基于序贯代理模型细化的贝叶斯全波形反演
Bayesian full waveform inversion with sequential surrogate model refinement
AI总结：
本文提出一种序贯细化代理模型的贝叶斯全波形反演方法，通过从低频到高频逐步扩展带宽并用后验样本迭代重训练代理模型，在二维跨孔GPR合成数据上以降低约两个数量级的计算成本获得优于传统方法的反演精度。
摘要：
反问题的贝叶斯表述因其能够纳入先验知识并在新数据可用时更新概率模型而具有吸引力。马尔可夫链蒙特卡洛（MCMC）方法对后验概率密度函数（pdf）进行采样，但需要准确的先验模型和大量的似然评估。主成分分析（PCA）等降维方法有助于定义先验并训练能够高效近似昂贵正演求解器的代理模型。然而，对于全波形反演等问题，复杂的输入/输出关系往往无法仅由基于先验样本训练的代理模型很好地捕捉，从而导致结果有偏。纳入来自高后验概率区域的样本可以提高精度，但这些区域很难事先识别。我们提出了一种逐步细化代理模型的迭代方法。从低频数据开始，我们训练一个初始代理模型并进行一次MCMC反演。然后将得到的后验样本用于重新训练代理模型，从而允许我们在下一步反演中扩展频率带宽。重复这一过程可减少模型误差，并提高代理模型在相关输入域上的精度。最终，我们在整个带宽上获得一个高精度代理模型，从而能够进行最终的MCMC反演。来自二维合成跨孔探地雷达（GPR）算例的数值结果表明，我们的方法优于基于射线的方法以及仅依赖先验采样的方法。与完整的时域有限差分正演模拟相比，总体计算成本降低了约两个数量级。
英文摘要：
Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability density functions (pdfs) but require accurate prior models and many likelihood evaluations. Dimensionality-reduction methods, such as principal component analysis (PCA), can help define the prior and train surrogate models that efficiently approximate costly forward solvers. However, for problems like full waveform inversion, the complex input/output relations often cannot be captured well by surrogate models trained only on prior samples, leading to biased results. Including samples from high-posterior-probability regions can improve accuracy, but these regions are hard to identify in advance. We propose an iterative method that progressively refines the surrogate model. Starting with low-frequency data, we train an initial surrogate and perform an MCMC inversion. The resulting posterior samples are then used to retrain the surrogate, allowing us to expand the frequency bandwidth in the next inversion step. Repeating this process reduces model errors and improves the surrogate's accuracy over the relevant input domain. Ultimately, we obtain a highly accurate surrogate across the full bandwidth, enabling a final MCMC inversion. Numerical results from 2D synthetic crosshole Ground Penetrating Radar (GPR) examples show that our method outperforms ray-based approaches and those relying solely on prior sampling. The overall computational cost is reduced by about two orders of magnitude compared to full finite-difference time-domain modeling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
