VTI介质速度和各向异性参数建模研究
|
摘要
结合最新的时距曲线公式和最新的参数化方法,给出了一种自动非双曲线速度分析方案,并将其分别应用到理论合成数据和野外实际数据中,并对处理结果进行了定性分析。
推导了基于非双曲线旅行时公式做动校正的微分相似性层速度和层非椭圆率反演公式,并在反演方案中使用了三次样条插值预条件算子,给出了约束最优化反演的具体流程,并对理论合成数据进行处理及定性分析。
提出了成层VTI介质的梯形块状建模思想,介绍了建模的具体实现过程,推导了倾斜界面情况下VTI介质中用慢度表示的Snell定律公式,给出反射波射线追踪的具体实现过程,并通过具体的模拟实验,分析了算法的精度和计算效率。推导了解结合正则化和预条件的混合l~1 /l~2范数反问题的反演公式,给出了解这种反问题的共轭梯度算法。
推导了适合成层VTI介质中梯形块模型的反射波旅行时反演公式,以及射线旅行时关于模型参数参数的Frechet导数。结合射线追踪技术和正则化的混合l~1 /l~2范数反演方案,给出了一种反射波层析成像反演算法,对合成数据进行反演并对结果进行定性分析,取得较满意的结果。
Firstly, we improved the approximate formula of the phase velocity for qP wave in VTI media proposed by Berryman(2009). By tracking in the current international advances about inhomogeneous viscoelastic waves in anisotropic media, we propose a new perturbation formulas for the phase velocity and the poloarization of inhomogeneous plane wave in dissipative anisotropic media, which are more accurate than that proposed by Cerveny. By numerical analysis and comparison with exact solutions and approximation solution, we found that the accuracy of the new formulas are much higher than that of the original one.
Seismic velocity analysis in seismic data processing is a popular technology. We summarizes the approximate formula proposed by predecessors and compares their accuracy by numerical mdeling. We also find that the q1-q2 parameterizaton proposed by Abadd(2009) is the best one. In recent years with the development of an automatic non-hyperbolic velocity analysis techniques, Siliqi(2000) and Abadd introduce the idear of automatic nonhyperoblic velocity analysis. Their method can estimate the moveout velocity and the anellipticity accurately. We combine the latest formulas derived by Alexiso(2009) and the model parameterization of time-distance curves proposed by Abadd(2009), while using the latest technology and the popular Curvelet denoising techniques instead of the Kriging filtering mentioned in Alexiso(2009) and Siliqi(2001). In order to test the performance of this scheme, we applied it to the synthetic data and the field data with large offset, respectively. The final results shows it is satisfactory.
Differential semblance velocity inversion is a technology to estimate the velocity from the the objective function of the differential semblance. In the chapter 4 of this thesis, according to the scheme given by Li, and Symes in 2007 for interval velocity inversion based on NMO correction using hyperbolic traveltime formula, we propose the idear of inversion of interval velocity and anellipticity based on NMO correction using the nonhyperbolic one. Through a series of complex mathematical derivation, we show the optimization problem for non-hyperbolic differential semblance inversion, and the derivative of the objective function function with respect to interval velocity and anellipticity. By combining the nonlinear conjugate gradient algorithm with the constrained optimaization frame, we prove the validity of the algorithm using the synthetic data.
Seismic tomography based on ray is still an important research topic. In order to realize it for layered VTI media, we firstly need to achieve the parameterization of the underground model and ray tracing in this parameterized model. Many Geophysicsts have proposed so much parameterization methods for ray tracing, in which the simplest one is to sample the underground model by discrete rectangular blocks. The layered underground medium can also be divided into a series of small trapezoidal block. For more complex models, we can discretize it into a series of irregular blocks. In chapter 5 of this thesis, according to the trapezoidal block modeling for isotropic medium by Zelt in 1988, we proposed a new schemes for trapezoidal block modeling.for VTI medium The layered VTI media is divided into a series of trapezoidal blocks, in which each node owns a group of Thomsen parameters. In addition, we also derive the Snell’s law for the VTI medium with a tilted interface, which can be used to estimate the phase slowness for reflected or transmitted ray tracing from that of the incident ray. The single-layer model , multi-layered model , and topology multi-layered model is investigated by the proposed scheme, which prove the algorithm's practicality.
In addition to computing traveltime by ray tracing in seismic tomography, it is also necessary to calculate Frechet derivative of the raveltime of rays with respect to the model parameters and resolve the inverse problem. In the chapter 6 of this thesis, we discusses the mathematical theory of tomography inverse problem. Moreover, according to the travel perturbation formula proposed by Cerveny, we present the Frechet derivative of the ray traveltime with respect to the model parameters in the trapezoidal blocks. In solving the inverse problem of tomography, according to Bube’s mixed l~1/l~2norm inversion theory, we derived a series of regularized and preconditioned mixed l~1/l~2norm inversion method and gives the corresponding algorithm process. Finally, we show a numerical experiment of reflective tomography and compare the results for reflected qP-wave, reflected qPqSV-wave as well as the joint of reflected qP- and reflected qPqSV- wave.
推导了基于非双曲线旅行时公式做动校正的微分相似性层速度和层非椭圆率反演公式,并在反演方案中使用了三次样条插值预条件算子,给出了约束最优化反演的具体流程,并对理论合成数据进行处理及定性分析。
提出了成层VTI介质的梯形块状建模思想,介绍了建模的具体实现过程,推导了倾斜界面情况下VTI介质中用慢度表示的Snell定律公式,给出反射波射线追踪的具体实现过程,并通过具体的模拟实验,分析了算法的精度和计算效率。推导了解结合正则化和预条件的混合l~1 /l~2范数反问题的反演公式,给出了解这种反问题的共轭梯度算法。
推导了适合成层VTI介质中梯形块模型的反射波旅行时反演公式,以及射线旅行时关于模型参数参数的Frechet导数。结合射线追踪技术和正则化的混合l~1 /l~2范数反演方案,给出了一种反射波层析成像反演算法,对合成数据进行反演并对结果进行定性分析,取得较满意的结果。
Firstly, we improved the approximate formula of the phase velocity for qP wave in VTI media proposed by Berryman(2009). By tracking in the current international advances about inhomogeneous viscoelastic waves in anisotropic media, we propose a new perturbation formulas for the phase velocity and the poloarization of inhomogeneous plane wave in dissipative anisotropic media, which are more accurate than that proposed by Cerveny. By numerical analysis and comparison with exact solutions and approximation solution, we found that the accuracy of the new formulas are much higher than that of the original one.
Seismic velocity analysis in seismic data processing is a popular technology. We summarizes the approximate formula proposed by predecessors and compares their accuracy by numerical mdeling. We also find that the q1-q2 parameterizaton proposed by Abadd(2009) is the best one. In recent years with the development of an automatic non-hyperbolic velocity analysis techniques, Siliqi(2000) and Abadd introduce the idear of automatic nonhyperoblic velocity analysis. Their method can estimate the moveout velocity and the anellipticity accurately. We combine the latest formulas derived by Alexiso(2009) and the model parameterization of time-distance curves proposed by Abadd(2009), while using the latest technology and the popular Curvelet denoising techniques instead of the Kriging filtering mentioned in Alexiso(2009) and Siliqi(2001). In order to test the performance of this scheme, we applied it to the synthetic data and the field data with large offset, respectively. The final results shows it is satisfactory.
Differential semblance velocity inversion is a technology to estimate the velocity from the the objective function of the differential semblance. In the chapter 4 of this thesis, according to the scheme given by Li, and Symes in 2007 for interval velocity inversion based on NMO correction using hyperbolic traveltime formula, we propose the idear of inversion of interval velocity and anellipticity based on NMO correction using the nonhyperbolic one. Through a series of complex mathematical derivation, we show the optimization problem for non-hyperbolic differential semblance inversion, and the derivative of the objective function function with respect to interval velocity and anellipticity. By combining the nonlinear conjugate gradient algorithm with the constrained optimaization frame, we prove the validity of the algorithm using the synthetic data.
Seismic tomography based on ray is still an important research topic. In order to realize it for layered VTI media, we firstly need to achieve the parameterization of the underground model and ray tracing in this parameterized model. Many Geophysicsts have proposed so much parameterization methods for ray tracing, in which the simplest one is to sample the underground model by discrete rectangular blocks. The layered underground medium can also be divided into a series of small trapezoidal block. For more complex models, we can discretize it into a series of irregular blocks. In chapter 5 of this thesis, according to the trapezoidal block modeling for isotropic medium by Zelt in 1988, we proposed a new schemes for trapezoidal block modeling.for VTI medium The layered VTI media is divided into a series of trapezoidal blocks, in which each node owns a group of Thomsen parameters. In addition, we also derive the Snell’s law for the VTI medium with a tilted interface, which can be used to estimate the phase slowness for reflected or transmitted ray tracing from that of the incident ray. The single-layer model , multi-layered model , and topology multi-layered model is investigated by the proposed scheme, which prove the algorithm's practicality.
In addition to computing traveltime by ray tracing in seismic tomography, it is also necessary to calculate Frechet derivative of the raveltime of rays with respect to the model parameters and resolve the inverse problem. In the chapter 6 of this thesis, we discusses the mathematical theory of tomography inverse problem. Moreover, according to the travel perturbation formula proposed by Cerveny, we present the Frechet derivative of the ray traveltime with respect to the model parameters in the trapezoidal blocks. In solving the inverse problem of tomography, according to Bube’s mixed l~1/l~2norm inversion theory, we derived a series of regularized and preconditioned mixed l~1/l~2norm inversion method and gives the corresponding algorithm process. Finally, we show a numerical experiment of reflective tomography and compare the results for reflected qP-wave, reflected qPqSV-wave as well as the joint of reflected qP- and reflected qPqSV- wave.
引文
[1]何樵登, and张中杰.横向各向同性介质中地震波及其数值模拟[M].长春:吉林大学出版社, 1996.
[2] McGullagh. Geometrical proposition applied to the wave theory of light[J]. The Transactions of the Royal Irish Academy. 1831, 17: 241-263.
[3] Thompson) L.K. On stresses and strains(XXI. Elements of a mathematical theory of elasticity. Part 1)[J]. Philosophical Transactions of The Royal Society. 1856, 166: 481-489.
[4] Christoffel E.B. Uber die Fortpflanzung von Stossen durch elastische feste Korper[J]. Annali di Mathematica. 1877, 8: 193-243.
[5] Rudzki M.P. Uber die Gestalt elastischer Wellen in Gesteinen[J]. Bulletin of the Academy of Science Cracow. 1897: 387-393.
[6] Rudzki M.P. Uber die Gestalt elastischer Wellen in Gesteinen, IV Studie aus der Theorie der Erdbebenwellen[J]. Bulletin of the Academy of Science Cracow. 1898: 373-384.
[7] Rudzki M.P. Parametrische Darstellung der elastischen Welle in anisotropen Medien[J]. Bulletin of the Academy of Science Cracow(A). 1911: 503-536.
[8] Rudzki M.P. Sur la propagation dPune onde elastique superficielle dans un millen transversalement isotrope[J]. Bulletin of the Academy of Science Cracow(IA). 1912: 47-58.
[9] Rudzki M.P. Essai d'application du principe de Fermat aux milieux anisotropes[J]. Bulletin of the Academy of Science Cracow(A). 1913.
[10] Rudzki M.P. Uber die Theorie der Erdebenwellen[J]. Die Naturwissenschaften. 1915, 3: 201-204.
[11] Love A.E.H. A treatise on the mathematical theory of elasticity[M]. Cambridge: Cambridge University Press, 1892.
[12] Bruggeman D.A.G. Berechnung verschiedener physikalischer konstanten von heterogenen substanzen[J]. Annals of Physics. 1935, 24: 636.
[13] Levin F.K. The reflection,refraction,and diffraction of waves in media with an elliptical velocity dependence[J]. Geophysics. 1978, 43(4): 528-537.
[14] Love A.E.H. A Treatise on the Mathematical Theory of Elasticity[M]. Dover: New York, 1944.
[15] Riznichenko Y.V. On seismic quasi anizotropy[J]. Geography and Geophysics. 1949, 6: 518–544.
[16] Stoneley R. The seismological implications of aeolotropy in continental structure[J]. Geophysical Journal International. 1949, 5(8): 343-353.
[17] Postma G.W. Wave propagation in a stratified medium[J]. Geophysics. 1955, 20(4): 780-806.
[18] Krey T., and Helbig K. A theorem concerning anisotropy of stratified media and its significance for reflection seismics[J]. Geophysical Prospecting. 1956, 4(3): 294-302.
[19] Backus G.E. Long-wave elastic anisotropy produced by horizontal layering[J]. Journal of Geophysical Research. 1962, 67(11): 4427-4440.
[20] Jolly R.N. Investigation of shear waves[J]. Geophysics. 1956, 21(4): 905-938.
[21] Nur A., and Simmons G. Stress-induced velocity anisotropy in rock: an experimental study[J]. Journal of Geophysical Research. 1969, 74(27): 6667-6674.
[22] Bachman R.T. Acoustic anisotropy in marine sediments and sedimentary rock[J]. Journal of Geophysical Research. 1979, 84(B13): 7661-7663.
[23] Crampin S., and Bamford D. Estimating crack parameters for observations of P wave velocity anisotropy[J]. Geophysics. 1980, 45(3): 345-360.
[24] Crampin S. A review of wave motion in anisotropic and cracked elastic media[J]. Wave Motion. 1981, 3(4): 343-391.
[25] Crampin S., Chesnokov E.M., and Hipkin R.A. Seismic anisotropy-the state of the art[J]. First Break. 1984, 20: 9-18.
[26] Alford R.M. Shear data in the presence of azimuthal anisotropy[C]. 56th SEG annual meeting. Dilley. 1986,
[27] Lynn H.B., and Thomsen L.A. Reflection shear-wave data along the principal axes of azimuthal anisotropy[C]. 56th SEG annual meeting. Dilley. 1986,
[28] Li X., and Crampin S. Approximations to shear-wave velocity and moveout equations in anisotropic media[J]. Geophysical Prospecting. 1993, 41(7): 833-857.
[29] Hudson J.A. Wave speeds and attenuation of elastic wave in material containing cracks[J]. Geophys.J.R.astr.Soc. 1981, 64(1): 133-150.
[30] Hudson J.A. Overall properties of a cracked solid[J]. Math Proc Camb phil. 1980, 88: 371-384.
[31] Hudson J.A. A higher order approximation to the wave propagation constants for a cracked solid[J]. Geophys J R Astr Soc. 1986, 87: 265-274.
[32] Hudson J.A. Overall properties of anisotropic materials containing cracks[J]. Geophysical Journal International. 1993, 116(2): 279-282.
[33] Thomson L. Elastic anisotropy due to aligned cracks in porous rock[J]. Geophysical Prospecting. 1995, 43(6): 805-829.
[34] Thomsen L. Weak elastic anisotropy[J]. Geophysics. 1986, 51(10): 661-672.
[35] Lysmer J., and Drake L.A. A finite element method for seismology[J]. Methods in Computational Physics. 1972, 11.
[36]杨宝俊, and何樵登.有限元素法的一种频率域计算方法及其应用[J].石油物探. 1982, 21(1): 56-64.
[37] Marfurt K.J. Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations[J]. Geophysics. 1984, 49(5): 533-549.
[38] Seron F.J., Sanz F.J., and Sabadell F.J. A numerical laboratory for simulation and visualization of seismic wavefields[J]. Geophysical Prospecting. 1996, 44(4): 603-642.
[39] Seron F.J., Sanz F.J., and Kindelan M., et al. Finite-element method for elastic wave propagation[J]. Communications in Applied Numerical Methods. 1990, 6(5): 359-368.
[40] Padovani E., and Seriani G. Low- and high-order finite element method: experience in seismic modeling[J]. Journal of Computational Acoustics. 1994, 2(1): 371-422.
[41] Sarma G.S., Mallick K., and Gadhinglajkar V.R. Nonreflecting boundary condition in finite-element formulation for an elastic wave equation[J]. Geophysics. 1998, 63(3): 1006-1023.
[42]牟永光.三维复杂介质地震物理模拟[M].北京:石油工业出版社, 2003.
[43]杨顶辉.孔隙各向异性介质中基于微观流场的BISQ理论[C].中国地球物理学会年刊.北京. 1998,:58-59
[44] Gazdag J. Modeling of the acoustic wave equation with transform method[J]. Geophysics. 1981, 46(6): 854-859.
[45] Reshef M., and Kosloff D. Three-dimensional acoustic modeling by the Fourier method[J]. Geophysics. 1988, 3(9): 1175-1183.
[46] Fornberg B. The pseudospectral method: Comarisons with finite-differences for the elastic wave equations[J]. Geophysics. 1987, 52(4): 483-501.
[47]侯安宁, and何樵登.各向异性介质中弹性波特征的伪谱法模拟研究[J].石油物探. 1995, 34(2): 36-45.
[48]张文生, and何樵登.二维横向各向同性介质的伪谱法正演模拟[J].石油地球物理勘探. 1998, 33(3): 310-319.
[49]傅旦丹, and何樵登.正交各向异性介质地震弹性波场的伪谱法正演模拟[J].石油物探. 2001, 40(3): 8-14.
[50] Pao Y.H., and Varatharajulu V. Huygens principle, radiation conditions, and integral formulas for the scattering of elastic waves[J]. THe Journal of the Acoustical Society of America. 1976.
[51] Bennett C.L., and Mieras H.J. Time domaln integral equation for acoustic scattering from fluid targets[J]. The Journal of the Acoustical Society of America. 1981, 69(5): 1261-1265.
[52] Bouchon M. Diffraction of elastic waves by cracks or cavities using the discrete wavenumber method[J]. Journal of the acoustical society of America. 1987, 81(6): 1871-1876.
[53] Bouchon M., Campillo M., and Gaffet S. A boundary integral equation-discrete wave number representation method to study wave propagation in multilayered media having irregular interfaces[J]. Geophysics. 1989, 54(9): 1134-1140.
[54] Bakamjian B. An efficient method for modeling seismic wave propagation in 3-D[C]. 62th SEG annual meeting. Tulsa. 1992,:1232-1235
[55]符力耘, and牟永光.弹性波边界元法正演模拟[J].地球物理学报. 1994, 37(4): 521-529.
[56]阎贫, and何樵登.二维横向各向同性介质中的格林函数积分法合成记录[J].物化探计算技术. 1995, 17(2): 1-6.
[57] Fu L.Y., Mu Y.G., and Yang H.J. Forward problem of nonlinear Fredholm integral equation in reference medium via velocity-weighted wavefield function[J]. Geophysics. 1997, 62(2): 650-656.
[58] Fu L.Y. Numerical study of generalized Lippmann-Schwinger integral equation including surface topography[J]. Geophysics. 2003, 68(2): 665-671.
[59] Dablain M.A. The application of higher order fifferencing to the scalar wave equation[J]. Geophysics. 1986, 51(1): 54-66.
[60] Virieux J. SH wave propagation in heterogeneous media: velocity-stress finite difference method[J]. Geophysics. 1984, 49(11): 1933-1957.
[61] Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method[J]. Geophysics. 1986, 51(4): 889-901.
[62] Igel H., Mora P., and Riollet B. Anisotropic wave propagation through finite difference grids[J]. Geophysics. 1995, 60(4): 1203-1216.
[63] Dong Z., and McMechan G.A. 3-D viscoelastic anisotropic modeling of data from multi-component, multi-azimuth experiment in northeast Texas[J]. Geophysics. 1995, 60(4): 1128-1150.
[64] Ramos-Martinez J., Ortega A.A., and McMechan G.A. Shear-wave splitting at vertical incidence in media containing intersecting fracture systems[C]. 68th SEG annual meeting. New Orleans. 1998,:960-963
[65] Robertsson J.O.A., Blanch J.O., and Symes W.W. Viscoelastic finite difference modeling[J]. Geophysics. 1994, 59(9): 1444-1456.
[66] Robertsson J.O.A. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography[J]. Geophysics. 1996, 61(6): 1921-1934.
[67] Graves R.W. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite-difference[J]. Bulletin of the Seismological Society of America. 1996, 86(4): 1091-1106.
[68]侯安宁, and何樵登.各向异性介质中弹性波动方程高阶差分及其稳定性研究[J].地球物理学报. 1995, 38(4): 519-527.
[69]裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分数值模拟[J].中国石油大学学报(自然科学版). 2004, 30(2): 608-615.
[70]裴正林.层状各向异性介质中横波分裂和再分裂数值模拟[J].石油地球物理勘探. 2006, 41(1): 17-25.
[71]裴正林.三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报(自然科学版). 2006, 30(2): 608-615.
[72] Dai N., Vafidis A., and Kamasewich E.R. Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method[J]. Geophysics. 1995, 60(2): 327-340.
[73] Ozdenvar T., and McMechan G. Algorithms for staggered-grid computations for poroelastic, elastic, acoustic, and scalar wave equation[J]. Geophysical Prospecting. 1997, 45(3): 403-420.
[74] Carcione J.M., and Helle H.B. Numerical solution of the poro viscoelastic wave equation on a staggered mesh[J]. Journal of computational physics. 1999, 154(2): 520-527.
[75]杨宽德,杨顶辉, and王书强.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探. 2002, 37(5): 463-468.
[76]孟庆生.基于BISQ机制双相裂隙介质弹性波场正演及其方位属性研究[D].吉林大学, 2003.
[77] Wang Z., He Q., and Wang D. The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model[J]. Applied Geophysics. 2008, 5(1): 24-34.
[78] Hestholm S.O., and Ruud B.O. 2D finite difference elastic wave modeling including surface topography[J]. Geophysical Prospecting. 1994, 42(5): 371-390.
[79] Tessmer E., and Kosloff D. 3D elastic modeling with surface topography by a chebychev spectral method[J]. Geophysics. 1994, 59(3): 464-473.
[80] Aleixo R., and Schleicher J. Traveltime approximations for qP waves in vertical transversely isotropic media[J]. Geophysical Prospecting. 2009: 1-11.
[81] Alkhalifah T., and Larner K. Migration error in transversely isotropic media[J]. Geophysics. 1994, 59(9): 1405-1418.
[82] Vestrum R.W., Lawton D.C., and Schmid R. Imaging structures below dipping TI media[J]. Geophysics. 1999, 64(4): 1239-1246.
[83] Mukherjee A., Sen M.K., and Stoffa P.L. Traveltime computation, pre-stack split step Fourier and Kirchhoff migration in transversely isotropic media[C]. 71st SEG annual meeting. San Antonio, USA. 2001,20:1093-1096
[84] Tsvankin I., and Thomsen L. Nonhyperbolic reflection moveout in anisotropic media[J]. Geophysics. 1994, 59(8): 1290–1304.
[85] Alkhalifah T., and Tsvankin I. Velocity analysis for transversely isotropic media[J]. Geophysics. 1995, 60: 1550–1566.
[86] Fomel S. Time migration velocity analysis by velocity continuation.[J]. Geophysics. 2003, 68: 1662–1672.
[87] Fomel S. Method of velocity continuation in the problem of seismic time migration[J]. Russian Geology and Geophysics. 1994, 35(5): 100-111.
[88] Hubral P., Tygel M., and Schleicher J. Seismic image waves[J]. Geophysicsl Journal International. 1996, 125: 431-442.
[89] Schleicher J., and Aleixo R. Time and depth remigration in elliptically anisotropic media[J]. Geophysics. 2007, 72(1): S1-S9.
[90] Dix C.H. Seismic velocities from surfaces measurements[J]. Geophysics. 1955, 20(1): 68–86.
[91] Thore P.D., de Bazelaire E., and Ray M.P. The three-parameter equation: an efficient tool to enhance the stack[J]. Geophysics. 1994, 59(2): 297-308.
[92] Alkhalifah T., Tsvankin I., and K.L.E.A. Velocity analysis and imaging in transversely isotropic media: Methodology and a case study[J]. The Leading Edge. 1996, 15(5): 371-378.
[93] Toldi J., Alkhalifah T., and Berthet P., et al. Case study of estimation of anisotropy[J]. The Leading Edge. 1999, 18(5): 588-593.
[94] Bolshix C.F. Approximate model for the reflected wave traveltime curve in multilayered media[J]. Applied Geophysics. 1956, 15: 3-14. (in Russian).
[95] Taner M.T., and Koehler F. Velocity spectra-digital computer derivation and applications of velocity functions[J]. Geophysics. 1969, 34: 859–881.
[96] May B.T., and Straley D.K. Higher-order moveout spectra[J]. Geophysics. 1979, 44(7): 1193-1207.
[97] Grechka V., and Tsvankin I. Feasibility of nonhyperbolic moveout inversion in transversely isotropic media[J]. Geophysics. 1998, 63(3): 957-969.
[98] Zhang F., and Uren N. Approximate explicit ray velocity functions and travel times for P-waves in TI media[C]. 71st SEG Meeting. San Antonio , Texas , USA. 2001,:106–109
[99] van der Baan M., and Kendall J.-. Estimating anisotropy parameters and traveltimes in the tau-p domain[J]. Geophysics. 2002, 67(4): 1076-1086.
[100] Stovas A., and Ursin B. New travel-time approximations for a transversely isotropic medium[J]. Journal of Geophysics and Engineering. 2004, 1: 128–133.
[101] Alkhalifah T. Velocity analysis using nonhyperbolic moveout in transversely isoropic media[J]. Geophysics. 1997, 62(6): 1839-1854.
[102] Guerrero C., Wookey J., and van der Baan M., et al. VTI anisotropy parameter estimation in the tau-p domain: An example from the North Sea[C]. 72nd SEG annual meeting. San Antonio, USA. 2002,21:137-140
[103] Malovichko A.A. A new representation of the traveltime curve of reflected waves in horizontally layered media[J]. Applied Geophysics. 1978: 47–53. (in Russian).
[104] Claerbout J.F. Datum shift and velocity estimation[R]. , 1987.
[105] de Bazelaire E. Normal moveout revisited: Inhomogeneous media and curved interfaces[J]. Geophysics. 1988, 53(2): 143–157.
[106] Castle R. A theory of normal moveout[J]. Geophysics. 1994, 59(6): 983–999.
[107] Siliqi R., and Bousquie N. Anelliptic time processing based on a shifted hyperbola approach[C]. 70th SEG Meeting. Calgary. 2000,:2245–2248
[108] Ursin B., and Stovas A. Traveltime approximations for a layered transversely isotropic medium[J]. Geophysics. 2006, 71(2): D23–D33.
[109] Fomel S. On anelliptic approximations for qP velocities in VTI media[J]. Geophysical Prospecting. 2004, 52: 247–259.
[110] Muir F., and Dellinger J. A practical anisotropic system[R]. , 1985.
[111] Douma H., and Calvert A. Nonhyperbolic moveout analysis in VTI media using rational interpolation[J]. Geophysics. 2006, 71(3): D59-D71.
[112] Li J., and Symes W.W. Interval velocity estimation via NMO-based differential semblance[J]. Geophysics. 2007, 72(6): U75-U88.
[113] Brandsberg-Dahl S., Ursin B., and de Hoop M.V. Seismic velocity analysis in the scattering-angle/azimuth domain[J]. Geophysical Prospecting. 2003, 51(4): 95-314.
[114] Shen P., Symes W.W., and Stolk C.C. Differential semblance velocity analysis by wave-equation migration[C]. 73rd SEG annual meeting. Dallas, USA. 2003,22:2132-2135
[115] Shen P., and Symes W.W. Automatic velocity analysis via shot profile migration[J]. Geophysics. 2008, 73(5): VE49-VE59.
[116] Khoury A., and Symes W. DSR Migration velocity analysis by differential semblance optimization[C]. SEG annual meeting. New Orleans, USA. 2006,25:2450-2454
[117] Symes W.W. Migration velocity analysis and waveform inversion[J]. Geophysical Prospecting. 2008, 56(6): 765-790.
[118] Plessix R.-. Automatic cross-well tomography: an application of the differential semblance optimization to two real examples[J]. Geophysical Prospecting. 2000, 48(5): 937-951.
[119] Plessix R.-., Kroode F.T., and Mulder W. Automatic crosswell tomography by differential semblance optimization[C]. 70th SEG annual meeting. Calgary, Canada. 2000,:2265-2268
[120] Plessix R.-., Mulder W.A., and Kroode A.P.E.T. Automatic cross-well tomography by semblance and differential semblance optimization: theory and gradient computation[J]. Geophysical Prospecting. 2001, 48(5): 913-935.
[121] Chauris H., and Noble M. Two‐dimensional velocity macro model estimation from seismic reflection data by local differential semblance optimization: applications to synthetic and real data sets[J]. Geophysical Journal International. 2001, 144(1): 14-26.
[122] Foss S.K., Ursin B., and Sollid A. A practical approach to PP seismic angle tomography[J]. Geophysical Prospecting. 2004, 52(6): 663-669.
[123] Sun D., and Symes W.W. A nonlinear differential semblance strategy for waveform inversion: Experiments in layered media[C]. SEG annual meeting. Houston, USA. 2009,:2526-2530
[124] Gao F., and Symes W. Differential semblance velocity analysis by reverse time migration: Image gathers and theory[C]. SEG annual meeting. Houston, USA. 2009,28:2317-2321
[125] Symes W.W. High frequency asymptotics, differential semblance, and velocity estimation[C]. 68th SEG annual meeting. New Orleans, USA. 1998,17:1616-1619
[126] Symes W.W. All stationary points of differential semblance are asymptotic global minimizers: layered acoustics[R]. Department of Computational and Applied Mathematics, Rice University, 1999.
[127] Li J., and Symes W.W. Fast interval velocity estimation via NMO-based differential semblance[C]. 75th SEG annual meeting. Houston, USA. 2005,:2265-2268
[128] Verm R.W., and Symes W.W. Practice and pitfalls in NMO-based differential semblance velocity analysis[C]. SEG annual meeting. New Orleans, USA. 2006,25:2112-2116
[129] Helbig K. Systematic classification of layer-induced transverse isotropy[J]. Geophysical Prospecting. 1981, 29(4): 550-577.
[130] Suchy K. Ray tracing in anisotropic absorbing medium[J]. Journal of Plasma Physics. 1972, 8(1): 53-65.
[131] Cerveny V. Seismic rays and ray intensities in inhomogeneous anisotropic media[J]. Geophysical Journal of the Royal Astronomical Society. 1972, 1972(1): 1-13.
[132] Cerveny V., Molotkov I.A., and Psencik I. Ray method in seismology[M]. Praha: Univerzita Karlova, 1977.
[133] Jech J. Computation of rays in an inhomogeneous transversely isotropic medium with a nonvertical axis of symmetry[J]. studia geophysica et geodaetica. 1983, 27(2): 114-121.
[134] Petrashen G.I., and Kashtan B.M. Theory of body-wave propagation in inhomogeneous anisotropic media[J]. Geophysical Journal of the Royal Astronomical Society. 1984, 76(1): 29-39.
[135] Cerveny V., and Psencik I. Gaussian beams in elastic 2-D laterally varying layered structures[J]. Geophysical Journal of the Royal Astronomical Society. 1984, 78(1): 65-91.
[136] Gajewski D., and Psencik I. Computation of high-frequency seismic wavefields in 3-D laterally inhomogeneous anisotropic media[J]. Geophysical Journal of the Royal Astronomical Society. 1987, 91(2): 383-411.
[137] Mochizuki E. Ray tracing of body waves in an anisotropic medium[J]. Geophysical Journal of the Royal Astronomical Society. 1987, 90(3): 627-634.
[138] Shearer P.M., and Chapman C.H. Ray tracing in azimuthally anisotropic media—I. Results for models of aligned cracks in the upper crust[J]. Geophysical Journal International. 1989, 96(1): 51-64.
[139] Gajewski D., and Psencik I. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures[J]. Geophysical Journal of the Royal Astronomical Society. 1990, 95(B7): 11301-11315.
[140] Gajewski D., and Psencik I. Vector wavefields for weakly attenuating anisotropic media by the ray method[J]. Geophysics. 1992, 57(1): 27-38.
[141] Farra V., and Begat S.L. Sensitivity of qP-wave traveltimes and polarization vectors to heterogeneity, anisotropy and interfaces[J]. Geophysical Journal International. 1995, 121(2): 371-384.
[142] Mensch T., and Farra V. Computation of qP-wave rays, traveltimes and slowness vectors in orthorhombic media[J]. Geophysical Journal International. 1999, 138(1): 244-256.
[143] Cerveny V. Seismic Ray Theory[M]. Cambridge: Cambridge University Press, 2001.
[144] Vavrycuk V. Ray tracing in anisotropic media with singularities[J]. Geophysical Journal International. 2001, 145(1): 265-276.
[145] Cardarelli E., and Cerreto A. Ray tracing in elliptical anisotropic media using the linear traveltime interpolation(LTI) method applied to traveltime seismic tomography[J]. Geophysical Prospecting. 2002, 50(1): 55-72.
[146] Dickens T.A. Ray tracing in tilted transversely isotropic media: a group velocity approach[C]. 74th SEG annual meeting. Denver, USA. 2004,23:973-976
[147] Iversion E. REFORMULATED KINEMATIC AND DYNAMIC RAY TRACING SYSTEMS FOR ARBITRARILY ANISOTROPIC MEDIA[J]. Studia Geophysica et Geodaetica. 2004, 48(1): 1-20.
[148] Bansal B., and Mrinal K.S. 3-D Two-point ray tracing in general anisotropic media[C]. 75th SEG annual meeting. Houston, USA. 2005,24:190-194
[149] Rogister Y., and Slawinski M.A. Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model[J]. Geophysics. 2005, 70(5): D37-D41.
[150] Psencik I., and Farra V. First-order ray tracing for qP waves in inhomogeneous, weakly anisotropic media[J]. Geophysics. 2005, 70(6): D65-D75.
[151] Farra V. First-order ray tracing for qS waves in inhomogeneous weakly anisotropic media[J]. Geophysical Journal International. 2005, 161(2): 309-324.
[152] Klimes L. Common-Ray tracing and dynamic ray tracing for s waves in a smooth elastic anisotropic medium[J]. Studia Geophysica et Geodaetica. 2006, 50(3): 449-461.
[153] Zhou B., and Greenhalgh S. Raypath and traveltime computations for 2D transversely isotropic media with dipping symmetry axes[J]. Exploration Geophysics. 2006, 37(2): 150-159.
[154] Dehghan K., Farra V., and Nicoletis L. Approximate ray-tracing for qP waves in weakly VTI media[C]. 76th SEG annual meeting. New Orleans. 2006,25:2221-2225
[155] Dehghan K., Farra V., and Nicoletis L. Approximate ray tracing for qP-waves in inhomogeneous layered media with weak structural anisotropy[J]. Geophysics. 2007, 72(5): SM47-SM60.
[156] Cores D., and Loreto M.C. A generalized two point ellipsoidal anisotropic ray tracing for converted waves[J]. Optimization and Engineering. 2007, 8(4): 373-396.
[157] Cerveny V. A NOTE ON DYNAMIC RAY TRACING IN RAY-CENTERED COORDINATES IN ANISOTROPIC INHOMOGENEOUS MEDIA[J]. Studia Geophysica et Geodaetica. 2007, 51(3): 1573-1626.
[158]常旭, and刘伊克.地震正反演与成像[M].北京:华文出版社, 2001.
[159]杨文采.应用地震层析成像[M].北京:地质出版社, 1993.
[160] Clayton R.W. Seismic tomography(abstract)[J]. Eos Trans. Am. Geophys. Union. 1984, 65: 236.
[161] Dziewonski A.M., and Gilber F. The effect of smal aspherical perturbations on travel time and re-examination of the corrections for ellipticity[J]. Geophysical Journal of Royal Astronomy Society. 1976, 44: 7-17.
[162] Tanimoto T., and Anderson D.L. Mapping convection in the mantle[J]. Geophysical Research Letter. 1984, 11(4): 287-290.
[163] Woodhouse J.H., and Dzeiwonski A.M. Mapping the upper mantle: Three-Dimensional modeling of earth structure by inversion of seismic waveform[J]. Journal of Geophysical Research. 1984, 89: 5953-5986.
[164] Anderson D.I., and Dziewonski A.M. Seismic tomography[J]. Scientific American. 1984, 251(4): 58-66.
[165] Dziewonski A.M., and Anderson D.L. Seismic tomography of the Earth interior[J]. American Scientist. 1984, 721: 483-494.
[166] Dziewonski A.M. Mapping the lower mantle: determination of lateral heterogneity in P velocity up to degree and order 6[J]. Journal of Geophysical Research. 1984, 89: 5929-5952.
[167] Tanimoto T., and Anderson D.L. Later heterogeneity and azimuthal anisotropy of the upper mantle: Love and Rayleigh waves 100-250s[J]. Journal of Geophysical Research. 1985, 90(2): 1842-1858.
[168] Woodhouse J.H., and Masters G. Global upper mantle strcture from loong-period differential travel times[J]. Journal of Geophysical Research. 1991, 96: 6351-6377.
[169] Woodhouse J.H., and Masters G. Upper mantle strcture from long-period differential traveltime and free oscillation data[J]. Geophysical Journal International. 1992, 109: 275-293.
[170] Clayton R.W., and Comer R. A tomographic analysis of mantle heterogeneities from body wave travel time(abstract)[J]. Eos, Transactions, American Geophysical Union. 1983, 64(45): 776.
[171] Hager B.H., Clayton R.W., and M.A.R.E.A. Lower mantle heterogeneity, dynamic topography and the geoid[J]. Nature. 1985, 313: 541-545.
[172] Tanimoto T. Long-wavelength S-wave velocity strcture throughout the mantle[J]. Geophysical Journal International. 1990, 100: 327-336.
[173] Inoue H., Fukao Y., and K.T.E.A. Whole mantle P-wave travel time tomography[J]. Physics of the Earth and Planetary Interiors. 1990, 59: 294-328.
[174] Fukao Y., Obayashi M., and H.I.E.A. Subducting slabs stagnant in the mantle transition zone[J]. Journal of Geophysical Research. 1992, 97(4): 809-822.
[175] Su W., Woodward R.L., and Dziewonski A.M. Degree 12 model of shear velocity heterogeneity in the mantle[J]. Journal of Geophysical Research. 1994, 99: 6945-6980.
[176] Vasco D.W., Johnson L.R., and Pullian R.J. Lateral variations in mantle velocity strcture and discontinuities determined from P, PP, S, SS, and SS-Sds travel time residuals[J]. Journal of Geophysical Research. 1995, 100(24): 24037-24059.
[177] Masters G., Jonhnson S., and G.L.E.A. A shear-velocity model of the mantle[J]. Phios. Trans. R. Soc. London Ser. A. 1996, 354: 1385-1411.
[178] Vasco D.W., and Johnson L.R. Whole earth strcture estimated from seismic arrival times[J]. Journal of Geophysical Research. 1998, 103: 2633-2671.
[179] Ristema J., van Heijst H.J., and Woodhouse J.H. Complex shear wave velocity strcture imaged beneath Africa and Iceland[J]. Science. 1999, 286: 1925-1928.
[180] Goes G., Spakman W., and Bijwaard H. A low source for central European volcanism[J]. Science. 1999, 283: 1928-1932.
[181] Tanimoto T. Mantle dynamics and seismic tomography[J]. Proceedings of the National Academy of Sciences of the United States of America. 2000, 97(23): 12409-12410.
[182] Zhao D., Maruyama S., and Omori S. Mantle dynamics of Western Pacific and East Asia: Insight from seismic tomography and mineral physics[J]. Gondwana research. 2007, 11(1-2): 120-131.
[183] Zhao D. Multiscale seismic tomography and mantle dynamics[J]. Gondwana Research. 2009, 15(3-4): 297-323.
[184] Achauer U., Evans J.R., and Stauber D.A. High-Resolution Seismic Tomography of Compressional Wave Velocity Structure at Newberry Volcano, Oregon Cascade Range[J]. Journal of Geophysical Research. 1988,93(B9): 10,135–10,147.
[185] Aloisi M., Cocina O., and G.N.E.A. Seismic tomography of the crust underneath the Etna volcano, Sicily[J]. Physics of the Earth and Planetary Interiors. 2002, 134(3): 139-155.
[186] Finlayson D.M., Gudmundsson O., and I.I.E.A. Rabaul volcano, Papua New Guinea: seismic tomographic imaging of an active caldera[J]. Journal of Volcanology and Geothermal Research. 2003, 124(3-4): 153-171.
[187] Rowlands D.P., White R.S., and Haines A.J. Seismic tomography of the Tongariro Volcanic Centre, New Zealand[J]. Geophysical Journal International. 2005, 163(3): 1180-1194.
[188] Lou H., Wang C., and Huangfu G. Three-dimensional seismic velocity tomography of the upper crust in Tengchong volcanic area, Yunnan Province[J]. Acta Seismologica Sinica. 2007, 15(3): 260-268.
[189] Aki K., and Lee W.H.K. Determination of three-dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes[J]. Journal of Geophysical Research. 1976, 81(B23): 4381-4399.
[190] Aki K., Christoffersson A., and Husebye E.S. Determination of the three-dimensional seismic structure of the lithosphere[J]. Journal of Geophysical Research. 1977, 82(B2): 277-296.
[191] Dziewonski A.M., and Gilbert F. The effect of small asphericial perturbations on travel times and a reexamination of the correction of ellipticity[J]. Geophysical Journal of the Royal Astronomical Society. 1976, 44: 7-17.
[192] Papazachos C.B. Crustal P- and S-velocity structure of the Serbomacedonian Massif (Northern Greece) obtained by non-linear inversion of traveltimes[J]. Geophysical Journal International. 2002, 134(1): 25-39.
[193] Godey S., Snieder R., and A.V.E.A. Surface wave tomography of North America and the Caribbean using global and regional broad-band networks: phase velocity maps and limitations of ray theory[J]. Geophysical Journal International. 2003, 152(3): 620-632.
[194] Paulatto M., Minshull T.A., and B.B.E.A. Upper crustal structure of an active volcano from refraction/reflection tomography, Montserrat, Lesser Antilles[J]. Geophysical Journal International. 2009, 180(2): 685-696.
[195] Arroyo G., Husen S., and E.R.F.E.A. Three-dimensional P-wave velocity structure on the shallow part of the Central Costa Rican Pacific margin from local earthquake tomography using off- and onshore networks[J]. Geophysical Journal International. 2009, 179(2): 827-849.
[196] Jech J., and Cerveny V. Iterative geophysical tomography[J]. Studia Geophysica et Geodaetica. 1986, 30(3): 242-256.
[197] Carrion P. Dual tomography for imaging complex structures[J]. Geophysics. 1991, 56(9): 1395-1404.
[198] Sheng J., and Schuster G.T. Finite-frequency resolution limits of wave path traveltime tomography for smoothly varying velocity models[J]. Geophysical Journal International. 2003, 152(3): 669-676.
[199] Sekiguchi S. Hierarchical traveltime tomography[J]. Geophysical Journal International. 2006, 166(3): 1105-1124.
[200] Koren Z., and Ravve I. Curved rays anisotropic tomography: Local and global approaches[C]. 76th SEG annual meeting. New Orleans, USA. 2006,:3373-3377
[201] Benxi K., Zhang J., and Baofu C. Fat-ray first-arrival seismic tomography and its application[C]. 77th SEG annual meeting. San antonio, USA. 2007,26:2822-2826
[202] Santos V.G.B.D. Seismic-ray reflection tomography using integral function norm[C]. 77th SEG annual meeting. San Antonio, USA. 2007,26:1888-1892
[203] Adler F., Baina R., and M.A.S.E.A. Nonlinear 3D tomographic least-squares inversion of residual moveout in Kirchhoff prestack-depth-migration common-image gathers[J]. Geophysics. 2008, 73(5): VE13-VE23.
[204] Denli H., and Huang L. Double-difference elastic waveform tomography in the time domain[C]. 79th SEG annual meeting. Houston, USA. 2009,28
[205] Wang X., and Tsvankin I. Stacking-velocity tomography with borehole constraints for tilted TI media[C]. 79th SEG annual meeting. Houston, USA. 2009,28:2352-2356
[206] Meng Z., and Peng C. Non-hyperbolic reflection tomography for better imaging and interpretation[C]. 79th SEG annual meeting. Houston, USA. 2009,28:3665-3669
[207] Bakulin A., Woodward M., and Nichols D. Localized anisotropic tomography with well information in VTI media[C]. 79th SEG annual meeting. Houston, USA. 2009,28:221-225
[208] Billette F., Lambare G., and Podvin P. Velocity macromodel estimation by stereotomography[C]. 67th SEG annual meeting. New Frontiers, USA. 1997,16:1889-1892
[209] Billette F., Podvin P., and Lambare G. Stereotomography with automatic picking: Application to the Marmousi dataset[C]. 68th SEG annual meeting. New Orleans, USA. 1998,17:1317-1320
[210] Lambare G., Alerini M., and R.B.E.A. Stereotomography : A fast approach for velocity macro-model estimation[C]. 73th SEG annual meeting. 2003,23:2076-2079
[211] Lavaud B., Baina R., and Landa E. Automatic robust velocity estimation by poststack Stereotomography[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2351-2354
[212] Lambare G. Stereotomography: past, present and future[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2367-2370
[213] Lambare G., Alerini M., and Podvin P. Stereotomographic picking in practice[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2343-2346
[214] Nag S., Alerini M., and E.D.E.A. 2D stereotomography for anisotropic media[C]. 76th SEG annual meeting. New Orleans, USA. 2006,25:3305-3309
[215] Neckludov D., Baina R., and Landa E. Residual stereotomographic inversion[J]. Geophysics. 2006, 71(4): E35-E39.
[216] Lambare G. Stereotomography[J]. Geophysics. 2008, 73(5): VE25-VE34.
[217] Gao F., and A.L.E.A. Velocity analysis by waveform tomography: A few examples[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2371-2374
[218] Rao Y., Wang Y., and Morgan J.V. Crosshole seismic waveform tomography– II. Resolution analysis[J]. Geophysical Journal International. 2006, 166(3): 1237-1248.
[219] de Hoop M., van H.R., and Shen P. Multi-scale aspects of wave-equation reflection tomography[C]. 76th SEG annual meeting. New Orleans, USA. 2006,25:3378-3382
[220] de Hoop M., van der Hilst R.D., and Shen P. Wave-equation reflection tomography: annihilators and sensitivity kernels[J]. Geophysical Journal International. 2006, 167(3): 1332-1352.
[221] Long M.D., de Hoop M.V., and van der Hilst R.D. Wave-equation shear wave splitting tomography[J]. Geophysical Journal International. 2008, 172(1): 311-330.
[222] Barnes C., Charara M., and Tsuchiya T. Feasibility study for an anisotropic full waveform inversion of cross-well seismic data[J]. Geophysical Prospecting. 2008, 56(6): 897-906.
[223] Shin C., and Cha Y.H. Waveform inversion in the Laplace domain[J]. Geophysical Journal International. 2008, 173(3): 922-931.
[224] Boonyasiriwat C., Valasek P., and P.R.E.A. An efficient multiscale method for time-domain waveform tomography[J]. Geophysics. 2009, 74(6): WCC59-WCC68.
[225] Virieux J., and Operto S. An overview of full-waveform inversion in exploration geophysics[J]. Geophysics. 2009, 74(6): WCC1-WCC26.
[226] Zhang Y., and Wang D. Traveltime information-based wave-equation inversion[J]. Geophysics. 2009, 74(6): WCC27-WCC36.
[227] Burstedde C., and Ghattas O. Algorithmic strategies for full waveform inversion: 1D experiments[J].Geophysics. 2009, 74(6): WCC37-WCC46.
[228] Abubakar A., Hu W., and T.M.H.E.A. Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data[J]. Geophysics. 2009, 74(6): WCC47-WCC58.
[229] Yang Y., Li Y., and Liu T. 1D viscoelastic waveform inversion for Q structures from the surface seismic and zero-offset VSP data[J]. Geophysics. 2009, 74(6): WCC141-WCC148.
[230] Plessix R.-. Three-dimensional frequency-domain full-waveform inversion with an iterative solver[J]. Geophysics. 2009, 74(6): WCC149-WCC157.
[231] Krebs J.R., Anderson J.E., and Hinkley D. Fast full-wavefield seismic inversion using encoded sources[J]. Geophysics. 2009, 74(6): WCC177-WCC188.
[232] Tarantola A. Inverse problem theory and methods for model parameter estimation[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2005.
[233] Bube K.P., and Langan R.T. Hybrid L1/L2 data minimization with applications to tomography[J]. Geophysics. 1997, 62(4): 1183-1195.
[234] Bube K.P., and Nemeth T. Fast line searches for the robust solution of linear systems in the hybrid L1/L2 and Huber norms[J]. Geophysics. 2007, 72(2): A13-A17.
[235]刘海飞,阮百尧, and柳建新等.混合范数下的最优化反演方法[J].地球物理学报. 2007, 50(6): 1877-1883.
[236] Bertero M. Regularization methods for linear inverse problems[M]. Heidelberg: Springer Berlin, 1986.
[237] Fomel S., and Claerbout J.F. Multidimensional recursive filter preconditioning in geophysical estimation problems[J]. Geophysics. 2003, 68(2): 577-588.
[238] Fomel S., and Guitton A. Regularizing seismic inverse problems by model reparameterization using plane-wave construction[J]. Geophysics. 2006, 71(5): A43-A47.
[239] Fomel S. Sharping regularization in geophysical-estimation problems[J]. Geophysics. 2007, 72(2): R29-R36.
[240] Berryman V. Exact seismic velocities for transversely isotropic media and extended Thomsen formulas for stronger anisotropies[J]. Geophysics. 2009, 73(1): D1-D10.
[241] Cerveny V., and Psencik I. Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media[J]. Geophysical Journal International. 2008, 172(2): 663-673.
[242] Abbad B., Ursin B., and Rappin D. Automatic nonhyperbolic velocity analysis[J]. Geophysics. 2009, 74(2): U1-U12.
[243] Zelt C., and Ellis R.M. Practical and efficient ray tracing in two-dimensional media for rapid traveltime and amplitude forward modelling[J]. Canadian Journal of Exploration Geophysics. 1988, 24(1): 16-31.
[244] Crampin S. Suggestios for a consistent terminology for seismic anisotropy[J]. Geophysical Prospecting. 1989, 37(7): 753-770.
[245] Tsvankin I. Seismic Signatures and analysis of reflection data in anisotropic media[M]. New York: Elsevier Science Publication Corporation, 2001.
[246] Zhu Y., and Tsvankin I. Plane-wave propagation in attenuation transversely isotropic media[J]. Geophysics. 2006, 71(2): T17-T30.
[247] Cerveny V., and Psencik I. Plane waves in viscoelastic anisotropic media I: Theory[J]. Geophysical Journal International. 2005, 161(1): 197-212.
[248] Cerveny V., and Psencik I. Plane waves in viscoelastic anisotropic media II: Numerical examples[J]. Geophysical Journal International. 2005, 161(1): 213-229.
[249] Zhu Y., and Tsvankin I. Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media[J]. Geophysics. 2007, 72(1): D1-D7.
[250] Fomel S., and Stovas A. Generalized non-hyperbolic moveout approximation[C]. 69th EAGE meeting.London, UK. 2007,:B041
[251] Siliqi R., and Meur D.L. How to estimate uncorrelated dense V-ηfields?[C]. 66th EAGE Conference and Exhibition. Paris, France. 2004,
[252]王永刚,乐喜友, and张军华.地震属性分析技术[M].北京:石油大学出版社, 2007.
[253] Starck J.L., EJCandès, and Donoho D.L. The curvelet transform for image denoising[J]. IEEE Transactions on Image Processing. 2000, 11(6): 670-684.
[254] Symes W.W., and Carazzone J.J. Velocity inversion by differential semblance optimization[J]. Geophysics. 1991, 56(5): 654-663.
[255] Symes W.W. A differential semblance algorithm for the inverse problem of reflection seismology[J]. Computers & Mathematics with Applications. 1991, 22(4-5): 147-178.
[256] Symes W.W., and Kern M. Velocity inversion by differential semblance optimization for 2-D common source data[C]. 62nd SEG annual meeting. New Orleans, USA. 1992,11:1210-1213
[257] Symes W.W., and Versteeg R. Velocity model determination using differential semblance optimization[C]. 63rd SEG Annual Meeting. Washinton, USA. 1993,12:696-699
[258] Symes W.W., and Kern M. Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples[J]. Geophysical Prospecting. 1994, 42(6): 565-614.
[259] Mulder W.A., and Kroode A.P.E.T. Automatic velocity analysis by differential semblance optimization[C]. 71st SEG annual meeting. San Antonio, USA. 2001,20:893-896
[260] Zhou B., and Greenhalgh S. Non-linear traveltime inversion for 3-D seismic tomography in strongly anisotropic media[J]. Geophysical Journal International. 2008, 172(1): 383-394.
[261] Langan R.T., Lerche T., and Cutler R.T. Tracing of rays through heterogeneous media, An accurate and efficient procedure[J]. Geophysics. 1985, 50(9): 1456-1465.
[262] Moser T.J. Shortest path calculation of seismic rays[J]. Geophysics. 1991, 56(1): 59-67.
[263] Xu T., and Xu G.M. Block modeling and segmentally iterative ray tracing in complex 3D media[J]. Geophysics. 2006, 71(3): T41-T51.
[264] Zelt C., and Smith R.B. Seismic traveltime inversion for 2-D crustal velocity structure[J]. Geophysical Journal International. 1992, 108(1): 16-34.
[265] GuiZiou J.L., Mallet J.L., and Madariaga R. 3D seismic reflection tomography on top of the GOCAD depth modeler[J]. Geophysics. 1996, 61(5): 1499-1510.
[266] Mao W.J., and Stuart W. Rapid multiwave-type ray tracing in complex 2D and 3D isotropic media[J]. Geophysics. 1997, 62(1): 298-308.
[267] Rawlinson N., Houseman G.A., and Collins C.D.N. Inversion of seismic refraction and wide-angle reflection traveltimes for threedimensional layered crustal structure[J]. Geophysical Journal International. 2001, 145(2): 381-400.
[268]徐果明,卫山, and高尔根等.二维复杂介质的块状建模及射线追踪[J].石油地球物理勘探. 2001, 36(2): 213-219.
[269]徐涛,徐果明, and高尔根等.复杂介质的折射波射线追踪[J].石油地球物理勘探. 2005, 39(6): 690-693.
[270]徐涛,徐果明, and高尔根等.三维试射射线追踪子三角形法[J].石油地球物理勘探. 2005, 40(4): 391-399.
[271] Cerveny V. Seismic Ray Theory[M]. Cambridge: Cambridge University Press, 2001.
[272] Press W.H., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in C++: : The Art of Scientific Computing. Second Edition[M]. Cambridge: Cambridge University Press, 2002.
[273]岳玉波,孙建国, and韩复兴.起伏地表下初值射线追踪的实现[J].勘探地球物理进展. 2007, 30(5):388-391.
[274] Paige C.C., and Saunders M.A. LSQR: an algorithm for sparse linear equations and sparse least squares[J]. ACM Transactions Mathematical Software. 1982, 8(1): 43-71.
[275] Paige C.C., and Saunders M.A. Algorithm 583; LSQR: Sparse linear equations and least-squares problems[J]. ACM Transactions Mathematical Software. 1982, 8(2): 195-209.
[276]袁亚湘, and孙文瑜.最优化理论与方法[M].北京:科学出版社, 2005.
[277] Nocedal J., and Wright S.J. Numerical optimization[M]. New York: Springer-Verlag, 1999.
[2] McGullagh. Geometrical proposition applied to the wave theory of light[J]. The Transactions of the Royal Irish Academy. 1831, 17: 241-263.
[3] Thompson) L.K. On stresses and strains(XXI. Elements of a mathematical theory of elasticity. Part 1)[J]. Philosophical Transactions of The Royal Society. 1856, 166: 481-489.
[4] Christoffel E.B. Uber die Fortpflanzung von Stossen durch elastische feste Korper[J]. Annali di Mathematica. 1877, 8: 193-243.
[5] Rudzki M.P. Uber die Gestalt elastischer Wellen in Gesteinen[J]. Bulletin of the Academy of Science Cracow. 1897: 387-393.
[6] Rudzki M.P. Uber die Gestalt elastischer Wellen in Gesteinen, IV Studie aus der Theorie der Erdbebenwellen[J]. Bulletin of the Academy of Science Cracow. 1898: 373-384.
[7] Rudzki M.P. Parametrische Darstellung der elastischen Welle in anisotropen Medien[J]. Bulletin of the Academy of Science Cracow(A). 1911: 503-536.
[8] Rudzki M.P. Sur la propagation dPune onde elastique superficielle dans un millen transversalement isotrope[J]. Bulletin of the Academy of Science Cracow(IA). 1912: 47-58.
[9] Rudzki M.P. Essai d'application du principe de Fermat aux milieux anisotropes[J]. Bulletin of the Academy of Science Cracow(A). 1913.
[10] Rudzki M.P. Uber die Theorie der Erdebenwellen[J]. Die Naturwissenschaften. 1915, 3: 201-204.
[11] Love A.E.H. A treatise on the mathematical theory of elasticity[M]. Cambridge: Cambridge University Press, 1892.
[12] Bruggeman D.A.G. Berechnung verschiedener physikalischer konstanten von heterogenen substanzen[J]. Annals of Physics. 1935, 24: 636.
[13] Levin F.K. The reflection,refraction,and diffraction of waves in media with an elliptical velocity dependence[J]. Geophysics. 1978, 43(4): 528-537.
[14] Love A.E.H. A Treatise on the Mathematical Theory of Elasticity[M]. Dover: New York, 1944.
[15] Riznichenko Y.V. On seismic quasi anizotropy[J]. Geography and Geophysics. 1949, 6: 518–544.
[16] Stoneley R. The seismological implications of aeolotropy in continental structure[J]. Geophysical Journal International. 1949, 5(8): 343-353.
[17] Postma G.W. Wave propagation in a stratified medium[J]. Geophysics. 1955, 20(4): 780-806.
[18] Krey T., and Helbig K. A theorem concerning anisotropy of stratified media and its significance for reflection seismics[J]. Geophysical Prospecting. 1956, 4(3): 294-302.
[19] Backus G.E. Long-wave elastic anisotropy produced by horizontal layering[J]. Journal of Geophysical Research. 1962, 67(11): 4427-4440.
[20] Jolly R.N. Investigation of shear waves[J]. Geophysics. 1956, 21(4): 905-938.
[21] Nur A., and Simmons G. Stress-induced velocity anisotropy in rock: an experimental study[J]. Journal of Geophysical Research. 1969, 74(27): 6667-6674.
[22] Bachman R.T. Acoustic anisotropy in marine sediments and sedimentary rock[J]. Journal of Geophysical Research. 1979, 84(B13): 7661-7663.
[23] Crampin S., and Bamford D. Estimating crack parameters for observations of P wave velocity anisotropy[J]. Geophysics. 1980, 45(3): 345-360.
[24] Crampin S. A review of wave motion in anisotropic and cracked elastic media[J]. Wave Motion. 1981, 3(4): 343-391.
[25] Crampin S., Chesnokov E.M., and Hipkin R.A. Seismic anisotropy-the state of the art[J]. First Break. 1984, 20: 9-18.
[26] Alford R.M. Shear data in the presence of azimuthal anisotropy[C]. 56th SEG annual meeting. Dilley. 1986,
[27] Lynn H.B., and Thomsen L.A. Reflection shear-wave data along the principal axes of azimuthal anisotropy[C]. 56th SEG annual meeting. Dilley. 1986,
[28] Li X., and Crampin S. Approximations to shear-wave velocity and moveout equations in anisotropic media[J]. Geophysical Prospecting. 1993, 41(7): 833-857.
[29] Hudson J.A. Wave speeds and attenuation of elastic wave in material containing cracks[J]. Geophys.J.R.astr.Soc. 1981, 64(1): 133-150.
[30] Hudson J.A. Overall properties of a cracked solid[J]. Math Proc Camb phil. 1980, 88: 371-384.
[31] Hudson J.A. A higher order approximation to the wave propagation constants for a cracked solid[J]. Geophys J R Astr Soc. 1986, 87: 265-274.
[32] Hudson J.A. Overall properties of anisotropic materials containing cracks[J]. Geophysical Journal International. 1993, 116(2): 279-282.
[33] Thomson L. Elastic anisotropy due to aligned cracks in porous rock[J]. Geophysical Prospecting. 1995, 43(6): 805-829.
[34] Thomsen L. Weak elastic anisotropy[J]. Geophysics. 1986, 51(10): 661-672.
[35] Lysmer J., and Drake L.A. A finite element method for seismology[J]. Methods in Computational Physics. 1972, 11.
[36]杨宝俊, and何樵登.有限元素法的一种频率域计算方法及其应用[J].石油物探. 1982, 21(1): 56-64.
[37] Marfurt K.J. Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations[J]. Geophysics. 1984, 49(5): 533-549.
[38] Seron F.J., Sanz F.J., and Sabadell F.J. A numerical laboratory for simulation and visualization of seismic wavefields[J]. Geophysical Prospecting. 1996, 44(4): 603-642.
[39] Seron F.J., Sanz F.J., and Kindelan M., et al. Finite-element method for elastic wave propagation[J]. Communications in Applied Numerical Methods. 1990, 6(5): 359-368.
[40] Padovani E., and Seriani G. Low- and high-order finite element method: experience in seismic modeling[J]. Journal of Computational Acoustics. 1994, 2(1): 371-422.
[41] Sarma G.S., Mallick K., and Gadhinglajkar V.R. Nonreflecting boundary condition in finite-element formulation for an elastic wave equation[J]. Geophysics. 1998, 63(3): 1006-1023.
[42]牟永光.三维复杂介质地震物理模拟[M].北京:石油工业出版社, 2003.
[43]杨顶辉.孔隙各向异性介质中基于微观流场的BISQ理论[C].中国地球物理学会年刊.北京. 1998,:58-59
[44] Gazdag J. Modeling of the acoustic wave equation with transform method[J]. Geophysics. 1981, 46(6): 854-859.
[45] Reshef M., and Kosloff D. Three-dimensional acoustic modeling by the Fourier method[J]. Geophysics. 1988, 3(9): 1175-1183.
[46] Fornberg B. The pseudospectral method: Comarisons with finite-differences for the elastic wave equations[J]. Geophysics. 1987, 52(4): 483-501.
[47]侯安宁, and何樵登.各向异性介质中弹性波特征的伪谱法模拟研究[J].石油物探. 1995, 34(2): 36-45.
[48]张文生, and何樵登.二维横向各向同性介质的伪谱法正演模拟[J].石油地球物理勘探. 1998, 33(3): 310-319.
[49]傅旦丹, and何樵登.正交各向异性介质地震弹性波场的伪谱法正演模拟[J].石油物探. 2001, 40(3): 8-14.
[50] Pao Y.H., and Varatharajulu V. Huygens principle, radiation conditions, and integral formulas for the scattering of elastic waves[J]. THe Journal of the Acoustical Society of America. 1976.
[51] Bennett C.L., and Mieras H.J. Time domaln integral equation for acoustic scattering from fluid targets[J]. The Journal of the Acoustical Society of America. 1981, 69(5): 1261-1265.
[52] Bouchon M. Diffraction of elastic waves by cracks or cavities using the discrete wavenumber method[J]. Journal of the acoustical society of America. 1987, 81(6): 1871-1876.
[53] Bouchon M., Campillo M., and Gaffet S. A boundary integral equation-discrete wave number representation method to study wave propagation in multilayered media having irregular interfaces[J]. Geophysics. 1989, 54(9): 1134-1140.
[54] Bakamjian B. An efficient method for modeling seismic wave propagation in 3-D[C]. 62th SEG annual meeting. Tulsa. 1992,:1232-1235
[55]符力耘, and牟永光.弹性波边界元法正演模拟[J].地球物理学报. 1994, 37(4): 521-529.
[56]阎贫, and何樵登.二维横向各向同性介质中的格林函数积分法合成记录[J].物化探计算技术. 1995, 17(2): 1-6.
[57] Fu L.Y., Mu Y.G., and Yang H.J. Forward problem of nonlinear Fredholm integral equation in reference medium via velocity-weighted wavefield function[J]. Geophysics. 1997, 62(2): 650-656.
[58] Fu L.Y. Numerical study of generalized Lippmann-Schwinger integral equation including surface topography[J]. Geophysics. 2003, 68(2): 665-671.
[59] Dablain M.A. The application of higher order fifferencing to the scalar wave equation[J]. Geophysics. 1986, 51(1): 54-66.
[60] Virieux J. SH wave propagation in heterogeneous media: velocity-stress finite difference method[J]. Geophysics. 1984, 49(11): 1933-1957.
[61] Virieux J. P-SV wave propagation in heterogeneous media: velocity-stress finite-difference method[J]. Geophysics. 1986, 51(4): 889-901.
[62] Igel H., Mora P., and Riollet B. Anisotropic wave propagation through finite difference grids[J]. Geophysics. 1995, 60(4): 1203-1216.
[63] Dong Z., and McMechan G.A. 3-D viscoelastic anisotropic modeling of data from multi-component, multi-azimuth experiment in northeast Texas[J]. Geophysics. 1995, 60(4): 1128-1150.
[64] Ramos-Martinez J., Ortega A.A., and McMechan G.A. Shear-wave splitting at vertical incidence in media containing intersecting fracture systems[C]. 68th SEG annual meeting. New Orleans. 1998,:960-963
[65] Robertsson J.O.A., Blanch J.O., and Symes W.W. Viscoelastic finite difference modeling[J]. Geophysics. 1994, 59(9): 1444-1456.
[66] Robertsson J.O.A. A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography[J]. Geophysics. 1996, 61(6): 1921-1934.
[67] Graves R.W. Simulating seismic wave propagation in 3D elastic media using staggered-grid finite-difference[J]. Bulletin of the Seismological Society of America. 1996, 86(4): 1091-1106.
[68]侯安宁, and何樵登.各向异性介质中弹性波动方程高阶差分及其稳定性研究[J].地球物理学报. 1995, 38(4): 519-527.
[69]裴正林.三维各向异性介质中弹性波方程交错网格高阶有限差分数值模拟[J].中国石油大学学报(自然科学版). 2004, 30(2): 608-615.
[70]裴正林.层状各向异性介质中横波分裂和再分裂数值模拟[J].石油地球物理勘探. 2006, 41(1): 17-25.
[71]裴正林.三维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报(自然科学版). 2006, 30(2): 608-615.
[72] Dai N., Vafidis A., and Kamasewich E.R. Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method[J]. Geophysics. 1995, 60(2): 327-340.
[73] Ozdenvar T., and McMechan G. Algorithms for staggered-grid computations for poroelastic, elastic, acoustic, and scalar wave equation[J]. Geophysical Prospecting. 1997, 45(3): 403-420.
[74] Carcione J.M., and Helle H.B. Numerical solution of the poro viscoelastic wave equation on a staggered mesh[J]. Journal of computational physics. 1999, 154(2): 520-527.
[75]杨宽德,杨顶辉, and王书强.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探. 2002, 37(5): 463-468.
[76]孟庆生.基于BISQ机制双相裂隙介质弹性波场正演及其方位属性研究[D].吉林大学, 2003.
[77] Wang Z., He Q., and Wang D. The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model[J]. Applied Geophysics. 2008, 5(1): 24-34.
[78] Hestholm S.O., and Ruud B.O. 2D finite difference elastic wave modeling including surface topography[J]. Geophysical Prospecting. 1994, 42(5): 371-390.
[79] Tessmer E., and Kosloff D. 3D elastic modeling with surface topography by a chebychev spectral method[J]. Geophysics. 1994, 59(3): 464-473.
[80] Aleixo R., and Schleicher J. Traveltime approximations for qP waves in vertical transversely isotropic media[J]. Geophysical Prospecting. 2009: 1-11.
[81] Alkhalifah T., and Larner K. Migration error in transversely isotropic media[J]. Geophysics. 1994, 59(9): 1405-1418.
[82] Vestrum R.W., Lawton D.C., and Schmid R. Imaging structures below dipping TI media[J]. Geophysics. 1999, 64(4): 1239-1246.
[83] Mukherjee A., Sen M.K., and Stoffa P.L. Traveltime computation, pre-stack split step Fourier and Kirchhoff migration in transversely isotropic media[C]. 71st SEG annual meeting. San Antonio, USA. 2001,20:1093-1096
[84] Tsvankin I., and Thomsen L. Nonhyperbolic reflection moveout in anisotropic media[J]. Geophysics. 1994, 59(8): 1290–1304.
[85] Alkhalifah T., and Tsvankin I. Velocity analysis for transversely isotropic media[J]. Geophysics. 1995, 60: 1550–1566.
[86] Fomel S. Time migration velocity analysis by velocity continuation.[J]. Geophysics. 2003, 68: 1662–1672.
[87] Fomel S. Method of velocity continuation in the problem of seismic time migration[J]. Russian Geology and Geophysics. 1994, 35(5): 100-111.
[88] Hubral P., Tygel M., and Schleicher J. Seismic image waves[J]. Geophysicsl Journal International. 1996, 125: 431-442.
[89] Schleicher J., and Aleixo R. Time and depth remigration in elliptically anisotropic media[J]. Geophysics. 2007, 72(1): S1-S9.
[90] Dix C.H. Seismic velocities from surfaces measurements[J]. Geophysics. 1955, 20(1): 68–86.
[91] Thore P.D., de Bazelaire E., and Ray M.P. The three-parameter equation: an efficient tool to enhance the stack[J]. Geophysics. 1994, 59(2): 297-308.
[92] Alkhalifah T., Tsvankin I., and K.L.E.A. Velocity analysis and imaging in transversely isotropic media: Methodology and a case study[J]. The Leading Edge. 1996, 15(5): 371-378.
[93] Toldi J., Alkhalifah T., and Berthet P., et al. Case study of estimation of anisotropy[J]. The Leading Edge. 1999, 18(5): 588-593.
[94] Bolshix C.F. Approximate model for the reflected wave traveltime curve in multilayered media[J]. Applied Geophysics. 1956, 15: 3-14. (in Russian).
[95] Taner M.T., and Koehler F. Velocity spectra-digital computer derivation and applications of velocity functions[J]. Geophysics. 1969, 34: 859–881.
[96] May B.T., and Straley D.K. Higher-order moveout spectra[J]. Geophysics. 1979, 44(7): 1193-1207.
[97] Grechka V., and Tsvankin I. Feasibility of nonhyperbolic moveout inversion in transversely isotropic media[J]. Geophysics. 1998, 63(3): 957-969.
[98] Zhang F., and Uren N. Approximate explicit ray velocity functions and travel times for P-waves in TI media[C]. 71st SEG Meeting. San Antonio , Texas , USA. 2001,:106–109
[99] van der Baan M., and Kendall J.-. Estimating anisotropy parameters and traveltimes in the tau-p domain[J]. Geophysics. 2002, 67(4): 1076-1086.
[100] Stovas A., and Ursin B. New travel-time approximations for a transversely isotropic medium[J]. Journal of Geophysics and Engineering. 2004, 1: 128–133.
[101] Alkhalifah T. Velocity analysis using nonhyperbolic moveout in transversely isoropic media[J]. Geophysics. 1997, 62(6): 1839-1854.
[102] Guerrero C., Wookey J., and van der Baan M., et al. VTI anisotropy parameter estimation in the tau-p domain: An example from the North Sea[C]. 72nd SEG annual meeting. San Antonio, USA. 2002,21:137-140
[103] Malovichko A.A. A new representation of the traveltime curve of reflected waves in horizontally layered media[J]. Applied Geophysics. 1978: 47–53. (in Russian).
[104] Claerbout J.F. Datum shift and velocity estimation[R]. , 1987.
[105] de Bazelaire E. Normal moveout revisited: Inhomogeneous media and curved interfaces[J]. Geophysics. 1988, 53(2): 143–157.
[106] Castle R. A theory of normal moveout[J]. Geophysics. 1994, 59(6): 983–999.
[107] Siliqi R., and Bousquie N. Anelliptic time processing based on a shifted hyperbola approach[C]. 70th SEG Meeting. Calgary. 2000,:2245–2248
[108] Ursin B., and Stovas A. Traveltime approximations for a layered transversely isotropic medium[J]. Geophysics. 2006, 71(2): D23–D33.
[109] Fomel S. On anelliptic approximations for qP velocities in VTI media[J]. Geophysical Prospecting. 2004, 52: 247–259.
[110] Muir F., and Dellinger J. A practical anisotropic system[R]. , 1985.
[111] Douma H., and Calvert A. Nonhyperbolic moveout analysis in VTI media using rational interpolation[J]. Geophysics. 2006, 71(3): D59-D71.
[112] Li J., and Symes W.W. Interval velocity estimation via NMO-based differential semblance[J]. Geophysics. 2007, 72(6): U75-U88.
[113] Brandsberg-Dahl S., Ursin B., and de Hoop M.V. Seismic velocity analysis in the scattering-angle/azimuth domain[J]. Geophysical Prospecting. 2003, 51(4): 95-314.
[114] Shen P., Symes W.W., and Stolk C.C. Differential semblance velocity analysis by wave-equation migration[C]. 73rd SEG annual meeting. Dallas, USA. 2003,22:2132-2135
[115] Shen P., and Symes W.W. Automatic velocity analysis via shot profile migration[J]. Geophysics. 2008, 73(5): VE49-VE59.
[116] Khoury A., and Symes W. DSR Migration velocity analysis by differential semblance optimization[C]. SEG annual meeting. New Orleans, USA. 2006,25:2450-2454
[117] Symes W.W. Migration velocity analysis and waveform inversion[J]. Geophysical Prospecting. 2008, 56(6): 765-790.
[118] Plessix R.-. Automatic cross-well tomography: an application of the differential semblance optimization to two real examples[J]. Geophysical Prospecting. 2000, 48(5): 937-951.
[119] Plessix R.-., Kroode F.T., and Mulder W. Automatic crosswell tomography by differential semblance optimization[C]. 70th SEG annual meeting. Calgary, Canada. 2000,:2265-2268
[120] Plessix R.-., Mulder W.A., and Kroode A.P.E.T. Automatic cross-well tomography by semblance and differential semblance optimization: theory and gradient computation[J]. Geophysical Prospecting. 2001, 48(5): 913-935.
[121] Chauris H., and Noble M. Two‐dimensional velocity macro model estimation from seismic reflection data by local differential semblance optimization: applications to synthetic and real data sets[J]. Geophysical Journal International. 2001, 144(1): 14-26.
[122] Foss S.K., Ursin B., and Sollid A. A practical approach to PP seismic angle tomography[J]. Geophysical Prospecting. 2004, 52(6): 663-669.
[123] Sun D., and Symes W.W. A nonlinear differential semblance strategy for waveform inversion: Experiments in layered media[C]. SEG annual meeting. Houston, USA. 2009,:2526-2530
[124] Gao F., and Symes W. Differential semblance velocity analysis by reverse time migration: Image gathers and theory[C]. SEG annual meeting. Houston, USA. 2009,28:2317-2321
[125] Symes W.W. High frequency asymptotics, differential semblance, and velocity estimation[C]. 68th SEG annual meeting. New Orleans, USA. 1998,17:1616-1619
[126] Symes W.W. All stationary points of differential semblance are asymptotic global minimizers: layered acoustics[R]. Department of Computational and Applied Mathematics, Rice University, 1999.
[127] Li J., and Symes W.W. Fast interval velocity estimation via NMO-based differential semblance[C]. 75th SEG annual meeting. Houston, USA. 2005,:2265-2268
[128] Verm R.W., and Symes W.W. Practice and pitfalls in NMO-based differential semblance velocity analysis[C]. SEG annual meeting. New Orleans, USA. 2006,25:2112-2116
[129] Helbig K. Systematic classification of layer-induced transverse isotropy[J]. Geophysical Prospecting. 1981, 29(4): 550-577.
[130] Suchy K. Ray tracing in anisotropic absorbing medium[J]. Journal of Plasma Physics. 1972, 8(1): 53-65.
[131] Cerveny V. Seismic rays and ray intensities in inhomogeneous anisotropic media[J]. Geophysical Journal of the Royal Astronomical Society. 1972, 1972(1): 1-13.
[132] Cerveny V., Molotkov I.A., and Psencik I. Ray method in seismology[M]. Praha: Univerzita Karlova, 1977.
[133] Jech J. Computation of rays in an inhomogeneous transversely isotropic medium with a nonvertical axis of symmetry[J]. studia geophysica et geodaetica. 1983, 27(2): 114-121.
[134] Petrashen G.I., and Kashtan B.M. Theory of body-wave propagation in inhomogeneous anisotropic media[J]. Geophysical Journal of the Royal Astronomical Society. 1984, 76(1): 29-39.
[135] Cerveny V., and Psencik I. Gaussian beams in elastic 2-D laterally varying layered structures[J]. Geophysical Journal of the Royal Astronomical Society. 1984, 78(1): 65-91.
[136] Gajewski D., and Psencik I. Computation of high-frequency seismic wavefields in 3-D laterally inhomogeneous anisotropic media[J]. Geophysical Journal of the Royal Astronomical Society. 1987, 91(2): 383-411.
[137] Mochizuki E. Ray tracing of body waves in an anisotropic medium[J]. Geophysical Journal of the Royal Astronomical Society. 1987, 90(3): 627-634.
[138] Shearer P.M., and Chapman C.H. Ray tracing in azimuthally anisotropic media—I. Results for models of aligned cracks in the upper crust[J]. Geophysical Journal International. 1989, 96(1): 51-64.
[139] Gajewski D., and Psencik I. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures[J]. Geophysical Journal of the Royal Astronomical Society. 1990, 95(B7): 11301-11315.
[140] Gajewski D., and Psencik I. Vector wavefields for weakly attenuating anisotropic media by the ray method[J]. Geophysics. 1992, 57(1): 27-38.
[141] Farra V., and Begat S.L. Sensitivity of qP-wave traveltimes and polarization vectors to heterogeneity, anisotropy and interfaces[J]. Geophysical Journal International. 1995, 121(2): 371-384.
[142] Mensch T., and Farra V. Computation of qP-wave rays, traveltimes and slowness vectors in orthorhombic media[J]. Geophysical Journal International. 1999, 138(1): 244-256.
[143] Cerveny V. Seismic Ray Theory[M]. Cambridge: Cambridge University Press, 2001.
[144] Vavrycuk V. Ray tracing in anisotropic media with singularities[J]. Geophysical Journal International. 2001, 145(1): 265-276.
[145] Cardarelli E., and Cerreto A. Ray tracing in elliptical anisotropic media using the linear traveltime interpolation(LTI) method applied to traveltime seismic tomography[J]. Geophysical Prospecting. 2002, 50(1): 55-72.
[146] Dickens T.A. Ray tracing in tilted transversely isotropic media: a group velocity approach[C]. 74th SEG annual meeting. Denver, USA. 2004,23:973-976
[147] Iversion E. REFORMULATED KINEMATIC AND DYNAMIC RAY TRACING SYSTEMS FOR ARBITRARILY ANISOTROPIC MEDIA[J]. Studia Geophysica et Geodaetica. 2004, 48(1): 1-20.
[148] Bansal B., and Mrinal K.S. 3-D Two-point ray tracing in general anisotropic media[C]. 75th SEG annual meeting. Houston, USA. 2005,24:190-194
[149] Rogister Y., and Slawinski M.A. Analytic solution of ray-tracing equations for a linearly inhomogeneous and elliptically anisotropic velocity model[J]. Geophysics. 2005, 70(5): D37-D41.
[150] Psencik I., and Farra V. First-order ray tracing for qP waves in inhomogeneous, weakly anisotropic media[J]. Geophysics. 2005, 70(6): D65-D75.
[151] Farra V. First-order ray tracing for qS waves in inhomogeneous weakly anisotropic media[J]. Geophysical Journal International. 2005, 161(2): 309-324.
[152] Klimes L. Common-Ray tracing and dynamic ray tracing for s waves in a smooth elastic anisotropic medium[J]. Studia Geophysica et Geodaetica. 2006, 50(3): 449-461.
[153] Zhou B., and Greenhalgh S. Raypath and traveltime computations for 2D transversely isotropic media with dipping symmetry axes[J]. Exploration Geophysics. 2006, 37(2): 150-159.
[154] Dehghan K., Farra V., and Nicoletis L. Approximate ray-tracing for qP waves in weakly VTI media[C]. 76th SEG annual meeting. New Orleans. 2006,25:2221-2225
[155] Dehghan K., Farra V., and Nicoletis L. Approximate ray tracing for qP-waves in inhomogeneous layered media with weak structural anisotropy[J]. Geophysics. 2007, 72(5): SM47-SM60.
[156] Cores D., and Loreto M.C. A generalized two point ellipsoidal anisotropic ray tracing for converted waves[J]. Optimization and Engineering. 2007, 8(4): 373-396.
[157] Cerveny V. A NOTE ON DYNAMIC RAY TRACING IN RAY-CENTERED COORDINATES IN ANISOTROPIC INHOMOGENEOUS MEDIA[J]. Studia Geophysica et Geodaetica. 2007, 51(3): 1573-1626.
[158]常旭, and刘伊克.地震正反演与成像[M].北京:华文出版社, 2001.
[159]杨文采.应用地震层析成像[M].北京:地质出版社, 1993.
[160] Clayton R.W. Seismic tomography(abstract)[J]. Eos Trans. Am. Geophys. Union. 1984, 65: 236.
[161] Dziewonski A.M., and Gilber F. The effect of smal aspherical perturbations on travel time and re-examination of the corrections for ellipticity[J]. Geophysical Journal of Royal Astronomy Society. 1976, 44: 7-17.
[162] Tanimoto T., and Anderson D.L. Mapping convection in the mantle[J]. Geophysical Research Letter. 1984, 11(4): 287-290.
[163] Woodhouse J.H., and Dzeiwonski A.M. Mapping the upper mantle: Three-Dimensional modeling of earth structure by inversion of seismic waveform[J]. Journal of Geophysical Research. 1984, 89: 5953-5986.
[164] Anderson D.I., and Dziewonski A.M. Seismic tomography[J]. Scientific American. 1984, 251(4): 58-66.
[165] Dziewonski A.M., and Anderson D.L. Seismic tomography of the Earth interior[J]. American Scientist. 1984, 721: 483-494.
[166] Dziewonski A.M. Mapping the lower mantle: determination of lateral heterogneity in P velocity up to degree and order 6[J]. Journal of Geophysical Research. 1984, 89: 5929-5952.
[167] Tanimoto T., and Anderson D.L. Later heterogeneity and azimuthal anisotropy of the upper mantle: Love and Rayleigh waves 100-250s[J]. Journal of Geophysical Research. 1985, 90(2): 1842-1858.
[168] Woodhouse J.H., and Masters G. Global upper mantle strcture from loong-period differential travel times[J]. Journal of Geophysical Research. 1991, 96: 6351-6377.
[169] Woodhouse J.H., and Masters G. Upper mantle strcture from long-period differential traveltime and free oscillation data[J]. Geophysical Journal International. 1992, 109: 275-293.
[170] Clayton R.W., and Comer R. A tomographic analysis of mantle heterogeneities from body wave travel time(abstract)[J]. Eos, Transactions, American Geophysical Union. 1983, 64(45): 776.
[171] Hager B.H., Clayton R.W., and M.A.R.E.A. Lower mantle heterogeneity, dynamic topography and the geoid[J]. Nature. 1985, 313: 541-545.
[172] Tanimoto T. Long-wavelength S-wave velocity strcture throughout the mantle[J]. Geophysical Journal International. 1990, 100: 327-336.
[173] Inoue H., Fukao Y., and K.T.E.A. Whole mantle P-wave travel time tomography[J]. Physics of the Earth and Planetary Interiors. 1990, 59: 294-328.
[174] Fukao Y., Obayashi M., and H.I.E.A. Subducting slabs stagnant in the mantle transition zone[J]. Journal of Geophysical Research. 1992, 97(4): 809-822.
[175] Su W., Woodward R.L., and Dziewonski A.M. Degree 12 model of shear velocity heterogeneity in the mantle[J]. Journal of Geophysical Research. 1994, 99: 6945-6980.
[176] Vasco D.W., Johnson L.R., and Pullian R.J. Lateral variations in mantle velocity strcture and discontinuities determined from P, PP, S, SS, and SS-Sds travel time residuals[J]. Journal of Geophysical Research. 1995, 100(24): 24037-24059.
[177] Masters G., Jonhnson S., and G.L.E.A. A shear-velocity model of the mantle[J]. Phios. Trans. R. Soc. London Ser. A. 1996, 354: 1385-1411.
[178] Vasco D.W., and Johnson L.R. Whole earth strcture estimated from seismic arrival times[J]. Journal of Geophysical Research. 1998, 103: 2633-2671.
[179] Ristema J., van Heijst H.J., and Woodhouse J.H. Complex shear wave velocity strcture imaged beneath Africa and Iceland[J]. Science. 1999, 286: 1925-1928.
[180] Goes G., Spakman W., and Bijwaard H. A low source for central European volcanism[J]. Science. 1999, 283: 1928-1932.
[181] Tanimoto T. Mantle dynamics and seismic tomography[J]. Proceedings of the National Academy of Sciences of the United States of America. 2000, 97(23): 12409-12410.
[182] Zhao D., Maruyama S., and Omori S. Mantle dynamics of Western Pacific and East Asia: Insight from seismic tomography and mineral physics[J]. Gondwana research. 2007, 11(1-2): 120-131.
[183] Zhao D. Multiscale seismic tomography and mantle dynamics[J]. Gondwana Research. 2009, 15(3-4): 297-323.
[184] Achauer U., Evans J.R., and Stauber D.A. High-Resolution Seismic Tomography of Compressional Wave Velocity Structure at Newberry Volcano, Oregon Cascade Range[J]. Journal of Geophysical Research. 1988,93(B9): 10,135–10,147.
[185] Aloisi M., Cocina O., and G.N.E.A. Seismic tomography of the crust underneath the Etna volcano, Sicily[J]. Physics of the Earth and Planetary Interiors. 2002, 134(3): 139-155.
[186] Finlayson D.M., Gudmundsson O., and I.I.E.A. Rabaul volcano, Papua New Guinea: seismic tomographic imaging of an active caldera[J]. Journal of Volcanology and Geothermal Research. 2003, 124(3-4): 153-171.
[187] Rowlands D.P., White R.S., and Haines A.J. Seismic tomography of the Tongariro Volcanic Centre, New Zealand[J]. Geophysical Journal International. 2005, 163(3): 1180-1194.
[188] Lou H., Wang C., and Huangfu G. Three-dimensional seismic velocity tomography of the upper crust in Tengchong volcanic area, Yunnan Province[J]. Acta Seismologica Sinica. 2007, 15(3): 260-268.
[189] Aki K., and Lee W.H.K. Determination of three-dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes[J]. Journal of Geophysical Research. 1976, 81(B23): 4381-4399.
[190] Aki K., Christoffersson A., and Husebye E.S. Determination of the three-dimensional seismic structure of the lithosphere[J]. Journal of Geophysical Research. 1977, 82(B2): 277-296.
[191] Dziewonski A.M., and Gilbert F. The effect of small asphericial perturbations on travel times and a reexamination of the correction of ellipticity[J]. Geophysical Journal of the Royal Astronomical Society. 1976, 44: 7-17.
[192] Papazachos C.B. Crustal P- and S-velocity structure of the Serbomacedonian Massif (Northern Greece) obtained by non-linear inversion of traveltimes[J]. Geophysical Journal International. 2002, 134(1): 25-39.
[193] Godey S., Snieder R., and A.V.E.A. Surface wave tomography of North America and the Caribbean using global and regional broad-band networks: phase velocity maps and limitations of ray theory[J]. Geophysical Journal International. 2003, 152(3): 620-632.
[194] Paulatto M., Minshull T.A., and B.B.E.A. Upper crustal structure of an active volcano from refraction/reflection tomography, Montserrat, Lesser Antilles[J]. Geophysical Journal International. 2009, 180(2): 685-696.
[195] Arroyo G., Husen S., and E.R.F.E.A. Three-dimensional P-wave velocity structure on the shallow part of the Central Costa Rican Pacific margin from local earthquake tomography using off- and onshore networks[J]. Geophysical Journal International. 2009, 179(2): 827-849.
[196] Jech J., and Cerveny V. Iterative geophysical tomography[J]. Studia Geophysica et Geodaetica. 1986, 30(3): 242-256.
[197] Carrion P. Dual tomography for imaging complex structures[J]. Geophysics. 1991, 56(9): 1395-1404.
[198] Sheng J., and Schuster G.T. Finite-frequency resolution limits of wave path traveltime tomography for smoothly varying velocity models[J]. Geophysical Journal International. 2003, 152(3): 669-676.
[199] Sekiguchi S. Hierarchical traveltime tomography[J]. Geophysical Journal International. 2006, 166(3): 1105-1124.
[200] Koren Z., and Ravve I. Curved rays anisotropic tomography: Local and global approaches[C]. 76th SEG annual meeting. New Orleans, USA. 2006,:3373-3377
[201] Benxi K., Zhang J., and Baofu C. Fat-ray first-arrival seismic tomography and its application[C]. 77th SEG annual meeting. San antonio, USA. 2007,26:2822-2826
[202] Santos V.G.B.D. Seismic-ray reflection tomography using integral function norm[C]. 77th SEG annual meeting. San Antonio, USA. 2007,26:1888-1892
[203] Adler F., Baina R., and M.A.S.E.A. Nonlinear 3D tomographic least-squares inversion of residual moveout in Kirchhoff prestack-depth-migration common-image gathers[J]. Geophysics. 2008, 73(5): VE13-VE23.
[204] Denli H., and Huang L. Double-difference elastic waveform tomography in the time domain[C]. 79th SEG annual meeting. Houston, USA. 2009,28
[205] Wang X., and Tsvankin I. Stacking-velocity tomography with borehole constraints for tilted TI media[C]. 79th SEG annual meeting. Houston, USA. 2009,28:2352-2356
[206] Meng Z., and Peng C. Non-hyperbolic reflection tomography for better imaging and interpretation[C]. 79th SEG annual meeting. Houston, USA. 2009,28:3665-3669
[207] Bakulin A., Woodward M., and Nichols D. Localized anisotropic tomography with well information in VTI media[C]. 79th SEG annual meeting. Houston, USA. 2009,28:221-225
[208] Billette F., Lambare G., and Podvin P. Velocity macromodel estimation by stereotomography[C]. 67th SEG annual meeting. New Frontiers, USA. 1997,16:1889-1892
[209] Billette F., Podvin P., and Lambare G. Stereotomography with automatic picking: Application to the Marmousi dataset[C]. 68th SEG annual meeting. New Orleans, USA. 1998,17:1317-1320
[210] Lambare G., Alerini M., and R.B.E.A. Stereotomography : A fast approach for velocity macro-model estimation[C]. 73th SEG annual meeting. 2003,23:2076-2079
[211] Lavaud B., Baina R., and Landa E. Automatic robust velocity estimation by poststack Stereotomography[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2351-2354
[212] Lambare G. Stereotomography: past, present and future[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2367-2370
[213] Lambare G., Alerini M., and Podvin P. Stereotomographic picking in practice[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2343-2346
[214] Nag S., Alerini M., and E.D.E.A. 2D stereotomography for anisotropic media[C]. 76th SEG annual meeting. New Orleans, USA. 2006,25:3305-3309
[215] Neckludov D., Baina R., and Landa E. Residual stereotomographic inversion[J]. Geophysics. 2006, 71(4): E35-E39.
[216] Lambare G. Stereotomography[J]. Geophysics. 2008, 73(5): VE25-VE34.
[217] Gao F., and A.L.E.A. Velocity analysis by waveform tomography: A few examples[C]. 74th SEG annual meeting. Denver, USA. 2004,23:2371-2374
[218] Rao Y., Wang Y., and Morgan J.V. Crosshole seismic waveform tomography– II. Resolution analysis[J]. Geophysical Journal International. 2006, 166(3): 1237-1248.
[219] de Hoop M., van H.R., and Shen P. Multi-scale aspects of wave-equation reflection tomography[C]. 76th SEG annual meeting. New Orleans, USA. 2006,25:3378-3382
[220] de Hoop M., van der Hilst R.D., and Shen P. Wave-equation reflection tomography: annihilators and sensitivity kernels[J]. Geophysical Journal International. 2006, 167(3): 1332-1352.
[221] Long M.D., de Hoop M.V., and van der Hilst R.D. Wave-equation shear wave splitting tomography[J]. Geophysical Journal International. 2008, 172(1): 311-330.
[222] Barnes C., Charara M., and Tsuchiya T. Feasibility study for an anisotropic full waveform inversion of cross-well seismic data[J]. Geophysical Prospecting. 2008, 56(6): 897-906.
[223] Shin C., and Cha Y.H. Waveform inversion in the Laplace domain[J]. Geophysical Journal International. 2008, 173(3): 922-931.
[224] Boonyasiriwat C., Valasek P., and P.R.E.A. An efficient multiscale method for time-domain waveform tomography[J]. Geophysics. 2009, 74(6): WCC59-WCC68.
[225] Virieux J., and Operto S. An overview of full-waveform inversion in exploration geophysics[J]. Geophysics. 2009, 74(6): WCC1-WCC26.
[226] Zhang Y., and Wang D. Traveltime information-based wave-equation inversion[J]. Geophysics. 2009, 74(6): WCC27-WCC36.
[227] Burstedde C., and Ghattas O. Algorithmic strategies for full waveform inversion: 1D experiments[J].Geophysics. 2009, 74(6): WCC37-WCC46.
[228] Abubakar A., Hu W., and T.M.H.E.A. Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data[J]. Geophysics. 2009, 74(6): WCC47-WCC58.
[229] Yang Y., Li Y., and Liu T. 1D viscoelastic waveform inversion for Q structures from the surface seismic and zero-offset VSP data[J]. Geophysics. 2009, 74(6): WCC141-WCC148.
[230] Plessix R.-. Three-dimensional frequency-domain full-waveform inversion with an iterative solver[J]. Geophysics. 2009, 74(6): WCC149-WCC157.
[231] Krebs J.R., Anderson J.E., and Hinkley D. Fast full-wavefield seismic inversion using encoded sources[J]. Geophysics. 2009, 74(6): WCC177-WCC188.
[232] Tarantola A. Inverse problem theory and methods for model parameter estimation[M]. Philadelphia: Society for Industrial and Applied Mathematics, 2005.
[233] Bube K.P., and Langan R.T. Hybrid L1/L2 data minimization with applications to tomography[J]. Geophysics. 1997, 62(4): 1183-1195.
[234] Bube K.P., and Nemeth T. Fast line searches for the robust solution of linear systems in the hybrid L1/L2 and Huber norms[J]. Geophysics. 2007, 72(2): A13-A17.
[235]刘海飞,阮百尧, and柳建新等.混合范数下的最优化反演方法[J].地球物理学报. 2007, 50(6): 1877-1883.
[236] Bertero M. Regularization methods for linear inverse problems[M]. Heidelberg: Springer Berlin, 1986.
[237] Fomel S., and Claerbout J.F. Multidimensional recursive filter preconditioning in geophysical estimation problems[J]. Geophysics. 2003, 68(2): 577-588.
[238] Fomel S., and Guitton A. Regularizing seismic inverse problems by model reparameterization using plane-wave construction[J]. Geophysics. 2006, 71(5): A43-A47.
[239] Fomel S. Sharping regularization in geophysical-estimation problems[J]. Geophysics. 2007, 72(2): R29-R36.
[240] Berryman V. Exact seismic velocities for transversely isotropic media and extended Thomsen formulas for stronger anisotropies[J]. Geophysics. 2009, 73(1): D1-D10.
[241] Cerveny V., and Psencik I. Weakly inhomogeneous plane waves in anisotropic, weakly dissipative media[J]. Geophysical Journal International. 2008, 172(2): 663-673.
[242] Abbad B., Ursin B., and Rappin D. Automatic nonhyperbolic velocity analysis[J]. Geophysics. 2009, 74(2): U1-U12.
[243] Zelt C., and Ellis R.M. Practical and efficient ray tracing in two-dimensional media for rapid traveltime and amplitude forward modelling[J]. Canadian Journal of Exploration Geophysics. 1988, 24(1): 16-31.
[244] Crampin S. Suggestios for a consistent terminology for seismic anisotropy[J]. Geophysical Prospecting. 1989, 37(7): 753-770.
[245] Tsvankin I. Seismic Signatures and analysis of reflection data in anisotropic media[M]. New York: Elsevier Science Publication Corporation, 2001.
[246] Zhu Y., and Tsvankin I. Plane-wave propagation in attenuation transversely isotropic media[J]. Geophysics. 2006, 71(2): T17-T30.
[247] Cerveny V., and Psencik I. Plane waves in viscoelastic anisotropic media I: Theory[J]. Geophysical Journal International. 2005, 161(1): 197-212.
[248] Cerveny V., and Psencik I. Plane waves in viscoelastic anisotropic media II: Numerical examples[J]. Geophysical Journal International. 2005, 161(1): 213-229.
[249] Zhu Y., and Tsvankin I. Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media[J]. Geophysics. 2007, 72(1): D1-D7.
[250] Fomel S., and Stovas A. Generalized non-hyperbolic moveout approximation[C]. 69th EAGE meeting.London, UK. 2007,:B041
[251] Siliqi R., and Meur D.L. How to estimate uncorrelated dense V-ηfields?[C]. 66th EAGE Conference and Exhibition. Paris, France. 2004,
[252]王永刚,乐喜友, and张军华.地震属性分析技术[M].北京:石油大学出版社, 2007.
[253] Starck J.L., EJCandès, and Donoho D.L. The curvelet transform for image denoising[J]. IEEE Transactions on Image Processing. 2000, 11(6): 670-684.
[254] Symes W.W., and Carazzone J.J. Velocity inversion by differential semblance optimization[J]. Geophysics. 1991, 56(5): 654-663.
[255] Symes W.W. A differential semblance algorithm for the inverse problem of reflection seismology[J]. Computers & Mathematics with Applications. 1991, 22(4-5): 147-178.
[256] Symes W.W., and Kern M. Velocity inversion by differential semblance optimization for 2-D common source data[C]. 62nd SEG annual meeting. New Orleans, USA. 1992,11:1210-1213
[257] Symes W.W., and Versteeg R. Velocity model determination using differential semblance optimization[C]. 63rd SEG Annual Meeting. Washinton, USA. 1993,12:696-699
[258] Symes W.W., and Kern M. Inversion of reflection seismograms by differential semblance analysis: algorithm structure and synthetic examples[J]. Geophysical Prospecting. 1994, 42(6): 565-614.
[259] Mulder W.A., and Kroode A.P.E.T. Automatic velocity analysis by differential semblance optimization[C]. 71st SEG annual meeting. San Antonio, USA. 2001,20:893-896
[260] Zhou B., and Greenhalgh S. Non-linear traveltime inversion for 3-D seismic tomography in strongly anisotropic media[J]. Geophysical Journal International. 2008, 172(1): 383-394.
[261] Langan R.T., Lerche T., and Cutler R.T. Tracing of rays through heterogeneous media, An accurate and efficient procedure[J]. Geophysics. 1985, 50(9): 1456-1465.
[262] Moser T.J. Shortest path calculation of seismic rays[J]. Geophysics. 1991, 56(1): 59-67.
[263] Xu T., and Xu G.M. Block modeling and segmentally iterative ray tracing in complex 3D media[J]. Geophysics. 2006, 71(3): T41-T51.
[264] Zelt C., and Smith R.B. Seismic traveltime inversion for 2-D crustal velocity structure[J]. Geophysical Journal International. 1992, 108(1): 16-34.
[265] GuiZiou J.L., Mallet J.L., and Madariaga R. 3D seismic reflection tomography on top of the GOCAD depth modeler[J]. Geophysics. 1996, 61(5): 1499-1510.
[266] Mao W.J., and Stuart W. Rapid multiwave-type ray tracing in complex 2D and 3D isotropic media[J]. Geophysics. 1997, 62(1): 298-308.
[267] Rawlinson N., Houseman G.A., and Collins C.D.N. Inversion of seismic refraction and wide-angle reflection traveltimes for threedimensional layered crustal structure[J]. Geophysical Journal International. 2001, 145(2): 381-400.
[268]徐果明,卫山, and高尔根等.二维复杂介质的块状建模及射线追踪[J].石油地球物理勘探. 2001, 36(2): 213-219.
[269]徐涛,徐果明, and高尔根等.复杂介质的折射波射线追踪[J].石油地球物理勘探. 2005, 39(6): 690-693.
[270]徐涛,徐果明, and高尔根等.三维试射射线追踪子三角形法[J].石油地球物理勘探. 2005, 40(4): 391-399.
[271] Cerveny V. Seismic Ray Theory[M]. Cambridge: Cambridge University Press, 2001.
[272] Press W.H., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in C++: : The Art of Scientific Computing. Second Edition[M]. Cambridge: Cambridge University Press, 2002.
[273]岳玉波,孙建国, and韩复兴.起伏地表下初值射线追踪的实现[J].勘探地球物理进展. 2007, 30(5):388-391.
[274] Paige C.C., and Saunders M.A. LSQR: an algorithm for sparse linear equations and sparse least squares[J]. ACM Transactions Mathematical Software. 1982, 8(1): 43-71.
[275] Paige C.C., and Saunders M.A. Algorithm 583; LSQR: Sparse linear equations and least-squares problems[J]. ACM Transactions Mathematical Software. 1982, 8(2): 195-209.
[276]袁亚湘, and孙文瑜.最优化理论与方法[M].北京:科学出版社, 2005.
[277] Nocedal J., and Wright S.J. Numerical optimization[M]. New York: Springer-Verlag, 1999.