Combined arrival-time imaging and time reversal for scatterer identification

The computational inverse problem of identifying a scatterer in a time-dependent wave field is considered. The wave speed of the background medium and the wave source are assumed to be known. Wave measurements, possibly noisy, are given at chosen discrete points in space (sensor locations) and time. The goal is to find scatterer parameters such as location, size and shape. The computational solution procedure consists of two steps. In the first step, a standard fast Arrival-Time Imaging (ATI) algorithm is employed. This results in a rough image which provides possible regions for the location of the scatterer. In the second step an optimization scheme based on Time Reversal (TR) is used to determine the location, size and shape of the scatterer. The preliminary ATI step has the effect of reducing considerably the search space for the TR optimization. Also, proposed here is an improved definition of the objective function used for the optimization, which tends to eliminate spurious solutions. Numerical experiments, based on a finite element discretization in space and an explicit Newmark time-stepping, show the identification capability of the proposed scheme, for a model problem involving the linear scalar wave equation in a bounded domain. Two types of scatterers are considered: a crack with a known orientation, whose location and size are sought, and a rectangular scatterer whose location, aspect ratio and size are sought. The performance of the scheme in the presence of measurement noise is also demonstrated.