New iterative method for solving inverse scattering problem of 3D wave equation
Abstract
In this paper, a new iterative method for solving scattering potential inverse problem of threedimensional wave equation with the boundary impulse response is proposed. The simple form of the Frechet derivative of the above inverse problem has been obtained, along with a linearized integral equation which will be reduced to the problem of reconstructing a threedimensional increment potential function from its integrals over a family of halfellipsoids of revolution with one focus fixed at the origin and at the other focus running over all the points of a plane z = 0. This is an interesting integral geometry problem. Tikhonov's technology to make an inversion of Radon's integral geometry problem is efficiently and suitably used. The iteration is stable and effective, and excellent numerical results are obtained.
 Publication:

Scientia Sinica Series Mathematical Physical Technical Sciences
 Pub Date:
 October 1988
 Bibcode:
 1988SSSMP..31.1195X
 Keywords:

 Inverse Scattering;
 Iterative Solution;
 Wave Equations;
 Boundary Value Problems;
 Computational Geometry;
 Convolution Integrals;
 Physics (General)