Porosity reconstruction based on Biot elastic model of porous media by homotopy perturbation method

Fluid-saturated porous media are two-phase media, which are composed of solid and liquid phases. Biot theory for fluid-saturated porous media holds that underground media are composed of porous elastic solid and com-pressible viscous fluid filled with pore space. Compared with the single-phase media theory, the fluid-saturated porous media theory can describe the subsurface media more precisely, and the elastic wave equations in the fluid-saturated porous media contain more parameters used to describe the formation properties. There-fore, fluid-saturated porous media theory is widely used in geophysical exploration, seismic engineering, and other fields.This paper considers the porosity reconstruction problem of the elastic wave equations in the fluid-saturated po-rous media based on Biot theory, which is a typically nonlinear ill-posed inverse problem from mathematical viewpoint. The proposed method is a novel iteration regularization scheme based on the homotopy perturbation technique. To verify the validity and applicability, numerical experiments of two-dimensional and three-dimensional porosity models have been carried out. Numerical results illustrate that this method can overcome the numerical instability and are robust to data noise in the reconstruction procedure. Furthermore, compared with the classical regularized Gauss-Newton method, the homotopy perturbation method greatly widens the convergence region while keeping the fast convergence rate.(c) 2022 Elsevier Ltd. All rights reserved.