We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory and the Wasserstein distance, with a novel transformation of the time series to ensure that necessary normalisation and positivity conditions are met. Our measure is differentiable, and can readily be employed within an optimization framework. We demonstrate performance with a variety of synthetic examples, including seismic source inversion, and observe substantially better convergence properties than achieved with conventional $L_2$ misfits. We also briefly discuss the relationship between Optimal Transport and Bayesian inference.

翻译：我们提出一种新的方法来衡量地震波形等两个悬浮时间序列之间的协议,并证明它可以被有效地用于反向问题。我们的方法基于最佳运输理论和瓦塞斯坦距离,对时间序列进行新的改造,以确保满足必要的正常化和积极性条件。我们的措施是不同的,可以在优化框架内随时使用。我们用各种合成例子,包括地震源的倒转,来展示我们的表现,并观察到比常规的2美元差价高得多的汇合特性。我们还简要地讨论了最佳运输与巴耶斯推断之间的关系。