Fast wave source localization with sparse measurements

Abstract

Source localization problems are encountered in a variety of engineering dis- ciplines. Applications include earthquake localization, damage identification, speaker localization and structural testing. In most realistic settings, measure- ment points are sparse with respect to the physical domain. Moreover, the experimenter may not have control over where to place measurement points. It is in these imperfect settings that we still need to estimate the location of a wave source. In this talk we will outline a method for source localization inspired by the topological derivative used in shape identification. We will draw parallels to phase conjugation mirror techniques and gradient optimization. We will make no assumptions about the nature of the ambient media nor the computational domain. Specifically we allow for energy loss. We will also outline implemen- tation within an existing massively parallel finite element solver. Our proposed algorithm is minimally invasive and fully exploits the underlying optimization in the existing solvers. Moreover we can extend the method to other physical contexts.