非完全弹性介质的地震波吸收与频散问题研究
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摘要
非完全弹性介质会引起地震波的传播能量衰减和相速度频散,从而影响地震成像分辨率。因此在地震波正演和反演中需要十分重视对能量衰减和相速度频散问题的研究。本文在分析造成能量衰减和相速度频散的机理及其诸多影响因素的基础上,基于Boltzmann提出的线性非弹性介质本构关系,以Kjartansson常Q模型为例,系统推导了该模型的吸收系数及相速度频散关系,并全面分析了8种非完全弹性介质模型的能量吸收、相速度频散关系与特征,可为非完全弹性介质品质因子Q值估计以及反Q补偿等问题的研究提供有益的借鉴。
Anelasticity of subsurface medium causes seismic energy absorption and phase-velocity dispersion and reduces the resolution of seismic image consequently.It has been one of the important objectives of seismic modeling and inversion.The micro-mechanism of seismic attenuation and dispersion is complicated and affected by many subsurface medium's environmental conditions.Based upon the Boltzmann superposition principle,the attenuation coefficient and phase-velocity dispersion equations of Kjartansson constant-Q model have been deduced systematically.The energy absorption and phase-velocity dispersion characteristics of eight anelastic models have been compared and analyzed completely.This research is contributive to study on the anelasticity of subsurface medium and related issues such as estimation of quality factor and inverse Q filtering.
Anelasticity of subsurface medium causes seismic energy absorption and phase-velocity dispersion and reduces the resolution of seismic image consequently.It has been one of the important objectives of seismic modeling and inversion.The micro-mechanism of seismic attenuation and dispersion is complicated and affected by many subsurface medium's environmental conditions.Based upon the Boltzmann superposition principle,the attenuation coefficient and phase-velocity dispersion equations of Kjartansson constant-Q model have been deduced systematically.The energy absorption and phase-velocity dispersion characteristics of eight anelastic models have been compared and analyzed completely.This research is contributive to study on the anelasticity of subsurface medium and related issues such as estimation of quality factor and inverse Q filtering.
引文
[1]Johnston D H,Toksoz M Nand Ti mur A.Attenua-tion of seismic waves in dry and saturated rocks,Ⅱ:mechanisms.Geophysics,1979,44(4):691~711
[2]O’Connell RJ and Budiansky B.Viscoelastic proper-ties of fluid-saturated cracked solid.J Geophys Res,1977,82(36):5719~5735
[3]Jackson D D,Anderson D L.Physical mechanisms ofseismic wave attenuation.Rev Geophys Space Phys,1970,8(1):1~8
[4]Clark V A,Spencer T Wand Titt mann B R.Theeffect of thermal cycling on the seismic quality factorQof some sedi mentary rocks.J Geophys Res,1981,86(B8):7087~7094
[5]Murphy WF,Winkler K Wand Kleinberg R L.A-coustic relaxation in sedi mentary rocks:dependenceon grain contacts and fluid saturation.Geophysics,1986,51(3):757~766
[6]Stacey F D,Gladwin M T,McKavanagh B,Linde AT and Hastie L M.Anelastic damping of acoustic andseismic pulses.Surveys in Geophysics,1975,2(2):133~151
[7]Winkler Kand Nur A.Seismic attenuation:effects ofpore fluids and frictional sliding.Geophysics,1982,47(1):1~15
[8]Kjartansson E.ConstantQwave propagation and at-tenuation.Journal of Geophysical Research,1979,84(B9):4737~4748
[9]Winkler Kand Nur A.Pore fluids and seismic atten-uation in rocks.Geophys Res Lett,1979,6(1):1~4
[10]Toksoz M N,Johnston D Hand Ti mur A.Attenua-tion of seismic waves in dry and saturated rocks,Ⅰ:laboratory measurements.Geophysics,1979,44(4):681~690
[11]席道瑛,邱文亮,程经毅,易良坤,张斌,谢端.饱和多孔岩石的衰减与孔隙率和饱和度的关系.石油地球物理勘探,1997,32(2):196~201Xi Dao-ying,Qiu Wen-liang,Cheng Jing-yi,Yi Li-ang-kun,Zhang Bin and Xie Duan.Relation betweenattenuation and porosity or saturation of rock.OGP,1997,32(2):196~201
[12]王大兴,辛可锋,李幼铭等.地层条件下砂岩含水饱和度对波速及衰减影响的实验研究.地球物理学报,2006,49(3):908~914Wang Da-xing,Xin Ke-feng,Li You-ming et al.Anexperi mental study of influence of water saturation onvelocity and attenuation in sandstone under stratumconditions.Chinese Journal of Geophysics,2006,49(3):908~914
[13]Kli mentos T and McCann C.Relationships amongcompressional wave attenuation,porosity,clay con-tent,and permeability in sandstones.Geophysics,1990,55(8):998~1014
[14]O'Connell RJ and Budiansky B.Measures of dissipa-tion in viscoelastic media.Geophys Res Lett,1978,5(1):5~8
[15]Kolsky H.The propagation of stress pulses in viscoe-lastic solids.Philosophical Magazine,1956,1(8):693~710
[16]Futterman WI.Dispersive body waves.Journal ofGeophysical Research,1962,67(13):5279~5291
[17]Strick E.The determination ofQ,dynamic viscosity,and creep curves from wave propagation measure-ments.J Geophys Res,1967,13(1~3):197~218
[18]Mller G.Rheological properties and velocity disper-sion of a medium with power-law dependence ofQonfrequency.Journal of Geophysics,1983,54(1):20~29
[19]Azi mi S A,Kalinin A Vand Pivovarov B L.I mpulseand transient characteristics of media with linear andquadratic absorption laws.Izv Earth Physics,1968,2,42~54
[20]Cole K S and Cole R H.Dispersion and absorptionindielectrics,I:alternating current characteristics.Journal of Chemical Physics,1941,9,342~351
[21]Ben-Menafem A and Singh S J.Seismic waves andsources.Spring-Verlag New York Inc,1981
[22]Ursin Tand Toverud B.Comparison of seismic atten-uation models using zero-offset vertical seismic profi-ling(VSP)data.Geophysics,2005,70(2):F17~F25
[23]Yih Jeng,Jing-Yih Tsai,and Song-Hong Chen.Ani mproved method of determining near-surfaceQ.Geo-physics,1999,64(5):1608~1617
[2]O’Connell RJ and Budiansky B.Viscoelastic proper-ties of fluid-saturated cracked solid.J Geophys Res,1977,82(36):5719~5735
[3]Jackson D D,Anderson D L.Physical mechanisms ofseismic wave attenuation.Rev Geophys Space Phys,1970,8(1):1~8
[4]Clark V A,Spencer T Wand Titt mann B R.Theeffect of thermal cycling on the seismic quality factorQof some sedi mentary rocks.J Geophys Res,1981,86(B8):7087~7094
[5]Murphy WF,Winkler K Wand Kleinberg R L.A-coustic relaxation in sedi mentary rocks:dependenceon grain contacts and fluid saturation.Geophysics,1986,51(3):757~766
[6]Stacey F D,Gladwin M T,McKavanagh B,Linde AT and Hastie L M.Anelastic damping of acoustic andseismic pulses.Surveys in Geophysics,1975,2(2):133~151
[7]Winkler Kand Nur A.Seismic attenuation:effects ofpore fluids and frictional sliding.Geophysics,1982,47(1):1~15
[8]Kjartansson E.ConstantQwave propagation and at-tenuation.Journal of Geophysical Research,1979,84(B9):4737~4748
[9]Winkler Kand Nur A.Pore fluids and seismic atten-uation in rocks.Geophys Res Lett,1979,6(1):1~4
[10]Toksoz M N,Johnston D Hand Ti mur A.Attenua-tion of seismic waves in dry and saturated rocks,Ⅰ:laboratory measurements.Geophysics,1979,44(4):681~690
[11]席道瑛,邱文亮,程经毅,易良坤,张斌,谢端.饱和多孔岩石的衰减与孔隙率和饱和度的关系.石油地球物理勘探,1997,32(2):196~201Xi Dao-ying,Qiu Wen-liang,Cheng Jing-yi,Yi Li-ang-kun,Zhang Bin and Xie Duan.Relation betweenattenuation and porosity or saturation of rock.OGP,1997,32(2):196~201
[12]王大兴,辛可锋,李幼铭等.地层条件下砂岩含水饱和度对波速及衰减影响的实验研究.地球物理学报,2006,49(3):908~914Wang Da-xing,Xin Ke-feng,Li You-ming et al.Anexperi mental study of influence of water saturation onvelocity and attenuation in sandstone under stratumconditions.Chinese Journal of Geophysics,2006,49(3):908~914
[13]Kli mentos T and McCann C.Relationships amongcompressional wave attenuation,porosity,clay con-tent,and permeability in sandstones.Geophysics,1990,55(8):998~1014
[14]O'Connell RJ and Budiansky B.Measures of dissipa-tion in viscoelastic media.Geophys Res Lett,1978,5(1):5~8
[15]Kolsky H.The propagation of stress pulses in viscoe-lastic solids.Philosophical Magazine,1956,1(8):693~710
[16]Futterman WI.Dispersive body waves.Journal ofGeophysical Research,1962,67(13):5279~5291
[17]Strick E.The determination ofQ,dynamic viscosity,and creep curves from wave propagation measure-ments.J Geophys Res,1967,13(1~3):197~218
[18]Mller G.Rheological properties and velocity disper-sion of a medium with power-law dependence ofQonfrequency.Journal of Geophysics,1983,54(1):20~29
[19]Azi mi S A,Kalinin A Vand Pivovarov B L.I mpulseand transient characteristics of media with linear andquadratic absorption laws.Izv Earth Physics,1968,2,42~54
[20]Cole K S and Cole R H.Dispersion and absorptionindielectrics,I:alternating current characteristics.Journal of Chemical Physics,1941,9,342~351
[21]Ben-Menafem A and Singh S J.Seismic waves andsources.Spring-Verlag New York Inc,1981
[22]Ursin Tand Toverud B.Comparison of seismic atten-uation models using zero-offset vertical seismic profi-ling(VSP)data.Geophysics,2005,70(2):F17~F25
[23]Yih Jeng,Jing-Yih Tsai,and Song-Hong Chen.Ani mproved method of determining near-surfaceQ.Geo-physics,1999,64(5):1608~1617
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