Full-waveform inversion (FWI) aims to update the long and short wavelengths of the perturbations, in which parameterization plays an important role in multiparameter updates. For the anisotropic inversion of a transversely isotropic medium with a vertical symmetry direction (VTI), the parameterization can be chosen as five elastic constants ( c 11 , c 13 , c 33 , c 44 and density) or in other forms of parameterizations. In this paper, the choose of parameterizations is briefly discussed. The gradients of four elastic constants(vertical P-wave velocity, horizontal P-wave velocity, vertical S-wave velocity and δ) are calculated. The comparison with the inversion of elastic constants demonstrates the inversion of a combination with P- and S-wave velocities and Thomson parameters reduces interparameter crosstalks. To improve the inversion and avoid influence of one parameter with higher range of value on the inversion result than the other, the hierarchical inversion strategy is also applied in this paper. A three-layer VTI model is used to illustrate the hierarchical inversion strategy. Finally, a synthetic model is inverted with a parameterization of vertical P-wave velocity, horizontal P-wave velocity, vertical S-wave velocity and δ are illustrated.
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