The paper presents an original approach to numerical simulation of sonic logging for tilted transversely isotropic media with attenuation. We suggest a new way to introduce attenuation to the stiffness tensor components for anisotropic media, so that the quality factors of the elastic waves are of a given quantity. The numerical approach itself is based on the Lebedev finite difference scheme on staggered grid applied to cylindrical coordinate system which is more efficient than well-known rotated staggered grid scheme. The numerical experiments, presented in the paper, were done to illustrate an impact of anisotropy and attenuation on a sonic logging, for example appearance of azimuthal component of the displacement velocity even in case of volumetric source acting at the axis of a fluid-filled borehole.


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