通过隐式微分与雅可比矩阵分解的高效单步面波层析成像

中文摘要 AI 辅助

面波层析成像为地壳和上地幔提供了重要的约束，但直接反演数百万个测量数据以获取三维结构在计算上仍然要求很高。我们开发了一种高效的高斯-牛顿框架，用于单步面波层析成像，该框架联合反演多周期台站间走时以获取剪切波速度，同时考虑横向波传播和深度敏感性。对收敛的离散程函方程进行隐式微分，可提供单个走时敏感性核，这些核通过跨接收器重用程函依赖结构而高效构建。分解的雅可比矩阵将这些核与共享的模型和频散映射分开保留，减少了每次线性化解中的存储和重复乘积成本。合成实验表明，该框架在相似的数据拟合下，以更少的模型更新和更低的模型误差恢复了三维速度异常，优于测试的比较工作流。计算基准测试表明，与使用显式组装的雅可比矩阵相比，在算子存储和线性化模型更新的成本方面有显著节省。我们将该框架应用于美国本土的634万条瑞利波相位走时。恢复的模型捕获了主要的地壳和上地幔顶部速度变化，包括构造活跃的美国西部与大陆内部之间的广泛对比，与先前面波研究一致。这些结果展示了一种实用的高斯-牛顿方法，用于利用大型面波数据集对地壳和上地幔进行成像。

英文摘要

Surface-wave tomography provides important constraints on the crust and upper mantle, but directly inverting millions of measurements for three-dimensional structure remains computationally demanding. We develop an efficient Gauss--Newton framework for one-step surface-wave tomography that jointly inverts multiperiod interstation traveltimes for shear-wave velocity, accounting for both lateral wave propagation and depth sensitivity. Implicit differentiation of the converged discrete Eikonal equations provides individual traveltime sensitivity kernels, which are constructed efficiently by reusing the Eikonal dependency structure across receivers. A factorized Jacobian retains these kernels separately from shared model and dispersion mappings, reducing storage and repeated-product costs within each linearized solve. Synthetic experiments show that the framework recovers three-dimensional velocity anomalies with fewer model updates and lower model errors than the tested comparison workflows at similar data fits. Computational benchmarks demonstrate substantial savings in operator storage and the cost of linearized model updates compared with using explicitly assembled Jacobians. We apply the framework to 6.34 million Rayleigh-wave phase traveltimes across the contiguous United States. The recovered model captures major crustal and uppermost mantle velocity variations, including the broad contrast between the tectonically active western United States and the continental interior, consistent with previous surface-wave studies. These results demonstrate a practical Gauss--Newton approach to imaging the crust and upper mantle using large surface-wave data sets.

发表机构

• Harbin Institute of Technology（哈尔滨工业大学）
• Nanyang Technological University（南洋理工大学）
• Peking University（北京大学）

机构由 AI 辅助整理，请以论文原文为准。