An Efficient Second-Order Finite-Difference Scheme for 3D Time-Space Domain Acoustic Wave Equation

2019 ◽  
Author(s):  
N. Amini ◽  
C. Shin
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Second Order ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space

Second-Order Implicit Finite-Difference Schemes for Acoustic Wave Equation in Time-Space Domain

Geophysics ◽  
2021 ◽  
pp. 1-83
Author(s):  
Navid Amini ◽  
Changsoo Shin ◽  
Jaejoon Lee
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Second Order ◽  
Numerical Dispersion ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space ◽  
Implicit Finite Difference ◽  
2D And 3D

We propose compact implicit finite-difference (FD) schemes in time-space domain based on second-order FD approximation for accurate solution of the acoustic wave equation in 1D, 2D, and 3D. Our method is based on weighted linear combination of the second-order FD operators with different spatial orientations to mitigate numerical error anisotropy and weighted averaging of the mass acceleration term over the grid-points of the second-order FD stencil to reduce the overall numerical dispersion error. We present derivation of the schemes for 1D, 2D, and 3D cases and obtain their corresponding dispersion equations, then we find optimum weights by optimization of the time-space domain dispersion function and finally tabulate the optimized weights for each case. We analyze the numerical dispersion, stability and convergence rates of the proposed schemes and compare their numerical dispersion characteristics with the standard high-order ones. We also discuss efficient solution of the system of equations associated with the proposed implicit schemes using conjugate gradient method. The comparison of dispersion curves and the numerical solutions with the analytical and the pseudo-spectral solutions reveals that the proposed schemes have better performance than the standard spatial high-order schemes and remain stable for relatively large time-steps.

A new staggered grid finite difference scheme optimised in the space domain for the first order acoustic wave equation

2018 ◽  
Vol 49 (6) ◽  
pp. 898-905 ◽  
Author(s):  
Wenquan Liang ◽  
Xiu Wu ◽  
Yanfei Wang ◽  
Jingjie Cao ◽  
Chaofan Wu ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Staggered Grid ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
First Order

Acoustic Wave Equation Modeling with New Time-Space Domain Finite Difference Operators

2013 ◽  
Vol 56 (6) ◽  
pp. 840-850 ◽  
Author(s):  
LIANG Wen-Quan ◽  
YANG Chang-Chun ◽  
WANG Yan-Fei ◽  
LIU Hong-Wei
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Equation Modeling ◽  
Difference Operators ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space ◽  
New Time

scholarly journals ONE-STEP EXTRAPOLATION METHOD USING CHEBYSHEV’S RECURRENCE RELATION APPLIED TO SEISMIC MODELING

2016 ◽  
Vol 34 (4) ◽  
Author(s):  
Laura Lara Ortiz ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Chebyshev Polynomials ◽  
Finite Difference Scheme ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
First Order ◽  
One Step

ABSTRACT. In this work we show that the solution of the first order differential wave equation for an analytical wavefield, using a finite-difference scheme in time, follows exactly the same recursion of modified Chebyshev polynomials. Based on this, we proposed a numerical...Keywords: seismic modeling, acoustic wave equation, analytical wavefield, Chebyshev polinomials. RESUMO. Neste trabalho, mostra-se que a solução da equação de onda de primeira ordem com um campo de onda analítico usando um esquema de diferenças finitas no tempo segue exatamente a relação de recorrência dos polinômios modificados de Chebyshev. O algoritmo...Palavras-chave: modelagem sísmica, equação da onda acústica, campo analítico, polinômios de Chebyshev.

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