期刊
EXPLORATION GEOPHYSICS
卷 49, 期 2, 页码 187-201出版社
CSIRO PUBLISHING
DOI: 10.1071/EG16094
关键词
acoustic wave equation; high-order finite difference; implicit scheme; least squares; spatial dispersion; Taylor-series expansion; temporal dispersion
资金
- National Natural Science Foundation of China (NSFC) [41474110]
- National High Technology Research and Development Program of China (863 Program) [2013AA064201]
- Shell's PhD scholarship
The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-WendroffFDscheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.
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