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Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could result in a biased estimation of formation properties but could provide a means to estimate in situ stress from sonic logging data. In order to properly account for the formation property alteration, we propose an iterative numerical approach to calculate the stress-induced anisotropy around a borehole by combining the rock physics model of Mavko et al. (1995) and a finite-element method.We show the validity and accuracy of our approach by comparing numerical results to laboratory measurements of the stress-strain relation of a sample of Berea sandstone, which contains a borehole and is subjected to uniaxial stress loading. Our iterative approach converges very fast and can be applied to calculate the spatially varying stiffness tensor of 1 the formation around a borehole for any given stress state.2

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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.