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Stability condition of finite difference solution for viscoelastic wave equations |
Chengyu Sun1, Yunfei Xiao1, Xingyao Yin1, Hongchao Peng2 |
1 China University of Petroleum, Qingdao 266555, China
2 BGP, China National Petroleum Corporation, Zhuozhou 072751, China |
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Abstract The stability problem is a very important aspect in seismic wave numerical modeling. Based on the theory of seismic waves and constitutive equations of viscoelastic models, the stability problems of finite difference scheme for Kelvin- Voigt and Maxwell models with rectangular grids are analyzed. Expressions of stability conditions with arbitrary spatial accuracies for two viscoelastic models are derived. With approximation of quality factor Q≥5, simplified expressions are developed and some numerical models are given to verify the validity of the corresponding theoretical results. Then this paper summarizes the influences of seismic wave velocity, frequency, size of grid and difference coefficients, as well as quality factor on stability condition. Finally the prerequisite conditions of the simplified stability equations are given with error analysis.
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Received: 31 March 2009
Published: 10 October 2009
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Corresponding Authors:
Chengyu Sun
E-mail: suncy@upc.edu.cn
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