论文标题
部分可观测时空混沌系统的无模型预测
The Quadratic Wasserstein Metric With Squaring Scaling For Seismic Velocity Inversion
论文作者
论文摘要
二次Wasserstein度量标准表明了其在衡量概率密度之间的差异方面的力量，该概率密度具有更好的优化目标函数，并且对数据噪声不敏感。然而，使地震信号适合使用二次瓦斯坦公制的地震信号始终是一个重要的问题。该平方缩放值得探索，因为它可以保证数据移位引起的凸度。但是，如[Commun。 inf。 Syst。，2019，19：95-145]，平方缩放可能会失去独特性，并导致更局部的最小值，使其适应不合适的功能。在我们以前的工作中[J。计算。 Phys。，2018，373：188-209]，成功地应用了具有平方尺度的二次瓦斯坦斯坦度量标准。但这只讨论了几个自由度的反问题。在这项工作中，我们将提出一项关于平方缩放技术和二次瓦斯汀公制的组合的更深入的研究。通过丢弃一些不适用的数据，选择地震阶段并开发了一种新的归一化方法，我们成功地基于平方缩放技术和二次Wasestein度量来成功地颠覆了地震速度结构。数值实验表明，这种新提出的方法是获得更准确的反转结果的有效方法。
The quadratic Wasserstein metric has shown its power in measuring the difference between probability densities, which benefits optimization objective function with better convexity and is insensitive to data noise. Nevertheless, it is always an important question to make the seismic signals suitable for comparison using the quadratic Wasserstein metric. The squaring scaling is worth exploring since it guarantees the convexity caused by data shift. However, as mentioned in [Commun. Inf. Syst., 2019, 19:95-145], the squaring scaling may lose uniqueness and result in more local minima to the misfit function. In our previous work [J. Comput. Phys., 2018, 373:188-209], the quadratic Wasserstein metric with squaring scaling was successfully applied to the earthquake location problem. But it only discussed the inverse problem with few degrees of freedom. In this work, we will present a more in-depth study on the combination of squaring scaling technique and the quadratic Wasserstein metric. By discarding some inapplicable data, picking seismic phases, and developing a new normalization method, we successfully invert the seismic velocity structure based on the squaring scaling technique and the quadratic Wasserstein metric. The numerical experiments suggest that this newly proposed method is an efficient approach to obtain more accurate inversion results.
