Relating Gravity, Density, Topography and State of Stress Inside a Planet
Current interpretations of gravimetric and topographic data rely either on isostasy or on thin plate bending theory. Introducing a fluid rheology constitutes an alternative for global interpretation. In this paper, we present a method that enables to directly relate gravity to deviatoric stresses without any rheological assumption. The relation is obtained by perturbing the equilibrium equation and Poisson’s equation around a static spherical configuration, and by introducing a set of suited variables. Namely, we consider the density variation over the equipotential surfaces and the height of interfaces above their corresponding equipotential surfaces. The Backus decomposition of second-order tensors in scalar potentials (Backus 1966) is also found to be very useful. Finally, we show that the method can provide a way to infer strength differences and crustal thickness in a way that generalizes the isostasy approach.
KeywordsPerturbation Topography Clairaut’s equation Gravity Stress density.
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