地震波干涉法研究进展综述
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摘要
地震波干涉法的提出与应用丰富了对地震波传播规律的认识和研究,被认为是地球物理发展的一大进展.其基本原理是对不同位置接收到的地震波信号进行相关而得到新的地震信号,该信号能反映原始地震波信号所不能反映的信息.本文详细介绍了地震波干涉法的原理及其在地球物理学特别是地震勘探领域中的应用.首先,重点介绍了地震波干涉法理论的提出、发展和完善的过程;其次,讨论了目前应用的地震波干涉法的不同的数学实现方式;最后,介绍了用地震波干涉法的数值实现过程以及用地震波干涉法进行成像的研究进展.
The development and application of seismic interferometry,which is assumed as one significant advancement in geophysical community,have enriched the knowledge and study of seismic wave propagation.The basic idea of seismic interferometry is that if we cross-correlate the different seismic signals at different locations,we could retrieve a new signal,which could reflect the information that could not be seen from the original seismic waves. In this paper,we briefly review the principles of seismic interferometry and the application in geophysical fields, especially in exploration geophysics.We first focus on the birth,historical development and enrichment of seismic interferometry,then discuss different mathematical ways to do seismic interferometry,and finally introduc the process of interferometry from a numerical point of view and introduc the advancement interferometric imaging.
The development and application of seismic interferometry,which is assumed as one significant advancement in geophysical community,have enriched the knowledge and study of seismic wave propagation.The basic idea of seismic interferometry is that if we cross-correlate the different seismic signals at different locations,we could retrieve a new signal,which could reflect the information that could not be seen from the original seismic waves. In this paper,we briefly review the principles of seismic interferometry and the application in geophysical fields, especially in exploration geophysics.We first focus on the birth,historical development and enrichment of seismic interferometry,then discuss different mathematical ways to do seismic interferometry,and finally introduc the process of interferometry from a numerical point of view and introduc the advancement interferometric imaging.
引文
[1] 单新建,马瑾,王长林,柳稼航.利用差分干涉雷达测量技术(D-InSAR)提取同震形变场[J].地震学报,2007,24(4) ,413-420． Shan X J, Ma J, Wang C L, Liu J H. Extracting coseismic deformation of the 1997 Mani earthquake with Differntial Interferometric SAR[J]. Acta Seismologica Sinica, 2007,24 (4) ,413-420．
[2] 朱新慧,孙付平.用甚长基线干涉测量数据检测冰期后地壳回弹[J].地球物理学报,2005,48(2) :308-313． Zhu X H, Sun F P. Detection of postglacial rebound by using VLBI data[J]. 2005,48(2) :308-313．
[3] 孙建宝,徐锡伟,沈正康,等.基于线弹性位错模型及干涉雷达同震形变场反演1997年玛尼Mw7． 5级地震参数-Ⅰ:均匀滑动反演[J].地球物理学报,2007,50(4) :1097-1100． Sun J B, Xu X W, Shen Z K, etal. Parameter inversion of the 1997 Mani earthquake from INSAR co-seismic deformation field based on linear elastic dislocation model-I. Uniform slip inversions[J]. Chinese Journal of Geophysics, 2007, 50 (4) : 1097-1100．
[4] Schuster G J, Yu J, Sheng J, and Rickett J. Interferometric/daylight seismic imaging [J]. Geophysical Journal International, 2004,157(2) : 838-852．
[5] Hill S J. Geophysics bright spots[J]. The Leading Edge, 2006, 25:1082-1092．
[6] Claerbout J F. Synthesis of a layered medium from its acoustic transmission response[J]. Geophysics, 1968, 33 ( 2 ) : 264-269．
[7] Rickett J,Claerbout J F. Acoustic daylight imaging via spectral factorization: helioseismology and reservoir monitoring[J]. The Leading Edge, 1999, 18:957-960．
[8] Wapenaar C P A, Draganov D, Thorbecke J, Fokkema J T. Theory of acoustic daylight imaging revisited[A]. In: 72~(nd) SEG annual meeting, Expanded Abstracts[C], 2002, 2269-2272．
[9] Cassereau D, Fink M. Focusing with plane time-reversal mirrors: an efficient alternative to closed cavities [J]. Journal of the Acoustical Society of America, 1993, 94(4) : 2373-2386．
[10] Fink M. Time reversed acoustics[J]. Physics Today, 1997, 50, 34-40．
[11] Roux P,Fink M. Green's function estimation using secondary sources in a shallow water environment[J]. Journal of the Acoustical Society of America, 2003, 113, 1406-1416．
[12] Schuster G T. Theory of daylight/interferometric imaging: tutorial [A]. 63rd Annual International Conference and Exhibition, EAGE, Extended Abstracts [C]. 2001, A32．
[13] Wapenaar K. Synthesis of an inhomogeneous medium from its acoustic transmission response. Geophysics , 2003, 68 (5) :1756-1759．
[14] Wapenaar K, Thorbecke J, Draganov D. Relations between reflection and transmission responses of 3-D inhomogeneous media: Geoph. J. Int., 2004,156(2) :179-194．
[15] Wapenaar K. Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation [J]. Phys. Rev. Lett., 2004,93(25) :254301-1-254301-4．
[16] Wapenaar K, Thorbecke J, Draganov D. Relations between reflection and transmission responses of 3-D inhomogeneous media. Geoph. J. Int., 2004, 156(2) :179-194．
[17] Wapenaar K. Green's function retrieval by cross-correlation in case of one-sided illumination [J]. Geophysical Research Letters, 2006, 33:L19304-1-L19304-6．
[18] Snieder R, Gret A, Douma H, Scales J. Coda wave interferometry for estimating nonlinear behavior in seismic velocity. Science, 2002, 295 :2253-2255．
[19] Snieder R. Coda wave interferometry and the equilibration of energy in elastic media[J]. Phys. Rev. E, 2002 , 66 :046615-1,8．
[20] Snieder R, Hagerty M. Monitoring change in Volcanic Interiors using Coda Wave Interferometry: Application to Arenal Volcano, Costa Rica. Geophys. Res. Lett., 2004, 31(9) :L09608． 1-L09608． 5．
[21] Gret A R, Snieder R, Aster C, Kyle P R. Monitoring rapid temporal changes in a volcano with coda wave interferometry. Geophys. Res. Lett. , 2005, 32(6) :L06304． 1-L06304． 4．
[22] Snieder R. The theory of coda wave interferometry, Pure and Appl. Geophysics, 2006, 163: 455-473．
[23] Wang B, Zhu P, Chen Y, et al. Continuous subsurface velocity measurement with coda wave interferometry[J]. J. Geophys. Res., 2006, 113, B12313, doi:10． 1029/2007JB005023．
[24] 汪承灏,魏炜.改进的时间反转法用于有界面时超声目标探测的鉴别[J].声学学报,2002,27(3) :193-197． Wang C H, Wei W. Distinguishing between target and interface in ultrasonic detection by a modified time reversal method[J]. Acta Acoustica,2002,27(3) :1933-197．
[25] 吴吴,张碧星,汪承灏.声波在固体板中的多径传播及其时间反转声场[J].声学学报,2005,30(3) :215-221． Wu h, Zhang B X, Wang C H. Multi-path propagation of acoustical wave and time reversal acoustical field in solid plate[J]. Acta Acoustica,2005,30(3) :215-221．
[26] 陆铭慧,张碧星,汪承灏.时间反转法在水下通信中的应用[J].声学学报,2005,30(4) :215-22l. Lu M H, Zhang B X, Wang C H. Application of time reversal in underwater communication [J]. Acta Acoustica, 2005,30(3) :349-354．
[27] Frasier C W. Discrete time solution of plane P-SV waves in a plane layered medium[J]. Geophysics, 1970, 35: 197-219．
[28] Kumar M R, Bostock M G. Transmission to reflection transformation of teleseismic wavefields [J]. J. Geophys. Res. , 2006, 111, B08306, doi:10． 1029/2005JB004104．
[29] Wapenaar K. Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation [J]. Phys. Rev. Lett. , 2006, 93(25) : 254301-1-254301-4．
[30] Wapenaar K, Slob E, Snieder R. Unified Green's function retrieval by cross-correlation[J]. Phys. Rev. Lett. , 2006, 97(23) : 234301-1-234301-4．
[31] Snieder R, Wapenaar K,Wegler U. Unified Green's function retrieval by cross-correlation; connection with energy principle[J]. Phys. Rev. E, 2007, 75: 036103．
[32] Andrew C, Peter G, Haruo S, Roel S, Kees W. Seismic interferometry-turning noise into signal [J]. The Leading Edge, 2006, 25: 1082-1092．
[33] Slob E, Wapenaar K. Electromagnetic Green's functions retrieval by cross-correlation and cross-convolution in media with losses [J]. Geophysical Research Letters, 2007, 34: L05307-1-L05307-5．
[34] Wapenaar K, Slob E, Snieder R. Seismic and electromagnetic controlled-source interferometry in dissipative media [J]. Geophysical Prospecting, 2008, 56: 419-434．
[35] Snieder R, Sheiman J, Calvert R. Equivalence of the virtual source method and wavefield deconvolution in seismic interferometry[J]. Phys. Rev. E, 2006, 73: 066620．
[36] Vasconcelos I, Snieder R. Interferometry by deconvolution, Part 1-Theory for acoustic waves and numerical examples [J]. Geophysics, 2008, 73, Sl15-S128．
[37] Vasconcelos I, Snieder R. Interferometry by deconvolution, Part 2-Theory for elastic waves and application to drill-bit seismic imaging[J]. Geophysics, 2008,73 : S129-S141．
[38] Weaver R L,Lobkis O I. Diffuse fields in open systems and the emergence of the Green's function[J]. J. Acoust. Soc. Am. , 2004, 116: 2731-2734．
[39] Weaver R L, Lobkis O I. Diffuse fields in ultrasonics and seismology[J]. Geophysics, 2006, 71(4) :SIS-SI9．
[40] Maxwell S C,Urbancic T I. The role of passive microseismic monitoring in the instrumented oil field[J]. The Leading Edge, 2001, 20(6) : 636-639．
[41] Wapenaar K. Nonreciprocal Green's function retrieval by cross correlation[J]. Journal of the Acoustical Society of America, 2006, 120(1) :EL7-EL13．
[42] Larose E, Margerin L, Derode A, et al. Correlation of random wavefields: An interdisciplinary review [J]. Geophysics, 2006, 71(4) : SIll-SI21．
[43] Draganov D, Wapenaar K, Thorbecke J. Seismic interferometry: Reconstructing the earth’ s reflection response[J]. Geophysics, 2006, 71(4) : SI61-SI70．
[44] Draganov D, Wapenaar K, Mulder W, et al. Retrieval of reflections from seismic background-noise measurements[J], Geophysical Research Letters, 2007, 34: L04305．
[45] Wapenaar K, Fokkema J. Green's function representations
for seismic interferometry [J]. Geophysics, 2006, 71 (4) : SI33-SI46．
[46] Godin O A. Emergence of the acoustic Green's function from thermal noise [J]. Journal of the Acoustical Society of America, 2007, 121(2) : EL96-EL102．
[47] Snieder R. , Extracting the Green's function of attenuating heterogeneous media from uncorrelated waves [J]. J. Acoust. Soc. Am., 2007, 121:2637-2643．
[48] Mehta K, Snieder R, Calvert R, Jonathan Sheiman J. Acquisition geometry requirements for generating virtualsource data[J]. The Leading Edge, 2008, 27: 620-629．
[49] WillisME, LuRR, CampmanX, ToksMN, ZhangY, and de Hoop M V. A novel application of time-reversed acoustics: Salt-dome flank imaging using walkaway VSP surveys[J]. Geophysics, 2006,71(2) :A7-A11．
[50] Lu R R, Willis M E, Campman X, et al. Imaging dipping sediments at a salt dome flank-VSP seismic interferometry and reverse-time migration[A]. In: SEG annual meeting, Expanded Abstracts[C]2006, 2191-2195．
[51] Lu R R, Willis M E, Campman X, et al. Redatuming through a salt canopy and target-oriented salt-flank imaging [J]. Geophysics, 2008, 73(3) : S63-S71．
[52] Snieder R, Wapenaar K, Lamer K. Spurious multiples in seismic interferometry of primaries[J]. Geophysics, 2006, 71 : SI111-SI124．
[53] Sava P, Poliannikov O. Interferometric imaging condition for wave-equation migration[J]. Geophysics, 2008, 73(2) : S47-S61．
[54] Jiang Z, Yu J, Hornby B, Schuster G T. Migration of multiples[J]. The Leading Edge, 2006, 315-318．
[55] He R Q, Hornby B, Schuster G T. 3D wave-equation interferometric migration of VSP free-surface multiples[J]. Geophysics, 2007,72(5) : 195-203．
[56] Vasconcelos I, Snieder R, Brian Hornby B. Imaging internal multiples from subsalt VSP data-Examples of targetoriented interferometry[J]. Geophysics, 2008, 73(4) : S157-S168．
[57] Bakulin A, Calvert R. The virtual source method: Theory and case study[J]. Geophysics, 2006, 71(4) : SI139-SI150．
[58] Korneev V, Bakulin A. On the fundamentals of the virtual source method[J]. Geophysics, 2006, 71(3) : A13-A17．
[59] Bakulin A, Mateeva A, Mehta K, et al. Virtual source applications to imaging and reservoir monitoring [J]. The Leading Edge, 2007, 26: 732-740．
[60] Artman B. Imaging passive seismic data [J]. Geophysics, 2006, 71(4) : SI177-SI187．
[61] Hohl D, Mateeva A. Passive seismic reflectivity imaging with ocean-bottom cable data[A]. In: 76th Annual International Meeting, SEG, Expanded Abstracts[C], 2006,1560-1564．
[62] Schuster G T. Fermat's interferometric principle for targetoriented traveltime tomography[J]. Geophysics, 2005, 70 (4) : 47-50．
[63] Hanafy H M, Schuster G T. Target-oriented interferometric tomography for GPR data[J]. Geophysics, 2007, 72(3) : 1-6．
[2] 朱新慧,孙付平.用甚长基线干涉测量数据检测冰期后地壳回弹[J].地球物理学报,2005,48(2) :308-313． Zhu X H, Sun F P. Detection of postglacial rebound by using VLBI data[J]. 2005,48(2) :308-313．
[3] 孙建宝,徐锡伟,沈正康,等.基于线弹性位错模型及干涉雷达同震形变场反演1997年玛尼Mw7． 5级地震参数-Ⅰ:均匀滑动反演[J].地球物理学报,2007,50(4) :1097-1100． Sun J B, Xu X W, Shen Z K, etal. Parameter inversion of the 1997 Mani earthquake from INSAR co-seismic deformation field based on linear elastic dislocation model-I. Uniform slip inversions[J]. Chinese Journal of Geophysics, 2007, 50 (4) : 1097-1100．
[4] Schuster G J, Yu J, Sheng J, and Rickett J. Interferometric/daylight seismic imaging [J]. Geophysical Journal International, 2004,157(2) : 838-852．
[5] Hill S J. Geophysics bright spots[J]. The Leading Edge, 2006, 25:1082-1092．
[6] Claerbout J F. Synthesis of a layered medium from its acoustic transmission response[J]. Geophysics, 1968, 33 ( 2 ) : 264-269．
[7] Rickett J,Claerbout J F. Acoustic daylight imaging via spectral factorization: helioseismology and reservoir monitoring[J]. The Leading Edge, 1999, 18:957-960．
[8] Wapenaar C P A, Draganov D, Thorbecke J, Fokkema J T. Theory of acoustic daylight imaging revisited[A]. In: 72~(nd) SEG annual meeting, Expanded Abstracts[C], 2002, 2269-2272．
[9] Cassereau D, Fink M. Focusing with plane time-reversal mirrors: an efficient alternative to closed cavities [J]. Journal of the Acoustical Society of America, 1993, 94(4) : 2373-2386．
[10] Fink M. Time reversed acoustics[J]. Physics Today, 1997, 50, 34-40．
[11] Roux P,Fink M. Green's function estimation using secondary sources in a shallow water environment[J]. Journal of the Acoustical Society of America, 2003, 113, 1406-1416．
[12] Schuster G T. Theory of daylight/interferometric imaging: tutorial [A]. 63rd Annual International Conference and Exhibition, EAGE, Extended Abstracts [C]. 2001, A32．
[13] Wapenaar K. Synthesis of an inhomogeneous medium from its acoustic transmission response. Geophysics , 2003, 68 (5) :1756-1759．
[14] Wapenaar K, Thorbecke J, Draganov D. Relations between reflection and transmission responses of 3-D inhomogeneous media: Geoph. J. Int., 2004,156(2) :179-194．
[15] Wapenaar K. Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation [J]. Phys. Rev. Lett., 2004,93(25) :254301-1-254301-4．
[16] Wapenaar K, Thorbecke J, Draganov D. Relations between reflection and transmission responses of 3-D inhomogeneous media. Geoph. J. Int., 2004, 156(2) :179-194．
[17] Wapenaar K. Green's function retrieval by cross-correlation in case of one-sided illumination [J]. Geophysical Research Letters, 2006, 33:L19304-1-L19304-6．
[18] Snieder R, Gret A, Douma H, Scales J. Coda wave interferometry for estimating nonlinear behavior in seismic velocity. Science, 2002, 295 :2253-2255．
[19] Snieder R. Coda wave interferometry and the equilibration of energy in elastic media[J]. Phys. Rev. E, 2002 , 66 :046615-1,8．
[20] Snieder R, Hagerty M. Monitoring change in Volcanic Interiors using Coda Wave Interferometry: Application to Arenal Volcano, Costa Rica. Geophys. Res. Lett., 2004, 31(9) :L09608． 1-L09608． 5．
[21] Gret A R, Snieder R, Aster C, Kyle P R. Monitoring rapid temporal changes in a volcano with coda wave interferometry. Geophys. Res. Lett. , 2005, 32(6) :L06304． 1-L06304． 4．
[22] Snieder R. The theory of coda wave interferometry, Pure and Appl. Geophysics, 2006, 163: 455-473．
[23] Wang B, Zhu P, Chen Y, et al. Continuous subsurface velocity measurement with coda wave interferometry[J]. J. Geophys. Res., 2006, 113, B12313, doi:10． 1029/2007JB005023．
[24] 汪承灏,魏炜.改进的时间反转法用于有界面时超声目标探测的鉴别[J].声学学报,2002,27(3) :193-197． Wang C H, Wei W. Distinguishing between target and interface in ultrasonic detection by a modified time reversal method[J]. Acta Acoustica,2002,27(3) :1933-197．
[25] 吴吴,张碧星,汪承灏.声波在固体板中的多径传播及其时间反转声场[J].声学学报,2005,30(3) :215-221． Wu h, Zhang B X, Wang C H. Multi-path propagation of acoustical wave and time reversal acoustical field in solid plate[J]. Acta Acoustica,2005,30(3) :215-221．
[26] 陆铭慧,张碧星,汪承灏.时间反转法在水下通信中的应用[J].声学学报,2005,30(4) :215-22l. Lu M H, Zhang B X, Wang C H. Application of time reversal in underwater communication [J]. Acta Acoustica, 2005,30(3) :349-354．
[27] Frasier C W. Discrete time solution of plane P-SV waves in a plane layered medium[J]. Geophysics, 1970, 35: 197-219．
[28] Kumar M R, Bostock M G. Transmission to reflection transformation of teleseismic wavefields [J]. J. Geophys. Res. , 2006, 111, B08306, doi:10． 1029/2005JB004104．
[29] Wapenaar K. Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation [J]. Phys. Rev. Lett. , 2006, 93(25) : 254301-1-254301-4．
[30] Wapenaar K, Slob E, Snieder R. Unified Green's function retrieval by cross-correlation[J]. Phys. Rev. Lett. , 2006, 97(23) : 234301-1-234301-4．
[31] Snieder R, Wapenaar K,Wegler U. Unified Green's function retrieval by cross-correlation; connection with energy principle[J]. Phys. Rev. E, 2007, 75: 036103．
[32] Andrew C, Peter G, Haruo S, Roel S, Kees W. Seismic interferometry-turning noise into signal [J]. The Leading Edge, 2006, 25: 1082-1092．
[33] Slob E, Wapenaar K. Electromagnetic Green's functions retrieval by cross-correlation and cross-convolution in media with losses [J]. Geophysical Research Letters, 2007, 34: L05307-1-L05307-5．
[34] Wapenaar K, Slob E, Snieder R. Seismic and electromagnetic controlled-source interferometry in dissipative media [J]. Geophysical Prospecting, 2008, 56: 419-434．
[35] Snieder R, Sheiman J, Calvert R. Equivalence of the virtual source method and wavefield deconvolution in seismic interferometry[J]. Phys. Rev. E, 2006, 73: 066620．
[36] Vasconcelos I, Snieder R. Interferometry by deconvolution, Part 1-Theory for acoustic waves and numerical examples [J]. Geophysics, 2008, 73, Sl15-S128．
[37] Vasconcelos I, Snieder R. Interferometry by deconvolution, Part 2-Theory for elastic waves and application to drill-bit seismic imaging[J]. Geophysics, 2008,73 : S129-S141．
[38] Weaver R L,Lobkis O I. Diffuse fields in open systems and the emergence of the Green's function[J]. J. Acoust. Soc. Am. , 2004, 116: 2731-2734．
[39] Weaver R L, Lobkis O I. Diffuse fields in ultrasonics and seismology[J]. Geophysics, 2006, 71(4) :SIS-SI9．
[40] Maxwell S C,Urbancic T I. The role of passive microseismic monitoring in the instrumented oil field[J]. The Leading Edge, 2001, 20(6) : 636-639．
[41] Wapenaar K. Nonreciprocal Green's function retrieval by cross correlation[J]. Journal of the Acoustical Society of America, 2006, 120(1) :EL7-EL13．
[42] Larose E, Margerin L, Derode A, et al. Correlation of random wavefields: An interdisciplinary review [J]. Geophysics, 2006, 71(4) : SIll-SI21．
[43] Draganov D, Wapenaar K, Thorbecke J. Seismic interferometry: Reconstructing the earth’ s reflection response[J]. Geophysics, 2006, 71(4) : SI61-SI70．
[44] Draganov D, Wapenaar K, Mulder W, et al. Retrieval of reflections from seismic background-noise measurements[J], Geophysical Research Letters, 2007, 34: L04305．
[45] Wapenaar K, Fokkema J. Green's function representations
for seismic interferometry [J]. Geophysics, 2006, 71 (4) : SI33-SI46．
[46] Godin O A. Emergence of the acoustic Green's function from thermal noise [J]. Journal of the Acoustical Society of America, 2007, 121(2) : EL96-EL102．
[47] Snieder R. , Extracting the Green's function of attenuating heterogeneous media from uncorrelated waves [J]. J. Acoust. Soc. Am., 2007, 121:2637-2643．
[48] Mehta K, Snieder R, Calvert R, Jonathan Sheiman J. Acquisition geometry requirements for generating virtualsource data[J]. The Leading Edge, 2008, 27: 620-629．
[49] WillisME, LuRR, CampmanX, ToksMN, ZhangY, and de Hoop M V. A novel application of time-reversed acoustics: Salt-dome flank imaging using walkaway VSP surveys[J]. Geophysics, 2006,71(2) :A7-A11．
[50] Lu R R, Willis M E, Campman X, et al. Imaging dipping sediments at a salt dome flank-VSP seismic interferometry and reverse-time migration[A]. In: SEG annual meeting, Expanded Abstracts[C]2006, 2191-2195．
[51] Lu R R, Willis M E, Campman X, et al. Redatuming through a salt canopy and target-oriented salt-flank imaging [J]. Geophysics, 2008, 73(3) : S63-S71．
[52] Snieder R, Wapenaar K, Lamer K. Spurious multiples in seismic interferometry of primaries[J]. Geophysics, 2006, 71 : SI111-SI124．
[53] Sava P, Poliannikov O. Interferometric imaging condition for wave-equation migration[J]. Geophysics, 2008, 73(2) : S47-S61．
[54] Jiang Z, Yu J, Hornby B, Schuster G T. Migration of multiples[J]. The Leading Edge, 2006, 315-318．
[55] He R Q, Hornby B, Schuster G T. 3D wave-equation interferometric migration of VSP free-surface multiples[J]. Geophysics, 2007,72(5) : 195-203．
[56] Vasconcelos I, Snieder R, Brian Hornby B. Imaging internal multiples from subsalt VSP data-Examples of targetoriented interferometry[J]. Geophysics, 2008, 73(4) : S157-S168．
[57] Bakulin A, Calvert R. The virtual source method: Theory and case study[J]. Geophysics, 2006, 71(4) : SI139-SI150．
[58] Korneev V, Bakulin A. On the fundamentals of the virtual source method[J]. Geophysics, 2006, 71(3) : A13-A17．
[59] Bakulin A, Mateeva A, Mehta K, et al. Virtual source applications to imaging and reservoir monitoring [J]. The Leading Edge, 2007, 26: 732-740．
[60] Artman B. Imaging passive seismic data [J]. Geophysics, 2006, 71(4) : SI177-SI187．
[61] Hohl D, Mateeva A. Passive seismic reflectivity imaging with ocean-bottom cable data[A]. In: 76th Annual International Meeting, SEG, Expanded Abstracts[C], 2006,1560-1564．
[62] Schuster G T. Fermat's interferometric principle for targetoriented traveltime tomography[J]. Geophysics, 2005, 70 (4) : 47-50．
[63] Hanafy H M, Schuster G T. Target-oriented interferometric tomography for GPR data[J]. Geophysics, 2007, 72(3) : 1-6．
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