Inverse Obstacle Scattering in an Unbounded Structure (Communications in Computational Physics, 2019)
This paper is concerned with the acoustic scattering of a point incident waveby a sound hard obstacle embedded in a two-layered lossy background medium whichis separated by an infinite rough surface. Given the point incident wave, the directscattering problem is to determine the acoustic wave field for the given obstacle andinfinite rough surface; the inverse scattering problem is to determine both the obstacleand the infinite rough surface from the reflected and transmitted wave fields measuredon two plane surfaces enclosing the structure. For the direct scattering problem, thewell-posedness is studied by using the method of boundary integral equations. For theinverse scattering problem, we prove that the obstacle and the infinite rough surfacecan be uniquely determined by the measured wave fields corresponding to a singlepoint incident wave. To prove the local stability, the domain derivative of the wavefield with respect to the change of the shapes of the obstacle and the infinite roughsurface is examined. The local stability indicates that the Hausdorff distance of twodomains is bounded above by the distance of corresponding wave fields if the twodomains are close enough.