Viscous relaxation of impact crater relief on Venus: Constraints on crustal thickness and thermal gradient

Because of the high surface temperature on Venus and the strong temperature dependence of strain rate in silicates, solid-state creep may be an important mechanism for the reduction of topographic relief on that planet. Venera 15/16 radar altimetric profiles of impact craters 30–140 km in diameter, however, indicate crater depths of several hundred meters, suggesting that substantial relaxation has not occurred for these features. On the basis of models for the viscous relaxation of impact crater topography we derive constraints on the thickness of the crust and the mean lithospheric thermal gradient beneath the craters. From the mean and variance of observed crater depth as a function of crater diameter on Venus and from estimates of the initial depths of fresh impact craters on Venus obtained by scaling from lunar observations, we formulate a statistical test for the maximum amount of viscous relaxation that is consistent with the observations at a specified confidence level. We develop a general formulation for gravity-driven flow in a linearly viscous fluid, incorporating the densities and temperature-dependent effective viscosities of distinct crust and mantle layers. The statistical comparison of predicted and observed depths yields linked upper limits to crustal thickness H and thermal gradient dT/dz. Since dT/dz. can be estimated from global heat loss arguments or thermal models, an upper bound to H may be derived. The preserved relief of the largest craters constrain H to be less than or equal to 10–20 km. Because the craters with measured depths appear to be representative of a larger population of impact structures in terms of regional elevation, geological unit, and degree of preservation of morphological detail, extrapolation of this result to lowlands and rolling plains regions on a global basis is not unreasonable. Such an extrapolation, together with isostatic considerations, yields an upper limit to the crustal volume of Venus of 1010 km3. This value is an order of magnitude less than the time-integrated volume of crust produced on Earth and implies either that the average rate of crustal generation has been much smaller on Venus than on Earth or that some form of crustal recycling has occurred on Venus.