Crack-Induced Shear-Wave Orthorhombic Anisotropy: Modeling and Inversion of Shear-Wave Borehole Measurements

Rocks in horizontally layered sediments often exhibit transversely isotropic (TI) characteristics and contain aligned fractures/cracks due to tectonic movement and stress. We model the effective elastic properties of the TI medium containing vertically aligned cracks using the sphere-equivalency of the effective scattering method. Results show that the corresponding anisotropy of the VTI background medium containing vertically fluid-filled ellipsoidal inclusions can be characterized by the orthorhombic anisotropy model. The shear-wave anisotropy of the model is governed by three anisotropy parameters, corresponding to the horizontal plane, and the two vertical planes that are normal and parallel to the crack plane, respectively. Effects on anisotropy parameters due to cracks are examined in detail, showing that one can use shear-wave measurements to evaluate both the TI and crack parameters of the cracked TI-rock. Based on the theoretical analysis, we develop an inversion method to estimate shear anisotropy parameters from the four-component shear- wave logging measurement in a vertical borehole penetrating the orthorhombic rock. The inversion method is validated with synthetic data and applied to interpret acoustic anisotropy from borehole measurements acquired in a fractured shale formation, where theoretical predictions and measurements are found in good agreement. Plain Language Summary Rock physics models provide the basis to link fracture properties to seismic attributes. The sphere-equivalency of the effective scattering method is a reliable tool for modeling the orthorhombic anisotropy of cracked TI rocks. Of the three shear anisotropy parameters, the one that relates to the background TI is almost unaffected by cracks while the remaining two are strongly related to cracks, indicating that one can use shear-wave measurements to evaluate both the TI and crack parameters of the cracked rock. Moreover, we develop an inversion method to estimate these three shear anisotropy parameters from borehole acoustic measurements, providing an efficient tool for fracture characterization of anisotropic sedimentary rocks.