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Issue ESAIM: Proc.
Volume 26, 2009
Mathematical methods for imaging and inverse problems
Page(s) 1 - 23
DOI http://dx.doi.org/10.1051/proc/2009002
Published online 25 April 2009

ESAIM: Proc., 2009, Vol. 26, pp. 1-23
DOI: 10.1051/proc/2009002

An inverse problem for faults in elastic half space

Darko Volkov

Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester MA 01609, United States;

darko@wpi.edu

Published online: 25 April 2009

Abstract
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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