Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping
Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping
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DOI：
10.1002/cpa.21990
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发表时间：
2020-01
影响因子：
3
通讯作者：
Bjorn Engquist;Yunan Yang
中科院分区：
文献类型：
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作者：
Bjorn Engquist;Yunan Yang
全波反演法是当今地震成像反问题的标准处理方法。PDE约束最优化用于确定波动方程中代表地球物理性质的未知参数。目标函数衡量观测数据和计算合成数据之间的失配，传统上它是最小二乘范数。在一系列的文章中，我们引入了来自最优运输的Wasserstein度量作为一种替代的失配函数，以减轻所谓的周期跳跃，即优化过程陷入局部极小。在本文中，我们首先给出了一个以Wasserstein度量的凸性为目标函数的更尖锐的定理。然后，我们关注两个新问题。一个是将地震信号转换为概率度量的必要标准化，以便最优传输理论适用。另一种超越了跳旋回的方法，即反射界面以下参数的反演。首先，我们提出了一类正规化，并证明了这类正规化的几个有利性质。对于后者，我们证明了使用最优传输的FWI可以从没有地震波通过的区域恢复地球物理性质。最后，我们通过成像盐包裹体的实际应用来说明这些性质，这一直是勘探地球物理中的一个重大挑战。©2021威利期刊有限责任公司。
Full‐waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE‐constrained optimization is used to determine unknown parameters in a wave equation that represent geophysical properties. The objective function measures the misfit between the observed data and the calculated synthetic data, and it has traditionally been the least‐squares norm. In a sequence of papers, we introduced the Wasserstein metric from optimal transport as an alternative misfit function for mitigating the so‐called cycle skipping, which is the trapping of the optimization process in local minima. In this paper, we first give a sharper theorem regarding the convexity of the Wasserstein metric as the objective function. We then focus on two new issues. One is the necessary normalization of turning seismic signals into probability measures such that the theory of optimal transport applies. The other, which is beyond cycle skipping, is the inversion for parameters below reflecting interfaces. For the first, we propose a class of normalizations and prove several favorable properties for this class. For the latter, we demonstrate that FWI using optimal transport can recover geophysical properties from domains where no seismic waves travel through. We finally illustrate these properties by the realistic application of imaging salt inclusions, which has been a significant challenge in exploration geophysics. © 2021 Wiley Periodicals LLC.