基于高阶广义标准线性体模型的三维黏弹性介质弹性波正演模拟
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摘要
吸收衰减是地震波在实际地球介质中传播的固有特征.在实际应用中,通常假设表征吸收衰减特征的品质因子Q在地震频带范围内不随频率变化.高阶广义流变模型能够在时间域内精确的表征品质因子Q不随频率变化的特征,为黏弹性介质波动方程精细模拟奠定了基础.基于广义标准线性体模型理论,采用最小二乘拟合方法对Q值不随频率变化特征进行拟合,分析了不同阶次广义标准线性体模型对黏弹性介质Q值特征的拟合程度,在权衡计算精度和三维计算量的基础上,确定了五阶广义标准线性体模型并建立了相应的三维黏弹性波的速度-应力方程,结合CFS-PML边界条件开展了高精度三维黏弹性波正演模拟.通过均匀介质正演模拟,验证算法的正确性,明确了地震波的传播时的吸收衰减特征,对三维盐丘模型进行数值模拟,表明了五阶广义标准线性体可以精确的模拟黏弹性介质地震波吸收衰减特征.
Absorption attenuation is an inherent characteristic of seismic waves propagating in the actual earth medium. In practical applications, it is usually assumed that the quality factor(Q)that characterizing absorption attenuation characteristics does not vary with frequency within the range of seismic frequency band. The high order generalized rheological model can accurately characterize that the quality factor Q does not vary with frequency in time domain which lays the foundation for fine simulation of wave equation in viscoelastic media. This paper is based on the theory of generalized standard linear model, use the least squares method to fit the characteristics that Q values do not change with the frequency, analyze the fitting degree of the Q value characteristics of the viscoelastic medium with different order generalized standard linear model, consider computation accuracy and the computation in 3 D forward modeling, choose five order generalized standard linear body model,establish the corresponding three-dimensional stress wave equation of viscoelastic wave, carry out forward modeling of high precision three-dimensional viscoelastic elastic wave with CFS-PML boundary conditions. Through forward simulation in homogeneous medium, verify the correctness of the algorithm,clear the absorption and attenuation characteristics of seismic waves clarefy. The numerical simulation of the three dimensional salt mound model shows that the five order generalized standard linear body can accurately simulate the attenuation characteristics of seismic wave absorption in viscoelastic medium.
Absorption attenuation is an inherent characteristic of seismic waves propagating in the actual earth medium. In practical applications, it is usually assumed that the quality factor(Q)that characterizing absorption attenuation characteristics does not vary with frequency within the range of seismic frequency band. The high order generalized rheological model can accurately characterize that the quality factor Q does not vary with frequency in time domain which lays the foundation for fine simulation of wave equation in viscoelastic media. This paper is based on the theory of generalized standard linear model, use the least squares method to fit the characteristics that Q values do not change with the frequency, analyze the fitting degree of the Q value characteristics of the viscoelastic medium with different order generalized standard linear model, consider computation accuracy and the computation in 3 D forward modeling, choose five order generalized standard linear body model,establish the corresponding three-dimensional stress wave equation of viscoelastic wave, carry out forward modeling of high precision three-dimensional viscoelastic elastic wave with CFS-PML boundary conditions. Through forward simulation in homogeneous medium, verify the correctness of the algorithm,clear the absorption and attenuation characteristics of seismic waves clarefy. The numerical simulation of the three dimensional salt mound model shows that the five order generalized standard linear body can accurately simulate the attenuation characteristics of seismic wave absorption in viscoelastic medium.
引文
Cao D P.2008.Mcthod Research of Multiseale Seismic Data Modeling and Inversion [Ph.D.thesis].Qingdao:China University of Petroleum (EsatChina).
Cao D P,Yin X Y.2013.Equivalence Relations of Generalized Rheological Models for Viscoelastic Seismic-Wave Modeling [J].Bulletin of the Seismological Society of America,104(1):260-268,doi:10.1785/0120130158.
Carcione J M,Kosloff D,Kosloff R.1988a.Viscoacoustic wave propagation simulation in the earth [J].Geophysics,53(6):769-777,doi:10.1190/1.1442512.
Carcione J M,Kosloff D,Kosloff R.1988b.Wave propagation simulation in a linear viscoelastic medium [J].Geophysical Journal International,95(3):597- 611.
Chen X H,He Z H,Huang D J,et al.2009.Low frequency shadow detection of gas reservoirs in time-frequency domain [J].Chinese Journal Of Geophysics (in Chinese),52(1):215-221.
Day S M,Minster J B.1984.Numerical simulation of attenuated wavefields using a Pade approximant method [J].Geophysical Journal of the Royal Astronomical Society,78(1):105-118.
Emmerich H,Korn M.1987.Incorporation of attenuation into time-domain computations of seismic wave fields [J].Geophysics,52(9):1252-1264,doi:10.1190/1.1442386.
Futterman W I.1962.Dispersive body waves [J].Journal of Geophysical Research,67(13):5279-5291.
Gorden R B,Davis L A.1968.Velocity and attenuation of seismic waves in imperfectly elastic rock [J].Journal of Geophysical Research,73(12):3917-3935,doi:10.1029/JB073i012p03917.
He B H,Wu G C.2015.The seismic forward modeling using Born approximation equation based on rheological body [J].Acta Seismologica Sinica (in Chinese),37(4):661- 677,doi:10.11939/jass.2015.04.012.
He B H,Wu Guochen.2012.Estimation of relative absorption coefficient using pre-stack seismic data [J].Oil Geophysical Prospection (in Chinese),47(4):610- 618.
He B H,Wu Guochen.2016.Inversion of characterization parameters of constant Q model based on generalized rheological body [J].Oil Geophysical Prospection (in Chinese),51(3):572-580,doi:10.13810/j.cnki.issn.1000-7210.2016.03.020.
Lian X M,Shan L Y,Sui Z Q.2015.An overview of research on perfectly matched layers absorbing boundary condition of seismic forward numerical simulation [J].Progress in Geophysics (in Chinese),30(4):1725-1733,doi:10.6038/pg20150427.
Liu H,Anderson D L,Kanamori H.1976.Velocity dispersion due to anelasticity;implications for seismology and mantle composition [J].Geophysical Journal International,47(1):41-58.
Mcdonal F J,Angona F A,Mills R L,et al.1958.Attenuation of shear and compressional waves in Pierre shale [J].Geophysics,23(3):421- 439,doi:10.1190/1.1438489.
Quintal B,Madonna C,Tisato N,et al.2014.Laboratory apparatuses for measuring seismic attenuation in fluid-saturated rocks.13th International Congress of the Brazilian Geophysical Society,1044-1047.
Sun C Y,Qiao Z H,Wu D S.2017.Modeling of wave equation with fractional derivative using optimal finite-difference method in constant-Q attenuation media [J].Acta Seismologica Sinica (in Chinese),39(3):343-355.
Sun C Y,YAN Y F,LAN Y.2015.Finite difference modeling of Love waves based on CFS-CPML boundary processing [J].Progress in Geophysics (in Chinese),30(06):2558-2565,doi:10.6038/pg20150613.
Tisato Nicola,Quintal Beatriz.2014.Laboratory measurements of seismic attenuation in sandstone:Strain versus fluid saturation effects [J].Geophysics,79(5):WB9-WB14,doi:10.1190/geo2013- 0419.1.
Zhang J H,Wang W M,Zhao L F,et al.2007.Modeling 3-D scalar waves using the Fourier finite-difference method [J].Chinese Journal Of Geophysics (in Chinese),50(6):1854-1862,doi:10.3321/j.issn:0001-5733.2007.06.028.
曹丹平.2008.多尺度地震资料正反演方法研究[博士论文].青岛:中国石油大学(华东).
陈学华,贺振华,黄德济,等.2009.时频域油气储层低频阴影检测[J].地球物理学报,52(1):215-221.
何兵红,吴国忱.2012.利用叠前地震资料提取地层相对吸收系数[J].石油地球物理勘探,47(4):610- 618.
何兵红,吴国忱.2015.基于流变体模型的波恩近似方程地震正演模拟[J].地震学报,37(04):661- 677,doi:10.11939/jass.2015.04.012.
何兵红,吴国忱.2016.广义流变体常Q模型表征参数反演[J].石油地球物理勘探,51(03):572-580,doi:10.13810/j.cnki.issn.1000-7210.2016.03.020.
廉西猛,单联瑜,隋志强.2015.地震正演数值模拟完全匹配层吸收边界条件研究综述[J].地球物理学进展,30(04):1725-1733,doi:10.6038/pg20150427.
孙成禹,乔志浩,伍敦仕,等.2017.常Q衰减介质分数阶波动方程优化有限差分模拟[J].地震学报,39(03):343-355,doi:10.11939/jass.2017.03.004.
孙成禹,闫月锋,蓝阳.2015.基于CFS-CPML边界处理的LOVE面波有限差分模拟[J].地球物理学进展,30(06):2558-2565,doi:10.6038/pg20150613.
张金海,王卫民,赵连锋.2007.傅里叶有限差分法三维波动方程正演模拟[J].地球物理学报,50(06):1854-1862,doi:10.3321/j.issn:0001-5733.2007.06.028.
Cao D P,Yin X Y.2013.Equivalence Relations of Generalized Rheological Models for Viscoelastic Seismic-Wave Modeling [J].Bulletin of the Seismological Society of America,104(1):260-268,doi:10.1785/0120130158.
Carcione J M,Kosloff D,Kosloff R.1988a.Viscoacoustic wave propagation simulation in the earth [J].Geophysics,53(6):769-777,doi:10.1190/1.1442512.
Carcione J M,Kosloff D,Kosloff R.1988b.Wave propagation simulation in a linear viscoelastic medium [J].Geophysical Journal International,95(3):597- 611.
Chen X H,He Z H,Huang D J,et al.2009.Low frequency shadow detection of gas reservoirs in time-frequency domain [J].Chinese Journal Of Geophysics (in Chinese),52(1):215-221.
Day S M,Minster J B.1984.Numerical simulation of attenuated wavefields using a Pade approximant method [J].Geophysical Journal of the Royal Astronomical Society,78(1):105-118.
Emmerich H,Korn M.1987.Incorporation of attenuation into time-domain computations of seismic wave fields [J].Geophysics,52(9):1252-1264,doi:10.1190/1.1442386.
Futterman W I.1962.Dispersive body waves [J].Journal of Geophysical Research,67(13):5279-5291.
Gorden R B,Davis L A.1968.Velocity and attenuation of seismic waves in imperfectly elastic rock [J].Journal of Geophysical Research,73(12):3917-3935,doi:10.1029/JB073i012p03917.
He B H,Wu G C.2015.The seismic forward modeling using Born approximation equation based on rheological body [J].Acta Seismologica Sinica (in Chinese),37(4):661- 677,doi:10.11939/jass.2015.04.012.
He B H,Wu Guochen.2012.Estimation of relative absorption coefficient using pre-stack seismic data [J].Oil Geophysical Prospection (in Chinese),47(4):610- 618.
He B H,Wu Guochen.2016.Inversion of characterization parameters of constant Q model based on generalized rheological body [J].Oil Geophysical Prospection (in Chinese),51(3):572-580,doi:10.13810/j.cnki.issn.1000-7210.2016.03.020.
Lian X M,Shan L Y,Sui Z Q.2015.An overview of research on perfectly matched layers absorbing boundary condition of seismic forward numerical simulation [J].Progress in Geophysics (in Chinese),30(4):1725-1733,doi:10.6038/pg20150427.
Liu H,Anderson D L,Kanamori H.1976.Velocity dispersion due to anelasticity;implications for seismology and mantle composition [J].Geophysical Journal International,47(1):41-58.
Mcdonal F J,Angona F A,Mills R L,et al.1958.Attenuation of shear and compressional waves in Pierre shale [J].Geophysics,23(3):421- 439,doi:10.1190/1.1438489.
Quintal B,Madonna C,Tisato N,et al.2014.Laboratory apparatuses for measuring seismic attenuation in fluid-saturated rocks.13th International Congress of the Brazilian Geophysical Society,1044-1047.
Sun C Y,Qiao Z H,Wu D S.2017.Modeling of wave equation with fractional derivative using optimal finite-difference method in constant-Q attenuation media [J].Acta Seismologica Sinica (in Chinese),39(3):343-355.
Sun C Y,YAN Y F,LAN Y.2015.Finite difference modeling of Love waves based on CFS-CPML boundary processing [J].Progress in Geophysics (in Chinese),30(06):2558-2565,doi:10.6038/pg20150613.
Tisato Nicola,Quintal Beatriz.2014.Laboratory measurements of seismic attenuation in sandstone:Strain versus fluid saturation effects [J].Geophysics,79(5):WB9-WB14,doi:10.1190/geo2013- 0419.1.
Zhang J H,Wang W M,Zhao L F,et al.2007.Modeling 3-D scalar waves using the Fourier finite-difference method [J].Chinese Journal Of Geophysics (in Chinese),50(6):1854-1862,doi:10.3321/j.issn:0001-5733.2007.06.028.
曹丹平.2008.多尺度地震资料正反演方法研究[博士论文].青岛:中国石油大学(华东).
陈学华,贺振华,黄德济,等.2009.时频域油气储层低频阴影检测[J].地球物理学报,52(1):215-221.
何兵红,吴国忱.2012.利用叠前地震资料提取地层相对吸收系数[J].石油地球物理勘探,47(4):610- 618.
何兵红,吴国忱.2015.基于流变体模型的波恩近似方程地震正演模拟[J].地震学报,37(04):661- 677,doi:10.11939/jass.2015.04.012.
何兵红,吴国忱.2016.广义流变体常Q模型表征参数反演[J].石油地球物理勘探,51(03):572-580,doi:10.13810/j.cnki.issn.1000-7210.2016.03.020.
廉西猛,单联瑜,隋志强.2015.地震正演数值模拟完全匹配层吸收边界条件研究综述[J].地球物理学进展,30(04):1725-1733,doi:10.6038/pg20150427.
孙成禹,乔志浩,伍敦仕,等.2017.常Q衰减介质分数阶波动方程优化有限差分模拟[J].地震学报,39(03):343-355,doi:10.11939/jass.2017.03.004.
孙成禹,闫月锋,蓝阳.2015.基于CFS-CPML边界处理的LOVE面波有限差分模拟[J].地球物理学进展,30(06):2558-2565,doi:10.6038/pg20150613.
张金海,王卫民,赵连锋.2007.傅里叶有限差分法三维波动方程正演模拟[J].地球物理学报,50(06):1854-1862,doi:10.3321/j.issn:0001-5733.2007.06.028.
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