Dispersion and anisotropy of elastic waves in cracked rocks

Abstract

Rocks in the Earth's crust contain variable amount of cracks, depending on the deviatoric and confining stress levels, pore pressure, and temperature conditions. Crack damage results in effects that have been investigated for a long time, in particular, a decrease in elastic wave velocity and the development of anisotropy. In this paper, we focus on cracked rocks and develop a method to calculate both the elastic wave anisotropy and the dispersion in a fluid‐saturated cracked rock. We show that analytic expressions can be derived for both properties in terms of the crack density tensor components. Two fundamental theoretical tools are used in this purpose. The first one is the effective medium theory and the second one is the anisotropic poroelastic theory. Using both, it is possible from first principles to predict anisotropy and dispersion. Results are shown to be valid up to a total crack density of 0.5. The failure threshold appears close to a total crack density of 1. Between 0.5 and 1, the model still gives reasonably good results. Anisotropy can increase up to 60% and dispersion up to 30%, depending on the crack distribution. These results point out important differences that could exist in fluid‐saturated rocks between laboratory (high frequency) data and field (low frequency) results.