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

机译：快速体积积分方程法对弹性半空间的逆散射分析

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摘要

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.
机译：提出了一种利用快速体积积分方程法对弹性半空间进行逆散射分析的方法。为了进行反向散射分析，修改了用于正向散射分析的体积积分方程，从而描述了在自由表面观察到的散射波与波场波动之间的关系。获得反演方程，用于根据观测到的由于自由表面上的点源而产生的散射波，重构空间扩展和波场的波动幅度。通过Born近似进行的线性化以及Tikhonov正则化方法被应用于反演方程。为了解决反演方程，还应用了快速广义傅立叶变换。进行数值计算以研究关于不同正则化参数的解的收敛性质。此外，还检查了点源数量对重建结果准确性的影响。

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