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Lax‐Wendroff and Nyström methods for seismic modelling
Author(s) -
Chen JingBo
Publication year - 2009
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2009.00802.x
Subject(s) - symplectic geometry , scalar (mathematics) , mathematics , stability (learning theory) , context (archaeology) , dispersion relation , partial differential equation , mathematical analysis , computer science , geology , physics , geometry , paleontology , quantum mechanics , machine learning
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.