Modelling of stress-induced anisotropy of seismic velocity of consolidated sandstone using a modified penny-shape crack model

Abstract

Summary Seismic velocities of porous rocks are sensitive to tectonic stress and understanding the effect of deformation of cracks contained in rocks is crucial in modelling the stress sensitivity of seismic velocity. In this study, we investigated the stress sensitivity of seismic velocities under both hydrostatic and anisotropic stress conditions based on ultrasonic velocity measurement results. First, assuming the penny-shape crack model, we inverted the crack properties using the relationship between measured P-wave velocities and hydrostatic pressure, which is necessary for modelling the anisotropic stress sensitivity of seismic velocity. Next, we extended the penny-shape crack model to estimate the sensitivity of seismic velocities under anisotropic stress conditions. The modelling results and the measured P-wave velocities under anisotropic stress conditions showed good agreement for all incident angles, demonstrating that the model can be used to estimate P-wave velocity in any direction given arbitrary anisotropic stress conditions based on the velocities measured under hydrostatic stress conditions. Furthermore, the results suggest that stress-induced velocity anisotropy has a linear relationship with initial cumulative crack porosity, and rocks with higher stress sensitivity of velocity have higher velocity anisotropy under anisotropic stress conditions.