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Solar System Evolution: A New Perspective. By Stuart Ross Taylor. Cambridge University Press: 1993. Pp. 307. £35, $49.95.

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.

In previous papers in this series the smoothed particle hydrodynamics method (SPH) has been used to explore the conditions in which a major planetary collision may have been responsible for the formation of the Moon. In Paper II (W. Benz, W.L. Slattery, and A.G.W. Cameron 1987, Icarus 71, 30-45) it was found that the optimum conditions were obtained when the mass ratio of the impactor to the protoearth was 0.136. In the present paper we investigate the importance of the equation of state by running this optimum case several times and varying the equation of state and other related parameters. The two equations of state compared are the Tillotson (used in the previous papers) and the CHART D/CSQ ANEOS. Because of differences in these equations of state, including the fact that different types of rocks were used in association with each, it was not possible to prepare initial planetary models that were comparable in every respect, so several different simulations were necessary in which different planetary parameters were matched between the equations of state. We also used a new version of the SPH code. The results reaffirmed the previous principal conclusions: the collisions produced a disk of rocky material in orbit, with most of the material derived from the impacting object. These results indicate that the equation of state is not a critical factor in determining the amount of material thrown into orbit. This confirms the conclusions of Paper II that gravitational torques, and not pressure gradients, inject the orbiting mass. However, the way this mass is distributed in orbit is affected by the equation of state and the choice of rock material, the Tillotson equation for granite giving slightly larger mean orbital radius for the particles left in orbit than the ANEOS dunite for the same impact parameter. We also find, compared to Paper II, that in all subsequent cases the new SPH code leads to a slightly less extended prelunar accretion disk. We think this is due to the new shape adopted for the kernel. A few additional calculations were made to test the effects of increasing the impact parameter on the calculations, other parameters remaining unchanged. The motivation for this was that solar tides will have reduced the Earth-Moon angular momentum somewhat over the course of time. An increment of 6% in the angular momentum of the collision increases the amount of iron-free material in orbit and its mean orbital radius, but more than that leaves increasing amounts of iron in orbit (the iron has a small mean orbital radius). The debris from the destroyed impacting object tends to form a straight rotating bar which is very effective in transferring angular momentum. If the material near the end of the bar extends well beyond the Roche lobe, it may become unstable against gravitational clumping.

We have determined the global fracture patterns resulting from combinations of stresses due to tidal despinning and contraction or expansion. We find that Mercury's lineament pattern is consistent with a history of despinning and contraction. According to our model, the observed tectonic pattern implies that the despinning process reached completion before the planet ceased contracting. Our model predicts a stress due to contraction which is up to 1.8 times the maximum despinning stress on Mercury. The maximum contractional stress could be as large as 4 times the maximum despinning stress if the oldest fractures on the planet are N-S thrust faults in the equatorial region.

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.

Studies of tectonic landforms associated with Caloris Basin on Mercury suggest that isostatic adjustment has occurred in response to basin excavation, and that the smooth plains inside Caloris were emplaced significantly before isostatic equilibrium was attained. Combined with dynamical considerations, this leads us to propose that the Caloris region is characterized by a circular negative or zero free air gravity anomaly centered inside Caloris, and an annular positive anomaly which coincides with extensive tracts of young smooth plains outside the basin. This proposed gravity pattern differs markedly from that associated with mare-filled basins on the Moon.

This paper describes the relationship between the shock wave produced by an impact and the excavation flow that opens the crater. The excavation flow velocity is shown to be a nearly constant fraction of the peak particle velocity in the wave. The existence of an excavation flow is due to thermodynamically irreversible processes in the shock. The excavation flow velocity is thus very sensitive to nonideal constitutive effects such as porosity, plastic yielding, and unreversed phase transformations. Cratering computations that do not model these effects correctly may produce misleading results.

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.

This paper investigates the effect of shear heating in the asthenosphere on the thermal structure of the upper mantle. Equations describing the motion of the lithosphere over the asthenosphere in the presence of a strongly temperature-dependent stress-strain rate relation are derived and solved with the help of several approximations. These approximations are shown to be valid under conditions appropriate for the earth. Two sets of solutions are found. For one set (the “subcritical” solutions) a normal shear stress—velocity relation is found for small stresses. The velocity increases as the stress increases, reaching a maximum velocity σc for a critical stress σc. The subcritical solutions have a negligible effect on the thermal structure of the earth, even at the critical stress. The other set of solutions (the “supercritical” solutions) has the bizarre property that a decrease of applied shear stress leads to an increase of velocity. Thus, as the shear stress goes to zero, the velocity becomes infinite. At larger shear stresses the velocity decreases until it reaches σc at a stress σc (the two sets of solutions share this point in common). There are no steady solutions of any kind for shear stresses in excess of σc. We discard the supercritical solutions as candidates for the thermal structure of the earth on the basis of their instability to small perturbations of applied stress and temperature. The realm of subcritical solutions (stress less than σc, velocity less than σc) thus defines a regime of plate motion in which the thermal effects of shear heating are negligible. If the shear stresses acting on plates exceed σc, however, new physical processes must come into play to dissipate the excess heat generated. Assuming that the velocities of plates on the earth today are less than σc, relative to the deep mantle, a strict upper limit of a few tens of bars can be derived for σc, corresponding to effective viscosities of ca. 1019 poise in the asthenosphere.

A model for the ejection of material from an impact crater which links ejection velocity, fragment size, and shock pressure through a simplified stress-wave propagation and reflection scheme is presented. It is shown that a small amount of material (0.01 to 0.05 projectile mass) may be ejected at high velocity without suffering petrologically detectable shock pressures. The largest fragments ejected at any velocity are spalls that originate from the target planet's surface. The spall size is proportional to the radius of the primary impactor and the target tensile strength and inversely proportional to ejection velocity. The shock level in the spalls is low, typically half of the dynamic crushing strength of the rock. The model also predicts the aspect ratio of the spalled fragments, the angle of ejection, and the sizes and shock level of other fragments originating deeper in the target. Comparison with observational and experimental data shows generally good agreement.

The study investigates the mechanics of ring formation in lunar basins by collapse or slumping. Two classes of models are presented in order to broaden the range of plausible mechanisms involved. Extrusion flow models which assume a weak layer underlying a strong layer as well as plastic flow models which assume a continuous decrease of cohesion strength with depth are considered. In both classes, strength or resistance to deformation decreases with depth. If this decrease is rapid enough, in either set of models, at least one concentric fault scarp forms. The ratio between the scarp radius and the crater radius varies between 1.2 and about 2.7 depending on the model, and is thus in the range of observed radius ratios.

Both geologic and free-air-gravity data suggest that the positive mass anomaly associated with the Tharsis volcanoes may have reoriented Mars' lithosphere by as much as 25°. Since Mars is oblate (with flattening ƒ ⋍0.005 ), rotation of the lithosphere over the equatorial bulge by 25° produces membrane stresses of several kilobars, large enough to initiate faulting. These stresses were first evaluated by F.A. Vening-Meinesz (1947, Trans. Amer. Geophys. Union 28, 1–61) who treated the lithosphere as a thin elastic shell. The fracture patterns which result from these stresses are determined by the relation between stress and faulting proposed by E.M. Anderson (1951, The Dynamics of Faulting, Oliver & Boyd, Edinburgh). Plots of the magnitude and direction of stresses in a reoriented planet show that near Tharsis the dominant fault type should be north-south- trending normal faults. This normal fault province is centered about 30°N latitude and extends about 45° east and west in longitude. Similar faults should occur at the antipodes, north of Hellas Planitia. The polar regions should be occupied by roughly north-south-trending thrust faults which extend close to the equator south of Tharsis and north of Hellas. The regions between Tharsis and Hellas are subject to compression on a NE-trending axis and extension along a NW axis east of Tharsis (west of Tharsis the directions are NW compression and NE extension), thus predicting a zone of NNW and ENE strike slip faults east of Tharsis (NNE and WNW west of Tharsis). Although these patterns, except for the north-south normal faults north of Tharsis, have not yet been recognized, the discovery of such a tectonic system of the same age as Tharsis would provide strong support for the reorientation idea. Stresses due to reorientation appear to have little to do with Valles Marineris, since the stress normal to the axis of the Valles is predicted to be compressive, whereas geologic evidence suggests extension.

The possibility that certain very young meteorites originated as impact melts on a large asteroid or asteroids is investigated. Calculations of the thermal evolution of impact melt show that the solidification time should be long enough to produce igneous or quasi-cumulate textures within rocks if the crater is large enough and if the initial clast concentration is low, at least in some portion of the melt sheet. The number of collisions within the asteroid belt which would produce craters of the requisite size is calculated. Using an estimate of the current size distribution of asteroids, it is found that over 3000 such collisions should have occurred during the lifetime of the solar system. Excavation and ejection of the solidified melt by a subsequent impact would be dynamically easy because of the low escape velocities of even the largest asteroids but improbable because of the depth that must be sampled. A second, sufficiently large impact is rare, so only the products of one such double event have been obtained up to now.

Tidal deformation of the lithosphere of a synchronously rotating planet or satellite produces stresses that may result in a distinctive tectonic pattern. The lithosphereis treated as a thin elastic shell which maintains the equilibrium shape of a tidally distorted body. Stresses develop as the equilibrium shape changes during orbital evolution. E. M. Anderson's theory of faulting is used to translate this stress pattern into a tectonic pattern of faults on the planet's surface ( The Dynamics of Faulting , Oliver & Boyd, Edinburgh, 1951). On a body such as the Moon, which has receded from the Earth, an originally large tidal bulge has collapsed. The predicted tectonic pattern includes N-S striking thrust faults over an area extending roughly 30° in latitude and longitude around the sub-Earth point and its antipode. The polar regions above roughly 70° latitude exhibit normal faults striking from the near side of the Moon toward the far side. Strike slip faults, with offsets consistent with east-west compression, occur near the limbs. Stress differences are largest at the equator on the limbs, and may have reached several hundreds bars over the last few billion years of the Moon's history. The existence of such a tectonic pattern on the Moon can only be resolved by photogeologic mapping. At present, there is little evidence of this pattern; however, the crucial evidence probably lies in the poorly mapped lunar polar regions. These tectonic patterns, which could provide geologic evidence for large tidal distortions, may also be present on the Galilean satellites of Jupiter.

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.

A model for the origin of the outer rise is proposed which does not require multi-kilobar deviatoric stresses in the lithosphere. The model includes stresses developed by viscous flow of the lower part of the lithosphere as it is subducted. Besides the outer rise, features similar to an oceanic trench and island arc develop in the model. The elastic upper part of the lithosphere, treated approximately, is subject to extensional stresses on the seaward side of the trench axis. The observed topography of an oceanic trench and outer rise can be produced by a 90 km thick lithosphere subducting at 60 mm/yr if the average viscosity of the lower lithosphere is about 1023 poise.

The recent discovery of meteorites from the moon and the strong probability that the 8 SNC (Shergottite, Nakhlite and Chassignite) meteorites originated on Mars indicate that large hypervelocity impacts eject some solid debris at very high speed (more than 2.5 and 5 km/sec in the above cases). The standard Hugoniot relation between particle velocity and shock pressure predicts that lunar ejecta should be very heavily shocked (40–50 GPa) and Martian ejecta should be vaporized (100–200 GPa). However, the lunar meteorite ALHA 81005 was in fact subjected to less than 15 GPa, while the most highly shocked SNC meteorite was exposed to ca. 50 GPa, while others showing no detectable shock damage at all. Theoretical work shows that the normal Hugoniot relation doesn't apply in the vicinity of a free surface. The free surface is, by definition, a pressure-free boundary, so shock pressures on it must be identically zero. On the other hand, the acceleration of debris is proportional to the pressure gradient , so that near-surface material may be accelerated to high speed and still escape compression to correspondingly high pressure. This process occurs only in a restricted zone near the free surface. The thickness of this zone is proportional to the rise time of the stress-wave pulse generated by the impact. The rise time of the stress wave generated by a large impact is typically a/v i , where a is the projectile radius and v i its impact velocity. The near-surface zone in this case is comparable in thickness to a fraction of the projectile radius. Since the cratering event itself displaces many thousands of times the projectile mass, the quantity of lightly-shocked, high speed ejecta is small, amounting to only a few percent of the projectile's mass (for ejecta speed>few km/sec). The fastest solid ejecta leave at about 1/2 the impact velocity. Although the total quantity of high speed solid ejecta is thus small in comparison to the total crater ejecta, it is significant because no other process yields such high velocity fragments. Many meteorites appear to be near-surface samples of their parent bodies (many are regolith samples and one is a vesicular lava) and so may have been ejected by this process.

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.

This paper investigates the physics of meteoroid breakup in the atmosphere and its implications for the observed features of strewn fields. There are several effects which cause dispersion of the meteoroid fragments: gravity, differential lift of the fragments, bow shock interaction just after breakup, centripetal separation by a rotating meteoroid, and possibly a dynamical transverse separation resulting from the crushing deceleration in the atmosphere. Of these, we show that gravity alone can produce the common pattern in which the largest crater occurs at the downrange end of the scatter ellipse. The average lift-to-drag ratio of the tumbling fragments must be less than about 10 −3 , otherwise small fragments would produce small craters downrange of the main crater, and this is not generally observed. The cross-range dispersion is probably due to the combined effects of bow shock interaction, crushing deceleration, and possibly spinning of the meteoroid. A number of terrestrial strewn fields are discussed in the light of these ideas, which are formulated quantitatively for a range of meteoroid velocities, entry angles, and crushing strengths. It is found that when the crater size exceeds about 1 km, the separation between the fragments upon landing is a fraction of their own diameter, so that the crater formed by such a fragmented meteoroid is almost indistinguishable from that formed by a solid body of the same total mass and velocity.

An attempt is made to clarify the relation between current quarks and constituent quarks. Assuming that the two are related by a unitary transformation, we outline the properties of this transformation and, in the process, discover a new U(6) \ifmmode\times\else\texttimes\fi{} U(6) \ifmmode\times\else\texttimes\fi{} O(3) classification algebra for the hadrons. An example of this transformation is constructed in the lightlikeplane formulation of the free-quark model, where the transformation is found to be essentially unique and is just the operator solution to the problem of saturating chiral SU(3) \ifmmode\times\else\texttimes\fi{} SU(3). Using the algebraic structure of the free-quark model phenomenologically, matrix elements of currents between different hadrons are related. This abstraction of free-quark algebraic properties works fairly well for the axial-charge and magnetic-moment operators, although it fails for bilocal operators. Nevertheless, we obtain many successful approximate relations between matrix elements of currents, not the least of which is the recovery of the ratio $\frac{{\ensuremath{\mu}}_{T}(\mathrm{proton})}{{\ensuremath{\mu}}_{T}(\mathrm{neutron})}=\ensuremath{-}\frac{3}{2}$.

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.

The results of finite element (FEM) computations based on elastic dislocation theory are presented. It is shown that the ratio of fault depth to the lithospheric thickness is a significant factor in the sign of the rebound. Subsidence occurs if the fault penetrates less than approximately 0.68 of the way through the lithosphere. An uplift occurs if the fault cuts deeper. The FEM employed consisted of a 546 node, 500 element grid and a quasi-plane strain algorithm. The situation modeled consisted of a 30 deg dip fault in an initially planar elastic lithosphere overlying a Maxwell viscoelastic asthenosphere. It is suggested that postseismic rebound may be measurable over a several year interval, thus providing data on lithosphere thicknesses.

A simplified model of a subduction zone is presented, which incorporates the mechanical asymmetry induced by the subducted slab to anchor the subducting plate during post-seismic rebound and thus throw most of the coseismic stream release into the overthrust plate. The model predicts that the trench moves with respect to the deep mantle toward the subducting plate at a velocity equal to one-half of the convergence rate. A strong extensional pulse is propagated into the overthrust plate shortly after the earthquake, and although this extension changes into compression before the next earthquake in the cycle, the period of strong extension following the earthquake may be responsible for extensional tectonic features in the back-arc region.

The thickness and viscosity of a planetary lithosphere increase with time as the mantle cools, with a thicker lithosphere leading to the formation of one (or very few) irregular normal faults concentric to the crater. Since a gravity wave or tsunami induced by impact into a liquid mantle would result in both radial and concentric extension features, which are not observed in the case of the large impact structures on Ganymede and Callisto, an alternative mechanism is proposed in which the varying ice/silicate ratios, tectonic histories, and erosional mechanisms of the two bodies are considered to explain the subtle differences in thin lithosphere ring morphology between Ganymede and Callisto. It is concluded that the present lithosphere thickness of Ganymede is too great to permit the development of any rings.

Abundant geomorphic evidence for fluvial processes on the surface of Mars suggests that during the era of heavy bombardment, Mars's atmospheric pressure was high enough for liquid water to flow on the surface. Many authors have proposed mechanisms by which Mars could have lost (or sequestered) an earlier, thicker atmosphere but none of these proposals has gained general acceptance. Here we examine the process of atmospheric erosion by impacts and show that it may account for an early episode of atmosphere loss from Mars. On the basis of this model, the primordial atmospheric pressure on Mars must have been in the vicinity of 1 bar, barring other sources or sinks of CO2. Current impact fluxes are too small to erode significantly the present martian atmosphere.

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

The sequence of events subsequent to the impact of a large meteoroid in an ocean differs in several respects from an impact on land. Even if the meteoroid is large enough to produce a crater on the sea floor (that is, larger than a few km in diameter), the presence of water affects the character of the early-time events. The principal difference between land and oceanic impacts is the expansion of shock-vaporized water following an oceanic impact. A steam explosion follows the meteoroid's deposition of energy in the target. Shocked water expands from an initial pressure of 3 to 6 Mbar for 20-30 km/second impacts, ejecting water vapor and dust from the vaporized meteoroid several hundred km into the atmosphere. The violent vapor plume thus formed may explain how dust with a dominantly meteoritic composition can be dispersed to form a world-wide dust layer, as required by the Alvarez hypothesis.

A large body of evidence strongly suggests that the shergottite, nakhlite, and Chassigny (SNC) meteorites are from Mars. Various mechanisms for the ejection of large rocks at Martian escape velocity (5 km/sec) have been investigated, but none has proved wholly satisfactory. This article examines a number of possible ejection and cosmic-ray exposure histories to determine which is most plausible. For each possible history, the Melosh (1984, 1985, 1987) spallation model is used to estimate the size of the crater required to produce ejecta fragments of the required size with velocities not less than 5 km/sec and to produce a total mass of solid ejecta consistent with the observed mass flux of SNC meteorites. Estimates of crater production rates on Mars are then used to evaluate the probability that sufficiently large craters have formed during the available time. The results indicate that the SNC meteorites were probably ejected from a very large crater (greater than 100 kilometers in diameter) about 200 million years ago, and that cosmic-ray exposure of the recovered meteorites was initiated after collisional fragmentation of the original ejecta in space at much later times (0.5 to 10 million years ago).

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.

We are deeply disturbed by the recent escalation of political assaults on scientists in general and on climate scientists in particular. All citizens should understand some basic scientific facts. There is always some uncertainty associated with scientific conclusions; science never absolutely proves anything. When someone says that society should wait until scientists are absolutely certain before taking any action, it is the same as saying society should never take action. For a problem as potentially catastrophic as climate change, taking no action poses a dangerous risk for our planet.

THERE is considerable interest1,2 in detecting gravitational radiation from pulsars, in particular NP 0532 (the Crab Nebula pulsar). In this article the gravitational radiation to be expected from NP 0532 is estimated on the basis of the oblique rotator model3–6. This is a “lighthouse” model which postulates that pulsars are rotating neutron stars with a frozen-in magnetic field (see Fig. 1). The axis of the magnetic field is skewed with respect to the axis of rotation. Rotation carries the magnetic poles around in a circle, with the consequent emission of low frequency electromagnetic radiation. This radiation is then converted into other forms of energy, such as relativistic electrons and pulsed, higher frequency radiation4–8.

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.

The recent discovery of ALHA81005, a small meteorite that undoubtedly came from the moon, has raised questions about how an intact rock fragment could survive acceleration to planetary escape velocities. This acceleration could only have been produced by a large impact on the lunar surface. A small amount of material (0.005 to 0.02 projectile volume) may be ejected from an impact crater at speeds exceeding lunar escape velocity without suffering petrographically detectable shock damage. The ejected material is protected by stress-wave interference close to the free surface. The existence and size of this zone depend upon parameters such as the rise time of the stress pulse produced by an impact. The fragment size is a function of ejection velocity. The lunar meteorite was ejected during an impact event that produced a crater at least 3.6 km in diameter. Other meteorites may have originated in a similar way.

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.