A linear sampling method for detecting fluctuations of the wavefield in an elastic half-space

A linear sampling method for an elastic half-space is developed to reconstruct fluctuations in the wavefield. The starting point of the formulation is the near-field equation that was also used by Baganas et al. (2006). Instead of examining the norm of the solution of the near-field equation, we define a solvability index in order to obtain the spatial distribution of the amplitude of the solvability index and thus describe the location of the fluctuations. A numerical method for the evaluation of the index is also provided for a simplified algorithm; this method is based on a projection theorem for a Hilbert space and a singular value decomposition. Numerical calculations were performed, and the results validated the efficiency of the proposed method for reconstructing the fluctuations of a wavefield.