An inverse random source problem for the biharmonic wave equation

TL;DR

This paper investigates an inverse problem for the stochastic biharmonic wave equation, demonstrating that the source strength can be uniquely identified from wave measurements, with numerical validation for white noise sources.

Contribution

It introduces a novel method to recover the covariance operator of a stochastic biharmonic source from wave data, establishing uniqueness and providing numerical evidence.

Findings

Unique determination of source strength from a single wave realization

Well-posedness of the direct stochastic biharmonic problem

Numerical validation for white noise sources

Abstract

This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical pseudo-differential operator. The well-posedness of the direct problem is examined in the distribution sense and the regularity of the solution is discussed for the given rough source. For the inverse problem, the strength of the random source, involved in the principal symbol of its covariance operator, is shown to be uniquely determined by a single realization of the magnitude of the wave field averaged over the frequency band with probability one. Numerical experiments are presented to illustrate the validity and effectiveness of the proposed method for the case that the random source is the white noise.