A method for the inverse scattering analysis is presented for an elastic half space. The volume integral equation method is introduced here to reconstruct fluctuation of the medium from scattered waves observed at the free surface. The Born approximation is applied to the volume integral equation to formulate the equation for the inverse scattering analysis. The equation is solved by means of the Krylov subspace iteration method and the fast generalized Fourier transform. Several numerical calculations are carried out to investigate the solutions of the inverse scattering analysis.

A volume integral equation method for the analysis of scattered elastic waves in a half space is presented. This method introduces the generalized Fourier and its inverse transforms during the Krylov subspace iterative method for obtaining the solutions. The derivation of the coefficient matrix for the integral equation is not required. Furthermore, the introduction of the fast method for the generalized Fourier transform enables us to reduce the large amount of the CPU time, which was observed in the previous article. Numerical calculations are carried out to examine the effects of the fluctuations of the wave field due to the Lamé constants as well as the mass density on scattered waves. The numerical results are also compared with the results of the Born approximation to check the accuracy of the present method.