弹性波交错网格高阶有限差分法波场分离数值模拟
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摘要
地震波中的弹性波传播会产生纵波和横波,所以用完全弹性波波动方程进行弹性波波场数值模拟时,只能得到纵横波耦合的混合波场。本文从P波波场为无旋场,而S波波场为无散场的思路出发,推出满足此条件的一阶速度—应力弹性波波场分离方程,并利用交错网格高阶有限差分法对波场分离方程进行数值模拟。模拟实例表明,此方法不但成功地将P波波场和S波波场从混合波场中分离出来,而且这种方法的稳定性好、模拟精度高,可用于弹性波传播规律研究及地震资料处理。
Elastic wave propagation of seismic waves can produce P-wave and S-wave,therefore, using full e-lastic wave equation to carry out numeric simulation of elastic wavefield can only get hybrid wavefield coupling P-wave with S-wave. Starting from the idea of P-wave wavefield being rotation-free field and S-wave divergence-free field,the paper deduced separation equation of first-order velocity-stress elastic wavefield, which meets this condition, and used staggering grid high-order finite-difference algorithm to carry out numeric simulation of wavefield separation equation. The simulated cases showed that the approach not only can successfully separate P-wave wavefield from S-wave wavefield in hybrid wavefield, but also is characterized by good stability and higher simulated precision, which can be used for studying the rule of elastic wave propagation and seismic data processing.
Elastic wave propagation of seismic waves can produce P-wave and S-wave,therefore, using full e-lastic wave equation to carry out numeric simulation of elastic wavefield can only get hybrid wavefield coupling P-wave with S-wave. Starting from the idea of P-wave wavefield being rotation-free field and S-wave divergence-free field,the paper deduced separation equation of first-order velocity-stress elastic wavefield, which meets this condition, and used staggering grid high-order finite-difference algorithm to carry out numeric simulation of wavefield separation equation. The simulated cases showed that the approach not only can successfully separate P-wave wavefield from S-wave wavefield in hybrid wavefield, but also is characterized by good stability and higher simulated precision, which can be used for studying the rule of elastic wave propagation and seismic data processing.
引文
[1]Dankbaar J W M.Separation of P-waves and S-waves.Geophysical Prospecting,1985,33:970～986
[2]Devaney AJ,Oristaglio M L.A plane-wave decomposi-tionfor elastic wave fields applied to the separation of P-waves and S-waves in vector seismic data.Geophysics,1986,51:419～423
[3]Dellinger J,Etnen J.Wave-field separationin two-di men-sion anisotropic media.Geophysics,1990,55:914～919
[4]马德堂,朱光明.弹性波波场P波和S波分解的数值模拟.石油地球物理勘探,2003,38(5):482～486
[5]White J E.Undergroundsound:applicationofseis-mic wave.Elsevier Sci Publ Co,1983
[6]杜世通.地震波动力学.山东东营:石油大学出版社,1996
[7]董良国.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(1):411～419
[8]吴国忱.各向异性介质地震波传播与成像.山东东营:中国石油大学出版社,2006,116～123
[9]董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):45～56
[10]Collino F and Sogka T.Application of the perfectly matched absorbing layer model to the linear elastody-namic problem in anisotropic heterogeneous media.Geophysics,2001,66(1):294～307
[11]裴正林.层状各向异性介质中横波分裂和再分裂数值模拟.石油地球物理勘探,2006,41(1):17～25
[12]陈伟.起伏地表条件下二维地震波场的数值模拟.勘探地球物理进展,2005,28(1):25～31
[2]Devaney AJ,Oristaglio M L.A plane-wave decomposi-tionfor elastic wave fields applied to the separation of P-waves and S-waves in vector seismic data.Geophysics,1986,51:419～423
[3]Dellinger J,Etnen J.Wave-field separationin two-di men-sion anisotropic media.Geophysics,1990,55:914～919
[4]马德堂,朱光明.弹性波波场P波和S波分解的数值模拟.石油地球物理勘探,2003,38(5):482～486
[5]White J E.Undergroundsound:applicationofseis-mic wave.Elsevier Sci Publ Co,1983
[6]杜世通.地震波动力学.山东东营:石油大学出版社,1996
[7]董良国.一阶弹性波方程交错网格高阶差分解法.地球物理学报,2000,43(1):411～419
[8]吴国忱.各向异性介质地震波传播与成像.山东东营:中国石油大学出版社,2006,116～123
[9]董良国.弹性波数值模拟中的吸收边界条件.石油地球物理勘探,1999,34(1):45～56
[10]Collino F and Sogka T.Application of the perfectly matched absorbing layer model to the linear elastody-namic problem in anisotropic heterogeneous media.Geophysics,2001,66(1):294～307
[11]裴正林.层状各向异性介质中横波分裂和再分裂数值模拟.石油地球物理勘探,2006,41(1):17～25
[12]陈伟.起伏地表条件下二维地震波场的数值模拟.勘探地球物理进展,2005,28(1):25～31
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