A theory for wave equation inverse problem: The union method for scattered wave extrapolation and velocity imaging

Abstract

A new theory for inverse problem of wave equation, that is, the union method for scattered wave extrapolation and velocity imaging, is proposed in this paper. This method is very different from the classical wave extrapolation for migration, because we relate directly the scattered wave extrapolation to velocity inversion. And also this method is different from any linearized inverse method of wave equation, because we needn’t use linearized approximation. Because of this, the method can be applied to strong scattering case effectively (i. e. the value of scattered wave is not small, which can not be neglected). This method, of course, is different from nonlinearized optimum inverse method, because in this paper, the nonlinear inverse problem is turned into two steps inverse problem, i. e. scattered wave extrapolated and velocity imaging, which can be solved easily. Hence, the problem how to get the global optimum solution by using the nonlinearized optimum inverse method doesn’t bother us by using the method in this paper.

Keywords

inverse problem / wave extrapolation / velocity imaging / nonlinearization / wavelet representation