Integral Equation Methods With Multiple Scattering and Gaussian Beams in Inhomogeneous Background Media for Solving Nonlinear Inverse Scattering Problems

Abstract

I develop inverse scattering methods for velocity reconstruction in the subsurface, based on multiple scattering theory, Gaussian beams and nonlinear Born approximation. This method is based on a new version of the distorted Born iterative inverse scattering method. It directly uses an explicit representation of the data sensitivity function in terms of Green functions, rather than the indirect optimization approach based on the adjoint state method. I propose three direct scattering methods for forward modeling, namely, Gaussian beam integral equation propagators, nonlinear Born approximation, and multiple scattering. First, I apply a sensitivity kernel incorporating the Gaussian beam summation-based integral equation method and compute the background medium Green’s function in an inhomogeneous medium. Then I extend an approximate solution of the Lippmann–Schwinger equation, referred to as nonlinear Born approximation to inverse scattering problem. I apply the nonlinear Born approximation to forward modeling at each iteration. Furthermore, I combine the Gaussian beams with the multiple scattering theory for nonlinear scattering problems. I obtain the inversion results using the proposed approaches, which shows the capability for inverse scattering imaging. I have carried out several numerical experiments that involve reconstructing the resampled Marmousi and Society of Exploration Geophysicists (SEG)/European Association of Geoscientists and Engineers (EAGE) salt models from its smoothed version.