We have developed and numerically tested a method for determining parameters of homogeneous viscoelastic anisotropy from measurements of wavefields generated by point sources. The method is based on complex algebra and consists of several steps. First, a complex energy velocity surface is constructed from the directionally dependent velocity and attenuation measured along a set of ray directions. Second, a complex slowness surface is computed using the relation of polar reciprocity between the energy velocity and slowness vectors. The energy velocity vectors are homogeneous, but the corresponding slowness vectors are inhomogeneous. Finally, the complex phase velocity surface is calculated and inverted using the Christoffel equation. The inversion is nonlinear and can be performed in iterations. Numerical tests for the P-wave in transversely isotropic media showed that the method performed well for a wide range of models covering strong as well as weak velocity anisotropy and various levels of attenuation. The method was compared with a simplified approximate inversion when the inhomogeneity of the complex slowness vector is neglected. The neglect of the slowness vector inhomogeneity results in a significantly lower accuracy of the retrieved attenuation parameters. Accuracy with errors less than 10% is achieved only if the attenuation anisotropy is weak. This condition is, however, strongly restrictive because attenuation anisotropy is usually significant being more pronounced than the velocity anisotropy for most of rocks.