Land seismic multi-parameter full waveform inversion in anisotropic media is challenging because of high medium contrasts and because of surface waves. With a data-residual least-squares misfit function, the surface wave energy usually masks the body waves and the gradient of the misfit function exhibits high values in the very shallow depths preventing from recovering the deeper part of the earth model parameters. An optimal transport objective function, coupled with a Gaussian time-windowing strategy, allows to overcome this issue by more focusing on phase shifts and by balancing the contributions of the different events in the adjoint-source and the gradients. First, we show how OT function balances events. We then discuss a vertical transverse isotropic (VTI) example starting from a quasi 1D isotropic initial model. Despite some cycle-skipping issues in the initial model, the inversion based on the windowed optimal transport approach converges. Both the near-surface complexities and the variations at depth are satisfactorily recovered.