The Conjugate Gradient Method For The Inversion Of Fluid Saturated Porous Media Wave Equations

Compared to single-phase medium, fluid saturated porous media is closer to the actual formation of the real layers, its wave equation can describe elastic wave propagation in the formation in more detail, which makes the inverse problem of fluid-saturated porous media wave equations have a wide range of applications in many fields such as geophysical exploration, earthquake engineering, and so on. However, it faces basic difficulties as the nonlinear of operator equation, ill-posedness of solution and heavy amount of calculate. Therefore, to solve these problems better will have a very valuable theoretical and practical value for the further expansion of inversion problem of fluid-saturated porous media wave equations.In this paper, the main difficulties of current fluid-saturated porous media wave equation inversion process are counted, and the two-dimensional fluid-saturated porous media wave equation is chosen as a concrete mathematical model. Tikhonov regularization method is applied to the nonlinear problem to realize appropriate regularization, the widely-convergent homotopy methods and conjugate gradient method for solving large scale optimization problems are combined to ultimately construct the regularization-homotopy-conjugate gradient method. It overcomes serious shortcomings of traditional iterative methods depend heavily on the initial selection and relax limit of the initial guess solution, so as to not only guarantee the convergence of the method, significantly reduce computational cost of inversion, but also achieve the purpose of quickly finding the global optimal solution of the nonlinear inverse problems.In the paper, constructed inversion method is applied to inverse problem of two-dimensional fluid saturated porous media wave equation to carry out numerical simulations to further test its feasibility, efficiency and stability. We selected and layered medium and single-abnormal medium as typical models, and solve for porosity, one of parameters of fluid saturated porous media wave equation. By comparing number of iterations, computer time and errors between the exact value and iterations, the various algorithms for different media model are compared and analyzed from practice. The results of numerical simulations fully demonstrated that the constructed numerical inversion methods can deal with non-linear ill-posed inversion of seismic exploration more effectively and overcome the above essence difficulties in some extent, which has not only theoretical innovation significance, but also strong feasibility and high efficiency.