Abstract
The diffraction problem for an elliptical crack in an anisotropic elastic medium is considered. For incident waves whose lengths are larger than the characteristic sizes of the crack, the problem is reduced to the calculation of two-dimensional absolutely converging integrals. In the case of a transversely isotropic medium, these integrals are simplified to one-dimensional integrals and can be calculated explicitly in some particular cases. The obtained solution for an isolated crack is used in the framework of a self-consistent method for calculation of the velocities and attenuation coefficients of the mean wave field propagating in the cracked medium. The cases of aligned elliptical cracks parallel or perpendicular to the isotropy axis of a transversely isotropic medium are considered in detail.
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