The Study Of Sparsity Constraint Regularization Method For The Inversion Problems Of Elastic Wave Equation In The Stratified Porous Media

The main content of the inverse problem of elastic dynamics is that using elastic waves spread in media to infer the physical properties, mechanical parameters distribution and structural characteristics of medium. The elastic wave equations in porous media can detailed describe waves spread in formation, the inversion problems of elastic wave equation in stratified porous media have very broad application prospects in some fields, such as, the petroleum engineering, geophysics, environmental engineering field and so on.This article based on elastic wave equations in porous media carries out a research in the sparse constraint regularization method. For the problems like the nonlinear of operator equations, the ill-posedness, and the existence of the noise on the observation data in the inversion process, the appropriate regularization process is necessary in order to obtain accurate and stable calculation results. The penalty item of traditional Tikhonov regularization method is quadratic which has a smoothing effect on the solution, and cause the solution over smooth; the sparse constraint regularization method could generate the sparse solution, which has potential advantages for dealing with exception point, boundary of angle, abnormal structure etc.(for example:the porous media).This article selects the two-dimensional elastic wave equation in the stratified porous media as the specific mathematical model. Firstly, using the sparse constraint regularization method to deal with the ill-posed mathematical model; Secondly, using the semi-smooth Newton algorithm method to solve the minimum point of sparse constraint functions, and research the convergence and stability estimation of the proposed algorithm; Finally, we make numerical simulations based on the inversion problem of the parameters of two-dimensional elastic wave equation in the stratified porous media. Theoretical analysis and numerical experiment’s results show that the sparse constrained regularization method for discontinuous medium model has good recognition ability, and the constructed numerical inversion method could solve the nonlinear and ill-posed seismic inversion problems more effectively. It has not only innovation significance in theoretically, but also some strong feasibility and high efficiency. These research results may provide a useful reference for some other area in the field of inverse problem.