Pseudo-projection approach to reconstruct locations of point-like scatterers characterized by Lamé parameters and mass densities in an elastic half-space
A method for reconstructing the locations of point-like scatterers in an elastic half-space is developed in this article. Point-like scatterers are characterized by fluctuations of the Lamé parameters and the mass densities from the background structure of the wavefield. A representation of the wavefield is realized with the monopole and dipole Green’s functions. The main contribution of the present work is to clarify the far-field properties of the Green’s functions for both the monopole and dipole sources, which yields the pseudo-projection approach to the wave problem. Indicator functions that reconstruct the locations of point-like scatterers are defined by the far-field operator derived from the pseudo-projections and the near-field observation. Numerical computations were carried out to verify the accuracy of the pseudo-projection method. The sensitivities of the accuracy of the reconstruction results for the proposed method to random noise, the grid resolution at the free surface, and the analyzed frequency were also examined.
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