A wavelet multiscale method for the inverse problems of a two-dimensional wave equation
This article considers the problem of estimating the velocity in a two-dimensional acoustic wave equation. The wavelet analysis is introduced and a wavelet multiscale method is constructed, based on the idea of hierarchical approximation. The inverse problem is decomposed into a sequence of inverse problems which rely on the scale variables and are solved successively according to the size of scale from the longest to the shortest. And in every inversion, at different scales, the regularized Gauss-Newton method is used, which is stable and fast, until the parameter of the primary inverse problem is found. The results of numerical simulations indicate that the method is a widely convergent optimization method (in some cases it may be global), and exhibits the advantages of conventional methods on computational efficiency and precision.