初至波菲涅尔体地震层析成像
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摘要
根据地震波传播的有限频理论,对于某个特定震相的观测信息,不仅射线路径上的点对该信息具有影响,射线领域上的其他点对接收信息也具有影响,这种影响可以用核函数来表达.本文基于波动方程的Born近似与Rytov近似,给出了非均匀介质情况下初至地震波振幅与走时菲涅尔体层析成像单频、带限层析核函数的计算方法.通过对均匀介质情况下初至地震波菲涅尔体层析成像核函数解析表达式的理论模型实验与分析,给出了不同维度振幅、走时单频菲涅尔体的空间分布范围,进而给出了带限菲涅尔体边界的确定方法.将本文的走时非涅尔体层析成像理论应用于表层速度结构反演中,理论模型试验与实际资料处理结果表明,初至波菲涅尔体地震层析成像方法比传统的初至波射线层析成像理沦具有更高的反演精度.
According to the finite-frequency theory, for a single source-receiver pair, not only the points on the raypath but also those outside the ray affect the wave propagation. This kind of effect can be described by sensitivity kernel. On the basis of the Born and Rytov approximations, we derive the amplitude and traveltime sensitivity kernels for Fresnel volume tomography corresponding to different dimensions in heterogeneous medium. The analytical expressions of the sensitivity kernels in homogeneous media are presented, through which we give the distribution ranges of the amplitude and traveltime sensivitity kernels under different dimensions. Furthermore, we present the calculation methods of band-limited sensitivity kernels and the corresponding distribution ranges. According to the first arrival information of the seismic wave, we apply Fresnel volume tomography to the inversion of the near surface velocity of the earth. The inversion results of the theoretical model and practical data indicate that first arrival Fresnel volume tomography has the advantage of higher accuracy than the conventional raypath tomography.
According to the finite-frequency theory, for a single source-receiver pair, not only the points on the raypath but also those outside the ray affect the wave propagation. This kind of effect can be described by sensitivity kernel. On the basis of the Born and Rytov approximations, we derive the amplitude and traveltime sensitivity kernels for Fresnel volume tomography corresponding to different dimensions in heterogeneous medium. The analytical expressions of the sensitivity kernels in homogeneous media are presented, through which we give the distribution ranges of the amplitude and traveltime sensivitity kernels under different dimensions. Furthermore, we present the calculation methods of band-limited sensitivity kernels and the corresponding distribution ranges. According to the first arrival information of the seismic wave, we apply Fresnel volume tomography to the inversion of the near surface velocity of the earth. The inversion results of the theoretical model and practical data indicate that first arrival Fresnel volume tomography has the advantage of higher accuracy than the conventional raypath tomography.
引文
[1] Bishop T N, Bube K P, Cutler R T, et al. Tomographic determination of velocity and depth in lateral varying media.Geophysics, 1985,50(4) :903-923
[2] Harlan W S. Tomographic estimation of shear velocities from shallow cross-well seismic data. 63~(th) Ann. Internat. Mtg. ,Soc. of Expl. Geophys, 1990． 86-89
[3] 杨文采.地球物理反演的理论与方法.北京:地质出版社,1997 Yang W C. Theory and Methods of Geophysical Inversion (in Chinese). Beijing; Geological Publishing House, 1997
[4] Yl-Yahya K. Velocity analysis by iterative profile migration.Geophysics, 1989,54(6) :718-729
[5] Liu Z, Bleistein N. Migration velocity analysis; Theory and an iterative algorithm. Geophysics, 1995,60;142-153
[6] 洪学海,朱介寿,曹家敏等.中国大陆地壳上地幔S波品质因子三维层析成像.地球物理学报,2003,46(5) :642-651 Hong X H, Zhu J T, Cao J M, et al. Tomography of the 3-D S-wave quality factor of the crust and upper mantle in China. Chinese J. Geophys. (in Chinese) , 2003, 46 (5) : 642-651
[7] Billette F, Lambare G. Velocity macro-model estimation from seismic reflection data by stereo-tomography. Geophys.J. Int. ,1998,135(2) :671-680
[8] 刘福田,吴华.中国大陆及其邻近地区的地震层析成象.地球物理学报,1989,32(3) :281-291 Liu F T, Wu H. Seismic tomography of the Chinese continent and adjacent region. Chinese J. Geophys. ( in Chinese), 1989,32(3) :281-291
[9] Zhu X H, Sixta D P, Angstman B G. Tomostatics: Turning-ray tomography + static corrections. The Leading Edge,1992,11:15-23
[10] 李录明,罗省贤,赵波.初至波表层模型层析反演.石油地球物理勘探,2000,35(5) :559-564 Li L M, Luo X X, Zhao B. Tomographic inversion of first break in surface model. Oil Geophysical Prospecting ( in Chinese) ,2000,35(5) : 559-564
[11] Liu Y Z, Dong L G. Regularizations in first arrival tomography. 13 th European Meeting of Environmental and Engineering Geophysics, Istanbul, Turkey, 2007
[12] 刘玉柱,董良国.近地表速度结构初至波层析影响因素分析.石油地球物理勘探,2007,42(5) :544-553 Liu Y Z, Dong L G. Analysis of influence factors of first-breaks tomography. Oil Geophysical Prospecting ( in Chinese), 2007,42(5) :544-553
[13] 刘玉柱,董良国,夏建军.初至波走时层析成像中的正则化方法.石油地球物理勘探,2007,42(6) :682-685,698 Liu Y Z, Dong L G , Xia J J. Normalized approach in tomographic imaging of first breaks travel time. Oil Geophysical Prospecting (in Chinese), 2007, 42 (6) : 682-685,698
[14] Vasco D W, Majer E L. Wavepath traveltime tomography.Geophys. J. Int. ,1993,115:1055-1069
[15] Marquering H, Dahlen F A, Nolet G. Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana-doughnut paradox. Geophys. J. Int. ,1999,137:805-815
[16] Kravtsov, Orlov. On the validity conditions of the geometrical optics method. In: Recent Problems of Propagation and Scattering of Waves. IRE Acad. Sci. USSR, Moscow ( in Russian), 1979
[17] Wielandt E. On the validity of the ray approximation for interpreting delay times. In: Nolet, Seismic Tomography.D. Reidel Publishing Company, 1987
[18] Woodward M J. Wave-equation tomography. Geophysics,1992,57(1) : 15-26
[19] Devanvey A J. Geophysical diffraction tomography. IEEE Trans . Geoscience and Remote Sensing ,1984 ,GE-22(1) :3-13
[20] Tarantola A. Inversion of seismic data in acoustic approximation. Geophysics, 1984,49:1259-1266
[21] Wu R S, Toksoz M N. Diffraction tomography and multisource holography applied to seismic imaging.Geophysics, 1987,52(1) :11-25
[22] Pratt R G, Goulty N R. Combining wave-equation imaging with traveltime tomography to form high-resolution images from crosshole data. Geophysics, 1991,56(2) :208-224
[23] Schuster G T, Aksel Quintus-Bosz. Wavepath eikonal traveltime inversion: Theory. Geophysics, 1993, 58 (9) : 1314-1323
[24] Schuster G T. Resolution limits for crosswell migration and traveltime tomography. Geophys. J. Int. , 1996,127 :427-440
[25] Luo Y, Schuster G T. Wave-equation traveltime inversion.Geophysics, 1991 ,56(5) : 645-653
[26] Sheng J, Leed A, Buddensiek M, et al. Early arrival waveform tomography on near-surface refraction data.Geophysics,2006,71(4) :47-57
[27] Zhou Bing. Crosshole inversion with normalized full-waveform amplitude data. Geophysics, 2003,68 (4) : 1320-1330
[28] Michelena R J, Harris J M. Tomographic traveltime inversion using natural pixels. Geophysics, 1991, 56:635-644
[29] Sheng Xu. Yu Zhang, Tony Huang. Enhanced tomography resolution by a fat ray technique. 76~(th) Ann. Internat. Mtg. ,Soc. of Expl. Geophys,2006． 3354-3357
[30] Tarantola A. Inverse Problem Theory, Methods for Data Fitting and Model Parameter Estimation. New York:Elsevier,1987
[31] Cerveny V, Soares J E P. Fresnel volume ray tracing. Geophysics, 1992,57 :902-915
[32] Slaney M, Kak A C, Larsen L. Limitations of imaging with first-order diffraction tomography. IEEE Transactions on Microwave Theory and Techniques , 1984,MTT-32:860-873
[33] Snieder R, Lomax A. Wavefield smoothing and the effect of rough velocity perturbations on arrival times and amplitudes.Geophysical Journal International ,1996 ,125 :796-812
[34] Marquering H, Nolet G, Dahlen F A. Three-dimensional waveform sensitivity kernels. Geophysical Journal International, 1998 ,132 : 521-534
[35] Spetzler G, Snieder R. The effect of small-scale heterogeneity on the arrival time of waves. Geophysical Journal International, 2001,145:786-796
[36] Spetzler G, Snieder R. The fresnel volume and transmitted waves. Geophysics, 2004,69 :653-663
[37] Dahlen F A, Hung S H, Nolet G. Frechet kernels for finite-frequency traveltimes-Ⅰ. Theory. Geophysical Journal International, 2000,141:157-174
[38] Dahlen F A. Finite-frequency sensitivity kernels for boundary topography perturbations. Geophysical Journal International,2005,162:525-540
[39] Hung S H, Dahlen F A, Nolet G. Wavefront healing: a banana-doughnut perspective. Geophysical Journal International,2001,146:289-312
[40] Zhang Z G, Shen Y, Zhao L. Finite-frequency sensitivity kernels for head waves. Geophysical Journal International,2007,171:847-856
[41] Jocker J, Spetzler J, Smeulders D, et al. Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves. Geophysics, 2006 ,71:1 67-177
[42] Liu Y Z, Dong L G, Wang Y W, et al. Sensitivity kernels for seismic Fresnel volume tomography. Geophysics, 2009,74(in press)
[2] Harlan W S. Tomographic estimation of shear velocities from shallow cross-well seismic data. 63~(th) Ann. Internat. Mtg. ,Soc. of Expl. Geophys, 1990． 86-89
[3] 杨文采.地球物理反演的理论与方法.北京:地质出版社,1997 Yang W C. Theory and Methods of Geophysical Inversion (in Chinese). Beijing; Geological Publishing House, 1997
[4] Yl-Yahya K. Velocity analysis by iterative profile migration.Geophysics, 1989,54(6) :718-729
[5] Liu Z, Bleistein N. Migration velocity analysis; Theory and an iterative algorithm. Geophysics, 1995,60;142-153
[6] 洪学海,朱介寿,曹家敏等.中国大陆地壳上地幔S波品质因子三维层析成像.地球物理学报,2003,46(5) :642-651 Hong X H, Zhu J T, Cao J M, et al. Tomography of the 3-D S-wave quality factor of the crust and upper mantle in China. Chinese J. Geophys. (in Chinese) , 2003, 46 (5) : 642-651
[7] Billette F, Lambare G. Velocity macro-model estimation from seismic reflection data by stereo-tomography. Geophys.J. Int. ,1998,135(2) :671-680
[8] 刘福田,吴华.中国大陆及其邻近地区的地震层析成象.地球物理学报,1989,32(3) :281-291 Liu F T, Wu H. Seismic tomography of the Chinese continent and adjacent region. Chinese J. Geophys. ( in Chinese), 1989,32(3) :281-291
[9] Zhu X H, Sixta D P, Angstman B G. Tomostatics: Turning-ray tomography + static corrections. The Leading Edge,1992,11:15-23
[10] 李录明,罗省贤,赵波.初至波表层模型层析反演.石油地球物理勘探,2000,35(5) :559-564 Li L M, Luo X X, Zhao B. Tomographic inversion of first break in surface model. Oil Geophysical Prospecting ( in Chinese) ,2000,35(5) : 559-564
[11] Liu Y Z, Dong L G. Regularizations in first arrival tomography. 13 th European Meeting of Environmental and Engineering Geophysics, Istanbul, Turkey, 2007
[12] 刘玉柱,董良国.近地表速度结构初至波层析影响因素分析.石油地球物理勘探,2007,42(5) :544-553 Liu Y Z, Dong L G. Analysis of influence factors of first-breaks tomography. Oil Geophysical Prospecting ( in Chinese), 2007,42(5) :544-553
[13] 刘玉柱,董良国,夏建军.初至波走时层析成像中的正则化方法.石油地球物理勘探,2007,42(6) :682-685,698 Liu Y Z, Dong L G , Xia J J. Normalized approach in tomographic imaging of first breaks travel time. Oil Geophysical Prospecting (in Chinese), 2007, 42 (6) : 682-685,698
[14] Vasco D W, Majer E L. Wavepath traveltime tomography.Geophys. J. Int. ,1993,115:1055-1069
[15] Marquering H, Dahlen F A, Nolet G. Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana-doughnut paradox. Geophys. J. Int. ,1999,137:805-815
[16] Kravtsov, Orlov. On the validity conditions of the geometrical optics method. In: Recent Problems of Propagation and Scattering of Waves. IRE Acad. Sci. USSR, Moscow ( in Russian), 1979
[17] Wielandt E. On the validity of the ray approximation for interpreting delay times. In: Nolet, Seismic Tomography.D. Reidel Publishing Company, 1987
[18] Woodward M J. Wave-equation tomography. Geophysics,1992,57(1) : 15-26
[19] Devanvey A J. Geophysical diffraction tomography. IEEE Trans . Geoscience and Remote Sensing ,1984 ,GE-22(1) :3-13
[20] Tarantola A. Inversion of seismic data in acoustic approximation. Geophysics, 1984,49:1259-1266
[21] Wu R S, Toksoz M N. Diffraction tomography and multisource holography applied to seismic imaging.Geophysics, 1987,52(1) :11-25
[22] Pratt R G, Goulty N R. Combining wave-equation imaging with traveltime tomography to form high-resolution images from crosshole data. Geophysics, 1991,56(2) :208-224
[23] Schuster G T, Aksel Quintus-Bosz. Wavepath eikonal traveltime inversion: Theory. Geophysics, 1993, 58 (9) : 1314-1323
[24] Schuster G T. Resolution limits for crosswell migration and traveltime tomography. Geophys. J. Int. , 1996,127 :427-440
[25] Luo Y, Schuster G T. Wave-equation traveltime inversion.Geophysics, 1991 ,56(5) : 645-653
[26] Sheng J, Leed A, Buddensiek M, et al. Early arrival waveform tomography on near-surface refraction data.Geophysics,2006,71(4) :47-57
[27] Zhou Bing. Crosshole inversion with normalized full-waveform amplitude data. Geophysics, 2003,68 (4) : 1320-1330
[28] Michelena R J, Harris J M. Tomographic traveltime inversion using natural pixels. Geophysics, 1991, 56:635-644
[29] Sheng Xu. Yu Zhang, Tony Huang. Enhanced tomography resolution by a fat ray technique. 76~(th) Ann. Internat. Mtg. ,Soc. of Expl. Geophys,2006． 3354-3357
[30] Tarantola A. Inverse Problem Theory, Methods for Data Fitting and Model Parameter Estimation. New York:Elsevier,1987
[31] Cerveny V, Soares J E P. Fresnel volume ray tracing. Geophysics, 1992,57 :902-915
[32] Slaney M, Kak A C, Larsen L. Limitations of imaging with first-order diffraction tomography. IEEE Transactions on Microwave Theory and Techniques , 1984,MTT-32:860-873
[33] Snieder R, Lomax A. Wavefield smoothing and the effect of rough velocity perturbations on arrival times and amplitudes.Geophysical Journal International ,1996 ,125 :796-812
[34] Marquering H, Nolet G, Dahlen F A. Three-dimensional waveform sensitivity kernels. Geophysical Journal International, 1998 ,132 : 521-534
[35] Spetzler G, Snieder R. The effect of small-scale heterogeneity on the arrival time of waves. Geophysical Journal International, 2001,145:786-796
[36] Spetzler G, Snieder R. The fresnel volume and transmitted waves. Geophysics, 2004,69 :653-663
[37] Dahlen F A, Hung S H, Nolet G. Frechet kernels for finite-frequency traveltimes-Ⅰ. Theory. Geophysical Journal International, 2000,141:157-174
[38] Dahlen F A. Finite-frequency sensitivity kernels for boundary topography perturbations. Geophysical Journal International,2005,162:525-540
[39] Hung S H, Dahlen F A, Nolet G. Wavefront healing: a banana-doughnut perspective. Geophysical Journal International,2001,146:289-312
[40] Zhang Z G, Shen Y, Zhao L. Finite-frequency sensitivity kernels for head waves. Geophysical Journal International,2007,171:847-856
[41] Jocker J, Spetzler J, Smeulders D, et al. Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves. Geophysics, 2006 ,71:1 67-177
[42] Liu Y Z, Dong L G, Wang Y W, et al. Sensitivity kernels for seismic Fresnel volume tomography. Geophysics, 2009,74(in press)
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