The Relationship between Topography and Gravity on Earth and Venus

Abstract

The measurement of the admittance between the topography and the gravity of a planet as a function of wavelength provides important constraints on its interior processes. A detailed discussion of the influence of noise on such measurements shows that at long wavelengths the admittance is best determined in the frequency domain, using gravity as input and topography as output. This procedure is used to estimate the admittance in the Pacific and Indian Oceans. The observed values are reduced by volcanism above plumes, which produces a contribution to the long-wavelength-compensated topography. When this effect is taken into account there is little evidence that the admittance is reduced by the presence of a low viscosity zone in the upper mantle. A similar study of Venus shows an excellent correlation between gravity g and topography h for wavelengths greater than 700 km, with an admittance of about 50 mgal km -1. This value agrees well with that expected from numerical axisymmetric models of plumes and can be used to construct maps of residual topography by calculating h - g/50, where h is in kilometers and g in milligals. The power spectrum of the gravity field and its skewness, with positive anomalies covering a smaller area, but being larger, than the negative ones, are also in agreement with those of the numerical models. Of the major topographic features, only Aphrodite and Ishtar Terrae behave differently, with a value of admittance of about one-third of other large structures. This difference requires their topography to be partly supported by variations in crustal thickness. By analogy with similar structures on Earth, both are likely to be supported by volcanically thickened crust on top of rising plumes, though the observed relationships do not rule out other models. The behavior of the admittance at long wavelengths is important, because it can constrain the thickness of the convecting layer. At wavelengths of more than 3000 km the gravity data provides some evidence that the layer depth is about 1000 km. Over the center of Beta and Phoebe Regiones there are short-wavelength anomalies of residual topography, produced by crust that is thinner than that elsewhere, flanked by positive anomalies of thicker crust. The regions of thin crust occur beneath rift zones. This behavior can be explained if crust flows down the flanks of elevated regions above plumes, and can generate coronae when the plume support disappears.