AI 中文总结
针对变形网格上的全度量无矩阵高斯-牛顿走时层析成像，提出利用有向图与强连通分量重构冻结传输，实现块三角分解复用，大幅降低内迭代成本，加速反演。
AI 中文摘要
初至走时层析成像提供了一种计算高效的地下速度结构成像方法，而边界拟合变形网格允许在不放弃逻辑结构化网格的情况下表示崎岖地形。然而，在无矩阵高斯-牛顿反演中，线性化的全度量Eikonal传输及其转置必须在固定背景模型上重复应用。因此，方向扫描对每个Krylov右端项都会重新访问相同的状态相关依赖结构。我们将冻结的切向传输重新表述为有向图，并区分背景走时排序的丢失与真正的代数循环性。强连通分量识别出传输的不可约部分，而其余依赖在重新排序后允许精确的标量替换。凝聚图和局部块分解为每个冻结的源状态构建一次，然后同时用于原传输和转置的应用。在变形网格和三维层析成像问题上的数值实验表明，所得的块三角公式保留了冻结灵敏度作用，同时大幅降低了重复传输成本。通过消除这一主导的内迭代成本，所提出的方法显著加速了高斯-牛顿计算，并使变形网格上的全度量无矩阵反演以低得多的成本变得实用。
英文摘要
First-arrival traveltime tomography provides a computationally efficient means of imaging subsurface velocity structure, while boundary-conforming deformed grids allow rugged topography to be represented without abandoning a logically structured mesh. In matrix-free Gauss-Newton inversion, however, the linearized full-metric Eikonal transport and its transpose must be applied repeatedly at a fixed background model. Directional sweeping consequently revisits the same state-dependent dependency structure for every Krylov right-hand side. We recast the frozen tangent transport as a directed graph and distinguish loss of the background-traveltime ordering from genuine algebraic cyclicity. Strongly connected components identify the irreducible part of the transport, whereas the remaining dependencies admit exact scalar substitution after reordering. The condensation graph and local block factorizations are constructed once for each frozen source state and then reused for both primal and transpose applications. Numerical experiments on deformed grids and a three-dimensional tomography problem show that the resulting block-triangular formulation preserves the frozen sensitivity action while substantially reducing the repeated transport cost. By eliminating this dominant inner-iteration cost, the proposed method markedly accelerates Gauss-Newton computation and makes full-metric matrix-free inversion on deformed grids practical at much lower cost.
Comments22 pages, 3 figures
