It is necessary to account for anisotropy in full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data in most geologic environments, for correct depth positioning of reflectors, and for reliable estimations of wave speeds as a function of the direction of propagation. In this framework, choosing a suitable anisotropic subsurface parameterization is a central issue in monoparameter and multiparameter FWI. This is because this parameterization defines the influence of each physical parameter class on the data as a function of the scattering angle, and hence the resolution of the parameter reconstruction, and on the potential trade-off between different parameter classes. We apply monoparameter and multiparameter frequency-domain acoustic vertical transverse isotropic FWI to synthetic and real wide-aperture data, representative of the Valhall oil field. We first show that reliable monoparameter FWI can be performed to build a high-resolution velocity model (for the vertical, the horizontal, or normal move-out velocity), provided that the background models of two Thomsen parameters describe the long wavelengths of the subsurface sufficiently accurately. Alternatively, we show the feasibility of the joint reconstruction of two wave speeds (e.g., the vertical and horizontal wave speeds) with limited trade-off effects, while Thomsen parameter is kept fixed during the inversion. The influence of the wave speeds on the data for a limited range of scattering angles when combined each other can, however, significantly hamper the resolution with which the two wave speeds are imaged. These conclusions inferred from the application to the real data are fully consistent with those inferred from the theoretical parameterization analysis of acoustic vertical transverse isotropic FWI performed in the companion report.