Stability and accuracy of a finite‐difference scheme for elastic wave equation modeling

1984 ◽  
Author(s):  
L. Nicoletis ◽  
A. Bamberger ◽  
S. Daudier ◽  
O. Gosselin ◽  
P. Lailly
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Equation Modeling ◽  
Elastic Wave Equation ◽  
Stability And Accuracy

The pseudospectral method: Comparisons with finite differences for the elastic wave equation

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 483-501 ◽  
Author(s):  
Bengt Fornberg
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Difference Scheme ◽  
Finite Differences ◽  
Finite Difference Scheme ◽  
Pseudospectral Method ◽  
Two Dimensions ◽  
Seismic Modeling ◽  
Elastic Wave Equation

The pseudospectral (or Fourier) method has been used recently by several investigators for forward seismic modeling. The method is introduced here in two different ways: as a limit of finite differences of increasing orders, and by trigonometric interpolation. An argument based on spectral analysis of a model equation shows that the pseudospectral method (for the accuracies and integration times typical of forward elastic seismic modeling) may require, in each space dimension, as little as a quarter the number of grid points compared to a fourth‐order finite‐difference scheme and one‐sixteenth the number of points as a second‐order finite‐difference scheme. For the total number of points in two dimensions, these factors become 1/16 and 1/256, respectively; in three dimensions, they become 1/64 and 1/4 096, respectively. In a series of test calculations on the two‐dimensional elastic wave equation, only minor degradations are found in cases with variable coefficients and discontinuous interfaces.

Three-dimensional acoustic wave equation modeling based on the optimal finite-difference scheme

2015 ◽  
Vol 12 (3) ◽  
pp. 409-420 ◽  
Author(s):  
Xiao-Hui Cai ◽  
Yang Liu ◽  
Zhi-Ming Ren ◽  
Jian-Min Wang ◽  
Zhi-De Chen ◽  
...  
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Equation Modeling ◽  
Acoustic Wave Equation
Sign in / Sign up

Export Citation Format

Share Document