Scattering theory and Volterra renormalization for wave modeling in heterogeneous acoustic media

Abstract

Scattering theory is a promising tool for seismic modeling and inversion. However, the Born series related to the governing Lippmann Schwinger equation(LSE) is limited by convergence. Various partial series summations are developed to separately model specific primary or multiple events. However, these nonlinear approximations also have limitations when the perturbation is large and/or spatially extended. We propose a novel renormalization technique to LSE for full wavefield modeling. The renormalized LSE is a Volterra type and possesses absolute convergence properties. The related renormalized Green’s function is one-way in space and two-way in time and has a set of unique properties, e.g., real value, triangular, etc. By introducing wavefield separation, the renormalized LSE is divided into two sub-Volterra type integral equations, which can be solved non-iteratively. The study has the potential to make the scattering theory into a useful component of seismic forward modeling methods. Besides, it also provides insight for developing a different inverse scattering based inversion method.