Some authors have recently published different parametrizations of viscoelastic anisotropic media of particular symmetry type (e.g., transversely isotropic or orthorhombic).The aim of this paper is to extend such work to media of arbitrary anisotropy type, that is to say to triclinic media. In contrast to previous work, our parametrization uses complex anisotropy parameters and constitutes a "natural" extension to viscoelastic media of previous work dealing with non-attenuating elastic media of arbitrary anisotropy type. The new parametrization allows to compute the complete directional dependence of approximate velocities and quality factors Q of the 3 bulk waves. These approximate formulas are checked on qP-wave experimental data in a moderately anisotropic sandstone sample. Compared to the exact solutions, the errors observed on the approximate velocity are small and hardly exceed 1%. The errors on the approximate quality factor Q is reasonable, typically smaller than 6%, considering the huge directional dependence of Q (with variations of more than 160%).


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