Pressure-dependent seismic velocities based on effective compliance theory and an asperity deformation model

Abstract

Seismic velocities of rocks depend strongly on confining pressure, which is often explained by the fracture compliances changes within the rocks. It is important to have an accurate model describing the relations between confining pressure and seismic velocities for applications such as time-lapse reservoir characterization. We propose a new model to address this problem by combining the existing effective compliance theory with new solutions for the pressure dependence of fracture compliances. Specifically, we assume the fracture contact surface can be represented by a set of elastic hemispheres with radii following power-law distribution, and the pressure dependence of seismic velocities can be expressed through pressure-dependent normal and tangential fracture compliances that are derived from Hertzian contact theory. Joint data fittings of P- and S-wave velocity laboratory data show that our model is accurate. We also implement fluid substitution using our model to explain the similar stress-induced velocity variations of fluid-saturated fractured rocks.