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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 157071, 10 pages
http://dx.doi.org/10.1155/2013/157071
Research Article

Staggered-Grid Finite Difference Method with Variable-Order Accuracy for Porous Media

1Institute of Wave and Information, Xi'an Jiaotong University, Xi'an 710049, China
2National Engineering Laboratory for Offshore Oil Exploration, Xi'an 710049, China

Received 9 January 2013; Accepted 7 April 2013

Academic Editor: Alex Elias-Zuniga

Copyright © 2013 Jinghuai Gao and Yijie Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The numerical modeling of wave field in porous media generally requires more computation time than that of acoustic or elastic media. Usually used finite difference methods adopt finite difference operators with fixed-order accuracy to calculate space derivatives for a heterogeneous medium. A finite difference scheme with variable-order accuracy for acoustic wave equation has been proposed to reduce the computation time. In this paper, we develop this scheme for wave equations in porous media based on dispersion relation with high-order staggered-grid finite difference (SFD) method. High-order finite difference operators are adopted for low-velocity regions, and low-order finite difference operators are adopted for high-velocity regions. Dispersion analysis and modeling results demonstrate that the proposed SFD method can decrease computational costs without reducing accuracy.