论文标题

{\ it {h}}上的大规模频域地震波建模 - 具有迭代求解器和多级域分解预处理器的自适应四面体网格

Large-scale frequency-domain seismic wave modeling on {\it{h}}-adaptive tetrahedral meshes with iterative solver and multi-level domain-decomposition preconditioners

论文作者

Dolean, Victorita, Jolivet, Pierre, Operto, Stéphane, Tournier, Pierre-Henri

论文摘要

频域全波倒置(FWI)适用于长偏移式固定录制采集,因为可靠的地下模型可以使用一些频率重建,并且在没有计算开销的情况下可以轻松实现衰减。在频域中,波浪建模是一个helmholtz型边界值问题,它需要求解具有多个右侧(来源)的每个频率的较大稀疏的线性方程系统。该系统可以通过直接或迭代方法解决。虽然前者适合在涵盖中等大小的空间域的3D密集OBC采集上应用FWI,但以后的选择是涵盖大型域的稀疏节点获取的选择方法(超过5000万未知数)。然而,由于Helmholtz操作员的非确定性,一侧和离散的约束,在高频制度中,迭代求解器的快速收敛仍然具有挑战性,以最大程度地减少给定频率的分散误差,从而在另一侧,因此需要有效的先验者。在这项研究中,我们使用Krylov子空间GMRES迭代求解器与两级域分解预处理相结合。离散化依赖于非结构化四面体网格上订单3的连续拉格朗日有限元素符合复杂的几何形状,并将元素的大小调整为局部波长($ h $ adpaptivity)。我们评估方法与声学3D SEG/EAGE OUPTHRAST模型的准确性,收敛性和可扩展性,最高频率为20〜Hz。

Frequency-domain full-waveform inversion (FWI) is suitable for long-offset stationary-recording acquisition, since reliable subsurface models can be reconstructed with a few frequencies and attenuation is easily implemented without computational overhead. In the frequency domain, wave modeling is a Helmholtz-type boundary-value problem which requires to solve a large and sparse system of linear equations per frequency with multiple right-hand sides (sources). This system can be solved with direct or iterative methods. While the former are suitable for FWI application on 3D dense OBC acquisitions covering spatial domains of moderate size, the later should be the approach of choice for sparse node acquisitions covering large domains (more than 50 millions of unknowns). Fast convergence of iterative solvers for Helmholtz problems remains however challenging in high frequency regime due to the non definiteness of the Helmholtz operator, on one side and on the discretization constraints in order to minimize the dispersion error for a given frequency, on the other side, hence requiring efficient preconditioners. In this study, we use the Krylov subspace GMRES iterative solver combined with a two-level domain-decomposition preconditioner. Discretization relies on continuous Lagrange finite elements of order 3 on unstructured tetrahedral meshes to comply with complex geometries and adapt the size of the elements to the local wavelength ($h$-adaptivity). We assess the accuracy, the convergence and the scalability of our method with the acoustic 3D SEG/EAGE Overthrust model up to a frequency of 20~Hz.

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