Near-Field Imaging Point-Like Scatterers and Extended Elastic Solid in a Fluid (Communications in Computational Physics, 2020)
Consider the time-harmonic acoustic scattering from an extended elasticbody surrounded by a finite number of point-like obstacles in a fluid. We assumepoint source waves are emitted from arrayed transducers and the signals of scatterednear-field data are recorded by receivers not far away from the scatterers (comparedto the incident wavelength). The forward scattering can be modeled as an interactionproblem between acoustic and elastic waves together with a multiple scattering problembetween the extend solid and point scatterers. We prove a necessary and sufficientcondition that can be used simultaneously to recover the shape of the extended elasticsolid and to locate the positions of point scatterers. The essential ingredient in ouranalysis is the outgoing-to-incoming (OtI) operator applied to the resulting near-fieldresponse matrix (or operator). In the first part, we justify the MUSIC algorithm for locatingpoint scatterers from near-field measurements. In the second part, we apply thefactorization method, the continuous analogue of MUSIC, to the two-scale scatteringproblem for determining both extended and point scatterers. Numerical examples in2D are demonstrated to show the validity and accuracy of our inversion algorithms.