地震勘探中小尺度非均匀性的描述及长波长理论
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摘要
地球物理成像解释的一个重要问题是,地震波传播时其本身受到地质体中小尺度非均匀性的影响,对该问题的研究具有重要的意义且备受关注.据此,本文首先从统计意义上的表示形式来描述小尺度非均匀性,给出一种拓展了小尺度非均匀性择优取向的随机介质建模新方法,重点阐述了建模过程中对误差处理的重要性.其次讨论了地震波在水平层状介质中传播时的长波长理论,并指出对该理论的适用条件进行研究的重要意义.且还基于1D随机层状介质,从局部各向异性因子曲线的角度对长波长理论进行了研究,并讨论了密度及泊松比扰动对曲线形态的影响.最后,从对1D和2D随机介质进行数值模拟的角度重点研究长波长理论不能满足的情况下地震记录的特点,为了便于对比分析,文中也计算了1D随机介质在不同平均化长度下,通过长波长理论得到的等效介质的理论走时(走时的计算是在弱各向异性假设条件下完成的),并给出有指导意义的结论.
That seismic wave propagation is itself affected by small scale inhomogeneities of geologic bodies is an important issue of interpreting geophysical images and receives much attention in recent years.In this work,first of all,a statistical representation is used to describe small-scale inhomogeneities in seismological studies and a new way to build random media in which the preferred orientation of the small-scale inhomogeneities is expanded is proposed.Then,the importance of dealing with the errors is stated.And the long-wavelength theory of seismic wave propagating in horizontal layered media is discussed and its significance is pointed out.Next,based on 1D random layered media,the long-wavelength theory is studied by the local anisotropy factors′ curves,and the influences of fluctuations in density and Poisson′s ratio on the curves′ pattern are analyzed.Finally,the characteristics of seismographic records of the 1D and 2D random media are studied especially when the long-wavelength theory can not be satisfied.For comparative analysis,we also compute the theoretical traveltimes of the equivalent media which is got by the long-wavelength theory when the 1D random layered media has different averaging lengths(The predicted traveltimes are got under the hypothesis that the anisotropy is weak),and then give some conclusions with guidance meanings.
That seismic wave propagation is itself affected by small scale inhomogeneities of geologic bodies is an important issue of interpreting geophysical images and receives much attention in recent years.In this work,first of all,a statistical representation is used to describe small-scale inhomogeneities in seismological studies and a new way to build random media in which the preferred orientation of the small-scale inhomogeneities is expanded is proposed.Then,the importance of dealing with the errors is stated.And the long-wavelength theory of seismic wave propagating in horizontal layered media is discussed and its significance is pointed out.Next,based on 1D random layered media,the long-wavelength theory is studied by the local anisotropy factors′ curves,and the influences of fluctuations in density and Poisson′s ratio on the curves′ pattern are analyzed.Finally,the characteristics of seismographic records of the 1D and 2D random media are studied especially when the long-wavelength theory can not be satisfied.For comparative analysis,we also compute the theoretical traveltimes of the equivalent media which is got by the long-wavelength theory when the 1D random layered media has different averaging lengths(The predicted traveltimes are got under the hypothesis that the anisotropy is weak),and then give some conclusions with guidance meanings.
引文
[1]Bergmann P G.Propagation of radiation in a medium with Random inhomogeneities.Physical Review,1946,70(7-8):486-492.
[2]Aki K.Analysis of the seismic coda of local earthquakes as scattered waves.J.Geophys.Res.,1969,74(2):615-631.
[3]de Hoop M V,Burridge R,Chang H W.Wave propagation with tunneling in a highly discontinuous layered medium.WaveMotion,1991,13(4):307-329.
[4]Kerner C.Anisotropy in sedimentary rocks modeled as random media.Geophysics,1992,57(4):564-576.
[5]Frankel A,Clayton R W.A finite-difference simulation of wave propagation in two-dimensional random media.Bull.Seis.Soc.Am.,1984,74(6):2167-2186.
[6]Ikelle L T,Yung S K,Daube F.2-D random media with ellipsoidal autocorrelation functions.Geophysics,1993,58(9):1359-1372.
[7]奚先,姚姚.二维随机介质及波动方程正演模拟.石油地球物理勘探,2001,36(5):546-552.Xi X,Yao Y.2-D random media and wave equation forward modeling.Oil Geophysical Prospecting(in Chinese),2001,36(5):546-552.
[8]奚先,姚姚.随机介质模型的模拟与混合型随机介质.地球科学———中国地质大学学报,2002,27(1):57-67.Xi X,Yao Y.Simulations of random medium model and intermixed random medium.Earth Science-Journal of China University of Geosciences(in Chinese),2002,27(1):57-67.
[9]奚先,姚姚.二维横各向同性弹性随机介质中的波场特征.地球物理学进展,2004,19(4):924-932.Xi X,Yao Y.The wave field characteristics of2-D transversely isotropic elastic random medium.Progress in Geophys.(in Chinese),2004,19(4):924-932.
[10]朱生旺,魏修成,曲寿利等.用随机介质模型方法描述孔洞型油气储层.地质学报,2008,82(3):420-427.Zhu S W,Wei X C,Qu L,et al.Description of the carbonate karst reservoir with random media model.Acta Geologica Sinica(in Chinese),2008,82(3):420-427.
[11]Postma G W.Wave propagation in a stratified medium.Geophysics,1955,20(4):780-806.
[12]Backus G.Long-wave elastic anisotropy produced by horizontal layering.J.Geophys.Res.,1962,67(11):4427-4440.
[13]Berryman J G.Long-wave elastic anisotropy in transversely isotropic media.Geophysics,1979,44(5):896-917.
[14]Daley P F,Hron F.Computation of synthetic seismograms for a thin layered periodic structure.Canadian Journal of Earth Sciences,1982,19(7):1449-1453.
[15]Melia P J,Carlson R L.An experimental test of P-wave anisotropy in stratified media.Geophysics,1984,49(4):374-378.
[16]Helbig K.Anisotropy and dispersion in periodically layered media.Geophysics,1984,49(4):364-373.
[17]Carcione J M,Kosloff D,Behle A.Long-wave anisotropy in stratified media:A numerical test.Geophysics,1991,56(2):245-254.
[18]Marion D,Mukerji T,Mavko G.Scale effects on velocity dispersion:From ray to effective medium theories in stratified media.Geophysics,1994,59(10):1613-1619.
[19]Mukerji T,Mavko G,Mujica D,et al.Scale-dependent seismic velocity in heterogeneous media.Geophysics,1995,60(4):1222-1233.
[20]Griffiths D J,Steinke C A.Waves in locally periodic media.American Journal of Physics,2000,69(2):137-154.
[21]Stovas A,Ursin B.Equivalent time-average and effective medium for periodic layers.Geophys.Prosp.,2007,55(6):871-882.
[22]Birch F.The velocity of compressional waves in rocks to10 kilobars,Part2.J.Geophys.Res.,1961,66(7):2199-2224.
[23]Marple S L.Digital Spectral Analysis with Applications.New Jersey:Prentice-Hall,1987.
[24]Levin F K.Seismic velocities in transversely isotropic media.Geophysics,1979,44(5):918-936.
[25]Daley P F,Hron F.Reflection and transmission coefficients for transversely isotropic media.Bull.Seis.Soc.Am.,1977,67(3):661-675.
[26]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[27]Kneib G,Pestana R,Kerner C.Accurate and efficient seismic modelling in random media.The53rd Ann.Internet.Mtg,EAGE,Expanded Abstracts,1991:628-629.
[28]Virieux J.P-SV-wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geophysics,1986,51(4):889-901.
[29]Levander A R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,53(11):1425-1436.
[30]Hastings F D,Schneider J B,Broschat S L.Application of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation.J.Acoust.Soc.Am.,1996,100(5):3062-3069.
[2]Aki K.Analysis of the seismic coda of local earthquakes as scattered waves.J.Geophys.Res.,1969,74(2):615-631.
[3]de Hoop M V,Burridge R,Chang H W.Wave propagation with tunneling in a highly discontinuous layered medium.WaveMotion,1991,13(4):307-329.
[4]Kerner C.Anisotropy in sedimentary rocks modeled as random media.Geophysics,1992,57(4):564-576.
[5]Frankel A,Clayton R W.A finite-difference simulation of wave propagation in two-dimensional random media.Bull.Seis.Soc.Am.,1984,74(6):2167-2186.
[6]Ikelle L T,Yung S K,Daube F.2-D random media with ellipsoidal autocorrelation functions.Geophysics,1993,58(9):1359-1372.
[7]奚先,姚姚.二维随机介质及波动方程正演模拟.石油地球物理勘探,2001,36(5):546-552.Xi X,Yao Y.2-D random media and wave equation forward modeling.Oil Geophysical Prospecting(in Chinese),2001,36(5):546-552.
[8]奚先,姚姚.随机介质模型的模拟与混合型随机介质.地球科学———中国地质大学学报,2002,27(1):57-67.Xi X,Yao Y.Simulations of random medium model and intermixed random medium.Earth Science-Journal of China University of Geosciences(in Chinese),2002,27(1):57-67.
[9]奚先,姚姚.二维横各向同性弹性随机介质中的波场特征.地球物理学进展,2004,19(4):924-932.Xi X,Yao Y.The wave field characteristics of2-D transversely isotropic elastic random medium.Progress in Geophys.(in Chinese),2004,19(4):924-932.
[10]朱生旺,魏修成,曲寿利等.用随机介质模型方法描述孔洞型油气储层.地质学报,2008,82(3):420-427.Zhu S W,Wei X C,Qu L,et al.Description of the carbonate karst reservoir with random media model.Acta Geologica Sinica(in Chinese),2008,82(3):420-427.
[11]Postma G W.Wave propagation in a stratified medium.Geophysics,1955,20(4):780-806.
[12]Backus G.Long-wave elastic anisotropy produced by horizontal layering.J.Geophys.Res.,1962,67(11):4427-4440.
[13]Berryman J G.Long-wave elastic anisotropy in transversely isotropic media.Geophysics,1979,44(5):896-917.
[14]Daley P F,Hron F.Computation of synthetic seismograms for a thin layered periodic structure.Canadian Journal of Earth Sciences,1982,19(7):1449-1453.
[15]Melia P J,Carlson R L.An experimental test of P-wave anisotropy in stratified media.Geophysics,1984,49(4):374-378.
[16]Helbig K.Anisotropy and dispersion in periodically layered media.Geophysics,1984,49(4):364-373.
[17]Carcione J M,Kosloff D,Behle A.Long-wave anisotropy in stratified media:A numerical test.Geophysics,1991,56(2):245-254.
[18]Marion D,Mukerji T,Mavko G.Scale effects on velocity dispersion:From ray to effective medium theories in stratified media.Geophysics,1994,59(10):1613-1619.
[19]Mukerji T,Mavko G,Mujica D,et al.Scale-dependent seismic velocity in heterogeneous media.Geophysics,1995,60(4):1222-1233.
[20]Griffiths D J,Steinke C A.Waves in locally periodic media.American Journal of Physics,2000,69(2):137-154.
[21]Stovas A,Ursin B.Equivalent time-average and effective medium for periodic layers.Geophys.Prosp.,2007,55(6):871-882.
[22]Birch F.The velocity of compressional waves in rocks to10 kilobars,Part2.J.Geophys.Res.,1961,66(7):2199-2224.
[23]Marple S L.Digital Spectral Analysis with Applications.New Jersey:Prentice-Hall,1987.
[24]Levin F K.Seismic velocities in transversely isotropic media.Geophysics,1979,44(5):918-936.
[25]Daley P F,Hron F.Reflection and transmission coefficients for transversely isotropic media.Bull.Seis.Soc.Am.,1977,67(3):661-675.
[26]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[27]Kneib G,Pestana R,Kerner C.Accurate and efficient seismic modelling in random media.The53rd Ann.Internet.Mtg,EAGE,Expanded Abstracts,1991:628-629.
[28]Virieux J.P-SV-wave propagation in heterogeneous media:Velocity-stress finite-difference method.Geophysics,1986,51(4):889-901.
[29]Levander A R.Fourth-order finite-difference P-SV seismograms.Geophysics,1988,53(11):1425-1436.
[30]Hastings F D,Schneider J B,Broschat S L.Application of the perfectly matched layer(PML)absorbing boundary condition to elastic wave propagation.J.Acoust.Soc.Am.,1996,100(5):3062-3069.
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