Abstract: The quadratic Wasserstein distance has recently been proposed as an alternative to the classical $L^2$ distance for measuring data mismatch in computational inverse problems. Extensive computational evidences showing the advantages of using the Wasserstein distance has been reported. The objective of this talk is to provide some simple observations that might help us explain the numerically-observed differences between results based on the quadratic Wasserstein distance and those based on the $L^2$ distance for general linear and nonlinear inverse problems.