地震勘探中波动方程反问题的小波、同伦方法一般力学与力学基础专业论文.docxVIP

Abstract Abstract – – III – Abstract Wavelet analysis is an international forward research field in recent years. It not only contains abundant mathematical theories, but also is a powerful method and tool in engineering — it brings new ideas to many fields. The homotopy method is a widely convergent method for solving nonlinear system of equations, and also has important applications in many fields. The theory and practice of inverse problem of wave equation in seismic prospecting indicate that local ex- tremum and ill-posedness are the bottlenecks restricting the development of the inversion theory. Therefore, this dissertation draws the wavelet analysis and the homotopy method into the inversion process, and carries out a series of studies of numerical inversion methods, which have the abilities of saving computational costs, noise suppression, global convergence and easy realization of the procedure. Consequently, we acquires some concrete wavelet, homotopy inversion methods. Firstly, the principle of wavelet multiscale inversion is introduced to the gen- eral parameter estimation problem. Basing on this principle and combining the mature and simple Galerkin method, we design a wavelet multiscale Galerkin inversion method. Numerical simulations are carried out for the inverse problem of one-dimensional wave equation in seismic prospecting. The numerical results and tests of noise suppression indicate the method’s effectiveness. Secondly, for the insufficiencies of traditional nonlinear minimization meth- ods, the wavelet multiscale inversion method and the stable and quickly conver- gent regularized Gauss Newton method are combined, and which are successfully applied to solve the velocity inverse problem of 2–D wave equation in seismic prospecting. Compared with simple iterative methods, the risk of trapped in local extremum is greatly reduced. Compared with the multigrid multiscale in- version method, it owns a quick decomposition and reconstruction algorithm.