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

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.