Wavelet Finite-Difference Method for the Numerical Simulation of Wave Propagation in Fluid-Saturated Porous Media

HE Ying; HAN Bo

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(11): 1355-1346

HE Ying, HAN Bo. Wavelet Finite-Difference Method for the Numerical Simulation of Wave Propagation in Fluid-Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1355-1346.

Citation:

HE Ying, HAN Bo. Wavelet Finite-Difference Method for the Numerical Simulation of Wave Propagation in Fluid-Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1355-1346.

Citation:

HE Ying, HAN Bo. Wavelet Finite-Difference Method for the Numerical Simulation of Wave Propagation in Fluid-Saturated Porous Media[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1355-1346.

PDF( 819 KB)

Wavelet Finite-Difference Method for the Numerical Simulation of Wave Propagation in Fluid-Saturated Porous Media

HE Ying,
HAN Bo

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P. R. China

Received Date: 2008-03-20
Rev Recd Date: 2008-09-23
Publish Date: 2008-11-15

Abstract

Abstract

The numerical simulation of wave propagation in fluid-saturated porous media is considered. A wavelet finite-difference method was proposed for solving the 2-D elastic wave equation. This algorithm combines the flexibility and computational efficiency of wavelet multiresolution method with the easy implementation of finite-difference method. And the orthogonal wavelet basis provides a natural framework, which adapts spatial grids to local wavefield properties. Numerical results illustrate the value of the approach as an accurate and stable tool for the simulation of wave propagation in fluid-saturated porous media.
- wavelet multiresolution method,
- numerical simulation,
- fluid-saturated porous medium,
- finite-difference method

FullText(HTML)

References(17)

References

[1]	Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid: low-frequency range[J].Acoustical Society of America,1956,28(2):168-178. doi: 10.1121/1.1908239
[2]	Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid: higher-frequency range[J].Acoustical Society of America,1956,28(2):168-178. doi: 10.1121/1.1908239
[3]	Dai N,Vafidis A,Kanasewich E R.Wave propagation in heterogeneous,porous media:A velocity-stress,finite-difference method[J].Geophysics,1995,60(2):327-340. doi: 10.1190/1.1443769
[4]	Prevost J H. Wave propagation in fluid-saturated porous media: an efficient finite element procedure[J].Soil Dynamics and Earthquake Engineering,1985,4(4):183-202. doi: 10.1016/0261-7277(85)90038-5
[5]	Narasimhan T N,Witherspoon P A.An integrated finite difference method for analyzing fluid flow in porous media[J].Water Resources Research,1976,12(1):57-64. doi: 10.1029/WR012i001p00057
[6]	Pedercini M,Patera A T,Cruz M E.Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows[J].International Journal for Numerical Methods in Fluids,1998,26(2):145-175. doi: 10.1002/(SICI)1097-0363(19980130)26:2<145::AID-FLD617>3.0.CO;2-O
[7]	邵秀民,蓝志凌. 流体饱和多孔介质波动方程的有限元解法[J]. 地球物理学报.2000,43(2):264-277.
[8]	SUN Wei-tao,YANG Hui-zhu.Elastic wavefield calculation for heterogeneous anisotropic porous media using the 3D irregular-grid finite-difference[J].Acta Mechanica Solida Sinica,2003,16(4):283-299.
[9]	Hong T K,Kennett B L N. A wavelet-based method for simulation of two-dimensional elastic wave propagation[J].Geophysical Journal International,2002,150(3):610-638. doi: 10.1046/j.1365-246X.2002.01714.x
[10]	Mustafa M T,Siddiqui A A. Wavelet optimized finite difference method with non-static regridding[J].Applied Mathematics and Computation,2007,18(6):203-211.
[11]	Xiang J W,Chen X F,He Z J,et al. The construction of 1D wavelet finite elements for structural analysis[J].Computational Mechanics,2007,40(2):325-339. doi: 10.1007/s00466-006-0102-5
[12]	张新明,刘克安,刘家琦.流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法[J].地球物理学报,2005,48(5):1156-1166.
[13]	LIAO Zhen-peng,Wong H L,YANG Bai-po,et al. A transmitting boundary for transient wave analyses[J].Scientia Sinica,A,1984,27(10):1063-1076.
[14]	LIAO Zhen-peng,Wong H L.A transmitting boundary for the numerical simulation of elastic wave propagation[J].Soil Dynamics and Earthquake Engineering,1984,3(4):174-183. doi: 10.1016/0261-7277(84)90033-0
[15]	Beylkin G. On the representation of operators in bases of compactly supported wavelets[J].SIAM Numerical Analysis,1992,29(1):1716-1740. doi: 10.1137/0729097
[16]	Hajji M A,Melkonian S,Vaillancourt V.Representation of differential opterator in wavelet basis[J].Computers and Mathematics with Applications,2004,47(6):1011-1033. doi: 10.1016/S0898-1221(04)90083-1
[17]	Kelly K R,Ward R W,Treitel S,et al.Synthetic seismograms: a finite-difference approach[J].Geophysies,1976,41(1):2-27.