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Full waveform inversion of real seismic data should take into account a realistic Earth model including the anisotropy of the medium. However, incorporation of anisotropy increases both the computational requirements as well as the complexity of the problem. Therefore isotropic elastic FWI are frequently applied to process the seismic cross-well data. However, the domain of application of such strategy is not well defined. Here for elastic anisotropic (VTI) cross-well seismic data, we analyze results of anisotropic and isotropic inversions; and study to what extent we can retrieve anisotropy parameters.