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