Quantifying Damage, Saturation and Anisotropy in Cracked Rocks by Inverting Elastic Wave Velocities

Abstract

Theoretically, crack damage results in a decrease of elastic wave velocities and in the development of anisotropy. Using non-interactive crack eective medium theory as a fundamental tool, we calculate dry and wet elastic properties of cracked rocks in terms of a crack density tensor, average crack aspect ratio and mean crack fabric orientation using the solid grains and uid elastic properties.Using this same tool, we show that both the anisotropy and shear wave splitting of elastic waves can be derived. Two simple crack distributions are considered for which the predicted anisotropy depends strongly on the saturation, reaching up to 60% in the dry case. Comparison with experimental data on two granites, a basalt and a marble, shows that the range of validity of our model extends up to total crack density of approximately 0.5, considering symmetries up to orthorhombic. In the isotropic case, Kachanov's [1994] non-interactive eective medium model was used in order to invert elastic wave velocities and infer both crack density and aspect ratio evolutions. Inversions are stable and give coherent results in term of crack density and aperture evolution. In the anisotropic cases -both transverse isotropic and orthorhombic symmetries were considered -anisotropy and saturation patterns were well reproduced by the modelling and mean crack fabric orientations is recovered. Inversion results agree very well with the laboratory data and are consistent with the rock microstructure in the dierent rocks investigated. Our results point out that: (1) it is possible to predict damage, anisotropy and saturation in terms of a crack density tensor and mean crack aspect ratio and orientation; (2) Using well constrained laboratory

A unified theory for elastic wave propagation through porous media containing cracks—An extension of Biot’s poroelastic wave theory

“…It is therefore necessary to include crack parameters, i.e., crack density and aspect ratio, in the elastic wave propagation modeling. Because these crack parameters have a substantial influence on the elastic wave velocities, they can be estimated or inverted from elastic wave velocity measurements (see Schubnel et al [35], Cheng and Toksoz [36]). …”

Common Evolution of Mechanical and Transport Properties in Thermally Cracked Westerly Granite at Elevated Hydrostatic Pressure

“…The scalar H has been calculated by many authors for a wide variety of crack geometries and fluid properties. In this work we use an appropriate and widely used scalar for non-interactive penny shaped cracks (KACHANOV, 1994;SCHUBNEL and GUÉGUEN, 2003;SCHUBNEL et al, 2006). One of the most straightforward methods is KACHANOV'S (1994) non-interactive effective medium theory, as it neglects stress interactions between cracks, and can therefore represent a valid approximation for low crack densities (up to *0.5).…”

“…In such a scheme, the evolution of elastic-wave velocities can be used to quantify uniquely both the crack density and aspect ratios. As all of these methods and concepts have been well discussed in previous publications (e.g., BENSON et al, 2006;SCHUBNEL et al, 2006), the precise details are not reproduced here. Figure 7 plots the dimensionless crack density q as a function of temperature.…”

“…The existence of embedded microcrack fabrics in rocks significantly influences the elastic moduli and inferred permeability (HEARD and PAGE, 1982), fracture toughness (K IC ) (NASSERI et al, 2005(NASSERI et al, , 2006, elastic wave velocities (REUSCHLE et al, 2006;SCHUBNEL and GUÉGUEN 2003;SCHUBNEL et al 2006), and the permeability of rocks (GUÉGUEN and SCHUBNEL 2003;BENSON et al, 2006).…”

Geophysical Properties of the Near Surface Earth: Seismic Properties

“…Numerous authors have attempted to use the shapes of either the strain curves (as in Figure 18) or wave speeds (as in Figure 19) to invert for various characteristics of the cracks and the distributions of their dimensions (e.g., Angus et al, 2009;Cheng and Toks€ oz, 1979;David and Zimmerman, 2012;Schubnel et al, 2006) under a variety of simplifying assumptions.…”