Multi-parameter full waveform inversion (FWI) for transversely isotropic (TI) media with a vertical axis of symmetry (VTI) suffers from the trade-off between the parameters. The trade-off results in the leakage of one parameter’s update into the other. It affects the accuracy and convergence of the inversion. The sensitivity analyses suggested a parameterization using the horizontal velocity vh, Thomsen’s parameter ϵ and the an-elliptic parameter η to reduce the trade-off for surface recorded seismic data. We aim to invert for this parameterization using the scattering integral (SI) method. The available Born sensitivity kernels, within this approach, can be used to calculate additional inversion information. We mainly compute the diagonal of the approximate Hessian, used as a conjugate-gradient preconditioner, and the gradients step lengths. We consider modeling in the frequency domain. The large computational cost of the scattering integral method can be avoided with direct Helmholtz equation solvers.We apply the proposed method to the VTI Marmousi II model for various inversion strategies. We show that we can invert the vh accurately. For the ϵ parameter, only the short wavelengths are well recovered. On the other hand, the η parameter impact is weak on the inversion results and can be fixed. However, a good background η, with accurate long wavelengths, is needed to correctly invert for vh.Furthermore, we invert a real data set acquired by CGG from offshore Australia. We invert simultaneously all three parameters using the proposed inversion approach. The velocity model is improved and additional layers are recovered. We confirm the accuracy of the results by comparing them with well-log information, as well as, looking at the data and angle gathers.