Inverse source problems for the stochastic wave equations: far-field patterns

2021/12/24 by Jianliang Li, Li, Jianliang, Peijun Li +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Ultrasonics and Acoustic Wave Propagation

paper · pdf · doi:10.48550/arxiv.2112.12918

openalex publication_date 2021/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally isotropic Gaussian random field, whose covariance and relation operators are classical pseudo-differential operators. Given the random source, the direct problems are shown to be well-posed in the sense of distributions and the regularity of the solutions are given. For the inverse problems, we demonstrate by ergodicity that the principal symbols of the covariance and relation operators can be uniquely determined by a single realization of the far-field pattern averaged over the frequency band with probability one.

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