Fast Acoustic Imaging for a 3D Penetrable Object Immersed in a Shallow Water Waveguide (Journal of Computational Mathematics, 2018)
The paper is concerned with the inverse problem for reconstructing a 3D penetrable object in a shallow water waveguide from the far-field data of the scattered fields with many acoustic point source incidences. An indicator sampling method is analyzed and presented for fast imaging the size, shape and location of such a penetrable object. The method has the advantages that a priori knowledge is avoided for the geometrical and material properties of the penetrable obstacle and the many complicated iterative techniques are avoided during the inversion. Numerical examples are given of successful shape reconstructions for several 3D penetrable obstacles having a variety of shapes. In particular, numerical results show that the proposed method is able to produce a good reconstruction of the size, shape and location of the penetrable target even for the case where the incident and observation points are restricted to some limited apertures.