William M. Kaula

Venus tectonics: An overview of Magellan observations

The nearly global radar imaging and altimetry measurements of the surface of Venus obtained by the Magellan spacecraft have revealed that deformational features of a wide variety of styles and spatial scales are nearly ubiquitous on the planet. Many areas of Venus record a superposition of different episodes of deformation and volcanism. This deformation is manifested both in areally distributed strain of modest magnitude, such as families of graben and wrinkle ridges at a few to a few tens of kilometers spacing in many plains regions, as well as in zones of concentrated lithospheric extension and shortening. The common coherence of strain patterns over hundreds of kilometers implies that even many local features reflect a crustal response to mantle dynamic processes. Ridge belts and mountain belts, which have characteristic widths and spacings of hundreds of kilometers, represent successive degrees of lithospheric shortening and crustal thickening. The mountain belts of Venus, as on Earth, show widespread evidence for lateral extension both during and following active crustal compression. Venus displays two principal geometrical variations on lithospheric extension: the quasi-circular coronae (75–2600 km diameter) and broad rises with linear rift zones having dimensions of hundreds to thousands of kilometers. Both are sites of significant volcanic flux, but horizontal displacements may be limited to only a few tens of kilometers. Few large-offset strike slip faults have been observed, but limited local horizontal shear is accommodated across many zones of crustal stretching or shortening. Several large-scale tectonic features have extremely steep topographic slopes (in excess of 20°–30°) over a 10-km horizontal scale; because of the tendency for such slopes to relax by ductile flow in the middle to lower crust, such regions are likely to be tectonically active. In general, the preserved record of global tectonics of Venus does not resemble oceanic plate tectonics on Earth, wherein large, rigid plates are separated by narrow zones of deformation along plate boundaries. Rather tectonic strain on Venus typically involves deformation distributed across broad zones tens to a few hundred kilometers wide separated by comparatively undeformed blocks having dimensions of hundreds of kilometers. These characteristics are shared with actively deforming continental regions on Earth. The styles and scales of tectonic deformation on Venus may be consequences of three differences from the Earth: (1) The absence of a hydrological cycle and significant erosion dictates that multiple episodes of deformation are typically well-preserved. (2) A high surface temperature and thus a significantly shallower onset of ductile behavior in the middle to lower crust gives rise to a rich spectrum of smaller-scale deformational features. (3) A strong coupling of mantle convection to the upper mantle portion of the lithosphere, probably because Venus lacks a mantle low-viscosity zone, leads to crustal stress fields that are coherent over large distances. The lack of a global system of tectonic plates on Venus is likely a combined consequence of a generally lesser strength and more limited horizontal mobility of the lithosphere than on Earth.

The Lunar Laser Ranging Experiment: Accurate ranges have given a large improvement in the lunar orbit and new selenophysical information

The lunar ranging measurements now being made at the McDonald Observatory have an accuracy of 1 nsec in round-trip travel time. This corresponds to 15 cm in the one-way distance. The use of lasers with pulse-lengths of less than 1 nsec is expected to give an accuracy of 2 to 3 cm in the next few years. A new station is under construction in Hawaii, and additional stations in other countries are either in operation or under development. It is hoped that these stations will form the basis for a worldwide network to determine polar motion and earth rotation on a regular basis, and will assist in providing information about movement of the tectonic plates making up the earths surface. Several mobile lunar ranging stations with telescopes having diameters of 1.0 m or less could, in the future, greatly extend the information obtainable about motions within and between the tectonic plates. The data obtained so far by the McDonald Observatory have been used to generate a new lunar ephemeris based on direct numerical integration of the equations of motion for the moon and planets. With this ephemeris, the range to the three Apollo retro-reflectors can be fit to an accuracy of 5 m by adjusting the differences in moments of inertia of the moon about its principal axes, the selenocentric coordinates of the reflectors, and the McDonald longitude. The accuracy of fitting the results is limited currently by errors of the order of an arc second in the angular orientation of the moon, as derived from the best available theory of how the moon rotates in response to the torques acting on it. Both a new calculation of the moons orientation as a function of time based on direct numerical integration of the torque equations and a new analytic theory of the moons orientation are expected to be available soon, and to improve considerably the accuracy of fitting the data. The accuracy already achieved routinely in lunar laser ranging represents a hundredfold improvement over any previously available knowledge of the distance to points on the lunar surface. Already, extremely complex structure has been observed in the lunar rotation and significant improvement has been achieved in our knowledge of lunar orbit. The selenocentric coordinates of the retroreflectors give improved reference points for use in lunar mapping, and new information on the lunar mass distribution has been obtained. Beyond the applications discussed in this article, however, the history of science shows many cases of previously unknown, phenomena discovered as a consequence of major improvements in the accuracy of measurements. It will be interesting to see whether this once again proves the case as we acquire an extended series of lunar distance observations with decimetric and then centimetric accuracy.

Venus: a contrast in evolution to Earth.

Of the planets, Venus and Earth are by far the most similar in primary properties, yet they differ markedly in secondary properties. A great impact into Earth is believed to have created its moon and removed its atmosphere; the lack of such an impact into Venus apparently led to a greatly differing atmospheric evolution. The lack of an ocean on Venus prevents the recycling of volatiles and inhibits subduction, so that its crust is probably more voluminous than Earths, although distorted and quite variable in thickness. Venuss upper mantle appears to be depleted in both volatiles and energy sources because, in addition to the lack of volatile recycling, melts of mantle rocks are more dense than their solid matrix at pressures above 8 gigapascals and hence sink if they occur at depths below 250 kilometers. Appreciable energy sources persist at great depths to sustain the few great mountain complexes. The greatest current problem is reconciling the likelihood of a voluminous crust with indications of considerable strength at shallow depths of 20 to 100 kilometers.

Venus Tectonics: Initial Analysis from Magellan

Radar imaging and altimetry data from the Magellan mission have revealed a diversity of deformational features at a variety of spatial scales on the Venus surface. The plains record a superposition of different episodes of deformation and volcanism; strain is both areally distributed and concentrated into zones of extension and shortening. The common coherence of strain patterns over hundreds of kilometers implies that many features in the plains reflect a crustal response to mantle dynamic processes. Ridge belts and mountain belts represent successive degrees of lithospheric shortening and crustal thickening; the mountain belts also show widespread evidence for extension and collapse both during and following crustal compression. Venus displays two geometrical patterns of concentrated lithospheric extension: quasi-circular coronae and broad rises with linear rift zones; both are sites of significant volcanism. No long, large-offset strike-slip faults have been observed, although limited local horizontal shear is accommodated across many zones of crustal shortening. In general, tectonic features on Venus are unlike those in Earths oceanic regions in that strain typically is distributed across broad zones that are one to a few hundred kilometers wide, and separated by stronger and less deformed blocks hundreds of kilometers in width, as in actively deforming continental regions on Earth.

A NUMERICAL TREATMENT OF GEODYNAMIC : VISCOUS FLOW PROBLEMS INVOLVING THE ADVECTION OF MATERIAL INTERFACES

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Earth's Gravity Field: Relation to Global Tectonics.

An improved solution for the gravity field shows ocean rises, as well as trench and island arcs, as mass excesses. Ocean basins, areas of recent glaciation, and the Asian portion of the Alpide belt are mass deficiencies. Most features appear interpretable as varying behavior of the lithosphere in response to asthenospheric flow.

Gravity field determination and characteristics: Retrospective and prospective

Gravimetry has had a long history, using pendulums, torsion balances, and static spring gravimeters. Relative accuracy adequate for many geophysical problems was already attained by 1900, but it took another half century to build readily portable gravimeters. Calibration and datum definition remained problems until the 1970s when free-fall absolute gravimeters were developed that now have a precision of 10 -3 mGal. The problems of geographic inaccessibility and field party costs (notably in areas of greatest tectonic interest) are now being overcome by airborne gravimetry that has already achieved accuracies of 1-3 mGal with resolutions of 10 to 20 km. Satellite techniques are the best way to determine the long-wavelength variations of the gravity field. The resolution of the models has steadily improved with the number of satellites and the precision of the observations. The best current model includes tracking data from more than 30 satellites, satellite altimetry, and surface gravimetry and has a resolution of about 290 km (harmonic degree 70) with the most recent improvements coming from Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking of the SPOT 2 satellite and satellite laser ranging (SLR), DORIS, and Global Positioning System (GPS) tracking of the TOPEX/POSEIDON satellite. Meanwhile, radar altimetry has become the dominant technique to infer the marine geoid with a resolution of tens of kilometers or shorter. Similarly, the gravity fields of the Moon, Venus, and Mars have been determined to harmonic degrees 70, 75, and 50, respectively, although tracking limitations result in variations of spatial resolution. Modeling Earths gravity field from the abundance of precise data has become an increasingly complex task, with which the development of computer capacity has kept pace. Contemporary solutions now entail about 10,000 parameters, half of them for effects other than the fixed gravity field of Earth. Temporal variations arising from tides have long been well modeled, and nontidal changes are now being identified. The improvement in gravitational models engendered corresponding advances in geophysical interpretation. Isostatic models were refined and expanded to account for regional thermal and tectonic histories. Interpretation of the long-wavelength gravity field determined by satellite techniques has been mainly in terms of plate tectonics as a manifestation of mantle convection. Gravity has been significant in inferring that there must be a large increase in viscosity with depth (most strongly, from the apparent slow sinking of subducted slabs). The prospects for increasing accuracy and resolution in the determination of Earths gravity field rest primarily with the development of new measurement systems. Airborne gravimetry is taking promising new steps using GPS, but significant global model improvement awaits a dedicated satellite gravimetry system, and future satellite altimeter missions will do more for ocean dynamics studies than geoid improvement. Advances in interpretation will occur through the development of other data, such as seismic tomography, and larger-scale computer modeling of tectonics and convection.

Geophysical implications of satellite determinations of the earth's gravitational field

The variations of the gravitational field have been determined from satellite orbit perturbations with fair reliability up to at least spherical harmonic degree 8.The largest departure from hydrostatic equilibrium by a factor of 2 is the oblateness, which, together with the observed rate of deceleration of the earths rotation, leads to an estimate of about 1026 poises for the viscosity of the lower mantle.The remaining variations in the field are too large to be associated solely with the crust; their origin must be mainly in the mantle. The positive correlation with topography for degrees l ⩾ 6 and the rate of decrease of the variations (proportionate to l-2 in potential coefficients, or to l-1 in gravity anomaly power spectrum) are such that their source must in part be in the upper mantle, less than 400 km deep. However, the lack of obvious correlation with other indicators of upper-mantle activity such as sea-floor spreading and heat flow suggests that the density variations are the consequence of relatively small imbalances between dynamic disturbing effects and compensating restorative effects. At least part of the variations, particularly for degrees l⩽ 5, probably have their source in the stiff lower mantle.

Self-lubricated mantle convection: Two-dimensional models

We present results from convection models allowing for self-lubrication of downflows. Models impose a line source of chemically light, low viscosity material at the top of a convecting layer of temperature-dependent viscosity material. Low viscosity surface material serves as an analog to hydrated sediment/crust and the high viscosity upper portion of the convecting layer as an analog to mantle lithosphere. Slow near surface motion in the convecting layer entrains low viscosity material into zones of downflow, which has a lubricating effect. Once entrained lubricant is deeper than the cold high viscosity portion of the convecting layer, rapid upper boundary layer overturn occurs and system properties change (e.g., heat flux doubles). This marks transition to a lubricated state. Before and after transition, transport properties are dominantly determined by, respectively, the viscosity of mantle lithosphere and that of interior mantle. Lubricated and nonlubricated states appear as distinct regions in system output space suggesting that exchange between them is akin to a phase transition. That such exchange depends on a near surface lubricant implies that the geodynamics of planets lacking such lubricants may fundamentally differ from that of planets possessing them.

A co-accretional model of satellite formation

Abstract Numerical calculation of a simple accretion model including the effects of tidal friction indicate that coformation is tenable only if the planets Q is less than about 103. The parameter which most strongly affects the final mass ratio of the pair is the time at which the secondary embryo is introduced. Our model yields the proper Moon-Earth mass ratio if the Moon embryo is introduced when the Earth is only about 1 10 of its final mass. The lunar orbit remains at about 10 Earth radii throughout most of the growth. This model of satellite formation overcomes two difficulties of the “circumterrestrial cloud” model of Ruskol (1960, 1963, 1972): (1) The difficulty of accumulating a mass as great as the entire Moon before gravitational instability reduces the cloud to a small number of moonlets is removed. (2) The differences between terrestrial and outer planet satellite systems is easily understood in terms of the differences in Q between these planets. The high Q of the outer planets does not allow a satellite embryo to survive a significant portion of the accretion process, thus only small bodies which formed very late in the accumulation of the planet remain as satellites. The low Q of the terrestrial planets allows satellite embryos of these planets to survive during accretion, thus massive satellites such as the Earths Moon are expected. The present lack of such satellites of the other terrestrial planets may be the result of tidal evolution, either infall following primary despinning (Burns, 1973) or escape due to increase in orbit eccentricity.