An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the m...

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Bibliographic Details
Published in:Journal of applied geophysics Vol. 138; pp. 161 - 171
Main Authors: Yang, Lei, Yan, Hongyong, Liu, Hong
Format: Journal Article
Language:English
Published: Elsevier B.V 01.03.2017
Subjects:
Elastic modeling
Implicit staggered-grid finite difference (ISFD)
Minimax approximation (MA)
Remez algorithm
Taylor-series expansion (TE)
Minimax approximation (MA)
Remez algorithm
Taylor-series expansion (TE)
Elastic modeling
Implicit staggered-grid finite difference (ISFD)
ISSN:0926-9851, 1879-1859
Online Access:Get full text
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Summary:Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling. •Optimizing implicit staggered-grid finite-difference by modified Taylor-series expansion•Modifying Taylor-series expansion by minimax approximation with Remez algorithm•The optimal scheme keeps great accuracy at both the small and large wavenumbers.•The optimal scheme achieves greater accuracy and efficiency in elastic modeling.
ISSN:0926-9851
1879-1859
DOI:10.1016/j.jappgeo.2017.01.020