Seismic Dispersion and Attenuation in Saturated Porous Rock With Aligned Slit Cracks

Abstract

©2018. American Geophysical Union. All Rights Reserved. We estimate the seismic attenuation and velocity dispersion induced by fluid pressure diffusion in a saturated porous medium containing a sparse distribution of aligned slit fractures. This is done by solving the scattering problem for a single crack and using Waterman-Truell scattering approximation for a distribution of cracks. This approach gives a numerical solution for the entire frequency range and analytical solutions for the low- and high-frequency limits. Analysis of the results shows that the characteristics of the seismic dispersion and attenuation for the slit cracks are similar to known results for penny-shaped crack. At high frequencies, the attenuation and dispersion are controlled by the crack density regardless of the crack geometry. At low frequencies, due to the different geometries of the slit and penny-shaped cracks, the characteristics of seismic dispersion and attenuation are different. For both the slit and penny-shaped crack case, the slope of the frequency dependence attenuation of factor (inverse quality factor) Q-1 tends to be 1. Yet the low-frequency asymptotic solutions for these two cases are somewhat different. For penny-shaped cracks, the Q-1(?) on the bilogarithmic scale has a straight line asymptote with slope 1, so that the attenuation factor at low frequencies is proportional to the frequency ?. However, for slit cracks, the asymptotic low-frequency solution contains a logarithmic function of ?, and no such asymptote exists. At the same time, similarly to the penny-shaped crack case, the solution for compressional velocity in the low-frequency limit is consistent with the anisotropic Gassmann theory.