Pressure dependence of velocity and attenuation and its relationship to crack closure in crystalline rocks

Abstract

Measurements of linear strain, ultrasonic velocity, and attenuation (Q−1) were made simultaneously as functions of confining pressure on core and outcrop samples from the Moodus, Connecticut, area. Strain measurements indicate the core samples contain cracks which formed in part by stress relief during recovery (Meglis et al., 1991). The outcrop samples have a small crack porosity compared with the cores. Closure of cracks with increasing confining pressure causes an increase in velocity and a decrease in attenuation. We present a form for the pressure dependence of the crack density parameter ε (the number of cracks of unit radius per unit volume), which was used to incorporate the influence of crack closure with pressure into models of wave velocity and attenuation in cracked solids. The crack density parameter is represented as an exponentially decreasing function of confining pressure. The pressure dependence of ε was determined from the strain measurements using the non‐self‐consistent effective modulus approach of O'Connell and Budiansky (1974), from the velocity data using the solutions of Garbin and Knopoff (1973) and Hudson (1981), and from the attenuation measurements using the frictional attenuation model of Walsh (1966). All of the models fit the data reasonably well using an exponentially decaying ε described by one decay constant τ. However, some of the data are better fit by a crack density parameter with two decay constants, reflecting a rapid decrease of ε at low pressure and a slower decrease at higher pressure. There is considerable variation among the predicted decay constants for a given sample from the different data sets. Several factors contribute to this variation. For example, the two velocity models predict a different dependence of velocity on ε, which results in a different dependence of ε on pressure. For the Q−1 data, approximating dε/dP by a function with a single decay constant results in lower τ values for Q−1 than for strain or velocity. Finally, a large anisotropy in attenuation measured in the deepest core samples indicates that scattering is a significant source of wave energy loss in these samples, and therefore a frictional attenuation mechanism alone cannot account for all the observed attenuation.