Integral modelling of propagation of incident waves in a laterally varying medium: An exploration in the frequency domain

Abstract

In this work we present a formalism that intends to solve the problem of modeling wave propagation in the context of seismic inversion. The formalism is based on the linear perturbation theory of Cauchy’s equations. Based on the foregoing, we derived an equivalent Helmholtz equation for the propagation of waves in a variable density media. Then, we defined a solution, by using the boundary conditions on a half plane. This solution is of an integral nature and resembles expansion in a Neumann series. We implemented the solution of the first terms in the series, considering only the incident wavefield and neglecting the reflections. We show how this approximation works in different media that include lateral in homogeneities in the velocity. The method presented hereunder is intended as a first step in the modelling process for the full wavefield, to be used in seismic inversion methods, Full Waveform Inversion, for example.

Homotopy scattering series for seismic forward modelling with variable density and velocity

“…Many forward modelling methods, most of them for the ultrasound imaging, have been developed with variable density (Kwon and Jeong, 1998; Lavarello and Oelze, 2009; Mojabi and LoVetri, 2015; Rao et al ., 2020). In recent years, some studies about integral equation methods for seismic forward modelling with variable density have been considered in several publications (Yang et al ., 2016; Yao et al ., 2016; Sun et al ., 2017; Jiménez et al ., 2018; Luo and Wu, 2018; Farshad and Chauris, 2020). Although these studies have been developed, there is still an important need to develop more accurate and efficient methods for seismic forward modelling with variable density.…”