Dispersion and anisotropy of elastic waves in cracked rocks

Abstract

[1] 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 fluidsaturated rocks between laboratory (high frequency) data and field (low frequency) results.

A model of deep crustal fluid flow following the Mw = 8.0 Antofagasta, Chile, earthquake

“…The evolution of hydrofractures in the direction of the anomaly is possible, when one considers perturbation to the principal stress state due to slab pull. Consequently, anisotropy [Schubnel and Guéguen, 2003] and aftershock migration equivalent to the pressure front migration [Miller et al, 2004] could result. Further analysis of the aftershock data and shear wave splitting could shed additional light on this mechanism.…”

Exploring Trends in Microcrack Properties of Sedimentary Rocks: An Audit of Dry and Water Saturated Sandstone Core Velocity–Stress Measurements

“…is a normalization factor [26], and i and i  are the anisotropic intact rock Young's modulus and Poisson ratio. This derivation yields an expression for the effective elasticity that can model stress-induced elastic anisotropy due to deviatoric stress fields.…”

Exploring trends in microcrack properties of sedimentary rocks: An audit of dry-core velocity-stress measurements

“…is a normalization factor (Schubnel and Guéguen, 2003), and E 0 i and ν 0 i are the anisotropic intact rock Young's modulus and Poisson's ratio. [Note that summation convention is not implied for equations [5][6][7].…”