scholarly journals A Fourth Order Accurate Finite Difference Scheme for the Elastic Wave Equation in Second Order Formulation

2011 ◽  
Vol 52 (1) ◽  
pp. 17-48 ◽  
Author(s):  
Björn Sjögreen ◽  
N. Anders Petersson
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Difference Scheme ◽  
Fourth Order ◽  
Finite Difference Scheme ◽  
Second Order ◽  
Elastic Wave Equation

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.

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