A NEW METHOD FOR SOLVING THE INVERSE PROBLEM OF 1-D WAVE EQUATION IN SEISMIC PROSPECTING

摘要

This paper gives an operator equation inverse problem of one-dimensional wave equation in seismic prospecting problems T(p)=F, and discusses the qualities of operator T carefully. It means that the possibility of solving the above equation with iterative method. It is devoted to the study of the following inverse problem: Given the one-dimensional seismic waves travel model:（σ(x)ux)x=σ(x)uuThe purpose of seismic exploration is the acoustical impedance deternined by above equations. We first give the introductions of the paper. Secondly we introduce how to discuss the nonlinear operator equation for the coefficient inverse problem of the wave equation Thirdly, discuss the characteristics of the nonlinear operator T. At last, the iterative method for solving the coefficient inverse problem of the wave equation is given.