In multi-parameter anisotropic full-waveform inversion (FWI) for surface seismic data, both the far-offset and near-offset data are required to obtain accurate estimations of anisotropic properties. However, in acoustic transversely isotropic media with a vertical symmetry axis (vertical transverse isotropy [VTI]), the near-offset data are insensitive to the high-resolution features of the two anisotropy parameters ε and δ in the typical parameterization (v_p, ε, δ), which results in the corresponding low-resolution reconstruction in acoustic anisotropic FWI. To improve performance in surface seismic FWI, we propose a novel parameterization for acoustic VTI media using the Thomsen parameters ε and δ, along with a relevant parameter C_s (associated with the combination of vertical velocity and the Thomsen parameters). Using the Born approximation, we derive analytical expressions for the radiation patterns under this new parameterization and compare them with those under different parameterizations. The radiation patterns are imperative for indicating the angular influence of the perturbation on the parameters. This indicates that introducing the new parameter C_s is crucial for improving the contributions of ε and δ to near-offset data. We also derive the corresponding three-dimensional gradients and adjoint wave equations for parameterization (C_s, ε, δ) in acoustic VTI media. Furthermore, we develop multi-parameter point spread functions to numerically evaluate sensitivity during inversion. As a result, we can perform acoustic VTI FWI using the parameterization (C_s, ε, δ), which is optimal for inverting both the low- and high-wavenumber components of the parameters (C_s, ε, and δ). Finally, we apply the synthetic data to test the accuracy and effectiveness of our multi-parameter acoustic VTI FWI algorithm. The results show that the proposed parameterization has the potential to invert near-offset records to high-resolution anisotropy parameters in an active-source seismic experiment.