Inversion of Permeability for the Two‐Dimensional Porous Medium Using Travel Times

Abstract

The permeability identification problem for the two‐dimensional porous medium is studied by both the direct method and the optimization method. The formulation is different from the previous work. We determine the permeability from travel‐times of the fluid at every point in the domain, which can be measured in the experiment. This inverse problem can be solved into two steps. So this inverse problem can be divided into two subproblems to research. The numerical algorithm of the inversion of velocity for the two‐dimensional porous medium from the travel‐time of the fluid is studied, followed by the study of the numerical algorithm of the inversion of permeability for the two‐dimensional porous medium from the velocity. Finally the numerical examples are presented. Numerical results indicate the effectiveness and validity of the numerical algorithm used in this work.