双空间指示函数方法在三维分层介质中声波的反散射问题的推广

Generalized Dual Space Indicator Method for Inverse Scattering of Acoustic Waves in a Stratified Medium

给出了双空间指示函数方法在三维分层介质中声波的反散射问题的推广。这个方法基于以下观察:当Green函数的点源在障碍物内部时,远域数据的赋权积分可以很好地近似估计Green函数,但是当Green函数的点源在障碍物外部时,远域数据的赋权积分则不能很好地近似估计Green函数。建立一个积分方程:它的右边是声源在所重构区域的Green函数,则这个积分方程的解的范数在未知障碍物的内部有最值,而这些取得最值的点所围成的区域恰好就是所重构的障碍物区域。这个方法最显著的优势在于它不依赖于未知障碍物的边界条件。

A generalized dual space indicator method is presented for inverse scattering of acoustic waves in a stratified medium.The method is based on the observation that the weighted integration of the meas-ured scattered field can approximate the Green＇s function very well when source point of the Green＇s func-tion is inside the obstacle,but not so well when the source is outside the obstacle.An integral equation whose right-hand side is the Green＇s function with a source point from a searching region is set up.Then it is known that the norm of the solution of the integral equation has local maximum that lies inside the unknown obstacle,and the region which is surrounded by the local maximal points is exactly the region of obstacle.The most remarkable advantage of this method is that no knowledge of boundary condition is needed.