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In this work, we present a modified Time-Reversal Mirror (TRM) Method, called Source Time Reversal (STR), to find the spatial distribution of a seismic source induced by mining activity. This methodology is based on a known full description of the temporal dependence of the source, the Duhamel's principle, and the time-reverse property of the wave equation. We also provide an error estimate of the reconstruction when the measurements are acquired over the entire boundary, and we show experimentally the influence of measuring on a subdomain of the boundary. Numerical results indicate that the methodology is able to recover continuous and discontinuous sources, and it remains stable for partial boundary measurements.

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We consider the data-driven acceleration of Galerkin-based finite element discretizations for the approximation of partial differential equations (PDEs) [1]. The aim is to obtain approximations on meshes that are very coarse, but nevertheless resolve quantities of interest with striking accuracy.Our work is inspired by the the machine learning framework of Mishra [2], who considered the data-driven acceleration of finite-difference schemes. The essential idea is to optimize a numerical method for a given coarse mesh, by minimizing a loss function consisting of errors with respect to the quantities of interest for obtained training data.