The Application Of Proximal Newton-Type Method In Seismic Full Waveform Inversion

Seismic full waveform inversion(FWI) is an important problem in seismic exploration and has gained vast attention recently. An efficient FWI strategy is beneficial for locating the subsurface sources and for relieving the energy crisis,Which is useful for realistic application.The background of the sparse constrained regularization and the full waveform inversion are given. Also the current states of FWI is briefly introduced. Because available methods can not simulate the physical parameters properly. A new method is proposed.Quasi-Newton method and proximal mapping are considered first. Then proximal Newton-type method is introduced. The essential difference between proximal Newton-type method and quasi-Newton method is analyzed. The theories and properties of proximal Newton-type method are also considered which guarantees the feasibility of the method in FWI. Then the corresponding algorithm is given. The convergence of the finite difference scheme is analyzed by solving the forward problem with a constant velocity. The solution of acoustic equation with a complex velocity model is also given.At last, the application of proximal Newton-type method in FWI is discussed. The method is applied in frequency domain acoustic equation. It is first used to reconstruct a simple velocity model. The result is satisfactory.Then it is used to solve Marmousi velocity model. The details of this method are reconstructed. Thus the proximal Newton-type method could be a good candidate for solving the FWI problem. Conjugate gradient method is also used to reconstruct the Marmousi velocity model as a contrast. Results of the two methods are compared and analysized.