Implicit finite difference wave equation forward modeling based on partial fraction expansion

Numerical dispersion caused by mesh discretization is a critical factor affecting finite difference numerical simulation accuracy. High-order implicit finite difference operator may be used to solve this problem because the convergence rate increases with the order, but the efficiency is low because...

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Bibliographic Details
Published in:Applied geophysics 2023-12, Vol.20 (4), p.364-373
Main Authors: Song, Jian-yong, Cao, Hong, Lu, Ming-hui, Yang, Zhi-fang, Hu, Xin-hai, Li, Hong-bing, Yan, Xin-fei
Format: Article
Language:English
Subjects:
Accuracy
Computation
Computational efficiency
Computer applications
Computing time
Dispersion
Earth and Environmental Science
Earth Sciences
Efficiency
Finite difference method
Finite differences
Finite element method
Geophysics/Geodesy
Geotechnical Engineering & Applied Earth Sciences
Linear equations
Mathematical analysis
Mathematical models
Matrices (mathematics)
Modelling
Numerical simulations
Operators (mathematics)
Plane waves
Simulation
Wave equations
Wave number
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Summary:Numerical dispersion caused by mesh discretization is a critical factor affecting finite difference numerical simulation accuracy. High-order implicit finite difference operator may be used to solve this problem because the convergence rate increases with the order, but the efficiency is low because of the computation of the band matrix. We derived a low-order implicit difference operator with partial fraction expansion in the wave number domain from the plane wave theory to improve the accuracy of numerical simulation. Using this operator, the routine multi-diagonal matrix is rewritten as multi-parallel linear tri-diagonal matrices in different directions to simplify the solution of the sparse linear equations. We adopted the chasing method to solve the linear equations composed of tri-diagonal matrices. This improves the computational efficiency of the space partial derivative in the implicit difference forward modeling process. Dispersion analysis and numerical simulations show that our method yields excellent results with high accuracy and acceptable computational efficiency.
ISSN:1672-7975
1993-0658
DOI:10.1007/s11770-022-0991-x