A computational inverse random source problem for elastic waves

TL;DR

This paper introduces a non-iterative computational method to reconstruct the variance of a random elastic source from boundary measurements, significantly reducing computational cost and applicable to stochastic Maxwell equations.

Contribution

A novel, non-iterative approach for inverse random source problems in elastic waves that requires only single-frequency data and includes rigorous error analysis.

Findings

Method accurately reconstructs source variance from boundary data.

Significant reduction in computational cost compared to iterative methods.

Effective in numerical examples and adaptable to stochastic Maxwell equations.

Abstract

This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance of the random source from the correlation boundary measurement of the wave field. Compared with existing multi-frequency iterative approaches, our method is non-iterative and requires data at only a single frequency. As a result, the computational cost is significantly reduced. Furthermore, rigorous error analysis is conducted for the proposed method, which gives a quantitative error estimate. Numerical examples are presented to demonstrate effectiveness of the proposed method. Moreover, this method can to be directly applied to stochastic Maxwell equations.