Full waveform inversion (FWI) is an important and popular technique in subsurface earth property estimation. However, using the least-squares norm in the misfit function often leads to the local minimum solution of the optimization problem, and this phenomenon can be explained with the cycle-skipping artifact. Several methods that apply optimal transport distances to mitigate the cycle-skipping artifact have been proposed recently. The optimal transport distance is designed to compare two probability measures. To overcome the mass equality limit, we introduce an unbalanced optimal transport (UOT) distance with KullbackLeibler divergence to balance the mass difference. Also, a mixed L1/Wasserstein distance is constructed that can preserve the convex properties with respect to shift, dilation, and amplitude change operation. An entropy regularization approach and scaling algorithms are used to compute the distance and the gradient efficiently. Two strategies of normalization methods that transform the seismic signals into non-negative functions are provided. Numerical examples are provided to demonstrate the efficiency and effectiveness of the new method.
翻译:完全波形反转(FWI)是地表下地产估计中的一种重要和流行的技术。 但是,使用偏差函数中最小平方标准往往导致优化问题的当地最低解决方案,这种现象可以用周期倾斜工艺来解释。最近提出了几种采用最佳运输距离以缓解周期倾斜工艺物的最佳方法。最佳运输距离旨在比较两种概率尺度。为了克服质量平等限度,我们引入了一种不平衡的最佳运输(UOT)距离,与 KullbackLeibeller 差,以平衡质量差异。此外,还构建了一个混合的 L1/Wasserstein 距离, 以在移动、变形和振荡变化操作方面保持锥形特性。使用了恒温的正规化方法和缩放算法来有效计算距离和梯度。提供了两种将地震信号转换为非负值功能的正常化方法战略。提供了数字示例,以证明新方法的效率和有效性。