Optimal transport full-waveform inversion: from theory to industrial applications with examples from the Sultanate of Oman

The optimal transport problem was formulated more than 200 years ago to calculate the optimal way of transporting piles of sand. Due to the interesting properties of its solutions with respect to shifts between the compared distributions, optimal transport has recently been adapted to full-waveform inversion to mitigate the cycle-skipping issue. Various formalisms have been proposed. Here we present an overview of these approaches, emphasizing more specifically the approach based on the bi-dimensional Kantorovich-Rubinstein norm, which has led to numerous successful full-waveform inversion applications. We illustrate these successes with two onshore case studies from the Sultanate of Oman.