Full-waveform inversion (FWI) has become the tool of choice for building high-resolution velocity models. Its success depends on producing seamless updates of the short- and long-wavelength model features while avoiding cycle skipping. Classic FWI implementations use the L2 norm to measure the data misfit in combination with a gradient computed by a crosscorrelation imaging condition of the source and residual wavefields. The algorithm risks converging to an inaccurate result if the data lack low frequencies and/or the initial model is far from the true one. Additionally, the model updates may display a reflectivity imprint before the long-wavelength features of the model are fully recovered. We propose a new solution to this fundamental challenge by combining the quadratic form of the Wasserstein distance (W2 norm) for measuring the data misfit with a robust implementation of a velocity gradient. The W2 norm reduces the risk of cycle skipping, whereas the velocity gradient effectively eliminates the reflectivity imprint and emphasizes the long-wavelength model updates. We illustrate the performance of the new solution on a field survey acquired offshore Brazil. We demonstrate how FWI successfully updates the earth model and resolves a high-velocity carbonate section missing from the initial velocity model.