Cracks universally exist in Earth's crustal rocks. Many rocks are intrinsically anisotropic, which, when coupled with crack-induced anisotropy, significantly affect seismic wave propagation through the rocks. Using the method of sphere equivalency of effective scattering, we have developed a technique to model the effective moduli of transversely isotropic (TI) media containing cracks. The modelling results show that the wave characteristics are significantly affected by the interaction of the two anisotropy mechanisms. To validate the validity and accuracy, the theory was applied to a recent experiment made with a vertical transverse isotropy (VTI) medium containing cracks and shows significantly better agreement with the data. For a more realistic situation, the new modelling was applied to interpret the borehole acoustic anisotropy measurement results from a fractured VTI formation, showing that the theory can adequately explain the anisotropic characteristics of the field data. With the validation and testing, the theoretical results advocated in this study can be used with confidence. [ABSTRACT FROM AUTHOR]