Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion
Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion
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DOI：
10.1190/geo2016-0663.1
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发表时间：
2016-12
期刊：
影响因子：
3.3
通讯作者：
Yunan Yang;Bjorn Engquist;Junzhe Sun;Brittany D. Froese
中科院分区：
文献类型：
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作者：
Yunan Yang;Bjorn Engquist;Junzhe Sun;Brittany D. Froese
使用最小二乘范数作为失配函数的传统全波形反演（FWI）存在周期跳变问题，这增加了计算失配的局部最小值而不是全局最小值的风险。二次瓦瑟斯坦度量已被证明具有许多理想的凸性和对噪声不敏感的性质。当观测和预测地震数据被认为是两个密度函数时，二次Wasserstein度量对应于将一个密度重新排列到另一个密度的最佳成本，其中运输成本是距离的二次。与最小二乘范数不同，二次Wasserstein度量不仅测量振幅差异，还测量全局相移，这有助于避免周期跳过问题。我们提出了一种利用二次Wasserstein度规的新方法，并通过求解Monge-Ampere方程将其与全局二次Wasserstein度规进行了比较。我们加入了二次元瓦塞尔…
Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function is known to suffer from cycle-skipping issues which increases the risk of computing a local rather than the global minimum of the misfit. The quadratic Wasserstein metric has been proved to have many ideal properties with regards to convexity and insensitivity to noise. When the observed and predicted seismic data are considered to be two density functions, the quadratic Wasserstein metric corresponds to the optimal cost of rearranging one density into the other, where the transportation cost is quadratic in distance. Unlike the least-squares norm, the quadratic Wasserstein metric measures not only amplitude differences but also global phase shifts, which helps to avoid cycle-skipping issues. We propose a new way of using the quadratic Wasserstein metric trace-by-trace in FWI and compare it to the global quadratic Wasserstein metric via the solution of the Monge-Ampere equation. We incorporate the quadratic Wasser...