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

Time-domain explicit finite-difference method based on the mixed-domain function approximation for acoustic wave equation

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. T237-T248 ◽  
Author(s):  
Zhikai Wang ◽  
Jingye Li ◽  
Benfeng Wang ◽  
Yiran Xu ◽  
Xiaohong Chen
Keyword(s):  
Wave Equation ◽  
Dispersion Relation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Function Approximation ◽  
High Accuracy ◽  
Acoustic Wave Equation ◽  
Space Domain ◽  
Time Space ◽  
Explicit Finite Difference

Explicit finite-difference (FD) methods with high accuracy and efficiency are preferred in full-waveform inversion and reverse time migration. The Taylor-series expansion (TE)-based FD methods can only obtain high accuracy on a small wavenumber zone. We have developed a new explicit FD method with spatial arbitrary even-order accuracy based on the mixed [Formula: see text] (wavenumber)-space domain function approximation for the acoustic wave equation, and we derived the FD coefficients by minimizing the approximation error in a least-squares (LS) sense. The weighted pseudoinverse of mixed [Formula: see text]-space matrix is introduced into the LS optimization problem to improve the accuracy. The new method has an exact temporal derivatives discretization in homogeneous media and also has higher temporal and spatial accuracy in heterogeneous media. Approximation errors and numerical dispersion analysis demonstrate that the new FD method has a higher numerical accuracy than conventional TE-based FD and TE-based time-space domain dispersion-relation FD methods. Stability analysis reveals that our proposed method requires a slightly stricter stability condition than the TE-based FD and TE-based time-space domain dispersion-relation FD methods. Numerical tests in the homogeneous model, horizontally layered model, and 2D modified Sigsbee2 model demonstrate the accuracy, efficiency, and flexibility of the proposed new FD method.

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.

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