发表机构
Institute of Geophysics, Polish Academy of Sciences; Department of Computer Science, University of Central Florida（波兰科学院地球物理研究所; 中佛罗里达大学计算机系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对走时层析成像的大规模贝叶斯反演，提出结合FMM、ADMM和SVGD的分布式近端算法，实现高效后验采样与不确定性量化。
AI 中文摘要
我们提出了一种用于受程函方程控制的大规模贝叶斯反问题的分布式框架，特别关注地震走时层析成像。传统的确定性方法往往无法为不适定问题提供必要的不确定性量化（UQ），而传统的贝叶斯采样方法如马尔可夫链蒙特卡洛（MCMC）在高维模型空间中遭受维数灾难和收敛缓慢的问题。所提出的框架通过三层计算策略应对这些挑战。首先，我们利用快速行进法（FMM）求解程函方程，确保高数值精度。其次，我们将全局层析目标重构为去中心化共识形式，允许反演分解为独立的子问题，并通过交替方向乘子法（ADMM）并行求解。该架构消除了显式构建大规模灵敏度矩阵的需要，显著减少了三维勘测的内存占用。最后，我们在ADMM工作节点内集成斯坦变分梯度下降（SVGD）以执行近似后验采样。通过沿平衡数据拟合力与基于核的排斥多样性力的函数梯度方向演化一组模型粒子，我们获得一个集成，从中计算后验摘要。我们利用伍德伯里矩阵恒等式推导出数据空间高斯-牛顿更新，以进一步加速大规模三维问题中的粒子演化。在复杂二维和三维模型上的数值实验表明，该算法实现了稳定收敛，产生高保真速度重建，并提供后验不确定性图。
英文摘要
We present a distributed framework for large-scale Bayesian inverse problems governed by the eikonal equation, with a specific focus on seismic traveltime tomography. Traditional deterministic approaches often fail to provide the uncertainty quantification (UQ) necessary for ill-posed problems, while conventional Bayesian sampling methods such as Markov chain Monte Carlo (MCMC) suffer from the curse of dimensionality and slow convergence in high-dimensional model spaces. The proposed framework addresses these challenges through a three-tier computational strategy. First, we utilize the Fast Marching Method (FMM) to solve the eikonal equation, ensuring high numerical accuracy. Second, we reformulate the global tomographic objective into a decentralized consensus form, allowing the inversion to be decomposed into independent subproblems solved in parallel via the Alternating Direction Method of Multipliers (ADMM). This architecture eliminates the need for the explicit construction of large-scale sensitivity matrices, significantly reducing the memory footprint for 3D surveys. Finally, we integrate Stein Variational Gradient Descent (SVGD) within the ADMM workers to perform approximate posterior sampling. By evolving a set of model particles along a functional gradient direction that balances data-fitting forces with a repulsive kernel-based diversity force, we obtain an ensemble from which posterior summaries are computed. We derive a data-space Gauss-Newton update using the Woodbury matrix identity to further accelerate the particle evolution in large-scale 3D problems. Numerical experiments on complex 2D and 3D models demonstrate that the algorithm achieves stable convergence, produces high-fidelity velocity reconstructions, and provides posterior uncertainty maps.
