随机弹性介质中地震波散射衰减分析(英文)
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摘要
地震波衰减一直是许多学科研究的热点,因为可以反映介质的特性。导致地震波衰减的因素很多,如:传播过程中由于能量扩散导致的几何衰减,固体岩石内部晶粒间相对滑移导致的摩擦衰减,岩石结构不均匀引起的地震波散射衰减。本文主要从统计的观点出发,通过多次数值模拟的方法研究纵波散射在随机弹性介质中所引发的衰减。首先用随机理论建立了二维空间随机弹性介质模型,然后用错格伪谱法的数值方法模拟了波在随机介质中的传播,再通过波场中虚拟检波器的记录,用谱比法估计了弹性波在随机介质中的散射衰减。不同非均匀程度随机弹性介质中的数值结果表明:介质不均匀程度越高,散射衰减越大;在散射体尺寸小于波长的前提下,不同散射体尺寸的计算结果说明:散射体尺寸越大,弹性波衰减越明显。最后提出了一种不均匀孔隙介质中流体流动衰减的方法。通过对随机孔隙介质中地震波的总衰减和散射衰减分别进行了计算,并定量得出了随机孔隙介质中流体流动衰减,结果表明:在实际地震频段下,当介质不均匀尺度101米量级时,散射衰减比流体流动衰减要大,散射衰减是地震波在实际不均匀岩石孔隙介质中衰减的主要原因。
Seismic attenuation has been an interesting topic of research, for it reflects the inherent media characteristics in which seismic waves propagate. There are many factors that cause seismic wave attenuation, such as geometry attenuation caused by energy dissipating during propagation, friction attenuation by relative sliding among rock grains, and scattering attenuation by rock heterogeneity. In this paper we study P-wave scattering attenuation in a random elastic medium by numerical simulations from a statistical point of view. A random elastic medium model is built based on general stochastic process theory. Then a staggered-grid pseudo-spectral method is used to simulate wave propagation. Scattering attenuation is estimated by the spectral ratio method based on virtual detector records. Random elastic media numerical scatter results with various heterogeneity levels show that the higher heterogeneous levels cause greater scattering attenuation. When the scatter sizes are smaller than a wave length, the larger scatters give a greater attenuation. Finally, we propose a method to evaluate fluid-flow attenuation in porous media. The fluidflow attenuation is derived from total attenuation and scattering attenuation in random porous media and the attenuation is estimated quantitatively. Results show that in the real seismic frequency range when the heterogeneous scale is about 10 1 meters (less than one wave length), scattering attenuation is larger than fluid-flow attenuation in random porous media and scattering attenuation is the main factor of seismic attenuation in real heterogeneous porous media.
Seismic attenuation has been an interesting topic of research, for it reflects the inherent media characteristics in which seismic waves propagate. There are many factors that cause seismic wave attenuation, such as geometry attenuation caused by energy dissipating during propagation, friction attenuation by relative sliding among rock grains, and scattering attenuation by rock heterogeneity. In this paper we study P-wave scattering attenuation in a random elastic medium by numerical simulations from a statistical point of view. A random elastic medium model is built based on general stochastic process theory. Then a staggered-grid pseudo-spectral method is used to simulate wave propagation. Scattering attenuation is estimated by the spectral ratio method based on virtual detector records. Random elastic media numerical scatter results with various heterogeneity levels show that the higher heterogeneous levels cause greater scattering attenuation. When the scatter sizes are smaller than a wave length, the larger scatters give a greater attenuation. Finally, we propose a method to evaluate fluid-flow attenuation in porous media. The fluidflow attenuation is derived from total attenuation and scattering attenuation in random porous media and the attenuation is estimated quantitatively. Results show that in the real seismic frequency range when the heterogeneous scale is about 10 1 meters (less than one wave length), scattering attenuation is larger than fluid-flow attenuation in random porous media and scattering attenuation is the main factor of seismic attenuation in real heterogeneous porous media.
引文
Aki,K.,1969,Analysis of the seismic coda of logicalearthquakes as scattered waves:Journal of GeophysicalResearch,74,615–631.
Aki,K.,1973,Scattering of P waves under the MontanaLASA:Journal of Geophysical Research,78,1334–1346.
Aki,K.,and Richards,P.G.,2002,Quantitative seismology.Second edition:University Science Books,Sausalito,CA.
Berteussen,K.A.,Christoffersson,A.E.S.,Husebye,E.S.,and Dahle,A.,1975,Wave scattering theory inanalysis of P wave anomalies at NORSAR and LASA:Geophysical Journal Royal Astronomical Society,42,403–417.
Carcione,J.M.,Helle,H.B.,and Pham,N.H.,2003,White’s model for wave propagation in partiallysaturated rocks:Comparison with poroelastic numericalexperiments:Geophysics,68(4),1389–1398.
Chemov,L.A.,1960,Wave propagation in a randommedium:McGraw-Hill Press,New York.
Frankel,A.,and Clayton,R.W.,1986,Finite-differencesimulations of seismic scattering implications forthe propagation of short-period seismic waves in thecrust and models of crustal heterogeneity:Journal ofGeophysics Research,91,6465–6489.
Gusmeroli,A.,Clark,R.G.,et al.,2010,Seismic waveattenuation in the uppermost glacier ice of Storglaciaren,Sweden:Journal of Glaciology,56,249–256.
Ikelle,L.T.,Yung,S.K.,and Daube,F.,1993,2-Drandom media with ellipsoidal autocorrelation function:Geophysics,58,1359–1372.
Li,X.,and Hudson,J.A.,1996,Multiple scattering ofelastic waves from a continuous and heterogeneousregion:Geophysical Journal International,126,845-862.
Liu,J.,Ba,J.,Ma,J.W.,et al,2010,An analysis of seismicattenuation in random porous media:Science in ChinaSeries G,53,628–637.
Liu J.,Ma J.W.,Yang H.Z.,et.al,2008,Staggered-gridpseudo-spectrum simulation of fracture and cave reservoir (in Chinese):Oil Geophysical Prospecting,43,723–727.
Mavko,G.,Mukerji,T.,and Dvorkin,J.,1998,The rockphysics handbook:Tools for seismic analysis in porousmedia:Cambridge University Press,London.
Ozdenvar,T.,and McMechan,G.A.,1996,Causes andreduction of numerical artifacts in pseudo-spectralwavefield extrapolation:Geophys J Int,126,819–828.
Sato,H.,1982a,Amplitude attenuation of impulsive wavesin random media based on travel time corrected meanwave formalism:Journal of Acoustic Society of America,71,559–564.
Sato,H.,1982b,Attenuation of S waves in the lithospheredue to scattering by it’s random velocity structure:Journal of Geophysics Research,87,7779–7785.
Toksoz,M.N.,Johnston,D.H.,and Timur,A.,1979,Attenuation of seismic waves in dry and saturated rocks:I.Laboratory measurements:Geophysics,44,681–690.
Tonn,R.,1991,The determination of seismic qualityfactor Q from VSP data:A comparison of differentcomputational methods:Geophys.Prosp.,39,1–27.
Wu,R.S.,1982,Attenuation of short period seismic wavesdue to scattering:Geophysics Research Letters,9,9–12.
Wu,R.S.,and Aki,K.,1985a,Scattering characteristics ofelastic waves by and elastic heterogeneity:Geophysics,50,582–595.
Wu,R.S.,and Aki,K.,1985b,Elastic wave scattering bya random medium and the small-scale inhomogeneitiesin the lithosphere:Journal of Geophysics Research,90,10261–10273.
Wu,R.S.,and Aki,K.,1988,Multiple scattering andenergy transfer of seismic waves separation of scatteringeffect from intrinsic attenuation II.Application ofthe theory to Hindu Kush region:Pure and AppliedGeophysics,128,49–80.
Wu,R.S.,1989,The perturbation method in elastic wavescattering:Pure and Applied Geophysics,131,605–637.
Wu,R.S.,1994,Wide-angle elastic wave one-waypropagation in heterogeneous media and an elasticwave complex-screen method:Journal of GeophysicsResearch,4,751–766.
Xi,X.,and Yao,Y.,2002,Simulations of random mediummodel and intermixed random medium:Earth Science-Journal of China University of Geosciences(in Chinese),27,67–71.
Aki,K.,1973,Scattering of P waves under the MontanaLASA:Journal of Geophysical Research,78,1334–1346.
Aki,K.,and Richards,P.G.,2002,Quantitative seismology.Second edition:University Science Books,Sausalito,CA.
Berteussen,K.A.,Christoffersson,A.E.S.,Husebye,E.S.,and Dahle,A.,1975,Wave scattering theory inanalysis of P wave anomalies at NORSAR and LASA:Geophysical Journal Royal Astronomical Society,42,403–417.
Carcione,J.M.,Helle,H.B.,and Pham,N.H.,2003,White’s model for wave propagation in partiallysaturated rocks:Comparison with poroelastic numericalexperiments:Geophysics,68(4),1389–1398.
Chemov,L.A.,1960,Wave propagation in a randommedium:McGraw-Hill Press,New York.
Frankel,A.,and Clayton,R.W.,1986,Finite-differencesimulations of seismic scattering implications forthe propagation of short-period seismic waves in thecrust and models of crustal heterogeneity:Journal ofGeophysics Research,91,6465–6489.
Gusmeroli,A.,Clark,R.G.,et al.,2010,Seismic waveattenuation in the uppermost glacier ice of Storglaciaren,Sweden:Journal of Glaciology,56,249–256.
Ikelle,L.T.,Yung,S.K.,and Daube,F.,1993,2-Drandom media with ellipsoidal autocorrelation function:Geophysics,58,1359–1372.
Li,X.,and Hudson,J.A.,1996,Multiple scattering ofelastic waves from a continuous and heterogeneousregion:Geophysical Journal International,126,845-862.
Liu,J.,Ba,J.,Ma,J.W.,et al,2010,An analysis of seismicattenuation in random porous media:Science in ChinaSeries G,53,628–637.
Liu J.,Ma J.W.,Yang H.Z.,et.al,2008,Staggered-gridpseudo-spectrum simulation of fracture and cave reservoir (in Chinese):Oil Geophysical Prospecting,43,723–727.
Mavko,G.,Mukerji,T.,and Dvorkin,J.,1998,The rockphysics handbook:Tools for seismic analysis in porousmedia:Cambridge University Press,London.
Ozdenvar,T.,and McMechan,G.A.,1996,Causes andreduction of numerical artifacts in pseudo-spectralwavefield extrapolation:Geophys J Int,126,819–828.
Sato,H.,1982a,Amplitude attenuation of impulsive wavesin random media based on travel time corrected meanwave formalism:Journal of Acoustic Society of America,71,559–564.
Sato,H.,1982b,Attenuation of S waves in the lithospheredue to scattering by it’s random velocity structure:Journal of Geophysics Research,87,7779–7785.
Toksoz,M.N.,Johnston,D.H.,and Timur,A.,1979,Attenuation of seismic waves in dry and saturated rocks:I.Laboratory measurements:Geophysics,44,681–690.
Tonn,R.,1991,The determination of seismic qualityfactor Q from VSP data:A comparison of differentcomputational methods:Geophys.Prosp.,39,1–27.
Wu,R.S.,1982,Attenuation of short period seismic wavesdue to scattering:Geophysics Research Letters,9,9–12.
Wu,R.S.,and Aki,K.,1985a,Scattering characteristics ofelastic waves by and elastic heterogeneity:Geophysics,50,582–595.
Wu,R.S.,and Aki,K.,1985b,Elastic wave scattering bya random medium and the small-scale inhomogeneitiesin the lithosphere:Journal of Geophysics Research,90,10261–10273.
Wu,R.S.,and Aki,K.,1988,Multiple scattering andenergy transfer of seismic waves separation of scatteringeffect from intrinsic attenuation II.Application ofthe theory to Hindu Kush region:Pure and AppliedGeophysics,128,49–80.
Wu,R.S.,1989,The perturbation method in elastic wavescattering:Pure and Applied Geophysics,131,605–637.
Wu,R.S.,1994,Wide-angle elastic wave one-waypropagation in heterogeneous media and an elasticwave complex-screen method:Journal of GeophysicsResearch,4,751–766.
Xi,X.,and Yao,Y.,2002,Simulations of random mediummodel and intermixed random medium:Earth Science-Journal of China University of Geosciences(in Chinese),27,67–71.
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