标题： 基于高斯随机场和集合卡尔曼滤波的声波全波形反演的不确定性感知频率域方法 显示英文标题

标题： Uncertainty-aware Frequency-domain Acoustic Full Waveform Inversion Using Gaussian Random Fields and Ensemble Kalman Inversion

摘要： 近年来，具有不确定性感知的全波形反演（FWI）引起了越来越多的关注，特别是在生成与反演结果相关的有意义的不确定性估计方面越来越重视。贝叶斯推理方法——特别是基于蒙特卡洛的方法——被广泛用于量化不确定性。然而，这些技术通常需要大量的后验采样，导致计算成本高昂。为了解决这一挑战并实现FWI中的高效不确定性量化，我们引入了一种具有不确定性感知的FWI框架——EKI-GRFs-FWI——该框架将高斯随机场（GRFs）与集合卡尔曼反演（EKI）算法相结合。这种方法能够联合推断地下速度场，并以计算高效的方式提供可靠的不确定性估计。EKI算法利用无导数更新机制，并采用有效的停止准则以确保快速收敛，使其适用于大规模逆问题。同时，GRFs结合了空间平滑性和相关长度尺度的先验知识，使得为EKI生成物理上合理的初始集合成为可能。数值结果显示，EKI-GRFs-FWI在提供合理准确的速度重构的同时，也提供了有意义的不确定性估计。 显示英文摘要

摘要： In recent years, uncertainty-aware full waveform inversion (FWI) has received increasing attention, with a growing emphasis on producing informative uncertainty estimates alongside inversion results. Bayesian inference methods--particularly Monte Carlo-based approaches--have been widely employed to quantify uncertainty. However, these techniques often require extensive posterior sampling, resulting in high computational costs. To address this challenge and enable efficient uncertainty quantification in FWI, we introduce an uncertainty-aware FWI framework--EKI-GRFs-FWI--that integrates Gaussian random fields (GRFs) with the ensemble Kalman inversion (EKI) algorithm. This approach jointly infers subsurface velocity fields and provides reliable uncertainty estimates in a computationally efficient manner. The EKI algorithm leverages a derivative-free update mechanism and employs effective stopping criteria to ensure rapid convergence, making it suitable for large-scale inverse problems. Meanwhile, GRFs incorporate prior knowledge of spatial smoothness and correlation length scales, enabling the generation of physically plausible initial ensembles for EKI. Numerical results demonstrate that EKI-GRFs-FWI yields reasonably accurate velocity reconstructions while delivering informative uncertainty estimates.