Improving full-waveform inversion to make it more robust to cycle-skipping has been the subject of a large number of studies. From the several families of approaches developed, one of the most documented consists in modifying the least-squares distance defining the discrepancy between observed and calculated data. From all the propositions made to improve and replace the least-squares distance, only a few of them have been applied to field data. One of the methods proposed recently, the graph space optimal transport distance, presents appealing properties for field data applications. This study compares it with the least-squares distance in an analysis performed on the three-dimensional ocean bottom cable data from the Valhall field. This data has already been at the heart of several full-waveform inversion studies, making it a good candidate to evaluate the properties of this new misfit function. We first perform this comparison starting the inversion from the reflection traveltime tomography model used in previous studies. We then perform a second comparison from a crude, linearly varying in-depth one-dimensional velocity model. Starting from this model, least-squares-based full-waveform inversion fails to provide a meaningful estimate of the pressure-wave velocity model due to cycle skipping. We illustrate how the graph-space optimal transport-based full-waveform inversion mitigates this issue. A meaningful estimate of the pressure-wave velocity model is obtained in the zone sampled by both diving and reflected waves, down to almost two kilometers depth. To our knowledge, this is the first application of a graph space optimal transport-based full-waveform inversion to three-dimensional field data.