Volume 26, 2009Mathematical methods for imaging and inverse problems
|Page(s)||1 - 23|
|Published online||25 April 2009|
An inverse problem for faults in elastic half space
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester MA 01609, United States;
Corresponding author: firstname.lastname@example.org
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 field. 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.
Mathematics Subject Classification: 35P15 / 45E99 / 74L05 / 86A15
Key words: Linear elasticity / Green's tensors in half space / surface displacements / faults in half space / inverse problems.
© EDP Sciences, ESAIM, 2009
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