Integrating surface wave information is challenging for land seismic full waveform inversion (FWI). Cycle-skipping of surface waves can easily occur due to their highly dispersive and oscillating properties. While this issue can be mitigated using wider basin objective functions, a more severe difficulty is related to the unbalanced amplitude distribution between surface waves and body waves. The energetic surface waves dominate the objective function and drive the inversion to update only the shallow structure. The contribution from body waves is masked and the deep structures are not recovered. In a recent study, we have shown how an optimal-transport based misfit function can help mitigating this issue, providing naturally a better balance between events (KR-OT approach). Here, we apply a newly introduced OT based misfit function, relying on a graph space approach (GS-OT), in this framework of elastic FWI for land data. GS-OT better handles cycle skipping than KR-OT. We show here that it also helps to balance the amplitude of different seismic events. We design a practical workflow based on the GS-OT misfit function, coupled with an on-the-fly source estimation wavelet and a Gaussian-time window strategy. The method is applied to a synthetic case study from the SEAM II Foothill model. From crude velocity models, high resolution of VP and especially VS are obtained, using only sixteen seismic sources.