基于散度和旋度的弹性波波场分离数值模拟方法
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摘要
弹性波波场分离数值模拟方法是研究混合波场中纯纵波和纯横波波场传播规律的一种重要手段,通常采用算子分裂来实现,这不但增加了计算量,而且还浪费了大量计算时间。因此提出了基于散度和旋度的弹性波波场分离数值模拟新方法,仅依赖于交错网格来计算出散度场(纯纵波)和旋度场(纯横波),从而提高计算效率。在人工截断边界处采用完全匹配层吸收边界条件(PML)。数值模拟结果表明,该方法能够从混合波场中准确地分离出纯纵横波波场,且精度高,边界吸收效果好,计算速度快,计算过程稳定,可用于指导实际多波多分量地震资料处理,同时指出本文算法对相互耦合的波型(如面波)无法实现准确分离。
Elastic wave field separation numerical modeling has been an important means to study the propagating rule of pure compress wave and pure shear wave of the hybrid elastic wave field.The general method is achieved by the operator separation,which not only increase the computed memory,but also waste a lot of computed time.Thus we put forward a new elastic wave field separation numerical modeling scheme base on divergence and curl,which is only depended on staggered grid to compute the divergence field(compress wave) and curl field(shear wave),so the computed efficiency is greatly improved.Perfect Matched Layer(PML) absorbing boundary condition is used to weaken the reflection wave from the boundary.The numerical result shows that this method can correctly and quickly separate pure compress wave and pure shear wave from hybrid wave field with high precision,good boundary absorption,and the numerical process is stable,so it can be used to guide multi-wave multi-components seismic datum processing,and also point out that the method has difficulty to separate the coupled wave type such as surface wave.
Elastic wave field separation numerical modeling has been an important means to study the propagating rule of pure compress wave and pure shear wave of the hybrid elastic wave field.The general method is achieved by the operator separation,which not only increase the computed memory,but also waste a lot of computed time.Thus we put forward a new elastic wave field separation numerical modeling scheme base on divergence and curl,which is only depended on staggered grid to compute the divergence field(compress wave) and curl field(shear wave),so the computed efficiency is greatly improved.Perfect Matched Layer(PML) absorbing boundary condition is used to weaken the reflection wave from the boundary.The numerical result shows that this method can correctly and quickly separate pure compress wave and pure shear wave from hybrid wave field with high precision,good boundary absorption,and the numerical process is stable,so it can be used to guide multi-wave multi-components seismic datum processing,and also point out that the method has difficulty to separate the coupled wave type such as surface wave.
引文
[1]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).
[2]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.
[3]Bengt Fornberg.The pseudospectral method:Comparision with fi-nite differences for the elastic wave equation[J].Geophysics,1975,52:483-501.
[4]李振春,张华,刘庆敏,等.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.
[5]Zhang Jianlei,Tian Zhenping,Wang Chengxiang.P-and S-waveseparated elastic wave equation numerical modeling using2D stag-gered-grid.[C].SEG/San Antonio 2007 Annual Meeting.
[6]裵正林,牟永光.地震波传播的数值模拟[J].地球物理学进展,2004,19(4):933-941.
[7]裴正林.层状各向异性介质中横波分裂和再分裂数值模拟[J].石油地球物理勘探,2006,41(1):17-25.
[8]程冰洁,李小凡,徐天吉.非均匀介质中交错网格高阶有限差分数值模拟[J].物探化探计算技术,2006,28(4).
[9]董良国.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(1):411~419.
[10]杜世通.地震波动力学[M].东营:石油大学出版社,1996.
[11]陆基孟.地震勘探原理:下册[M].北京:石油大学出版社,2004.
[12]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).
[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]王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):20-23.
[15]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.
[16]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.
[17]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]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.
[3]Bengt Fornberg.The pseudospectral method:Comparision with fi-nite differences for the elastic wave equation[J].Geophysics,1975,52:483-501.
[4]李振春,张华,刘庆敏,等.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.
[5]Zhang Jianlei,Tian Zhenping,Wang Chengxiang.P-and S-waveseparated elastic wave equation numerical modeling using2D stag-gered-grid.[C].SEG/San Antonio 2007 Annual Meeting.
[6]裵正林,牟永光.地震波传播的数值模拟[J].地球物理学进展,2004,19(4):933-941.
[7]裴正林.层状各向异性介质中横波分裂和再分裂数值模拟[J].石油地球物理勘探,2006,41(1):17-25.
[8]程冰洁,李小凡,徐天吉.非均匀介质中交错网格高阶有限差分数值模拟[J].物探化探计算技术,2006,28(4).
[9]董良国.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(1):411~419.
[10]杜世通.地震波动力学[M].东营:石油大学出版社,1996.
[11]陆基孟.地震勘探原理:下册[M].北京:石油大学出版社,2004.
[12]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).
[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]王永刚,邢文军,谢万学,等.完全匹配层吸收边界条件的研究[J].中国石油大学学报:自然科学版,2007,31(1):20-23.
[15]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.
[16]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.
[17]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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