Analysis of the Attenuation Characteristics of an Elastic Wave Due to the Wave-Induced Fluid Flow in Fractured Porous Media

A theoretical model is presented to describe the elastic wave propagation characteristics in porous media of periodically arranged fractures. The effects of fracture geometric parameters on a compressional wave (p-wave) are considered through analysis of the wave induced fluid flow (WIFF) process between the fractures and the background media. The diffusion equation in porous media is used to reveal how the entire diffusion process affects the wave propagation. When the thickness proportion of fractures tends to 0 and 1, the WIFF does not take place almost between fractures and background matrix porosity, and therefore the media elasticity modulus is perfectly elastic. When the fracture thickness fraction achieves a certain value, the peak of the attenuation curve reaches the maximum value at a particular frequency, which is controlled by the fluid mass conservation and stress continuity conditions on each fracture boundary. That is, the inter-coupling of fluid diffusion between the adjacent layers is important for waves attenuation. Physically speaking, the dissipation of a wave is associated with the fluid flux essentially.