Quadratic Wasserstein metric(W2) and its application on seismic inversion

Optimal transport has become a well developed topic in analysis since it was first proposed by Monge in 1781. Due to their ability to incorporate differences in both intensity and spatial information, the related Wasserstein metrics have been adopted in a variety of applications, including seismic inversion. Quadratic Wasserstein metric (W2) has ideal properties like convexity and insensitivity to noise, while conventional L2 norm is known to suffer from local minima. We propose two ways of using W2 in seismic inversion, a trace-by-trace comparison solved by sorting, and the global comparison which requires numerical solution to Monge-Ampere equation.