ANALYSIS AND INTERPRETATION OF THE SURFACE-TOPOGRAPHY AND GRAVITATIONAL POTENTIAL OF VENUS

The relationship between the surface topography and gravitational pote ntial of Venus and the Earth is investigated over the spherical harmon ics of degree and order up to 75. The covarying harmonics of the topog raphy and the potential, i.e. the harmonics having nonnegative degree/ order correlation coefficients, are treated separately from the antiva rying harmonics,those with negative degree/order correlation coefficie nts. The covarying harmonics provide reliable estimates of the compens ation depth of the surface topography. The surface topography of the E arth specified by spherical harmonics of degree higher than 11 is esse ntially compensated isostatically at the Moho discontinuity, whereas t he lower-degree harmonics are largely supported by mantle dynamics. Fo r Venus the harmonics of degree lower than 9 are probably supported by mantle dynamics, while those of degree higher than 35 are most likely supported isostatically at a depth of about 45 km. There is a gradual increase in the compensation depth of the surface topography as the d egree of harmonics decreases from 35 to 9, implying a combination of i sostatic and dynamic support of these harmonics. Part of the topograph y specified by antivarying harmonics of degree greater than about 20 c annot be maintained by an isostatic compensation or a steady state dyn amic support; it is more likely time dependent. Assuming that this par t of the topography arises from viscous deformation of mantle under su rface loading, the gravity and topography relationship provides a firs t-order estimate of 5x10(24) Pa s for the viscosity of the Venusian ma ntle, This high viscosity results in a Rayleigh number of about 12000 for the mantle, which is only about 17 times greater than the critical Rayleigh number for convection, implying a very slow quasisteady conv ection in the mantle.