Lax‐Wendroff and Nyström methods for seismic modelling
Lax‐Wendroff and Nyström methods for seismic modelling
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DOI：
10.1111/j.1365-2478.2009.00802.x
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发表时间：
2009-11
影响因子：
2.6
通讯作者：
Jing‐Bo Chen
中科院分区：
文献类型：
--
作者：
Jing‐Bo Chen
Lax‐Wendroff和Nyström方法是用于求解微分方程的时间近似的数值算法。这些方法为高精度地震建模提供了有效的算法。在空间伪谱离散的背景下，我探索这两种方法的比较。详细讨论了它们的稳定性和色散关系。四阶Lax‐Wendroff方法与四阶Nyström方法的比较表明，Nyström方法的稳定极限较小，但色散关系较好，更接近六阶Lax‐Wendroff方法。这些方法的结构保持性能也被揭示。Lax‐Wendroff方法是一种二阶辛算法，与方法的阶数无关。这一结果有助于理解Lax‐Wendroff方法的误差增长。基于标量波动方程的数值实验验证了所提出格式的有效性，并证明了辛方法优于非辛方法。
Lax‐Wendroff and Nyström methods are numerical algorithms of temporal approximations for solving differential equations. These methods provide efficient algorithms for high‐accuracy seismic modeling. In the context of spatial pseudospectral discretizations, I explore these two kinds of methods in a comparative way. Their stability and dispersion relation are discussed in detail. Comparison between the fourth‐order Lax‐Wendroff method and a fourth‐order Nyström method shows that the Nyström method has smaller stability limit but has a better dispersion relation, which is closer to the sixth‐order Lax‐Wendroff method. The structure‐preserving property of these methods is also revealed. The Lax‐Wendroff methods are a second‐order symplectic algorithm, which is independent of the order of the methods. This result is useful for understanding the error growth of Lax‐Wendroff methods. Numerical experiments based on the scalar wave equation are performed to test the presented schemes and demonstrate the advantages of the symplectic methods over the nonsymplectic ones.