Detecting buried wave-penetrable scatterers in a two-layered medium

In a two-layered medium, we prove that a buried inhomogeneous scatterer is uniquely determined from the wave field data measured in the upper half-space with respect to many incident point sources. Moreover, we extend the multilevel sampling method in Liu and Zou (2013) to numerically reconstruct the buried scatterer applying only few incident fields and partial scattered data. The extended recovery scheme only involves matrix-vector operations and does not need to solve any large-scale ill-posed linear systems or any optimization process. It is feasible to deal with the scatterers of different features and easy to implement, highly tolerant to noise and computationally quite cheap. We can regard it as an effective yet simple computational method to provide a reliable initial guess for the implementation in existing more accurate and refined optimization-type reconstruction algorithms.