Application Of Semi-Smooth Newton Method For Solving Elastic Wave Parameters Inversion Problem In Porous Media

Porous media is closer to the actual strata than traditional single-phase elastic medium, it can reflect the relationship between earthquake information and underground rock mechanical properties more realistic. Inversion and direct problem have a good application prospect based on this.In this paper, we carry out precise and efficient research of retrieval algorithm based on convex optimization theory for the problem of fluid saturated elastic medium parameters wave equation inversion. Firstly, using a unsplit staggered grid finite difference method solves the pore medium elastic wave equation forward problem which provides the high-quality computational data for inversion. Secondly, most of the various existing inversion algorithm are based on Gaussian noise model assumptions, however, observational data often contains a large amount of non-Gaussian noise in practice which mainly show up as large error of some of observational data, while other points remain intact, observational data like this has sparseness that can’t use the representation of normal distribution. The L1data fitting is able to detect the outliers accurately, and repair them automatically from the inversion program. Therefore, this paper uses the L1norm data fitting. However, focusing on the non-differentiable problem of the-norm optimization objective function, we adopt a family of smooth functions to approach this non-differentiable objective functional, build and analyze the semi-smooth Newton method solving the nonlinear optimization problems. Under appropriate assumptions, we complete the superlinear convergence analysis of the semi-smooth Newton method. Finally, considering the models of three horizontal layers medium and the porous medium, inversion of solid density parameters is realized by using our designed algorithm, the numerical results prove the effectiveness.of this method.