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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 muchdoi:10.4208/jcm.1304-m3983 fatcat:s47pvzdw4ng5bemo7evvl6jzp4