Analysis and extensions of the Multi-Layer Born method

TL;DR

This paper improves the multi-layer Born method for scalar wave simulation in complex media by including evanescent modes, analyzing errors, and proposing high-order, cost-effective schemes.

Contribution

It introduces solutions to incorporate evanescent modes into the multi-layer Born method and develops high-order versions for better accuracy and efficiency.

Findings

One method is more accurate based on error analysis.

High-order schemes reduce computational cost for given accuracy.

Optimal discretization parameters are identified through rigorous analysis.

Abstract

Simulating scalar wave propagation in strongly heterogeneous media comes at a steep computational cost, and the widely used approach to simplification - split-step operators - sacrifices accuracy. The recently proposed multi-layer Born method has sought to resolve that problem, but because it discards evanescent modes, also produces large errors. In this work our main goal is to propose solutions to this critical issue by including evanescent modes in the simulation. We work in a setting where backscattering can be neglected, allowing us to only calculate forward propagation, and derive two possible schemes. A rigorous mathematical analysis of the numerical errors shows one method is more accurate. This analysis is also helpful for choosing optimally the discretization parameters. In addition, we propose high order versions of the multi-layer Born method that offer a lower computational cost for a given tolerance.