A tentative approach based on unified asperity deformation model and effective compliance theory to explain the pressure-dependence of anisotropic velocity in sandstones

Abstract

Seismic velocity variation with stress in fractured rocks can be explained as a consequence of fracture deformation, which results in changes in fracture compliance. Laboratory and field observations often show that the fractured rocks may contain preferentially aligned fractures distributed through the rock volume, and thus any model used to represent the pressure-dependent seismic properties of such materials must take alignment into account to explain velocity anisotropy phenomena in these rocks. We apply a model that accomplishes this goal by combining expressions relating fracture compliance to effective rock properties with an asperity deformation model. The compliance model allows a straightforward combination of multiple fracture sets, and the asperity deformation model represents the stress-dependence of fracture compliances. Previous applications have considered only isotropic media, but here we consider anisotropic velocity variations in two sandstones that include both measurements of the directional variation of velocity and its stress dependence. We approximate the anisotropic velocity variation using a single set of aligned fractures, but the data measuring velocity change with pressure shows that this set alone will not correctly model the rock. Combining the aligned set of fractures with a set of randomly oriented fractures causing isotropic velocity variation does accurately fit the observed data.