黏声波动方程变机制数有限差分正演
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摘要
实际地下介质普遍具有黏弹性,一般采用品质因子Q表征介质黏弹性程度。在勘探地震频带范围内,通常认为Q不随频率变化,这种常Q特征可以用广义标准线性固体模型进行较好地刻画,因此广义标准线性固体模型成为了黏弹性地震波正演模拟的首选。但是目前这类黏弹介质地震波正演方法往往使用固定的松弛机制数,存在模拟精度与计算效率不能较好统一的缺陷。本文基于广义标准线性体模型,提出了一种黏声波动方程变松弛机制数有限差分地震波场正演方法,即在模型不同区域使用不同松弛机制数、不同模拟精度的求解方式,以达到计算效率与模拟精度的统一。将本文模拟结果与解析解对比,分析模拟精度与机制数、Q值和传播距离的关系,确定不同机制数的适用范围;进一步对比变松弛机制数模拟结果与固定松弛机制数模拟结果的精度和计算效率,结果表明前者适用范围广,模拟精度高,并可有效提高计算效率。
Subsurface media are generally not elastic but viscoelastic,and the viscoelasticity is normally depicted by a dimensionless quantity,i.e.,quality factor Q.Within the frequency band of seismic exploration,Q is widely considered frequency-independent,which can be properly characterized by the generalized standard linear solid(GSLS)model.Thus,the GSLS model has become the mainstream while viscoelastic seismic wave modeling.However,when GSLS model has been chosen,the current modeling schemes commonly adopt a fixed number of relaxation mechanisms,which leads to a shortcoming,not being able to integrate the computational efficiency and precision.In this paper,we propose a finite difference viscoelastic seismicwave modeling scheme with variable mechanisms based on GSLS model.More precisely,we use different number of mechanisms to approximate the Q in different areas of earth model,thereby integrating both computational efficiency and precision.We compare our results with the analytical solution,and analyze the relation between the precision and the number of mechanisms,and Qand the traveling distance to determine the appropriate applicable range of different mechanisms.We also compare the precision and efficiency of variable mechanisms with those of a fixed number of mechanisms,and analyze the applicability of the proposed method.The results indicate some merits of the proposed scheme:wider applicability,higher computational precision,and more efficient simulation.
Subsurface media are generally not elastic but viscoelastic,and the viscoelasticity is normally depicted by a dimensionless quantity,i.e.,quality factor Q.Within the frequency band of seismic exploration,Q is widely considered frequency-independent,which can be properly characterized by the generalized standard linear solid(GSLS)model.Thus,the GSLS model has become the mainstream while viscoelastic seismic wave modeling.However,when GSLS model has been chosen,the current modeling schemes commonly adopt a fixed number of relaxation mechanisms,which leads to a shortcoming,not being able to integrate the computational efficiency and precision.In this paper,we propose a finite difference viscoelastic seismicwave modeling scheme with variable mechanisms based on GSLS model.More precisely,we use different number of mechanisms to approximate the Q in different areas of earth model,thereby integrating both computational efficiency and precision.We compare our results with the analytical solution,and analyze the relation between the precision and the number of mechanisms,and Qand the traveling distance to determine the appropriate applicable range of different mechanisms.We also compare the precision and efficiency of variable mechanisms with those of a fixed number of mechanisms,and analyze the applicability of the proposed method.The results indicate some merits of the proposed scheme:wider applicability,higher computational precision,and more efficient simulation.
引文
[1] Carcione J M.Wave propagation in anisotropic linear viscoelastic media:Theory and simulated wavefields[J].Geophysical Journal International,1990,101(3):739-750.
[2] Liu H P,Anderson D L,Kanamori H.Velocity dispersion due to anelasticity:implications for seismology and mantle composition[J].Geophysical Journal International,1976,47(1):41-58.
[3] Day S M,Bernard M J.Numerical simulation of atte-nuated wavefields using a Padé approximate method[J].Geophysical Journal of the Royal Astronomical Society,1984,78(1):105-118.
[4] Emmerich H,Korn M.Incorporation of attenuation into time-domain computations of seismic wave fields[J].Geophysics,1987,52(9):1252-1264.
[5] Robertsson J O A,Blanch J O,Levander A,et al.3-D viscoelastic finite difference modeling[C].SEG Technical Program Expanded Abstracts,1994,13:994-997.
[6] Robertsson J O A,Blanch J O,Symes W W.Visco-elastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456.
[7] Blanch J O,Robertsson J O A,Symes W W.Modeling of a constant Q:methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique[J].Geophysics,1995,60(1):176-184.
[8] Bohlen T.Parallel 3-D viscoelastic finite difference seismic modelling[J].Computers & Geosciences,2002,28(8):887-899.
[9] Saenger E H,Bohlen T.Finite difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid[J].Geophysics,2004,69(2):583-591.
[10] 杜启振,杨慧珠.线性黏弹性各向异性介质速度频散和衰减特征研究[J].物理学报,2002,51(9):2101-2108.DU Qizhen,YANG Huizhu.Velocity dispersion and attenuation in anisotropic linear viscoelastic media[J].Acta Physica Sinica,2002,51(9):2101-2108.
[11] 杜启振.各向异性黏弹性介质伪谱法波场模拟[J].物理学报,2004,53(12):4428-4434.DU Qizhen.Wavefield forward modeling with the pseudo-spectral method in viscoelastic and azimuthally anisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434.
[12] 牛滨华.黏弹性介质与地震波传播[M].北京:地质出版社,2007.
[13] 严红勇,刘洋.黏弹TTI介质中旋转交错网格高阶有限差分数值模拟[J].地球物理学报,2012,55(4):1354-1365.YAN Hongyong,LIU Yang.Rotated staggered grid high order finite difference numerical modeling for wave propagation in viscoelastic TTI media[J].Chinese Journal of Geophysics,2012,55(4):1354-1365.
[14] 何兵红,吴国忱,许冲.基于FFD算子的衰减介质地震波模拟[J].石油地球物理勘探,2014,49(1):153-160.HE Binghong,WU Guochen,XU Chong.Seismic wave simulation in attenuation medium based on FFD operator[J].Oil Geophysical Prospecting,2014,49(1):153-160.
[15] 罗文山,陈汉明,王成祥,等.时间域黏滞波动方程及其数值模拟新方法[J].石油地球物理勘探,2016,51(4):707-713.LUO Wenshan,CHEN Hanming,WANG Cheng- xiang,et al.A novel time-domain viscoacoustic wave equation and its numerical simulation[J].Oil Geophysical Prospecting,2016,51(4):707-713.
[16] 姚振岸,孙成禹,谢俊法,等.黏弹TTI介质旋转交错网格微地震波场模拟[J].石油地球物理勘探,2017,52(2):253-263.YAO Zhen’an,SUN Chengyu,XIE Junfa,et al.Micro-seismic forward modeling in visco-elastic TTI media based on rotated staggered grid finite-difference method[J].Oil Geophysical Prospecting,2017,52(2):253-263.
[17] Talezer H.An accurate and efficient scheme for wave propagation in linear viscoelastic media[J].Geophy-sics,1990,55(10):1366-1379.
[18] 杨仁虎,常旭,刘伊克.基于非均匀各向同性介质的黏弹性波正演数值模拟[J].地球物理学报,2009,52(9):2321-2327.YANG Renhu,CHANG Xu,LIU Yike.Viscoelastic wave modeling in heterogeneous and isotropic media[J].Chinese Journal of Geophysics,2009,52(9):2321-2327.
[19] 陈康,吴国忱,印兴耀,等.基于反射率法的TTI介质正演模拟[J].石油地球物理勘探,2013,48(5):717-727.CHEN Kang,WU Guochen,YIN Xingyao,et al.The modeling based on the reflectivity method in TTImedia[J].Oil Geophysical Prospecting,2013,48(5):717-727.
[20] Zhu T,Carcione J M.Theory and modelling of constant-Q P- and S-waves using fractional spatial deri-vatives[J].Geophysical Journal International,2014,196(3):1787-1795.
[21] Krohn C E,Murray T J.Shallow near-surface effects[J].Geophysics,2016,81(5):T221-T231.
[22] 陈志德,王成,刘国友,等.近地表Q值模型建立方法及其地震叠前补偿应用[J].石油学报,2015,36(2):188-196.CHEN Zhide,WANG Cheng,LIU Guoyou,et al.Modeling method of near-surface Q value and its seismic pre-stack compensation application[J].Acta Petrolei Sinica,2015,36(2):188-196.
[23] 杨宇,黄建平,雷建设,等.Lebedev网格黏弹性介质起伏地表正演模拟[J].石油地球物理勘探,2016,51(4):698-706.YANG Yu,HUANG Jianping,LEI Jianshe,et al.Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface[J].Oil Geophysical Prospecting,2016,51(4):698-706.
[24] Cai R Q,Sun C Y,Wu D S,et al.Finite-difference numerical modeling with variable mechanism for viscoacoustic wave equation[C].Extended Abstracts of 80th EAGE Conference & Exhibition,2018,Tu P903.
[25] Zener C M,Siegel S.Elasticity and Anelasticity of Metals[M].University of Chicago Press,Chicago,Illinois,1948.
[26] O’Connell R J,Budiansky B.Measures of dissipation in viscoelastic media[J].Geophysical Research Letters,1978,5(1):5-8.
[27] Carcione J M,Dan K,Ronnie K.Wave propagation simulation in a linear viscoelastic medium[J].Geophysical Journal of the Royal Astronomical Society,1988,93(2):597-611.
[2] Liu H P,Anderson D L,Kanamori H.Velocity dispersion due to anelasticity:implications for seismology and mantle composition[J].Geophysical Journal International,1976,47(1):41-58.
[3] Day S M,Bernard M J.Numerical simulation of atte-nuated wavefields using a Padé approximate method[J].Geophysical Journal of the Royal Astronomical Society,1984,78(1):105-118.
[4] Emmerich H,Korn M.Incorporation of attenuation into time-domain computations of seismic wave fields[J].Geophysics,1987,52(9):1252-1264.
[5] Robertsson J O A,Blanch J O,Levander A,et al.3-D viscoelastic finite difference modeling[C].SEG Technical Program Expanded Abstracts,1994,13:994-997.
[6] Robertsson J O A,Blanch J O,Symes W W.Visco-elastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456.
[7] Blanch J O,Robertsson J O A,Symes W W.Modeling of a constant Q:methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique[J].Geophysics,1995,60(1):176-184.
[8] Bohlen T.Parallel 3-D viscoelastic finite difference seismic modelling[J].Computers & Geosciences,2002,28(8):887-899.
[9] Saenger E H,Bohlen T.Finite difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid[J].Geophysics,2004,69(2):583-591.
[10] 杜启振,杨慧珠.线性黏弹性各向异性介质速度频散和衰减特征研究[J].物理学报,2002,51(9):2101-2108.DU Qizhen,YANG Huizhu.Velocity dispersion and attenuation in anisotropic linear viscoelastic media[J].Acta Physica Sinica,2002,51(9):2101-2108.
[11] 杜启振.各向异性黏弹性介质伪谱法波场模拟[J].物理学报,2004,53(12):4428-4434.DU Qizhen.Wavefield forward modeling with the pseudo-spectral method in viscoelastic and azimuthally anisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434.
[12] 牛滨华.黏弹性介质与地震波传播[M].北京:地质出版社,2007.
[13] 严红勇,刘洋.黏弹TTI介质中旋转交错网格高阶有限差分数值模拟[J].地球物理学报,2012,55(4):1354-1365.YAN Hongyong,LIU Yang.Rotated staggered grid high order finite difference numerical modeling for wave propagation in viscoelastic TTI media[J].Chinese Journal of Geophysics,2012,55(4):1354-1365.
[14] 何兵红,吴国忱,许冲.基于FFD算子的衰减介质地震波模拟[J].石油地球物理勘探,2014,49(1):153-160.HE Binghong,WU Guochen,XU Chong.Seismic wave simulation in attenuation medium based on FFD operator[J].Oil Geophysical Prospecting,2014,49(1):153-160.
[15] 罗文山,陈汉明,王成祥,等.时间域黏滞波动方程及其数值模拟新方法[J].石油地球物理勘探,2016,51(4):707-713.LUO Wenshan,CHEN Hanming,WANG Cheng- xiang,et al.A novel time-domain viscoacoustic wave equation and its numerical simulation[J].Oil Geophysical Prospecting,2016,51(4):707-713.
[16] 姚振岸,孙成禹,谢俊法,等.黏弹TTI介质旋转交错网格微地震波场模拟[J].石油地球物理勘探,2017,52(2):253-263.YAO Zhen’an,SUN Chengyu,XIE Junfa,et al.Micro-seismic forward modeling in visco-elastic TTI media based on rotated staggered grid finite-difference method[J].Oil Geophysical Prospecting,2017,52(2):253-263.
[17] Talezer H.An accurate and efficient scheme for wave propagation in linear viscoelastic media[J].Geophy-sics,1990,55(10):1366-1379.
[18] 杨仁虎,常旭,刘伊克.基于非均匀各向同性介质的黏弹性波正演数值模拟[J].地球物理学报,2009,52(9):2321-2327.YANG Renhu,CHANG Xu,LIU Yike.Viscoelastic wave modeling in heterogeneous and isotropic media[J].Chinese Journal of Geophysics,2009,52(9):2321-2327.
[19] 陈康,吴国忱,印兴耀,等.基于反射率法的TTI介质正演模拟[J].石油地球物理勘探,2013,48(5):717-727.CHEN Kang,WU Guochen,YIN Xingyao,et al.The modeling based on the reflectivity method in TTImedia[J].Oil Geophysical Prospecting,2013,48(5):717-727.
[20] Zhu T,Carcione J M.Theory and modelling of constant-Q P- and S-waves using fractional spatial deri-vatives[J].Geophysical Journal International,2014,196(3):1787-1795.
[21] Krohn C E,Murray T J.Shallow near-surface effects[J].Geophysics,2016,81(5):T221-T231.
[22] 陈志德,王成,刘国友,等.近地表Q值模型建立方法及其地震叠前补偿应用[J].石油学报,2015,36(2):188-196.CHEN Zhide,WANG Cheng,LIU Guoyou,et al.Modeling method of near-surface Q value and its seismic pre-stack compensation application[J].Acta Petrolei Sinica,2015,36(2):188-196.
[23] 杨宇,黄建平,雷建设,等.Lebedev网格黏弹性介质起伏地表正演模拟[J].石油地球物理勘探,2016,51(4):698-706.YANG Yu,HUANG Jianping,LEI Jianshe,et al.Numerical simulation of Lebedev grid for viscoelastic media with irregular free-surface[J].Oil Geophysical Prospecting,2016,51(4):698-706.
[24] Cai R Q,Sun C Y,Wu D S,et al.Finite-difference numerical modeling with variable mechanism for viscoacoustic wave equation[C].Extended Abstracts of 80th EAGE Conference & Exhibition,2018,Tu P903.
[25] Zener C M,Siegel S.Elasticity and Anelasticity of Metals[M].University of Chicago Press,Chicago,Illinois,1948.
[26] O’Connell R J,Budiansky B.Measures of dissipation in viscoelastic media[J].Geophysical Research Letters,1978,5(1):5-8.
[27] Carcione J M,Dan K,Ronnie K.Wave propagation simulation in a linear viscoelastic medium[J].Geophysical Journal of the Royal Astronomical Society,1988,93(2):597-611.