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ELASTIC SCATTERER RECONSTRUCTION VIA THE REGULARIZED SAMPLING METHOD

A three-dimensional inverse problem dealing with the reconstruction of cavities in a uniform semi-infinite solid from surface elastodynamic waveforms is investigated via the linear sampling method. To cater for active imaging applications that are often characterized by a limited density of illuminating sources, the existing near-field formulation of the linear sampling method is advanced in terms of its adjoint statement that features integration over the receiver surface rather than its source counterpart. To deal with an ill-posedness of the integral equation that is used to reconstruct the obstacle, the problem is solved by alternative means of Tikhonov regularization and a preconditioned conjugate gradient method. Computational details of the imaging procedure, including evaluation of the featured integrals as well as the implementation of the regularization approach, are highlighted. An example dealing with the reconstruction of an ellipsoidal void from noise-polluted synthetic measurements is included to illustrate the effectiveness of the proposed methodology.