Anderson Acceleration for Seismic Inversion
Anderson Acceleration for Seismic Inversion
复制标题
DOI：
10.1190/geo2020-0462.1
复制
发表时间：
2020-08
期刊：
影响因子：
--
通讯作者：
Yunan Yang
中科院分区：
文献类型：
--
作者：
Yunan Yang
最先进的地震成像技术将全波形反演（FWI）和最小二乘逆时偏移（LSRTM）等反演任务视为偏微分方程约束的优化问题。由于大规模的性质，在实践中，基于梯度的优化算法是迭代更新模型的首选算法。高阶方法在更少的迭代中收敛，但通常需要更高的计算成本、更多的行搜索步骤和更大的内存存储。必须考虑到这些方面之间的平衡。我们使用安德森加速（AA）进行了评估，这是一种加速定点迭代收敛的流行策略，以加速最陡下降算法，我们创新地将其视为定点迭代。在不考虑未知参数维数的情况下，实现该方法的计算成本可以简化为一个极低维的最小二乘问题。通过低级别更新可以进一步降低成本。我们确定了AA与其他著名的优化方法（如L-BFGS和重启广义最小残差法）之间的理论联系和差异，并比较了它们的计算成本和内存需求。应用于Marmousi基准的FWI和LSRTM数值算例验证了AA的加速效应。与最陡下降法相比，AA法收敛速度更快，并能与某些拟牛顿方法相媲美，是一种有吸引力的地震反演优化策略。
State-of-the-art seismic imaging techniques treat inversion tasks such as full-waveform inversion (FWI) and least-squares reverse time migration (LSRTM) as partial differential equation-constrained optimization problems. Due to the large-scale nature, gradient-based optimization algorithms are preferred in practice to update the model iteratively. Higher-order methods converge in fewer iterations but often require higher computational costs, more line-search steps, and bigger memory storage. A balance among these aspects has to be considered. We have conducted an evaluation using Anderson acceleration (AA), a popular strategy to speed up the convergence of fixed-point iterations, to accelerate the steepest-descent algorithm, which we innovatively treat as a fixed-point iteration. Independent of the unknown parameter dimensionality, the computational cost of implementing the method can be reduced to an extremely low dimensional least-squares problem. The cost can be further reduced by a low-rank update. We determine the theoretical connections and the differences between AA and other well-known optimization methods such as L-BFGS and the restarted generalized minimal residual method and compare their computational cost and memory requirements. Numerical examples of FWI and LSRTM applied to the Marmousi benchmark demonstrate the acceleration effects of AA. Compared with the steepest-descent method, AA can achieve faster convergence and can provide competitive results with some quasi-Newton methods, making it an attractive optimization strategy for seismic inversion.