Source time reversal (STR) method for linear elasticity

We study the problem of source reconstruction for a linear elasticity problem applied to seismicity induced by mining. We assume the source is written as a variable separable function $\mathit{f}\left(\mathit{x}\right)g\left(t\right)$. We first present a simple proof a local decay result for elasticity in the case of homogeneous media. We then extend the source time reversal method, originally developed for acoustic waves, to an elastic system of waves. Additionally, we present a fast reconstruction implementation for large data sets. This is especially useful in the elastic case, in which the numerical cost is higher than in fluid acoustics. We complement this work with several 2D and 3D numerical experiments and an analysis of the results.