二阶弹性波动方程高精度交错网格波场分离数值模拟
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摘要
给出了一种等价的二阶弹性波动方程,以解决弹性波场中完全弹性波动方程不能完全分离耦合的纵、横波波场问题。应用高阶交错网格有限差分法求解该波动方程,并使用通量校正技术(FCT)进一步压制频散,采用均匀介质模型和层状介质模型进行波场分离数值试验,精确得到了混合波场、完全分离的纯纵波及纯横波波场。数值结果分析表明,本文方法在均匀介质情况下准确可靠,在分离后的纯纵、横波波场中可观察到较为丰富的能量转换信息,这对认识复杂弹性波的传播规律及弹性波理论具有重要意义。
This paper proposes an equivalent second order elastic wave equation to solve the problem of being unable to completely separate the coupled P and S wave by full elastic wave equation.Through solving this equivalent wave equation by high-order staggered-grid finite difference scheme together with Flux Correction Technology(FCT) and separating wave fields of the isotropic model and layered model,the authors accurately obtained the hybrid wave field and completely separated fields of pure P wave and pure S wave fields.An analysis of the numerical results shows that the method is effective and reliable in isotropic media,and there exists abundant energy transform information in separated pure P and pure S wave field.The result of the study is of significance in understanding the propagating law and the elastic wave theory in the complex wave field.
This paper proposes an equivalent second order elastic wave equation to solve the problem of being unable to completely separate the coupled P and S wave by full elastic wave equation.Through solving this equivalent wave equation by high-order staggered-grid finite difference scheme together with Flux Correction Technology(FCT) and separating wave fields of the isotropic model and layered model,the authors accurately obtained the hybrid wave field and completely separated fields of pure P wave and pure S wave fields.An analysis of the numerical results shows that the method is effective and reliable in isotropic media,and there exists abundant energy transform information in separated pure P and pure S wave field.The result of the study is of significance in understanding the propagating law and the elastic wave theory in the complex wave field.
引文
[1]Dankbaar J W M.Separation of P-waves and S-waves[J].Geo-physical Prospecting,1985,33:970-986.
[2]Dellinger J,Etnen J.Wave-field separation in two-dimension aniso-tropic media[J].Geophysics,1990,55:914-919.
[3]Devaney A J,Oristaglio ML.A plane-wave decomposition for elas-tic wave fields applied to the separation of P waves and S waves invector seismic data[J].Geophysics,1986,51:419-423.
[4]马德堂,朱光明.弹性波波场P波和S波分解的数值模拟[J].石油地球物理勘探,2003,30(5).
[5]马永旺,詹正彬,顾汉明.伪谱法地震波传播数值模拟[J].石油物探,2001,40(20):42-48.
[6]Bengt Fornberg.The pseudospectral method:Comparision with fi-nite differences for the elastic wave equation[J].Geophysics,1975,52:483-501.
[7]李振春,张华,刘庆敏,韩文功.弹性波交错网格高阶有限差分法波场分离数值模拟[J].石油地球物理勘探,2007,42(5):510-515.
[8]Zhang Jianlei,Tian Zhenping,Wang Chengxiang.P-and S-waveseparated elastic wave equation numerical modeling using2D stag-gered-grid[R].SEG/San Antonio 2007 Annual Meeting.
[9]杜世通.地震波动力学[M].东营:石油大学出版社,1996.
[10]DONG Liangguo,MA Zaitian,CAO Jingzhong.The staggered-gridhigh-order difference method of one-order elastic equation[J]Chi-nese J Geophys(in Chinese),2000,43(3):411-419.
[11]宁刚,熊章强,陈持逊.波动方程有限差分正演模拟误差来源分析[J].物探与化探,2008,32(2):203-206.
[12]李万万,裴正林.井间地震弹性波传播特征数值模拟[J].物探与化探,2008,32(2):207-211.
[13]陈可洋,刘洪林,杨微,吴清岭,等.随机介质模型的改进方法及应用[J].大庆石油地质与开发.2008,27(5):124-126,131.
[14]王?,杨长春,冯英杰.用优化通量校正传输技术压制数值模拟的频散[J].勘探地球物理进展,2007,30(4):16-21.
[15]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6).
[16]陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79.
[2]Dellinger J,Etnen J.Wave-field separation in two-dimension aniso-tropic media[J].Geophysics,1990,55:914-919.
[3]Devaney A J,Oristaglio ML.A plane-wave decomposition for elas-tic wave fields applied to the separation of P waves and S waves invector seismic data[J].Geophysics,1986,51:419-423.
[4]马德堂,朱光明.弹性波波场P波和S波分解的数值模拟[J].石油地球物理勘探,2003,30(5).
[5]马永旺,詹正彬,顾汉明.伪谱法地震波传播数值模拟[J].石油物探,2001,40(20):42-48.
[6]Bengt Fornberg.The pseudospectral method:Comparision with fi-nite differences for the elastic wave equation[J].Geophysics,1975,52:483-501.
[7]李振春,张华,刘庆敏,韩文功.弹性波交错网格高阶有限差分法波场分离数值模拟[J].石油地球物理勘探,2007,42(5):510-515.
[8]Zhang Jianlei,Tian Zhenping,Wang Chengxiang.P-and S-waveseparated elastic wave equation numerical modeling using2D stag-gered-grid[R].SEG/San Antonio 2007 Annual Meeting.
[9]杜世通.地震波动力学[M].东营:石油大学出版社,1996.
[10]DONG Liangguo,MA Zaitian,CAO Jingzhong.The staggered-gridhigh-order difference method of one-order elastic equation[J]Chi-nese J Geophys(in Chinese),2000,43(3):411-419.
[11]宁刚,熊章强,陈持逊.波动方程有限差分正演模拟误差来源分析[J].物探与化探,2008,32(2):203-206.
[12]李万万,裴正林.井间地震弹性波传播特征数值模拟[J].物探与化探,2008,32(2):207-211.
[13]陈可洋,刘洪林,杨微,吴清岭,等.随机介质模型的改进方法及应用[J].大庆石油地质与开发.2008,27(5):124-126,131.
[14]王?,杨长春,冯英杰.用优化通量校正传输技术压制数值模拟的频散[J].勘探地球物理进展,2007,30(4):16-21.
[15]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6).
[16]陈可洋.声波完全匹配层吸收边界条件的改进算法[J].石油物探,2009,48(1):76-79.
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