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

The conventional least-squares misfit function compares the synthetic data to the observed data in a point by point style. The Wasserstein distance function, also called optimal transport function, matches patterns. The kinematic information of a 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 inter-receiver coherency. The main difficulty of extending to 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 to full waveform inversion, we demonstrate 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.