da Silva Sérgio Luiz E F, de Araújo João M, de la Barra Erick, Corso Gilberto
Department of Applied Science and Technology, Politecnico di Torino, 10129 Torino, Italy.
Geoscience Institute, Fluminense Federal University, Niterói 24210-346, RJ, Brazil.
Entropy (Basel). 2023 Jun 28;25(7):990. doi: 10.3390/e25070990.
Data-centric inverse problems are a process of inferring physical attributes from indirect measurements. Full-waveform inversion (FWI) is a non-linear inverse problem that attempts to obtain a quantitative physical model by comparing the wave equation solution with observed data, optimizing an objective function. However, the FWI is strenuously dependent on a robust objective function, especially for dealing with cycle-skipping issues and non-Gaussian noises in the dataset. In this work, we present an objective function based on the Kaniadakis κ-Gaussian distribution and the optimal transport (OT) theory to mitigate non-Gaussian noise effects and phase ambiguity concerns that cause cycle skipping. We construct the κ-objective function using the probabilistic maximum likelihood procedure and include it within a well-posed version of the original OT formulation, known as the Kantorovich-Rubinstein metric. We represent the data in the graph space to satisfy the probability axioms required by the Kantorovich-Rubinstein framework. We call our proposal the κ-Graph-Space Optimal Transport FWI (κ-GSOT-FWI). The results suggest that the κ-GSOT-FWI is an effective procedure to circumvent the effects of non-Gaussian noise and cycle-skipping problems. They also show that the Kaniadakis κ-statistics significantly improve the FWI objective function convergence, resulting in higher-resolution models than classical techniques, especially when κ=0.6.
以数据为中心的反问题是一个从间接测量中推断物理属性的过程。全波形反演（FWI）是一个非线性反问题，它试图通过将波动方程解与观测数据进行比较，优化一个目标函数来获得定量物理模型。然而，FWI严重依赖于一个稳健的目标函数，特别是在处理数据集中的周跳问题和非高斯噪声时。在这项工作中，我们提出了一个基于卡尼亚达基斯κ-高斯分布和最优传输（OT）理论的目标函数，以减轻导致周跳的非高斯噪声影响和相位模糊问题。我们使用概率最大似然过程构建κ-目标函数，并将其纳入原始OT公式的一个适定版本中，即康德罗维奇-鲁宾斯坦度量。我们在图空间中表示数据，以满足康德罗维奇-鲁宾斯坦框架所需的概率公理。我们将我们的提议称为κ-图空间最优传输FWI（κ-GSOT-FWI）。结果表明，κ-GSOT-FWI是一种有效规避非高斯噪声影响和周跳问题的方法。结果还表明，卡尼亚达基斯κ统计显著改善了FWI目标函数的收敛性，从而得到比传统技术更高分辨率的模型，特别是当κ = 0.6时。
