This paper starts from a model in geophysics for the quasi static evolution of displacement fields occurring during the destabilization of fractured plates. We use the equations of linear elasticity in half space with traction free conditions on the surface and given tangential dislocations on the fault. We first discuss the derivation of the adequate Green's tensor for this problem. We then use this Green's tensor to obtain a simple and efficient approximation to the surface displacement

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... Next we show how to solve the fault inverse problem from measurements of surface displacements. We first give the solution in closed form. We then illustrate it on numerical examples which demonstrate the robustness of our reconstruction algorithm. Article published by EDP Sciences and available at http://www.edpsciences.org/proc or http://dx.