Inverse Boundary Value and Inverse Scattering Problems

主要研究者：James Ralston/Gregory EskinDMS-0139192摘要当人们希望从远距离观测或在不穿透内部的情况下在物体表面进行的测量中恢复物体的物理性质时，就会出现逆散射问题。广义地解释，它们包括无损检测和医学成像的方法。这里提出的问题包括表明，从原理上讲，可以根据非均匀弹性体对表面压力的响应来确定其性质，也可以根据反射声波来确定固体障碍物周围介质和障碍物本身的声学性质。更具体地说，我们提出的问题包括：1）证明了由非均匀弹性体对无穷小边界变形的响应唯一地确定其拉梅参数是可能的。2）对于非均匀介质中的障碍物，我们提出了证明，障碍物和声速在介质中可以恢复从散射振幅在一个固定的频率。3）做问题2）在技术上更困难的情况下，两个空间维，它成为一个“确定”的反问题。

PI: James Ralston/Gregory EskinDMS-0139192Abstract Inverse scattering problems arise when one wishes to recover physical properties of anobject from data obtained by remote observations or from measurements made on its surface without penetrating the interior. Interpreted broadly they include methods of nondestructive testing and medical imaging. The problems proposed here include showing that it is possible, in principle, to determine the properties of an inhomogeneous elastic body from its response to pressures on its surface, and to determine both the acoustic properties of a medium surrounding a solid obstacle and the obstacle itself from reflected sound waves.More specifically, the problems we propose include:1) showing that it is possible to uniquely determinethe Lame' parameters of an inhomogeneous elastic bodyfrom its response to infinitesimal boundary deformations.2) For an obstacle in an inhomogeneous medium we propose to show that both the obstacle and the sound speed in the medium can be recovered from the scattering amplitude ata fixed frequency.3) Do problem 2) in the more technically difficult caseof two space dimensions, where it becomes a "determined"inverse problem.