虚谱法一阶应力—速度方程地震数值模拟
|
摘要
地震波场模拟是正确认识复杂条件下地震波传播机理、规律及波场特征的有效手段。交错网格高阶差分常用于一阶应力—速度声波方程数值模拟,但空间差分的固有特性使得数值频散难以避免。虚谱法利用模型空间的全部信息对波场函数进行傅氏变换,可得到精确的波场空间导数;由于它克服了对高频成分的限制,因而可实现全频带的地震波场模拟。将完美匹配层边界条件引入虚谱法数值模拟可更有效地消除边界反射,有利于更精确地模拟地震波的传播过程。数值算例表明,虚谱法一阶应力—速度声学方程模拟结果具有较高的时间分辨率,在同等模拟精度条件下则具有更高的计算效率。
Seismic wave field simulation is an effective method to correctly understand the spreading mechanism and the wave field characteristic for seismic wave in complex conditions.Staggered mesh high order difference is often used in one order stress-velocity acoustic equation seismic simulation,however the numerical dispersion caused by the algorithm can not be avoided.By using all information in model space and applying Fourier transformation to wave field function,accurate wave field space derivative is obtained in the Pseudo spectral method,as in this method the restriction to high frequency was overcame,the seismic wave field simulation with full frequency bandwidth was realized.With the use of perfected matched layers condition in Pseudo spectral seismic simulation,the reflection wave from artificial boundary can be eliminated efficiently,and the seismic wave penetrating process can be better and accurately simulated.In this paper the numerical test shows that simulation results with pseudo spectral method one order stress-velocity equation has good resolution in time domain and it has high calculating efficiency with the same simulation precision.
Seismic wave field simulation is an effective method to correctly understand the spreading mechanism and the wave field characteristic for seismic wave in complex conditions.Staggered mesh high order difference is often used in one order stress-velocity acoustic equation seismic simulation,however the numerical dispersion caused by the algorithm can not be avoided.By using all information in model space and applying Fourier transformation to wave field function,accurate wave field space derivative is obtained in the Pseudo spectral method,as in this method the restriction to high frequency was overcame,the seismic wave field simulation with full frequency bandwidth was realized.With the use of perfected matched layers condition in Pseudo spectral seismic simulation,the reflection wave from artificial boundary can be eliminated efficiently,and the seismic wave penetrating process can be better and accurately simulated.In this paper the numerical test shows that simulation results with pseudo spectral method one order stress-velocity equation has good resolution in time domain and it has high calculating efficiency with the same simulation precision.
引文
[1]陆基孟.地震勘探原理.北京:石油工业出版社,1982
[2]贺振华.反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989
[3]陈耿毅,余钦范,蔡希玲等.地震模拟技术新进展——第67届EAGE年会论文综述.勘探地球物理进展,2005,28(6):439～448
[4]张永刚.地震波场数值模拟方法.石油物探,2003,42(2):143～148
[5]Altermen Z S and Loewenthal D.Seismic wave in a quarter and three quarter p1ane.Geophysics J Roy Astr Soc,1970,20(1):101～126
[6]Alford R M,Kelly K Rand Boore D M.Accuracy of finite difference modeling of the acoustic wave equa-tion.Geophysics,1974,39(6):834～842
[7]Virieux J.SH wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geo-physics,1984,49(11):1933～1957
[8]Levander A R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,53(11):1425～1436
[9]Crase E.High-order(space and ti me)finite-differ-ence modeling of elastic wave equation.Expanded Abstracts of60th SEG Annual Meeting,1990,987～991
[10]Carcione J M.Staggered mesh for the anisotropic and viscoelastic wave equation.Geophysics,1999,64(6):1863～1866
[11]Magnier S A,Mora P and Tarantola A.Finite differ-ence on mini ma1grids.Geophysics,1994,59(9):1435～1443
[12]Kosloff D D and Baysalt E.Forward modeling by a Fourier method.Geophysics,1982,47(10):1402～1412
[13]Fornberg B.The pseudo-spectral method:Accurate representation in elastic wave calculations.Geophys-ics,1988,53(5):625～637
[14]Reshef M,Kosloff D,Edwards M and Hsiung C.Three-di mensional acoustic modeling by the Fourier method.Geophysics,1988,53(9):1175～1183
[15]Reshef M,Kosloff D,Edwards M and Hsiung C.Three-di mensional elastic modeling by the Fourier method.Geophysics,1988,53(9):1184～1193
[16]傅旦丹,何樵登.正交各向异性介质地震弹性波场的伪谱法正演模拟.石油物探,2001,40(3):8～14
[17]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005
[18]庄东海,王超,肖斌.虚谱法三维地震波动方程正演模拟.江汉石油学院学报,1998,20(4):30～33
[19]Collino F and Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastody-namic problem in anisotropic heterogeneous media.Geophysics,2001,66(1):294～307
[20]王守东.声波方程完美匹配层吸收边界.石油地球物理勘探,2003,38(1):31～34
[21]Cerjan C,Kosloff Dand Kosloff Ret al.Anonreflecting boundary condition for discrete acoustic and elastic wave equation.Geophysics,1985,50(9):705～708
[22]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.地球物理学报,2000,43(6):856～859
[23]刘文革,贺振华,黄德济等.高精度傅里叶有限差分法模型正演.石油地球物理勘探,2007,42(6):629～633
[24]RistowD.Fourierfinite-difference migration.Geophys-ics,1994,59(12):1882～1893
[2]贺振华.反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989
[3]陈耿毅,余钦范,蔡希玲等.地震模拟技术新进展——第67届EAGE年会论文综述.勘探地球物理进展,2005,28(6):439～448
[4]张永刚.地震波场数值模拟方法.石油物探,2003,42(2):143～148
[5]Altermen Z S and Loewenthal D.Seismic wave in a quarter and three quarter p1ane.Geophysics J Roy Astr Soc,1970,20(1):101～126
[6]Alford R M,Kelly K Rand Boore D M.Accuracy of finite difference modeling of the acoustic wave equa-tion.Geophysics,1974,39(6):834～842
[7]Virieux J.SH wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geo-physics,1984,49(11):1933～1957
[8]Levander A R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,53(11):1425～1436
[9]Crase E.High-order(space and ti me)finite-differ-ence modeling of elastic wave equation.Expanded Abstracts of60th SEG Annual Meeting,1990,987～991
[10]Carcione J M.Staggered mesh for the anisotropic and viscoelastic wave equation.Geophysics,1999,64(6):1863～1866
[11]Magnier S A,Mora P and Tarantola A.Finite differ-ence on mini ma1grids.Geophysics,1994,59(9):1435～1443
[12]Kosloff D D and Baysalt E.Forward modeling by a Fourier method.Geophysics,1982,47(10):1402～1412
[13]Fornberg B.The pseudo-spectral method:Accurate representation in elastic wave calculations.Geophys-ics,1988,53(5):625～637
[14]Reshef M,Kosloff D,Edwards M and Hsiung C.Three-di mensional acoustic modeling by the Fourier method.Geophysics,1988,53(9):1175～1183
[15]Reshef M,Kosloff D,Edwards M and Hsiung C.Three-di mensional elastic modeling by the Fourier method.Geophysics,1988,53(9):1184～1193
[16]傅旦丹,何樵登.正交各向异性介质地震弹性波场的伪谱法正演模拟.石油物探,2001,40(3):8～14
[17]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005
[18]庄东海,王超,肖斌.虚谱法三维地震波动方程正演模拟.江汉石油学院学报,1998,20(4):30～33
[19]Collino F and Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastody-namic problem in anisotropic heterogeneous media.Geophysics,2001,66(1):294～307
[20]王守东.声波方程完美匹配层吸收边界.石油地球物理勘探,2003,38(1):31～34
[21]Cerjan C,Kosloff Dand Kosloff Ret al.Anonreflecting boundary condition for discrete acoustic and elastic wave equation.Geophysics,1985,50(9):705～708
[22]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.地球物理学报,2000,43(6):856～859
[23]刘文革,贺振华,黄德济等.高精度傅里叶有限差分法模型正演.石油地球物理勘探,2007,42(6):629～633
[24]RistowD.Fourierfinite-difference migration.Geophys-ics,1994,59(12):1882～1893
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心