Optimal transport (OT) distances have been recently proposed to mitigate the non-convexity of the L 2 misfit function in FWI. However, OT is only applicable to positive and normalized data. To overcome this difficulty, we have proposed two strategies, one based on the Kantorovich-Rubinstein (KR) norm, which extends a specific OT distance to the comparison of signed data, the other based on the interpretation of the discrete graph space of the data through OT. In this study, we compare these two approaches for the inversion of 3D OBC data from the Valhall field, using a visco-acoustic time-domain FWI algorithm. Starting from a crude initial velocity model, both KR and graph space approaches provide more reliable results than L 2 , the best results being obtained with the graph space approach. Thanks to a recently developed numerical approach, the computational cost increase is limited in this case to approximately 15 % compared to standard L 2 FWI.