The circular‐crack model has been widely used in seismology to infer earthquake stress drop. A common assumption is that the background medium is isotropic, although many earthquakes occur in geologically anisotropic settings. In this article, we study the effect of anisotropy on stress drop for a circular crack model and present explicit formalism in both static and kinematic cases. In the static case, we obtain the relationship between stress drop and slip for a circular crack model in an arbitrarily anisotropic medium. Special attention is given to the transversely isotropic (TI) medium. The static formalism is useful in understanding stress drop, but not all quantities are observables. Therefore, we resort to the kinematic case, from which we can infer stress drop using recorded far‐field body waves. In the kinematic case, we assume that the crack ruptures circularly and reaches the final displacement determined by the static solutions. The far‐field waveforms show that the corner frequency will change with different anisotropic parameters. Finally, we calculate the stress drops for cracks in isotropic and anisotropic media using the far‐field waveforms. We find that in an isotropic medium, only shear stress acting on the crack surface contributes to shear slip. However, in a TI medium, if the anisotropy symmetry axis is not perpendicular or parallel to the crack surface, a normal stress (normal to the crack surface) can produce a shear slip. In calculating stress drop for an earthquake in an anisotropic medium using far‐field body waves, a large error may be introduced if we ignore the possible anisotropy in the inversion. For a TI medium with about 18% anisotropy, the misfit of inferred stress drop could be up to 41%. Considering the anisotropic information, we can further improve the accuracy of stress‐drop inversion.

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