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Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

Numerical dispersion analysis for three-dimensional Laplace-Fourier-domain scalar wave equation

Jing-Bo Chen
+ Author Affiliations
- Author Affiliations

Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, PO Box 9825, Beijing 100029, China. Email: chenjb@mail.iggcas.ac.cn

Exploration Geophysics 47(2) 158-167 https://doi.org/10.1071/EG15022
Submitted: 17 March 2015  Accepted: 4 June 2015   Published: 25 June 2015

Abstract

Based on the phase velocity and attenuation propagation velocity, a method for performing numerical dispersion analysis of three-dimensional Laplace-Fourier-domain scalar wave equation is presented. This method is applied to a 27-point average-derivative optimal scheme and a 27-point finite-element scheme. Within the relative error of 1%, the 27-point average-derivative optimal scheme requires seven grid points per wavelength and pseudo-wavelength while the 27-point finite-element scheme requires 23 grid points per wavelength and pseudo-wavelength for equal and unequal directional sampling intervals. Numerical examples show that the 27-point Laplace-Fourier-domain average-derivative optimal scheme is more accurate than the 27-point Laplace-Fourier-domain finite-element scheme for the same computational cost. By using larger directional sampling intervals while maintaining accuracy, the 27-point Laplace-Fourier-domain average-derivative optimal scheme can greatly reduce the computational cost of three-dimensional Laplace-Fourier-domain modelling.

Key words: 3D modelling, dispersion analysis, finite difference, Laplace-Fourier domain, optimisation.


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