Inverse scattering analysis of an elastic half-space by means of the fast volume integral equation method

A method for inverse scattering analysis of an elastic half-space using the fast volume integral equation method is presented. For the formulation of the inverse scattering analysis, the volume integral equation for the forward scattering analysis is modified so that it describes the relationship between the observed scattered waves at the free surface and the fluctuation of the wavefield. The inversion equation is obtained for reconstructing spatial spreads and the amplitude of fluctuations of the wavefield from the observed scattered waves due to point sources at the free surface. Linearization by the Born approximation as well as the Tikhonov regularization method is applied to the inversion equation. The fast generalized Fourier transform is also applied in order to solve the inversion equation. Numerical calculations are performed in order to investigate the convergence properties of the solution with respect to different regularization parameters. In addition, the effects of the number of point sources on the accuracy of the reconstruction results are examined.