Abstract
This paper is concerned with an inverse problem for two-dimensional elastic solids. It seeks to recover the subsurface density profile based on the measurements obtained at the boundary. The method considers a temporal interval for which time dependent measurements are provided. It formulates an optimal estimation problem which seeks to minimize the error difference between the given data and the response from the system. It uses a boundary regularization term to stabilize the inversion. The method leads to an iterative algorithm which, at every iteration, requires the solution to a two-point boundary value problem. Several numerical results are presented which indicate that a close estimate of the unknown density function can be obtained based on the boundary measurements only.
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