acceleration of 4.27×106 m/s2, or 4.36×105×g. Approximately 107 spores were centrifuged in phosphate-buffered saline for 24, 48, 50 and 72 h. Spores were inactivated with simple exponential kinetics, and 65 h of centrifugation was required to inactivate 90% of the spore population. To test for resistance to jerk, spores of B. subtilis or cells of D. radiodurans were loaded into the rear cavities of lead pellets fired from a compressed-air pellet rifle into a target consisting of plasticene modeling clay, previously chilled to 4°C. The velocity of each pellet was measured using a chronograph and the depth of penetration of each pellet into the target was measured before removing the pellet from the clay using sterile forceps. Two different rifles were used, one with a measured pellet velocity of ∼100 m/s and the other with a velocity of ∼300 m/s. These correspond to estimated accelerations of 1.5×106 and 4.5×106 m/s2 and jerks of 1.5×1010 and 1.5×1011 m/s3, respectively. The percent survival for both organisms ranged from 40 to 100%. The samples in the ballistic experiments were subjected to jerks and accelerations 2.5–25 times larger than those estimated to prevail during ejection according to the computer simulation. We therefore conclude that acceleration and jerk are not important lethal factors during the ejection of viable microorganisms from planetary surfaces.

A seismic reflection and three-dimensional wide-angle tomographic study of the buried, V200-km diameter, Chicxulub impact crater in Mexico reveals the kinematics of central structural uplift and peak-ring formation during large-crater collapse. The seismic data show downward and inward radial collapse of the transient cavity in the outer crater, and upward and outward collapse within the central structurally uplifted region. Peak rings are formed by the interference between these two flow regimes, and involve significant radial transport of material. Hydrocode modeling replicates the observed collapse features. Impact-generated melt rocks lie mostly inside the peak ring; the melt appears to be clast-rich and undifferentiated, with a maximum thickness of 3.5 km in the center. fl 2000 Elsevier Science B.V. All rights reserved.

[1] Images of Mercury’s northern volcanic plains taken by the MESSENGER spacecraft reveal a large number of buried impact craters and basins discernible by wrinkle-ridge rings that overlie their rims. Many of these “ghost” craters and basins contain interior graben of diverse widths and orientations. Here we use finite element models to test a variety of mechanisms for the formation of these graben and ridges. Results show that graben are best explained by cooling of large thicknesses of flood lavas within the craters and basins; conservation of surface area during cooling induces the required extensional stress state. In contrast, the development of wrinkle-ridge rings is best explained as the result of cooling and contraction of Mercury’s interior, during which a reduction in Mercury’s surface area led to a compressional state of stress. The critical factor in determining where large graben form is the thickness of the youngest cooling unit, the topmost sequence of lavas that cooled coevally. A thicker cooling unit leads to a deeper initiation of normal faulting (wider graben floors). Consistent with observations, the widest graben are predicted to occur where pooled lavas were thickest, and no graben are predicted within generally thinner plains outside of major craters. Observed concentrically oriented graben can be explained by variations in the thickness of the youngest cooling unit. In contrast, none of the basin uplift mechanisms considered, including isostatic response to crater topography, inward flow of the lower crust, or exterior loading by volcanic plains, can account for concentrically oriented graben.

[1] Our data suggest that the presence of a layer of regolith covering the lunar surface results in a portion of the high-velocity ejection phase occurring in the fine-grained regolith, reducing the population of large blocks available for ejection at high velocities. This conclusion is supported by a study of boulder distributions around 10 lunar craters. The boulder ejection velocities were calculated by applying crater ejecta scaling relations and assuming a ballistic trajectory. Regolith depths were estimated by analyzing the morphology of small craters (tens of meters in diameter). Because both meteorites and distant secondary craters are produced by solid fragments within the highest-velocity ejecta, we conclude that less regolith cover at the impact site will favor the formation of meteorites and distant secondary craters.

The dynamic fragmentation in impacts into solids is examined using a physical model for the formation and growth of cracks in rocks. The physical model is then inserted into a numerical model (hydrocode) of stress wave propagation and interaction, from which the outcome of a given impact event can be computed. The hydrocode model predicts fragment sizes due to impact in terms of shock waves propagating in a homogeneous elastic medium containing a distribution of crack nucleation centers known as Weibull flaws.

The tectonics of planetary loading is investigated using an analytical model for determining the stresses in an arbitrarily thick spherical shell due to an idealized axisymmetric load. The model includes the flat plate and thin shell membrane approximations as end members, and makes it possible to determine the nature of the transition between them. Using this model, the stress states and the resulting tectonic patterns due to an idealized exponential load are determined as functions of five dimensionless parameters: the ratio of the lithospheric thickness to the planetary radius; the decay width of the load; the 'support parameter', which is the ratio of the buoyancy to the flexural support; the angular distance from the load center; and the normalized radial distance from the planet center.

Summary. Subduction zones are expressed topographically by long linear oceanic trenches flanked by a low outer rise on the seaward side and an island arc on the landward side. This topographic structure is reflected in free air gravity anomalies, suggesting that much of the topography originates from dynamical forces applied at the base of the crust. We have successfully reproduced the general topographic features of subduction zones by supposing that the stresses generated by the bending of the viscous lower lithosphere as it subducts are transmitted through the thin elastic upper portion of the lithosphere. The trench is due to a zone of extensional flow (associated with low pressure) in the upper part of the viscous lithosphere. The stresses in the subducting slab are computed using a finite element technique, assuming a Maxwell viscoelastic constitutive relation. Various dips (10 to 90") were investigated, as well as depth dependent and nonNewtonian (power law, n = 3) viscosities. Observed subduction zone dimensions are well reproduced by these models. The effective viscosity required at mid-depth in the lithosphere is about 6 x lo2* P. This low value is probably due to the stress dependence of the effective viscosity. However, these models also show that the topography of the subduction zone depends primarily upon the geometry of the subducting slab (dip, radius of curvature of the bend) rather than upon' its rheology. Shear stresses beneath the trench reach maxima of approximately 50 MPa. An interesting feature of some solutions is a dynamically supported bench or platform between the trench and island arc.

This letter reports the discovery of a relation between the moments of inertia of the mascons (taken about the moon's center) and the moon's moments of inertia. It is found that the principal axes of the mascons alone are nearly parallel to those of the moon. Possible explanations of this parallelism are discussed. If the mascons are associated with a layer of uncompensated basalt on the moon's nearside, then the parallelism can be adequately explained on the grounds that the mascons and basalts together determined the moon's orientation. On the other hand, the third-order harmonics of the moon's gravity field indicate that the excess mass controlling the moon's orientation is on the farside. It thus appears that the mascons have been emplaced in special sites whose position was controlled by the processes which produced the farside highlands.

Summary. Motion of the lithosphere over a low viscosity asthenosphere concentrates shear and thus energy dissipation in the asthenosphere. This heat source warms the asthenosphere and, in extreme circumstances, may lead to thermal instabilities. The conditions for thermal stability have been investigated by Melosh who supposed that constant stress acted on the plate, and by Yuen & Schubert who assumed constant velocity boundary conditions. In this paper we investigate a simple analytical model which behaves qualitatively like the more complex systems. This model reproduces the results of Melosh for constant stress and of Yuen & Schubert for constant velocity. The velocity-shear stress characteristic curve for this model shows three branches. The stability of solutions on each branch is a function of the boundary conditions, whether constant stress or constant velocity. The simplicity of the model allows us to investigate stability when neither constant stress nor constant velocity apply and to study the structure of the solutions as these limits are approached. A relation between the velocity of a plate and the driving force is constructed. A loading-line analysis specifies the actual stress and velocity of the plate. Although the solutions are unique for many combinations of the loading-line parameters, there is a region of multiple solutions. These solutions exhibit the characteristics of a ‘cusp catastrophe’; both a low velocity and a high velocity state are stable, while an intermediate state is unstable. Continental lithosphere may lie in this region, leading to epirogenic movements when the plate changes its velocity with respect to the mantle. Oceanic lithosphere almost certainly moves in the low velocity state.

This paper outlines a new method, the “split node technique” for introducing fault displacements into finite element numerical computations. The value of the displacement at a single node point shared between two elements depends upon which element it is referred to, thus introducing a displacement discontinuity between the two elements. We show that the modification induced by this splitting can be contained in the load vector, so that the stiffness matrix is not altered. The number of degrees of freedom is not increased by splitting. This method can be implemented entirely on the local element level, and we show rigorously that no net forces or moments are induced on the finite element grid when isoparametric elements are used. This method is thus of great utility in many geological and engineering applications.

This paper investigates the idea that large impact events have caused the moon to change its orientation in space. It is found that the very largest impact events, such as those which formed Imbrium and Orientale, probably did reorient the moon. This reorientation is primarily due to the change in the moon's moments of inertia consequent upon crater formation. The impulse delivered by the impact can at most unlock the moon's synchronous rotation for a few thousand years, and is thus not of major importance. The moon will attain its new orientation in less than a few times 10 4 years as a result of tidal friction. Since the large craters eventually are filled by isostatic rebound and extrusive igneous activity, the moon may eventually regain its original orientation unless other phenomena cause new changes in the distribution of mass on its surface.

The mechanics of the initial stages of graben formation are examined, showing that the configuration of a graben (a pair of antithetically dipping normal faults) is the most energetically favorable fault configuration in elastic-brittle rocks subjected to pure extension. The stress field in the vicinity of a single initial normal fault is computed with a two-dimensional FEM. It is concluded that the major factor controlling graben width is the depth of the initial fault.

By H. Ramberg. Academic Press, xii + 452 pp., cloth bound (£32.80) (ISBN 12 576860 5).

This paper consists of two parts. The first is theoretical and extends Elsasser's theory of stress propagation in the upper mantle to an asthenosphere with nonlinear rheology. Exact solutions of the nonlinear equations are found for two geologically important problems. The second part uses these theoretical results as the basis for a measurement of the rheology of the asthenosphere. The seaward migration pattern of aftershocks from the February 4, 1965, Rat Island earthquake is analyzed, and strong evidence for a non-Newtonian stress-strain relation in the asthenosphere is presented. It is found that an individual large earthquake can influence the regional stress pattern only to a distance of about 300 km perpendicular to the line of rupture. Excellent agreement is found between the stress propagation coefficient calculated from the aftershock migration pattern and that calculated from laboratory measurements of high-temperature creep in olivine. We thus arrive at a picture of stress propagation in the upper mantle which is consistent both with theoretical expectation and with observational evidence.

We propose that asymmetric sea-floor spreading occurs as a consequence of the relative motion between ridges and slow-moving mantle material below. A fluid mechanical model of asymmetric spreading predicts that the trailing flank of a ridge migrating with respect to the mantle spreads fastest. Observed asymmetries are compared to those predicted by ridge migration velocities. Although the magnitude of the asymmetry appears to depend as much on local effects as on the migration of the ridge, the direction of asymmetry agrees with our prediction in most locations. In contrast, models in which the ridge attempts to remain above a source fixed in the mantle predict the opposite direction of asymmetry. Other models, which attribute asymmetric spreading to asymmetric cooling, require large deviations from the standard depth-age relationship, while our model does not.

Viking orbiter images show grooves and chains of pits crossing the surface of Phobos, many of which converge toward the large crater Stickney or its antipode. Although it has been proposed that the pits and grooves are chains of secondary craters, their morphology and geometric relations suggest that they are the surface traces of fractures in the underlying solid body of Phobos. Several models have been proposed to explain the pits, of which the most plausible are gas venting and drainage of regolith into open fractures. the latter mechanism is best supported by the image data and is the mechanism studied in this investigation. Drainage pits and fissures are modeled experimentally by using two rigid substrate plates placed edge to edge and covered by uniform thicknesses of dry fragmental debris (simulated regolith). Fracture extension is simulated by drawing the plates apart, allowing drainage of regolith into the newly created void. A typical drainage experiment begins with a shallow depression on the surface of the regolith, above the open fissure. Increased drainage causes local drainage pits to form; continued drainage causes the pits to coalesce, forming a cuspate groove. The resulting experimental patterns of pits and grooves have pronounced similarities to those observed on Phobos. Characteristics such as lack of raised rims, linearity of grooves and chains of pits, uniform spacing of pits, and progression from discrete pits to cuspate grooves are the same in the experiments and on Phobos. In contrast, gas-venting pits occur in irregular chains and have raised rims. These experiments thus indicate that the Phobos grooves and pits formed as drainage structures. The pit spacing in an experiment is measured at the time that the maximum number of pits forms, prior to groove development. The average pit spacing is compared to the regolith thickness for each material. Regression line fits indicate that the average spacing of drainage pits in unconsolidated, noncohesive regolith is nearly equal to the thickness of regolith and appears to gbe independent of the angle of repose, within the resolution of our experiments. This provides a simple means of estimating regolith thickness where drainage pits are present. On Phobos, two locations differing by 90 degrees in longitude have average pit spacings that suggest regolith thicknesses of 290 and 300 m, suggesting that large areas of Phobos have a nearly uniform regolith thickness of approximately 300 m.

A phenomenological Bingham plastic model has previously been shown to provide an adequate description of the collapse of impact craters. This paper demonstrates that the Bingham parameters may be derived from a model in which acoustic energy generated during excavation fluidizes the rock debris surrounding the crater. Experimental support for the theoretical flow law is presented. Although the Bingham yield stress cannot be computed without detailed knowledge of the initial acoustic field, the Bingham viscosity is derived from a simple argument which shows that it increases as the 3/2 power of crater diameter, consistent with observation. Crater collapse may occur in material with internal dissipation Q as low as 100, comparable to laboratory observations of dissipation in granular materials. Crater collapse thus does not require that the acoustic field be regenerated during flow.

The deformation induced by a vertical dip slip earthquake is examined using a variety of rheologic models. In this way the complications of dipping faults are avoided, and the phenomenon of transient peripheral warping is clearly revealed. A thrust fault dipping at 30 deg is investigated, and the important effects of dip and the existence of a slab on the asymmetry of strain pulses propagated into the overthrust and subducted lithosphere are demonstrated. One of the signal results of the study is the essential similarity of the strain patterns for Newtonian and non-Newtonian flow laws: the two rheologies give nearly identical strain field geometries. The principal difference between the two, which is readily observable, is in their time evolution. Relaxation in non-Newtonian rheologies tends to be initially fast, then slow at times that are late in comparison with relaxation in a Newtonian rheology. The possibility of simply recalling the time dependence of a Newtonian solution to obtain an approximate solution to a non-Newtonian problem is demonstrated.

Two of the proposed explanations for the coronae seen on Miranda involve mantle convection driven by density anomalies. In the sinker model, the coronae result from late-accreting large silicate bodies slowly sinking through an icy mantle toward the body's center; in the riser model, they result from a compositionally produced, low-density, rising diapir. The present study determines the surface stresses induced by such density anomalies and the expected surface expressions. The results are in good agreement with the predictions of the sinker model.

The Valhalla basin on Callisto is a multiringed structu-e that extends over much of the satellite's surface. Although its appearance differs in detail from lunar multiringed basins, its origin may also be attributed to lithospheric fragmentation accompanying collapse of the transient crater formed by an impact event. This paper explores the mechanics of the collapse process by treating the lithosphere as a thin elastic-Von Mises plastic sheet (plane geometry) or shell (spherical geometry). Flow of the underlying asthenosphere inward toward the crater cavity induces plastic failure of the lithosphere and produces a characteristic pattern of faults in the disrupted lithosphere. The pattern and extent of faulting is a function of a single dimensionless parameter that involves the strength and thickness of the lithosphere, the crater depth and diameter, and the surface gravity of the planet. The tectonic structures of Valhalla correspond well with the failure pattern expected for a large crater produced in a thin (circa 30 km) weak (strength