Effective Elastic Properties of Rocks With Transversely Isotropic Background Permeated by Aligned Penny-Shaped Cracks

Seismic characterization of fractures is of great importance in many disciplines, for which rock physics models provide the basis to link fracture properties to seismic attributes. However, to date, most rock physics models neglect the background anisotropy that may exist in many fractured formations. Hence, in this work, we developed a theoretical model for rock effective elastic properties with penny-shaped cracks embedded in the transversely isotropic (TI) background medium. We first derived analytical solutions for the case with dry or fluid-filled penny-shaped cracks parallel to the isotropic plane of TI background medium. Further, the results were extended to the case with cracks inclined to the isotropic plane with any angles. We then studied, based on the developed theoretical model, two tight sand samples with TI and isotropic background, respectively, to illustrate effects of background anisotropy on effective elastic properties of fractured rocks. The results show that the background anisotropy has significant influence on P and S wave velocity anisotropy, as well as on shear wave splitting. The background anisotropy can either increase or decrease P and SH wave velocity anisotropy depending on crack inclination angles, whereas it has relatively small influence on SV wave velocity anisotropy. To further illustrate the important effects of background anisotropy, we compared theoretical predictions to ultrasonic measurements on a synthetic fractured sandstone sample with TI background medium. The results show notable improvement of the agreement between theoretical predictions and experimental results after considering background anisotropy.