基于非均质体的波动方程有限元正演模拟
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摘要
通常地震波声波方程正演模拟所采用的方程是描述波在均匀介质中传播的波动方程,该方程用于非均质介质时,其模拟结果存在较大误差,因此需要在界面处引入过渡层,即认为弹性参数是连续变化的。采用有限元方法求解非均质声波方程,将单元内的弹性参数插值,使介质上任意一点的位移和应力始终是一个连续函数,这样对于突变界面就能通过过渡层来近似模拟,当该层单元格足够小时可以有效控制误差,提高正演模拟精度。最终通过数值模型算例验证了该方法的有效性。
Acoustic wave equation is usually used for modeling in homogeneous media,but for modeling in heterogeneous media,some calculation errors will appear.So a transition layer at the interface is used for overcoming this problem to take the elastic parameters as continuous change.Here,the heterogeneous acoustic wave equation is solved with the finite-element method,so the elastic parameters in each element are interpolated and satisfied the modeling requirement in heterogeneous body.By altering the discontinuous interface into transition layer,the computing errors can be controlled when the size of element is small enough,in order to improve the accuracy of modeling.Finally,several numerical examples verified the validity of this method.
Acoustic wave equation is usually used for modeling in homogeneous media,but for modeling in heterogeneous media,some calculation errors will appear.So a transition layer at the interface is used for overcoming this problem to take the elastic parameters as continuous change.Here,the heterogeneous acoustic wave equation is solved with the finite-element method,so the elastic parameters in each element are interpolated and satisfied the modeling requirement in heterogeneous body.By altering the discontinuous interface into transition layer,the computing errors can be controlled when the size of element is small enough,in order to improve the accuracy of modeling.Finally,several numerical examples verified the validity of this method.
引文
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[8]赵海波,王秀明,王东.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报,2007,50(02):581-591Zhao H B,Wang X M,Wang D.Applications of theboundary absorption using aperfectly matched layerfor elastic wave simulation in poroelastic media[J].Chinese Journd of Geophysics,2007,50(2):581-591
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[10]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34Wang S D.Absorbing boundary condition for acous-tic wave equation by perfectly matched layer[J].OilGeophysical Prospectiong,2003,38(1):31-34
[2]Wu R S.Wide-angle elastic wave one way propaga-tion in heterogeneous media and an elastic wavecomplex screen method[J].Journal of GeophysicalResearch,1994,99(13):751-766
[3]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005:1-215Mou Y G,Pei Z L.Seismic numerical modeling for 3-D complex media[M].Beijing:Petroleum IndustryPress,2005:1-215
[4]Claerbout J F,Johnson A G.Extrapolation of timedependent waveforms along their path of propaga-tion[J].Geophysics,1971,26(3):285-295
[5]Alterman Z S,Loewenthal D.Seismic waves in aquarter and three quarter plane[J].GeophysicalJournal Royal Astronomical Society,1970,20(9):1090-1098
[6]Carcione J.M,Hermanz G.C,Kroode A P E.Seis-mic modeling[J].Geophysics,2002,67(4):1304-1325
[7]Kelly K R,Ward R W,Treitel S A,et al.A finitedifference approach[J].Geophysics,1976,41(1):2-27
[8]赵海波,王秀明,王东.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报,2007,50(02):581-591Zhao H B,Wang X M,Wang D.Applications of theboundary absorption using aperfectly matched layerfor elastic wave simulation in poroelastic media[J].Chinese Journd of Geophysics,2007,50(2):581-591
[9]薛东川,王尚旭.有限元解波动方程求取初至时间[J].石油地球物理勘探,2009,43(2):223-229Xue D C,Wang S X.Computation of first breakstime by using finite-element algorithm for solvingwave equation[J].Oil Geophysical Prospecting,2009,43(2):223-229
[10]王守东.声波方程完全匹配层吸收边界[J].石油地球物理勘探,2003,38(1):31-34Wang S D.Absorbing boundary condition for acous-tic wave equation by perfectly matched layer[J].OilGeophysical Prospectiong,2003,38(1):31-34
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