论文标题
地球物理反转和最佳运输
Geophysical Inversion and Optimal Transport
论文作者
论文摘要
我们提出了一种新的方法，用于衡量两个振荡时间序列（例如地震波形）之间的一致性，并证明它可以在反问题中有效使用。我们的方法基于最佳运输理论和Wasserstein距离，并具有时间序列的新变化，以确保满足必要的归一化和阳性条件。我们的措施是可区分的，并且可以轻松地用于优化框架中。我们通过各种合成示例（包括地震源反演）展示了性能，并且比传统的$ L_2 $ MISFITS相比，观察到的收敛属性要好得多。我们还简要讨论了最佳运输与贝叶斯推断之间的关系。
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.
