| A numerical study of 1-D nonlinear P-wave propagation in solid |
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| 作者姓名： | 郑海山 张中杰 杨宝俊 |
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| 作者单位： | Institute of Geology and Geophysics，Chinese Academy of Sciences，Institute of Geology and Geophysics，Chinese Academy of Sciences，Department of Geophysics，Jilin University Beijing 100101，China，Beijing 100101，China，Changchun 130026，China |
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| 基金项目： | Project of Knowledge Innovation Program from Chinese Academy of Sciences (KZCX2-109). |
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| 摘 要： | IntroductionBecauseoftheextensivedistributionofruptures,micro-cracksandcrystalfracturesintheearth,therelationshipsbetweenthestressandstrainarenolongerlinear,infact,theyarenonlinear.Inordertoinvestigateandusethenonlinearcharacteristicsofsolidmediumintheearth,weshouldconsidertheinfluenceofnonlinearresponseduringthecourseofseismicmodelingandinversion.Thisisoneoftheimportantstudyfieldsthathavebeenpaidgreatattentionsinthere-centyearsintheworld(Minster,etal,1991;ZHANG,TENG,1993).Thenonlinearchar…
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A numerical study of 1-D nonlinear P-wave propagation in solid |
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| ZHENG Hai-shanZHANG Zhong-jieYANG Bao-jun Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing ,China.A numerical study of 1-D nonlinear P-wave propagation in solid[J].Acta Seismologica Sinica(English Edition),2004,17(1):80-86. |
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| Authors: | ZHENG Hai-shanZHANG Zhong-jieYANG Bao-jun Institute of Geology and Geophysics Chinese Academy of Sciences Beijing China |
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| Institution: | 1. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100101, China
2. Department of Geophysics, Jilin University, Changchun 130026, China |
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| Abstract: | Two central schemes of finite difference (FD) up to different accuracy orders of space sampling step Dx (Fourth order and Sixth order respectively) were used to study the 1-D nonlinear P-wave propagation in the nonlinear solid media by the numerical method. Distinctly different from the case of numerical modeling of linear elastic wave, there may be several difficulties in the numerical treatment to the nonlinear partial differential equation, such as the steep gradients, shocks and unphysical oscillations. All of them are the great obstacles to the stability and conver-gence of numerical calculation. Fortunately, the comparative study on the modeling of nonlinear wave by the two FD schemes presented in the paper can provide us with an easy method to keep the stability and convergence in the calculation field when the product of the absolute value of nonlinear coefficient and the value of u/x are small enough, namely, the value of bu/x is much smaller than 1. Several results are founded in the numerical study of nonlinear P-wave propagation, such as the waveform aberration, the generation and growth of harmonic wave and the energy redistribution among different frequency components. All of them will be more violent when the initial amplitude A0 is larger or the nonlinearity of medium is stronger. Correspondingly, we have found that the nonlinear P-wave propagation velocity will change with different initial frequency f of source wave or the wave velocity c (equal to the P-wave velocity in the same medium without considering nonlinearity). |
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| Keywords: | nonlinear wave numerical simulation central schemes of finite difference |
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