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.
翻译:夸度瓦塞斯坦测量仪显示了测量概率密度差异的力量,这种概率密度有利于优化目标功能,而且对数据噪音不敏感。然而,让地震信号适合使用夸度瓦塞斯坦测量仪进行比较,总是一个重要问题。夸度比例值值得探索,因为它保证了数据变化造成的共性。然而,如[Commun.Inf.Syst., 2019, 19:95-145]所述,比例缩放可能会失去独特性,导致更多的本地迷你功能。在我们以往的工作中[J.Comput. Phys., 2018, 373:18:209],使地震信号适合使用夸度瓦塞斯坦测量仪与夸度测量仪成功地应用于地震位置问题。但是,它只是用很少的自由度来讨论反向问题。在这项工作中,我们将更深入地研究如何将缩放技术与夸度瓦塞斯坦测量仪相结合,通过丢弃某些可比较的数据,选择地震阶段,37:188-209],用夸度度度测量度度度度度度度度测量度测量度度度度度度测量测量测量测量测量方法成功地测量了新的标准,我们建议的平流平流度标准,以获得新的平流度标准。