Seismic attenuation and dispersion in a cracked porous medium: An effective medium model based on poroelastic linear slip conditions

Abstract

Mechanical and hydraulic properties of a crack can significantly affect seismic wave propagation. To explore these effects, we developed an effective medium model that describes the P-wave dispersion and attenuation in inhomogeneous porous media containing a distribution of aligned cracks. Although there are numerous theoretical models for quantifying the seismic dispersion and attenuation, some of them are restricted to low frequencies at which only effects of the wave-induced fluid flow (WIFF) are considered but the influences of elastic scattering are ignored. Others only consider crack mechanical properties without incorporating crack permeability. The others describe the crack by a thin layer with infinitely lateral extension, neglecting the crack length information. To improve the applicability of previous theoretical models and overcome some of these restrictions, we consider a crack of finite size as a porous medium having different poroelastic properties from the matrix material and use poroelastic linear slip conditions to describe the jumps in the stress and displacement across the crack. We first study the scattering of a normally incident fast-P wave by a single circular crack. Then, by combining the theoretical solution and Foldy's scattering method, we develop an effective medium model that can relate seismic characteristics to mechanical compliance and hydraulic permeability of the cracks. Finally, we perform comprehensive parametrical analysis to study the role played by different characteristics of crack on the seismic signatures. We show that the P-wave phase velocity and attenuation are sensitive to the crack mechanical properties, fluid mobility inside the crack and crack size. The findings provide deep understandings on seismic characteristics in cracked rocks and may allow for extracting these properties from seismic data.