An inverse problem for the one-dimensional wave equation in multilayer media

Abstract

We consider half-line media which consist of many kinds of substances. We assume that the waves through this media are described by the one-dimensional wave equation. We can directly observe the data near the boundary point of the half-line, but we cannot directly observe the data of things away from the boundary point. In this situation, we try to identify these unknown things by creating an artificial explosion and observing on the boundary point the waves generated by the explosion. In the previous works related to this problem, only the speeds of the waves were treated, but we also take into account the impedances of the media in our setting.