The back-and-forth method for the quadratic Wasserstein distance-based full-waveform inversion

The conventional least-squares misfit function compares synthetic data to observed data in a point-by-point style. The Wasserstein distance function, also called the optimal transport function, matches patterns. The kinematic information of seismograms is therefore efficiently extracted. This property makes it more convex than the conventional least-squares function. Computing the 1D Wasserstein function is fast. Processing the 2D or 3D seismic data volume trace by trace, however, loses the interreceiver coherency. The main difficulty of extending to the high-dimensional Wasserstein function is the heavy computation cost. This computational challenge can be alleviated by a back-and-forth method. After explaining the computation strategy and incorporating it into full-waveform inversion, we illustrate the superior performances of the high-dimensional Wasserstein function with a Camembert model and the Marmousi model. The superiority is also demonstrated with the Chevron 2014 blind test.