求解3D弹性波方程的并行WNAD方法及其TI介质中的波场模拟
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摘要
准确模拟TTI介质中弹性波的传播是研究地震各向异性、AVO反演的基础.在二维加权近似解析离散化(WNAD)算法的基础上,本文发展的并行WNAD算法是一种研究三维横向各向同性(TI)介质中弹性波传播的、快速高效的数值模拟方法.我们首先介绍三维WNAD方法的构造过程,然后与经典的差分格式——交错网格(SG)算法进行了比较.理论分析和数值算例表明,WNAD算法比交错网格算法更适合在高性能计算机上进行大规模弹性波场模拟.同时,本文利用并行的WNAD方法研究了弹性波在TTI介质中的传播规律,观测了TI介质中弹性波传播的重要特征:横波分离、体波耦合和速度各向异性等.在TTI介质分界面处,弹性波产生更加复杂的折射、反射和波型转化,使得波场非常复杂,研究和辨别不同类型的波能够加深我们对由裂隙诱导的各向异性介质的认识.
The accurate modeling of elastic wave propagation in TTI media is significantly important for the study of the anisotropy,amplitude versus offset(AVO) analysis,and other inverse problems.A new numerical algorithm named parallel weighted nearly-analytical discrete(WNAD) method is presented in this paper.As an extension of 2D WNAD,the parallel WNAD method is a fast and efficient algorithm for simulating the elastic wave propagation in TTI media.We first show how to formulate the 3D WNAD method,and then compare the wavefield generated by this method with the wavefield computed by a conventional staggered-grid method.The numerical results show that the WNAD algorithm is more suitable for the simulations of the large-scale seismic wavefield by using the high-performance computers.Using the parallel WNAD algorithm,we study the elastic wave propagation in the TTI media and observe the important feature of TI media: shear-wave splitting,the quasi body wave coupling and velocity anisotropy.The reflected,refracted,and converted waves are generated at the interfaces.This makes the wavefield complex.To better understand the anisotropic media induced by fracture,it′s useful to study and identify those waves.
The accurate modeling of elastic wave propagation in TTI media is significantly important for the study of the anisotropy,amplitude versus offset(AVO) analysis,and other inverse problems.A new numerical algorithm named parallel weighted nearly-analytical discrete(WNAD) method is presented in this paper.As an extension of 2D WNAD,the parallel WNAD method is a fast and efficient algorithm for simulating the elastic wave propagation in TTI media.We first show how to formulate the 3D WNAD method,and then compare the wavefield generated by this method with the wavefield computed by a conventional staggered-grid method.The numerical results show that the WNAD algorithm is more suitable for the simulations of the large-scale seismic wavefield by using the high-performance computers.Using the parallel WNAD algorithm,we study the elastic wave propagation in the TTI media and observe the important feature of TI media: shear-wave splitting,the quasi body wave coupling and velocity anisotropy.The reflected,refracted,and converted waves are generated at the interfaces.This makes the wavefield complex.To better understand the anisotropic media induced by fracture,it′s useful to study and identify those waves.
引文
[1]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[2]牛滨华,何樵登,孙春岩.六方各向异性介质方位矢量波动方程及其相速度.石油物探,1994,33(1):19-29.Niu B H,He Q D,Sun C Y.Azimuth vector wave equationand its phase velocity in hexagonal anisotropy medium.Geophys.Prospect.Petrol.(in Chinese),1994,33(1):19-29.
[3]吴国忱,梁楷,印兴耀.TTI介质弹性波相速度与偏振特征分析.地球物理学报,2010,53(8):1914-1923.Wu G C,Liang K,Yin X Y.The analysis of phase velocityand polarization feature for elastic wave in TTI media.Chinese J.Geophys.(in Chinese),2010,53(8):1914-1923.
[4]郝重涛,姚陈.任意空间取向TI介质中体波速度特征.地球物理学报,2007,50(2):546-555.Hao C T,Yao C.A theoretical study on the effect of ozonebelow cloud on total ozone retrieved by TOMS and a newinversion algorithm.Chinese J.Geophys.(in Chinese),2007,50(2):546-555.
[5]杜向东,翁斌,刘军荣等.TI介质偏移速度建模研究.地球物理学报,2008,51(2):538-545.Du X D,Weng B,Liu J R,et al.Migration velocity modelingstrategies of TI media.Chinese J.Geophys.(in Chinese),2008,51(2):538-545.
[6]Crampin S.An introduction to wave propagation in 2Danisotropic media.Geophys.J.Roy.Astron.Soc.,1984,76(1):17-28.
[7]Carcione J M,Kosloff D,Behle A,et al.A spectral schemefor wave propagation simulation in 3-D elastic-anisotropicmedia.Geophysics,1992,57(12):1593-1607.
[8]Igel H,Mora P,Riollet B.Anisotropic wave propagationthrough finite-difference grids.Geophysics,1995,60(4):1203-1261.
[9]Juhlin C.Finite-difference elastic wave propagation in 2Dheterogeneous transversely isotropic media.Geophys.Prospect.,1995,43(6):843-858.
[10]侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究.地球物理学报,1995,38(2):243-251.Hou A N,He Q D.Study of a elastic wave high-orderdifference method and its stability in anisotropic media.Chinese J.Geophys.(in Chinese),1995,38(2):243-251.
[11]吴国忱.各向异性介质地震波传播与成像.东营:中国石油大学出版社,2006.Wu G C.Seismic Wave Propagation and Imaging inAnisotropic Media(in Chinese).Dongying:China Universityof Petroleum Press,2006.
[12]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005.Mou Y G,Pei Z L.Seismic Numerical Modeling for 3-DComplex Media(in Chinese).Beijing:Petrolum IndustryPress,2005.
[13]郝奇.三维TTI介质地震波场正演模拟[硕士学位论文].长春:吉林大学,2006Hao Q.Seismic wavefield modeling in 3D TTI media(inChinese)[Master′s thesis].Changchun:Jilin University,2006.
[14]Dablain M A.The application of high-order differencing tothe scale wave equation Laser.Geophysics,1986,1(51):54-66.
[15]Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method.Geophysics,1986,51(4):889-901.
[16]Yang D H,Teng J W,Zhang Z J,et al.A nearly analyticdiscrete method for acoustic and elastic wave equations inanisotropic media.Bull.Seis.Soc.Am.,2003,93(2):882-890.
[17]王磊,杨顶辉,邓小英.非均匀介质中地震波应力场的WNAD方法及其数值模拟.地球物理学报,2009,52(6):1526-1535.Wang L,Yang D H,Deng X Y.A WNAD method forseismic stress-field modeling in heterogeneous media.ChineseJ.Geophys.(in Chinese),2009,52(6):1526-1535.
[18]Yang D H,Song G J,Hua B L,et al.Simulation of acousticwavefields in heterogeneous media:A robust method forautomatic suppression of numerical dispersion.Geophysics,2010,75(3):99-110.
[19]宋国杰,杨顶辉,陈亚丽等.基于WNAD方法的非一致网格算法及其弹性波场模拟.地球物理学报,2010,53(8):1985-1992.Song G J,Yang D H,Chen Y L,et al.Non-uniform gridalgorithm based on the WNAD method and elastic wave-fieldsimulations.Chinese J.Geophys.(in Chinese),2010,53(8):1985-1992.
[20]http://www.top500.org/lists/2010/11/press-release[2010-09-28].
[21]Olsen K B,Archuleta R J,Matarese J R.3-dimensionalsimulation of a magnitude 7.75 earthquake on the SanAndreas fault.Sciences,1995,270(5242):1628-1632.
[22]Bohlen T.Parallel 3-D viscoelastic finite difference seismicmodelling.Comput.Geosci-UK,2002,28(8):887-899.
[23]Komatitsch D,Ritsema J,Tromp J.The spectral-elementmethod,Beowulf computing,and global seismology.Science,2002,298(5599):1737-1742.
[24]Gao H W,Zhang J F.Parallel 3-D simulation of seismic wavepropagation in heterogeneous anisotropic media:a gridmethod approach.Geophys.J.Int.,2006,165(3):875-888.
[25]Tape C,Liu QY,Maggi A,et al.Adjoint tomography of theSouthern California crust.Science,2009,325(5943):988-992.
[26]Ting T C T.Anisotropic Elasticity:Theory andApplications.New York:Oxford University Press,1996.
[27]Yang D H,Song G J,Lu M.Optimally accurate nearlyanalytic discrete scheme for wave-field simulation in 3Danisotropic media.Bull.Seis.Soc.Am.,2007,97(5):1557-1569.
[28]Grama A,Gupta A,Karypis G,et al.Introduction toParallel Computing.Beijing:China Machine Press,2003.
[2]牛滨华,何樵登,孙春岩.六方各向异性介质方位矢量波动方程及其相速度.石油物探,1994,33(1):19-29.Niu B H,He Q D,Sun C Y.Azimuth vector wave equationand its phase velocity in hexagonal anisotropy medium.Geophys.Prospect.Petrol.(in Chinese),1994,33(1):19-29.
[3]吴国忱,梁楷,印兴耀.TTI介质弹性波相速度与偏振特征分析.地球物理学报,2010,53(8):1914-1923.Wu G C,Liang K,Yin X Y.The analysis of phase velocityand polarization feature for elastic wave in TTI media.Chinese J.Geophys.(in Chinese),2010,53(8):1914-1923.
[4]郝重涛,姚陈.任意空间取向TI介质中体波速度特征.地球物理学报,2007,50(2):546-555.Hao C T,Yao C.A theoretical study on the effect of ozonebelow cloud on total ozone retrieved by TOMS and a newinversion algorithm.Chinese J.Geophys.(in Chinese),2007,50(2):546-555.
[5]杜向东,翁斌,刘军荣等.TI介质偏移速度建模研究.地球物理学报,2008,51(2):538-545.Du X D,Weng B,Liu J R,et al.Migration velocity modelingstrategies of TI media.Chinese J.Geophys.(in Chinese),2008,51(2):538-545.
[6]Crampin S.An introduction to wave propagation in 2Danisotropic media.Geophys.J.Roy.Astron.Soc.,1984,76(1):17-28.
[7]Carcione J M,Kosloff D,Behle A,et al.A spectral schemefor wave propagation simulation in 3-D elastic-anisotropicmedia.Geophysics,1992,57(12):1593-1607.
[8]Igel H,Mora P,Riollet B.Anisotropic wave propagationthrough finite-difference grids.Geophysics,1995,60(4):1203-1261.
[9]Juhlin C.Finite-difference elastic wave propagation in 2Dheterogeneous transversely isotropic media.Geophys.Prospect.,1995,43(6):843-858.
[10]侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究.地球物理学报,1995,38(2):243-251.Hou A N,He Q D.Study of a elastic wave high-orderdifference method and its stability in anisotropic media.Chinese J.Geophys.(in Chinese),1995,38(2):243-251.
[11]吴国忱.各向异性介质地震波传播与成像.东营:中国石油大学出版社,2006.Wu G C.Seismic Wave Propagation and Imaging inAnisotropic Media(in Chinese).Dongying:China Universityof Petroleum Press,2006.
[12]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005.Mou Y G,Pei Z L.Seismic Numerical Modeling for 3-DComplex Media(in Chinese).Beijing:Petrolum IndustryPress,2005.
[13]郝奇.三维TTI介质地震波场正演模拟[硕士学位论文].长春:吉林大学,2006Hao Q.Seismic wavefield modeling in 3D TTI media(inChinese)[Master′s thesis].Changchun:Jilin University,2006.
[14]Dablain M A.The application of high-order differencing tothe scale wave equation Laser.Geophysics,1986,1(51):54-66.
[15]Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method.Geophysics,1986,51(4):889-901.
[16]Yang D H,Teng J W,Zhang Z J,et al.A nearly analyticdiscrete method for acoustic and elastic wave equations inanisotropic media.Bull.Seis.Soc.Am.,2003,93(2):882-890.
[17]王磊,杨顶辉,邓小英.非均匀介质中地震波应力场的WNAD方法及其数值模拟.地球物理学报,2009,52(6):1526-1535.Wang L,Yang D H,Deng X Y.A WNAD method forseismic stress-field modeling in heterogeneous media.ChineseJ.Geophys.(in Chinese),2009,52(6):1526-1535.
[18]Yang D H,Song G J,Hua B L,et al.Simulation of acousticwavefields in heterogeneous media:A robust method forautomatic suppression of numerical dispersion.Geophysics,2010,75(3):99-110.
[19]宋国杰,杨顶辉,陈亚丽等.基于WNAD方法的非一致网格算法及其弹性波场模拟.地球物理学报,2010,53(8):1985-1992.Song G J,Yang D H,Chen Y L,et al.Non-uniform gridalgorithm based on the WNAD method and elastic wave-fieldsimulations.Chinese J.Geophys.(in Chinese),2010,53(8):1985-1992.
[20]http://www.top500.org/lists/2010/11/press-release[2010-09-28].
[21]Olsen K B,Archuleta R J,Matarese J R.3-dimensionalsimulation of a magnitude 7.75 earthquake on the SanAndreas fault.Sciences,1995,270(5242):1628-1632.
[22]Bohlen T.Parallel 3-D viscoelastic finite difference seismicmodelling.Comput.Geosci-UK,2002,28(8):887-899.
[23]Komatitsch D,Ritsema J,Tromp J.The spectral-elementmethod,Beowulf computing,and global seismology.Science,2002,298(5599):1737-1742.
[24]Gao H W,Zhang J F.Parallel 3-D simulation of seismic wavepropagation in heterogeneous anisotropic media:a gridmethod approach.Geophys.J.Int.,2006,165(3):875-888.
[25]Tape C,Liu QY,Maggi A,et al.Adjoint tomography of theSouthern California crust.Science,2009,325(5943):988-992.
[26]Ting T C T.Anisotropic Elasticity:Theory andApplications.New York:Oxford University Press,1996.
[27]Yang D H,Song G J,Lu M.Optimally accurate nearlyanalytic discrete scheme for wave-field simulation in 3Danisotropic media.Bull.Seis.Soc.Am.,2007,97(5):1557-1569.
[28]Grama A,Gupta A,Karypis G,et al.Introduction toParallel Computing.Beijing:China Machine Press,2003.
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