Source Inversion Based on Distributed Acoustic Sensing-Type Data

Litao Shen, Tian-Yi Wang () and Haoran Zhang
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Litao Shen: School of Science, Wuhan University of Technology, Wuhan 430070, China
Tian-Yi Wang: School of Science, Wuhan University of Technology, Wuhan 430070, China
Haoran Zhang: Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China

Mathematics, 2024, vol. 12, issue 12, 1-24

Abstract: In this study, we investigate the inverse problem of the two-dimensional wave equation source term, which arises from the Distributed Acoustic Sensing (DAS) data on the boundary. We construct a new integral operator that maps the interior sources to the DAS-type data at the boundary. Due to the noninjectivity and instability of the integral operator, which violates the well posedness of the inverse problem, a minimization problem on a compact convex subset is formulated, and the existence and uniqueness of the minimizer are obtained. Numerical examples for different cases are illustrated.

Keywords: inverse problem; source term; DAS-type data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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