Stability estimates of inverse random source problems for the wave equations by using correlation-based data
Year: 2024
Type: preprint
Abstract: This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined by its covariance operator in the form of a classical pseudo-differential operator. The inverse problem is to determine the strength function of the principal symbol by exploiting the correlation of far-field patterns associated with the stochastic wave equations at a single frequency. For the first time, we show in a unified framework that the optimal Lipschitz-type stability can be attained across all the considered wave equations through the utilization of correlation-based data.
Source: arXiv (Cornell University)
Authors: Li, Peijun, Liang, Ying, Wang, Xu
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403365190