Relating Gravity, Density, Topography and State of Stress Inside a Planet

  • B. Valette
  • F. Chambat
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 127)


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.


Perturbation Topography Clairaut’s equation Gravity Stress density. 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • B. Valette
    • 1
  • F. Chambat
    • 2
  1. 1.LGIT, IRDUniversité de SavoieLe Bourget du Lac CedexFrance
  2. 2.ENS LyonLSTLyon Cedex 07France

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