Poroelastic scattering potentials and inversion sensitivities
Wenyong Pan, Kristopher A. Innanen
Estimating the seismic wavefields response corresponding to the small model parameters perturbations is a classical problem in inverse scattering problem of exploration geophysics. The Frechet derivatives or sensitive matrices play a crucial role in perturbation analysis and are considered as sensitivity kernels in least-squares inverse problems. The forward modeling problem in poroelastic media has been studied by many researchers, while the inverse problem for poroelastic media has rarely been investigated. The scattering potentials indicating the perturbations of model parameters can be considered as engines for seismic wave scattering. And they are closely related to the Frechet derivatives. In this research, we reviewed the Biot's theory for poroelastic wave equations and derived the poroelastic scattering potentials represented by different field variables firstly. And then we derived the coupled poroelastic Frechet derivatives with respect to 9 poroelastic parameters, namely, the Lame coefficients of the dry frame dry and , porosity/fluid term f, density of saturated medium sat, fluid density f, C, M, , and mobility of the fluid m using perturbation method and non-perturbation method. The porosity/fluid term f involved by Russell et al. (2011) for linearized AVO analysis is considered as a poroelastic parameter for sensitivity analysis. The explicit expressions for these Frechet derivatives with respect to different poroelastic parameters are provided. When wave propagating in poroelastic media, there are two kinds of compressional waves: the fast compressional wave and the slow compressional wave. In this research, we also derived the P-SV Frechet derivatives in which the fast compressional wave and slow compressional wave are coupled together.