Multiparameter identification of fluid-saturated porous medium with the wavelet multiscale method

In this article, the problem of estimating the parameters of the fluid-saturated porous medium is considered. To overcome ill conditioning and multiple minima, a wavelet multiscale method is presented and applied to the multiparameter identification of the fluid-saturated porous medium. On the basis of a multiscale inversion strategy, the parameter identification is decomposed to multiple scales with wavelet transform. The original inverse problem is reformulated to be a set of subinverse problems that rely on different scale variables and is solved successively according to the size of the scale from the smallest to the largest. At each scale, the regularized Gauss-Newton method is carried out, which is stable and fast, until the optimum solution of the original inverse problem is found. The wavelet multiscale method is described as the combination of three operators: a restriction operator, a relaxation operator, and a prolongation operator. The restriction operator matrix and the prolongation operator matrix are available by adopting the compactly supported orthonormal waveletDaubechies wavelets. The results of numerical simulations demonstrate that the wavelet multiscale method is a fast and widely convergent inversion algorithm.