A numerical solution of the parabolic elastic wave equation

1995 ◽  
Vol 98 (5) ◽  
pp. 2953-2953
Author(s):  
Raymond J. Nagem ◽  
Ding Lee ◽  
Gongquin Li
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Numerical Solution ◽  
Elastic Wave Equation

Full elastic wave-equation based seismic-to-well tying: A real data example from onshore Australia

2022 ◽  
Author(s):  
P. Haffinger ◽  
D. Gisolf ◽  
J. Coffin ◽  
N. Chasnikov ◽  
P. Doulgeris
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Real Data ◽  
Elastic Wave Equation

An average-derivative optimal scheme for modeling of the frequency-domain 3D elastic wave equation

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. T209-T234 ◽  
Author(s):  
Jing-Bo Chen ◽  
Jian Cao
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Frequency Domain ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Wave Phase Velocity ◽  
Point Scheme ◽  
Grid Points

Because of its high computational cost, we needed to develop an efficient numerical scheme for the frequency-domain 3D elastic wave equation. In addition, the numerical scheme should be applicable to media with a liquid-solid interface. To address these two issues, we have developed a new average-derivative optimal 27-point scheme with arbitrary directional grid intervals and a corresponding numerical dispersion analysis for the frequency-domain 3D elastic wave equation. The novelty of this scheme is that its optimal coefficients depend on the ratio of the directional grid intervals and Poisson’s ratio. In this way, this scheme can be applied to media with a liquid-solid interface and a computational grid with arbitrary directional grid intervals. For media with a variable Poisson’s ratio, we have developed an effective and stable interpolation method for optimization coefficients. Compared with the classic 19-point scheme, this new scheme reduces the required number of grid points per wavelength for equal and unequal directional grid intervals. The reduction of the number of grid points increases as the Poisson’s ratio becomes larger. In particular, the numerical S-wave phase velocity of this new scheme becomes zero, whereas the classic 19-point scheme produces a spurious numerical S-wave phase velocity, as Poisson’s ratio reaches 0.5. We have performed numerical examples to develop the theoretical analysis.

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