A New Non-Iterative Reconstruction Method for Solving a Class of Inverse Problems

Abstract

Several classes of inverse reconstruction problems are written in the form of overdetermined boundary value problems. The general idea consists in rewriting them as an optimization problem. Therefore, a cost functional measuring the misfit between observed and predicted data is minimized with respect to a set of admissible solutions, leading to a non-iterative second order reconstruction algorithm. As a result, the reconstruction process becomes very robust with respect to noisy data and independent of any initial guess. In particular, we are interested in the spatial reconstruction and characterization of (micro-) seismic events via joint source location and moment tensor inversion from pointwise boundary measurements.