起伏地表下流体填充裂缝的地震波场模拟(英文)
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摘要
我们发展了一种模拟复杂地表下含裂缝介质地震波场的方法,这对于解释山地地区的地震资料具有重要意义。基于Coates-Schoenberg方法,把裂缝引入到有限差分法(FD)中,从而使包含裂缝的单元里的弹性介质就具有了局部的各向异性。为了模拟起伏的地表地形,我们借助于贴体网格,将笛卡尔坐标系的具有水平对称轴的横向各向同性介质(HTI)的弹性波方程和自由边界条件变换到曲线坐标系中,采用一种稳定的、显式的二阶精度的有限差分方法离散(曲线坐标系)HTI介质中的弹性波方程。数值实例充分地展现了在不规则地球表面的影响下裂缝介质中地震波传播的复杂性。合成地震记录和波场快照表明裂缝端点产生的散射波在地表处会受不规则地表地形的作用,再次被散射;同理,地表地形产生的散射波,经过裂缝端点时也会被再次散射,尤其是瑞利面波产生的散射波,因其能量很强,严重污染了地震记录,使得识别地下裂缝等产生的有效信息变得异常困难。这对山地地震勘探中资料的解释具有重要意义。
We present a finite difference(FD) method for the simulation of seismic wave fields in fractured medium with an irregular(non-flat) free surface which is beneficial for interpreting exploration data acquired in mountainous regions.Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded.To implement surface topography,we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one.We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations(in a curvilinear coordinate system) in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry(HTI).Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration.The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography.The scattered waves provoked by the topography are re-scattered by the fractures,especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.
We present a finite difference(FD) method for the simulation of seismic wave fields in fractured medium with an irregular(non-flat) free surface which is beneficial for interpreting exploration data acquired in mountainous regions.Fractures are introduced through the Coates-Schoenberg approach into the FD scheme which leads to local anisotropic properties of the media where fractures are embedded.To implement surface topography,we take advantage of the boundary-conforming grid and map a rectangular grid onto a curved one.We use a stable and explicit second-order accurate finite difference scheme to discretize the elastic wave equations(in a curvilinear coordinate system) in a 2D heterogeneous transversely isotropic medium with a horizontal axis of symmetry(HTI).Efficiency tests performed by different numerical experiments clearly illustrate the influence of an irregular free surface on seismic wave propagation in fractured media which may be significant to mountain seismic exploration.The tests also illustrate that the scattered waves induced by the tips of the fracture are re-scattered by the features of the free surface topography.The scattered waves provoked by the topography are re-scattered by the fractures,especially Rayleigh wave scattering whose amplitudes are much larger than others and making it very difficult to identify effective information from the fractures.
引文
Appelo,D.,and Petersson,N.A.,2009,A stable finite difference method for the elastic wave equation on complex geometries with free surfaces:Commun. Comput.Phys.,5,84-107.
Campilio,M.,and Bouchon,M.,1985,Synthetic SH seismograms in a laterally varying medium by the discrete wavenumber method:Geophys.J.R.Astr.Soc, 83,307-317.
Coates,R.T.,and Schoenberg,M,1995,Finite-difference modeling of faults and fractures:Geophysics,60,1514 - 1526.
Crampin,S.,1984,Effective anisotropic elastic constants for wave propagation through cracked solids:Geophys.J. Int.,76,135-145.
Durand,S.,Gaffet,S.,and Virieux,J.,1999,Seismic diffracted waves from topography using 3-D discrete wavenumber-boundary integral equation simulation: Geophysics,64,572 - 578.
Fornberg,B.,1988,The pseudo-spectral method:Accurate representation in elastic wave calculations:Geophysics, 53,625 - 637.
Gao,H.,and Zhang,J.,2006,Parallel 3-D simulation of seismic wave propagation in heterogeneous anisotropic medium:a grid method approach:Geophys.J.Int.,165, 875-888.
Guan,X.Z.,Fu,L.Y,Tao,Y.,Yu,G.X.,2011,Boundary-volume integral equation numerical modeling for complex near surface:Chinese J.Geophys.(in Chinese), 54(9),2357 - 2367.
Hestholm,S.,and Ruud,B.,1994,2-D finite-difference elastic wave modeling including surface topography: Geophys.Prosp.,42,371 - 390.
Hsu,C.J.,and Schoenberg,M.,1993,Elastic waves through a simulated fractured medium:Geophysics,58, 964 - 977.
Hudson,J.A.,1981,Wave speeds and attenuation of elastic waves in material containing cracks:Geophys.J.Int.,64, 133-150.
Hvid,S.L.,1994,Three dimensional algebraic grid generation:PhD Thesis,Technical University of Denmark.
Komatitsch,D.,and Tromp,J.,2002,Spectral-element simulations of global seismic wave propagation-I. Validation:Geophys.J.Int.,149,390 - 412.
Lan,H.Q.,and Zhang,Z.J.,2011a,Three-dimensional wave-field simulation in heterogeneous transversely isotropic medium with irregular free surface:Bull. Seismol.Soc.Am.,101(3),1354- 1370.
——,2011b,Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation:Journal of Geophysics and Engineering,8,275 - 286.
Lan,H.Q.,Liu,J.,and Bai,Z.M.,2011,Wave-field simulation in VTI media with irregular free surface: Chinese J.Geophys.(in Chinese),54(8),2072 - 2084.
Lan,H.Q.,Xu T.,and Bai,Z.M,2012,Study of the effects due to the anisotropic stretching of the surface-fitting grid on the traveltime computation for irregular surface by the coordinate transforming method:Chinese J.Geophys.(in Chinese),accepted.
Liu,E.,Crampin,S.,Queen,J.H.,and Rizer,W.D., 1993,Velocity and attenuation anisotropy caused by microcracks and microfractures in a multiazimuth reverse VSP:Can.J.Explor.Geophys.,29,177 - 188.
Liu,E.,Hudson,J.A.,and Pointer,T.,2000,Equivalent medium representation of fractured rock:J.Geophys. Res.,105,2981-3000.
Moczo,P.,Bystricky,E.,Kristek,J.,Carcione,J.,and Bouchon,M.,1997,Hybrid modelling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures:Bull.Seism.Soc.Am.,87,1305 - 1323.
Nielsen,P.,If,R,Berg,P.,and Skovgaard,O.,1994,Using the pseudospectral technique on curved grids for 2D acoustic forward modelling:Geophys.Prospect.,42,321 -342.
Nilsson,S.,Petersson,N.A.,Sjogreen,B.,and Kreiss,H. O.,2007,Stable difference approximations for the elastic wave equation in second order formulation:SIAM J. Numer.Anal.,45,1902 - 1936.
Pei,Z.L.,He,H.M.,and Xie,F.,2010,Elastic wave equation forward modeling for complex surface and complex structure model:Oil Geophysical Prospecting, 45(6),807-818.
Pyrak-Nolte,L.J.,Myer,L.R.,and Cook,N.G.W.,1990, Transmission of seismic waves across single natural fractures:Journal of Geophysical Research,95,8617- 8638.
Robertsson,J.O.A.,1996,A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography:Geophysics,61, 1921 - 1934.
Robertsson,J.O.A.,and Holliger,K.,1997,Modeling of seismic wave propagation near the earth's surface:Phys. Earth Planet.Inter.,104,193 - 211.
Sanchez-Sesma,R J.,Bravo,M.A.,and Herrear,I.,1985, Surface motion of topographical irregularities for incident P,SV,and Rayleigh waves:Bull.Seismol.Soc. Am.,75,263 - 269.
Schoenberg,M.,1980,Elastic wave behavior across linear slip interfaces:Journal of the Acoustical Society of America,68,1516-1521.
Schoenberg,M,and Muir,R,1989,A calculus for finely layered anisotropic medium:Geophysics,54,581-589.
Schoenberg,M.,and Sayers,C,1995,Seismic anisotropy of fractured rocks:Geophysics,60,204 -211.
Tessmer,E.,and Kosloff,D.,1994,3-D clastic modeling with surface topography by a Chcbychev spectral method:Geophysics,59,464 - 473.
Thompson,J.R,Warsi,Z.U.A.,and Mastin,C.W.,1985, Numerical grid generation:foundations and applications: North-Holland,Amsterdam.
Thomsen,L.,1995,Elastic anisotropy due to aligned cracks in porous rock:Geophys.Prosp.,43,805 - 829.
Tian,X.B.,Zhao,D.P.,Zhang,H.S.,Tian,Y.,and Zhang,Z.J.,2010a,Mantle transition zone topography and structure beneath the central Tien Shan orogenic belt:J.Geophys.Res.,115,B10308,doi:10.1029/ 2008JB006229.
Tian,X.B.,Teng,J.W.,Zhang,H.S.,Zhang,Z.J.,Zhang,Y. Q.,Yang,H,2010b,Structure of crust and upper mantle beneath the Ordos Block and the Yinshan Mountains revealed by receiver function analysis:Phys.Earth Planet.Inter.,194,186-193.
Wu,C,Harris,J.M? Nihei,K.T.,and Nakagawa,S.,2005, Two-dimensional finite-difference seismic modeling of an open fluid-filled fracture:Comparison of thin-layer and linear-slip models:Geophysics,70,T57 - T62.
Yan,S.X.,Liu,H.S.,and Yao,X.G.,2000,Geophysical exploration technology in the mountainous area: Petroleum Industry Press,Beijing.
Yilmaz,O.,and Dohcrty,S.M.,2001,Seismic data analysis:Society of Exploration Geophysicists. Zhang,J.R,2005,Elastic wave modeling in fractured media with an explicit approach:Geophysics,70,T75 - T85.
Zhang,W.,and Chen,X.,2006,Traction image method for irregular free surface boundaries in finite difference seismic wave simulation:Geophys.J.Int.,167,337 - 353.
Zhang,Z.J.,Wang,G.,and Harris,J.M.,1999,Multi-component wavefield simulation in viscous extensively dilatancy anisotropic medium:Phys.Earth Planet.Inter., 114,25-38.
Zhang,Z.J.,and Klemperer,S.L.,2010,Crustal structure of the Tethyan Himalaya,south Tibet:new constraints from old wide-angle seismic data:Geophys.J.Int.,181, 1247-1260.
Zhang,Z.J.,Yuan,X.,Chen,Y,Tian,X.,Kind,R.,Li,X., and Teng,J.,2010,Seismic signature of the collision between the east Tibetan escape flow and the Sichuan Basin:Earth Planet Sci Lett,292,254 - 264.
Campilio,M.,and Bouchon,M.,1985,Synthetic SH seismograms in a laterally varying medium by the discrete wavenumber method:Geophys.J.R.Astr.Soc, 83,307-317.
Coates,R.T.,and Schoenberg,M,1995,Finite-difference modeling of faults and fractures:Geophysics,60,1514 - 1526.
Crampin,S.,1984,Effective anisotropic elastic constants for wave propagation through cracked solids:Geophys.J. Int.,76,135-145.
Durand,S.,Gaffet,S.,and Virieux,J.,1999,Seismic diffracted waves from topography using 3-D discrete wavenumber-boundary integral equation simulation: Geophysics,64,572 - 578.
Fornberg,B.,1988,The pseudo-spectral method:Accurate representation in elastic wave calculations:Geophysics, 53,625 - 637.
Gao,H.,and Zhang,J.,2006,Parallel 3-D simulation of seismic wave propagation in heterogeneous anisotropic medium:a grid method approach:Geophys.J.Int.,165, 875-888.
Guan,X.Z.,Fu,L.Y,Tao,Y.,Yu,G.X.,2011,Boundary-volume integral equation numerical modeling for complex near surface:Chinese J.Geophys.(in Chinese), 54(9),2357 - 2367.
Hestholm,S.,and Ruud,B.,1994,2-D finite-difference elastic wave modeling including surface topography: Geophys.Prosp.,42,371 - 390.
Hsu,C.J.,and Schoenberg,M.,1993,Elastic waves through a simulated fractured medium:Geophysics,58, 964 - 977.
Hudson,J.A.,1981,Wave speeds and attenuation of elastic waves in material containing cracks:Geophys.J.Int.,64, 133-150.
Hvid,S.L.,1994,Three dimensional algebraic grid generation:PhD Thesis,Technical University of Denmark.
Komatitsch,D.,and Tromp,J.,2002,Spectral-element simulations of global seismic wave propagation-I. Validation:Geophys.J.Int.,149,390 - 412.
Lan,H.Q.,and Zhang,Z.J.,2011a,Three-dimensional wave-field simulation in heterogeneous transversely isotropic medium with irregular free surface:Bull. Seismol.Soc.Am.,101(3),1354- 1370.
——,2011b,Comparative study of the free-surface boundary condition in two-dimensional finite-difference elastic wave field simulation:Journal of Geophysics and Engineering,8,275 - 286.
Lan,H.Q.,Liu,J.,and Bai,Z.M.,2011,Wave-field simulation in VTI media with irregular free surface: Chinese J.Geophys.(in Chinese),54(8),2072 - 2084.
Lan,H.Q.,Xu T.,and Bai,Z.M,2012,Study of the effects due to the anisotropic stretching of the surface-fitting grid on the traveltime computation for irregular surface by the coordinate transforming method:Chinese J.Geophys.(in Chinese),accepted.
Liu,E.,Crampin,S.,Queen,J.H.,and Rizer,W.D., 1993,Velocity and attenuation anisotropy caused by microcracks and microfractures in a multiazimuth reverse VSP:Can.J.Explor.Geophys.,29,177 - 188.
Liu,E.,Hudson,J.A.,and Pointer,T.,2000,Equivalent medium representation of fractured rock:J.Geophys. Res.,105,2981-3000.
Moczo,P.,Bystricky,E.,Kristek,J.,Carcione,J.,and Bouchon,M.,1997,Hybrid modelling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures:Bull.Seism.Soc.Am.,87,1305 - 1323.
Nielsen,P.,If,R,Berg,P.,and Skovgaard,O.,1994,Using the pseudospectral technique on curved grids for 2D acoustic forward modelling:Geophys.Prospect.,42,321 -342.
Nilsson,S.,Petersson,N.A.,Sjogreen,B.,and Kreiss,H. O.,2007,Stable difference approximations for the elastic wave equation in second order formulation:SIAM J. Numer.Anal.,45,1902 - 1936.
Pei,Z.L.,He,H.M.,and Xie,F.,2010,Elastic wave equation forward modeling for complex surface and complex structure model:Oil Geophysical Prospecting, 45(6),807-818.
Pyrak-Nolte,L.J.,Myer,L.R.,and Cook,N.G.W.,1990, Transmission of seismic waves across single natural fractures:Journal of Geophysical Research,95,8617- 8638.
Robertsson,J.O.A.,1996,A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography:Geophysics,61, 1921 - 1934.
Robertsson,J.O.A.,and Holliger,K.,1997,Modeling of seismic wave propagation near the earth's surface:Phys. Earth Planet.Inter.,104,193 - 211.
Sanchez-Sesma,R J.,Bravo,M.A.,and Herrear,I.,1985, Surface motion of topographical irregularities for incident P,SV,and Rayleigh waves:Bull.Seismol.Soc. Am.,75,263 - 269.
Schoenberg,M.,1980,Elastic wave behavior across linear slip interfaces:Journal of the Acoustical Society of America,68,1516-1521.
Schoenberg,M,and Muir,R,1989,A calculus for finely layered anisotropic medium:Geophysics,54,581-589.
Schoenberg,M.,and Sayers,C,1995,Seismic anisotropy of fractured rocks:Geophysics,60,204 -211.
Tessmer,E.,and Kosloff,D.,1994,3-D clastic modeling with surface topography by a Chcbychev spectral method:Geophysics,59,464 - 473.
Thompson,J.R,Warsi,Z.U.A.,and Mastin,C.W.,1985, Numerical grid generation:foundations and applications: North-Holland,Amsterdam.
Thomsen,L.,1995,Elastic anisotropy due to aligned cracks in porous rock:Geophys.Prosp.,43,805 - 829.
Tian,X.B.,Zhao,D.P.,Zhang,H.S.,Tian,Y.,and Zhang,Z.J.,2010a,Mantle transition zone topography and structure beneath the central Tien Shan orogenic belt:J.Geophys.Res.,115,B10308,doi:10.1029/ 2008JB006229.
Tian,X.B.,Teng,J.W.,Zhang,H.S.,Zhang,Z.J.,Zhang,Y. Q.,Yang,H,2010b,Structure of crust and upper mantle beneath the Ordos Block and the Yinshan Mountains revealed by receiver function analysis:Phys.Earth Planet.Inter.,194,186-193.
Wu,C,Harris,J.M? Nihei,K.T.,and Nakagawa,S.,2005, Two-dimensional finite-difference seismic modeling of an open fluid-filled fracture:Comparison of thin-layer and linear-slip models:Geophysics,70,T57 - T62.
Yan,S.X.,Liu,H.S.,and Yao,X.G.,2000,Geophysical exploration technology in the mountainous area: Petroleum Industry Press,Beijing.
Yilmaz,O.,and Dohcrty,S.M.,2001,Seismic data analysis:Society of Exploration Geophysicists. Zhang,J.R,2005,Elastic wave modeling in fractured media with an explicit approach:Geophysics,70,T75 - T85.
Zhang,W.,and Chen,X.,2006,Traction image method for irregular free surface boundaries in finite difference seismic wave simulation:Geophys.J.Int.,167,337 - 353.
Zhang,Z.J.,Wang,G.,and Harris,J.M.,1999,Multi-component wavefield simulation in viscous extensively dilatancy anisotropic medium:Phys.Earth Planet.Inter., 114,25-38.
Zhang,Z.J.,and Klemperer,S.L.,2010,Crustal structure of the Tethyan Himalaya,south Tibet:new constraints from old wide-angle seismic data:Geophys.J.Int.,181, 1247-1260.
Zhang,Z.J.,Yuan,X.,Chen,Y,Tian,X.,Kind,R.,Li,X., and Teng,J.,2010,Seismic signature of the collision between the east Tibetan escape flow and the Sichuan Basin:Earth Planet Sci Lett,292,254 - 264.
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