The Diagonalized Contrast Source Inversion Approach for Elastic Wave Inversion

Abstract

This study focuses on the inverse scattering of objects embedded in a homogeneous elastic background. The medium is probed by ultrasonic sources, and the scattered fields are observed along a receiver array. The goal is to retrieve the shape, location, and constitutive parameters of the objects through an inversion procedure. The problem is formulated using a vector integral equation. As is well-known, this inverse scattering problem is nonlinear and ill-posed. In a realistic configuration, this nonlinear inverse scattering problem involves a large number of unknowns, hence the application of full nonlinear inversion approaches such as Gauss-Newton or nonlinear gradient methods might not be feasible, even with present-day computer power. Hence, in this study we use the so-called diagonalized contrast source inversion (DCSI) method in which the nonlinear problem is approximately transformed into a number of linear problems. We will show that, by using a three-step procedure, the nonlinear inverse problem can be handled at the cost of solving three constrained linear inverse problems. The robustness and efficiency of this approach is illustrated using a number of synthetic examples.