论文标题

弹性完整波形反演中的基于预处理的BFG的不确定性定量

Preconditioned BFGS-based Uncertainty Quantification in elastic Full Waveform Inversion

论文作者

Liu, Qiancheng, Beller, Stephen, Lei, Wenjie, Peter, Daniel, Tromp, Jeroen

论文摘要

全波形反演(FWI)在重建地球物理结构中起着至关重要的作用。关于反转结果的不确定性量化同样重要,但在当前的大多数地球物理反演中都缺少。从数学上讲,不确定性定量涉及逆Hessian(或后协方差矩阵),该矩阵在计算和存储中对于实用的地球物理FWI问题而言却是过于良好的。 L-BFGs填充了最有效的高斯牛顿法。但是,在这项研究中,我们将其赋予了访问FWI中不确定性量化的逆Hessian的新可能性。为了促进逆检索,我们将BFG(本质上是全历史的L-BFG)组合在一起,它们具有随机的奇异值分解,以朝着黑esian逆的低级别近似。等级编号等于迭代的数量,即使对于大规模反转,该解决方案也使该解决方案有效且可支配。同样,基于伴随方法,我们将不同的对角线Hessian首字母缩写为预处理,并比较其在弹性FWI中的性能。我们用弹性的Marmousi基准强调了我们的方法,证明了预处理的BFG在大规模FWI和不确定性定量中的适用性。

Full Waveform Inversion (FWI) plays a vital role in reconstructing geophysical structures. The Uncertainty Quantification regarding the inversion results is equally important but has been missing out in most of the current geophysical inversions. Mathematically, uncertainty quantification is involved with the inverse Hessian (or the posterior covariance matrix), which is prohibitive in computation and storage for practical geophysical FWI problems. L-BFGS populates as the most efficient Gauss-Newton method; however, in this study, we empower it with the new possibility of accessing the inverse Hessian for uncertainty quantification in FWI. To facilitate the inverse-Hessian retrieval, we put together BFGS (essentially, full-history L-BFGS) with randomized singular value decomposition towards a low-rank approximation of the Hessian inverse. That the rank number equals the number of iterations makes this solution efficient and memory-affordable even for large-scale inversions. Also, based on the adjoint method, we formulate different diagonal Hessian initials as preconditioners and compare their performances in elastic FWI. We highlight our methods with the elastic Marmousi benchmark, demonstrating the applicability of preconditioned BFGS in large-scale FWI and uncertainty quantification.

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