The principal purpose of this paper is to examine whether membrane stresses can support topographic loads on planetary elastic lithospheres. It is found that the ability of a spherical shell to support loads through membrane stresses is determined by the nondimensional parameter r = Ed/ApgR 2 where d is the thickness of the elastic lithosphere, AO is the density difference between the mantle and crust, and R is the radius of the planetary body. When this parameter is large membrane stresses can fully support topographic loads without flexure, and when it is small the influence of membrane stresses can be neglected. Solutions of the equation governing the behavior of a spherical shell are obtained for a topographic load expressed in terms of spherical harmonics. Spherical harmonic expansions of the measured gravity and topography for Mars and the moon are compared with the theory. It is found that for Mars the support of topography is primarily due to membrane stresses for n < 8 and for the moon for n < 17. For Mars the data for 4 _< n _< 7 give •-= 0.5. For the moon the data have considerable scatter that is attributed to the mascons but generally correlate with •-= 0.5. If bending stresses are neglected, the governing equation for the deflection of the spherical shell is Legendre's equation. A general solution is obtained for an axisymmetric load. This solution is applied to the Tharsis region on Mars. The 60-65% compensation of this region requires that •-= 0.6. The well defined fracture pattern surrounding the Tharsis region is attributed to tensional membrane stresses.

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PHY 94-07882 (H.E.S. 26. Because the crossover line is spacelike, the "bow-30. , Commun. Math. Phys. 25, 152 (1972). and L.S.); by NSF grants AST 91 -19475 and PHY legqedness" of the diagram is to some extent due to 31. We thank D. Eardley, R. Geroch, R. Gomez, J. M. 94-08378 and ~ational Aeronautics and Space Adair-choice of coordinates. A different choice of simultaneity can change the qualitative shape but must leave invariant the smooth merger of the spacelike crossover line with the light ray lines leaving the cusps. helpful comments on this work. We are especially grateful to J. M a s d and P. Walker for producing Fig. 10 and for contributing significantly to the analysis in this paper. We also thank MMultibeam bathymetry and magnetometer data from the Pitman fracture zone (FZ) permit construction of a plate motion history for the South Pacific over the past 65 million years.Reconstructions show that motion between the Antarctic and Bellingshausen plates was smaller than previously hypothesized and ended earlier, at chron C27 (61 million years ago). The fixed hot-spot hypothesis and published paleomagnetic data require additional motion elsewhere during the early Tertiary, either between East Antarctica and West Antarctica or between the North and South Pacific. A plate reorganization at chron C27 initiated the Pitman FZ and may have been responsible for the other right-stepping fracture zones along the ridge. An abrupt (8") clockwise rotation in the abyssal hill fabric along the Pitman flowline near the young end of chron C3a (5.9 million years ago) dates the major change in Pacific-Antarctic relative motion in the late Neogene.

In regions of slowly varying lateral density changes, the gravity and geoid anomalies may be expressed as power series expansions in topography. To a good approximation, geoid anomalies in isostatically compensated regions can be directly related to the local dipole moment of the density‐depth distribution. This relationship is used to obtain theoretical geoid anomalies for different models of isostatic compensation. The classical Pratt and Airy models give geoid height‐elevation relationships which differ in their functional form but which predict geoid anomalies of comparable magnitude. The thermal cooling model which explains ocean floor subsidence away from mid‐ocean ridges predicts a linear age‐goid height relationship of 0.16 m/m.y. Geos 3 altimetry profiles were examined to test these theoretical relationships. A profile over the mid‐Atlantic ridge is closely matched by the geoid curve derived from the thermal cooling model. The observed geoid anomaly over the Atlantic margin of North America can be explained by Airy compensation. The relation between geoid anomaly and bathymetry across the Bermuda Swell is consistent with Pratt compensation with a 100‐km depth of compensation.