海洋波导中三维可穿透目标的快速声学成像

研究了用声传播远场分布信息来成像海洋波导环境中三维可穿透目标的反问题.建立了求解这类反问题的远场方程,基于内透射边界值问题的分析,讨论了远场方程解的唯一性和可解性,证明了总能找到远场方程的一个在最小平方意义下的近似解,其模在可穿透目标内部的取值是小的,而在外部的取值是大的,进而发展了一种快速成像可穿透目标的一种指示器样本方法.数值试验表明了这种方法是有效的,即使在有限孔径测量方式的情况,也能够得到未知目标的一个理想成像,而且不需要先验知道可穿透目标的任何几何与物理信息.

FAST ACOUSTIC IMAGING FOR A 3D PENETRABLE OBJECT IMMERSED IN AN OCEANIC WAVEGUIDE

The paper is concerned with the inverse problem for reconstructing a 3D unknown penetrable object in an oceanic waveguide from the far-field data of the scattered fields with many acoustic incidences.A far field equation for solving this problem is obtained. Based on the analysis of a boundary value problem called the interior transmission problem, the uniqueness of the solution and solvability for the far field equation are discussed.An approximated least-square solution,whose norm is small inside whereas is large outside the penetrable object,is obtained for the far field equation.An indicator sampling method for fast imaging the penetrable object is presented.The numerical results show that the proposed method is valid for obtaining a good reconstruction of the unknown penetrable object.A particular feature of the method is that it does not need the knowledge of any prior physical and geometrical information of the unknown object.