Source Inversion Based on Distributed Acoustic Sensing-Type Data

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.