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Article << Previous     |     Next >>   Contents Vol 42(3)

3D acoustic wave modelling with time-space domain dispersion-relation-based finite-difference schemes and hybrid absorbing boundary conditions

Yang Liu 1 3 Mrinal K. Sen 2

1 State Key Laboratory of Petroleum Resources and Prospecting (China University of Petroleum, Beijing), Beijing, 102249, China.
2 The Institute for Geophysics, John A. and Katherine G. Jackson School of Geosciences, The University of Texas, 10100 Burnet Road, R2200 Austin, TX 78758, USA.
3 Corresponding author. Email: wliuyang@vip.sina.com

Exploration Geophysics 42(3) 176-189 http://dx.doi.org/10.1071/EG11007
Submitted: 23 January 2011  Accepted: 7 July 2011   Published: 2 September 2011


 
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Abstract

Most conventional finite-difference methods adopt second-order temporal and (2M)th-order spatial finite-difference stencils to solve the 3D acoustic wave equation. When spatial finite-difference stencils devised from the time-space domain dispersion relation are used to replace these conventional spatial finite-difference stencils devised from the space domain dispersion relation, the accuracy of modelling can be increased from second-order along any directions to (2M)th-order along 48 directions. In addition, the conventional high-order spatial finite-difference modelling accuracy can be improved by using a truncated finite-difference scheme. In this paper, we combine the time-space domain dispersion-relation-based finite difference scheme and the truncated finite-difference scheme to obtain optimised spatial finite-difference coefficients and thus to significantly improve the modelling accuracy without increasing computational cost, compared with the conventional space domain dispersion-relation-based finite difference scheme. We developed absorbing boundary conditions for the 3D acoustic wave equation, based on predicting wavefield values in a transition area by weighing wavefield values from wave equations and one-way wave equations.

Dispersion analyses demonstrate that high-order spatial finite-difference stencils have greater accuracy than low-order spatial finite-difference stencils for high frequency components of wavefields, and spatial finite-difference stencils devised in the time-space domain have greater precision than those devised in the space domain under the same discretisation. The modelling accuracy can be improved further by using the truncated spatial finite-difference stencils. Stability analyses show that spatial finite-difference stencils devised in the time-space domain have better stability condition. Numerical modelling experiments for homogeneous, horizontally layered and Society of Exploration Geophysicists/European Association of Geoscientists and Engineers salt models demonstrate that this modelling scheme has greater accuracy than a conventional scheme and has better absorbing effects than Clayton-Engquist absorbing boundary conditions.

Key words: absorbing boundary conditions, dispersion-relation-based finite difference, 3D acoustic wave equation, time-space domain, truncated finite difference.


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