地震逆散射理论与深度成像
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摘要
地震数据处理方法中，地震偏移、地震层析成像和波动方程系数反演构成了二十世纪后期研究的主要方向，其中以地震偏移研究地球内部细结构最为成功，地震层析成像和波动方程系数反演取得了很大进展。然而，这些方法存在的一个根本性问题是在进行反演时需要建立一个速度模型，反演结果的好坏在很大程度上依赖于速度模型建立得恰当与否。而地震波的传播速度是地震勘探中一个至关重要的参数，如果已知了传播速度，那就没必要再进行反演了。因此，解决这一根本性的矛盾是现在和以后研究的重大课题。
地震波反演的另一个障碍，主要是所记录的地震波响应中频率信息及相应的振幅真值的不完整与严重缺失。其中高频信息的缺失，直接影响地震波对地层层位识别的分辨率；低频成分的缺失导致重构波阻抗的失败。采集系统特性和技术指标决定了所记录的地震波振幅值为近似的相对振幅，用这样的相对振幅作为地震波参数反演的振幅真值依据，必然导致反演参数值的严重失真。这样使得即使在满足弱散射的条件，运用Born近似反演技术，也仅可以获得界面位置，而得不到反射系数的真值。实际上，从地球物理的实用观点出发，人们特别关心的往往并不是要求恢复全部的物性参数，而是要知道它的间断性及梯度变化较大的状况和位置(即奇性点)。
考虑到上述问题，本文在Bleistein和Cohen等人对Born近似的深入研究基础上，运用地震逆散射理论进行深度成像，反演地层奇性界面的位置。Born近似反演由于只利用了散射序列中的第一项，它只适应于小扰动量的成像，对于大扰动量的成像，它会产生很大的误差。本文提出的反演理论，考虑到散射序列中高阶项对成像结果的影响，在反演时利用逆散射序列中的高阶项以弥补散射场数据的丢失，使得在大扰动量的情况下同样能够实现界面位置和形态的精确成像，解决了大对比度情况下的成像问题。
本文第二章对Born近似反演算法进行了深入研究和分析，指出了Born近似反演存在的问题。Born近似成像对于小扰动量的情况，能够取得较好的结果，但其反演的奇性界面位置，除第一个界面较准确外，其余均与真实位置有一定偏差，并且这种偏差随着界面的反射系数的增加而迅速增大。
本文第三章和第四章，就散射理论和逆散射理论进行了研究。在第三章，首先对散射理论进行了研究，分析了散射序列中各项的物理意义，并推导了一维情况下多层介质的散射场表达式。然后，就一维情况下的逆散射序列奇性反演算法进行了推导，运用摄动法求解逆散射序列，得到了一套理论公式，并用模型数据验证了算法的有效性。在第四章，主要研究了三维情况下的逆散射奇性反演算法。通过2.5维模型数据的检验，证明了算法的有效性。
本文提出的反演理论，主要是基于声波波动方程展开讨论和研究的，其研究方法对于弹性波方程和粘弹性波方程同样适应。
In seismic data processing, the main research directions are seismic migration, seismic tomography and wave equation coefficient inversion in late 20th century. In these methods, seismic migration is the most successful to study the subtle structure in the earth. Seismic tomography and wave equation coefficient inversion have greatly improved. But, these methods have a dead problem, i.e., the velocity model is necessary. The inverse results depend on the velocity model. If the model is correct, then the result is credible. Otherwise, the result is false. But the velocity of seismic wave is an important parameter in seismic prospecting. If we obtain the velocity model, it is not necessary to do inversion. So solving the problem is a great subject at present and in the future.
The other problem in seismic inversion is that the frequency information and amplitude real value recorded by seismograph are incomplete and severely absent. The absence of high frequency information influences distinguishing location of layer. And the absence of low frequency information leads to fail to reconstruct the wave impedance. Technical parameters and characters of sampling system determine that seismic wave amplitude recorded by seismograph is approximate relative amplitude. Using these data necessarily leads to serious distortion of inverse parameters. So using Born approximation can only obtain the location of interface even if the earth medium is little disturbance. In fact, our aims are not to obtain all parameters, only know the discontinuity or singularity of interface in most case by applied opinion.
Considering problem mentioned in above part and founding on Bleistein's and Cohen's researches on Born approximation, the author carries out depth imaging inversion by using inverse scattering series for obtaining the singularity locations of layers. Because of taking only advantage of the first item in scattering series, method of Born approximation inversion is only suitable to little disturbance imaging. And it will produce great error in condition of great perturbation. The inversion theory advanced in this paper can also obtain the real location and shape of interface in great perturbation as a result of using the high items in scattering series. It solves the imaging problem in great contrast.
In chapter 2, the author deeply studies and analyzes the arithmetic of the method of Born approximation inversion and points out the limitations and disadvantage of the method. The good inverse results can be obtained in little disturbance by Born approximation. But the singularity location inversed by Born approximation inversion
is false except the first interface. With reflect coefficients increasing, the error is rapidly enlarged.
In chapter 3, the author studies the scattering theory and analyzes the physical meaning of each item in scattering series. At same time, the author deduces the formula of scattering fields in one dimension. Then, the singularity inversion arithmetic of inverse scattering series is deduced in one dimension. Using perturbation method to solve inverse scattering series, the author obtains a set of inverse formula and verifies its validity through model data. In chapter 4, the author studies the singularity inversion arithmetic of inverse scattering series in three dimensions and proves validity of arithmetic through 2.5D theoretic model data.
The study in the paper is based on acoustic wave equation, but its research methods are also suitable to elastic and viscoelastic wave equation.
地震波反演的另一个障碍，主要是所记录的地震波响应中频率信息及相应的振幅真值的不完整与严重缺失。其中高频信息的缺失，直接影响地震波对地层层位识别的分辨率；低频成分的缺失导致重构波阻抗的失败。采集系统特性和技术指标决定了所记录的地震波振幅值为近似的相对振幅，用这样的相对振幅作为地震波参数反演的振幅真值依据，必然导致反演参数值的严重失真。这样使得即使在满足弱散射的条件，运用Born近似反演技术，也仅可以获得界面位置，而得不到反射系数的真值。实际上，从地球物理的实用观点出发，人们特别关心的往往并不是要求恢复全部的物性参数，而是要知道它的间断性及梯度变化较大的状况和位置(即奇性点)。
考虑到上述问题，本文在Bleistein和Cohen等人对Born近似的深入研究基础上，运用地震逆散射理论进行深度成像，反演地层奇性界面的位置。Born近似反演由于只利用了散射序列中的第一项，它只适应于小扰动量的成像，对于大扰动量的成像，它会产生很大的误差。本文提出的反演理论，考虑到散射序列中高阶项对成像结果的影响，在反演时利用逆散射序列中的高阶项以弥补散射场数据的丢失，使得在大扰动量的情况下同样能够实现界面位置和形态的精确成像，解决了大对比度情况下的成像问题。
本文第二章对Born近似反演算法进行了深入研究和分析，指出了Born近似反演存在的问题。Born近似成像对于小扰动量的情况，能够取得较好的结果，但其反演的奇性界面位置，除第一个界面较准确外，其余均与真实位置有一定偏差，并且这种偏差随着界面的反射系数的增加而迅速增大。
本文第三章和第四章，就散射理论和逆散射理论进行了研究。在第三章，首先对散射理论进行了研究，分析了散射序列中各项的物理意义，并推导了一维情况下多层介质的散射场表达式。然后，就一维情况下的逆散射序列奇性反演算法进行了推导，运用摄动法求解逆散射序列，得到了一套理论公式，并用模型数据验证了算法的有效性。在第四章，主要研究了三维情况下的逆散射奇性反演算法。通过2.5维模型数据的检验，证明了算法的有效性。
本文提出的反演理论，主要是基于声波波动方程展开讨论和研究的，其研究方法对于弹性波方程和粘弹性波方程同样适应。
In seismic data processing, the main research directions are seismic migration, seismic tomography and wave equation coefficient inversion in late 20th century. In these methods, seismic migration is the most successful to study the subtle structure in the earth. Seismic tomography and wave equation coefficient inversion have greatly improved. But, these methods have a dead problem, i.e., the velocity model is necessary. The inverse results depend on the velocity model. If the model is correct, then the result is credible. Otherwise, the result is false. But the velocity of seismic wave is an important parameter in seismic prospecting. If we obtain the velocity model, it is not necessary to do inversion. So solving the problem is a great subject at present and in the future.
The other problem in seismic inversion is that the frequency information and amplitude real value recorded by seismograph are incomplete and severely absent. The absence of high frequency information influences distinguishing location of layer. And the absence of low frequency information leads to fail to reconstruct the wave impedance. Technical parameters and characters of sampling system determine that seismic wave amplitude recorded by seismograph is approximate relative amplitude. Using these data necessarily leads to serious distortion of inverse parameters. So using Born approximation can only obtain the location of interface even if the earth medium is little disturbance. In fact, our aims are not to obtain all parameters, only know the discontinuity or singularity of interface in most case by applied opinion.
Considering problem mentioned in above part and founding on Bleistein's and Cohen's researches on Born approximation, the author carries out depth imaging inversion by using inverse scattering series for obtaining the singularity locations of layers. Because of taking only advantage of the first item in scattering series, method of Born approximation inversion is only suitable to little disturbance imaging. And it will produce great error in condition of great perturbation. The inversion theory advanced in this paper can also obtain the real location and shape of interface in great perturbation as a result of using the high items in scattering series. It solves the imaging problem in great contrast.
In chapter 2, the author deeply studies and analyzes the arithmetic of the method of Born approximation inversion and points out the limitations and disadvantage of the method. The good inverse results can be obtained in little disturbance by Born approximation. But the singularity location inversed by Born approximation inversion
is false except the first interface. With reflect coefficients increasing, the error is rapidly enlarged.
In chapter 3, the author studies the scattering theory and analyzes the physical meaning of each item in scattering series. At same time, the author deduces the formula of scattering fields in one dimension. Then, the singularity inversion arithmetic of inverse scattering series is deduced in one dimension. Using perturbation method to solve inverse scattering series, the author obtains a set of inverse formula and verifies its validity through model data. In chapter 4, the author studies the singularity inversion arithmetic of inverse scattering series in three dimensions and proves validity of arithmetic through 2.5D theoretic model data.
The study in the paper is based on acoustic wave equation, but its research methods are also suitable to elastic and viscoelastic wave equation.
引文
1．程建春，韦钰．Born近似二维弹性波方程的双参数反演．应用科学学报，1988，6(3)：203—208
2．陈生昌，曹景忠，马在田．基于拟线性Born近似的叠前深度偏移方法．地球物理学报，2001，44(5)：704—709
3．陈小宏，牟永光．二维地震资料波动方程非线性反演．地球物理学报，1996，39(3)：401—408
4．陈祖权．最佳加权叠加．海上油气，1982，No．2
5．陈祖传．多次波剩余时差分析法．北京：石油工业出版社，1997
6．大港油田科技丛书编委会．地震勘探资料处理和解释技术．北京：石油工业出版社，1999
7．丁科，宋守根等．层状介质模型散射波场的研究．中南工业大学学报，2001，32(6)：555—558
8．丁科，宋守根．逆散射序列的研究．中国地球物理学会年刊(2001)(中国地球物理学会 编)．云南科技出版社，2001：348
9．董泽斌，吴良元．地震资料数据处理．北京：石油工业出版社，1992
10．段虞荣，郑继明，段绍光．小波分析在油气田地球物理勘探中的应用．重庆大学学报(自然科学版)，1996，19(6)：44—53
11．范祯祥，郑仙种．变背景速度2.5维反散射技术在地震勘探中的应用问题．地球物理学报，1995，38(增刊1)：112—122
12．顾德淦 主编．摄动方法及其在某些力学问题中的应用．北京：高等教育出版社，1993
13．何樵登主编．地震勘探原理与方法．北京：地质出版社，1986
14．黄联捷，杨文采．参考波速线性变化时声波方程逆散射反演．地球物理学报，1991，34(1)：89—98
15．黄联捷，杨文采．声波方程逆散射反演的近似方法．地球物理学报，1991，34(5)：626—634
16．李庆春，朱光明．基于小波变换的薄层地震信号奇点的检测．地震学报，2000，22(1)：54—58
17．李世雄，林其彭，叶雅菊．沿曲线族的Radon变换．地球物理学报，1990，33(专辑Ⅱ)：81—88
18．李世雄．一维波动方程的奇性反演与小波．地球物理学报，1995，38(1)：93—104
19．刘洪，李幼铭，吴如山．三维散射算子及其在逆散射中的应用．地球物理学进展，1994，9(2)：54—83
20．刘继军，王元明．层状不均匀介质的一维地球模型物性参数反演．高校应用数学学报，1994，9(A辑Ⅱ)：109—117
21．刘继军．2.5维介质Born近似波速反演唯一性．应用数学学报，1998，21(1)：66—73
22．刘继军，王元明．一类双曲反问题的逼近算法及收敛性．数学物理学报，1997，17(2)：134—144
23．栾文贵．我国地球物理反演问题研究的某些进展．地球物理学报，1990，33(5)：501—508
24．栾文贵．关于一维弹性波动方程的反问题．地球物理学报，1990，33(专辑Ⅱ)：39—53
25．陆基孟 主编．地震勘探原理(上、下)．北京：石油大学出版社，2001
26．陆振球，谭春虎，薛强，陶智勇．普遍声逆散射微扰论与形式参数展开法．南开大学学报(自然科学版)，1999，32(3)：75—82
27．马在田．高阶方程偏移的分裂算法．地球物理学报，1983，31(5)：678—686
28．马在田．标量波动方程全倾角有限差分偏移．地球物理学报，1988，39(5)：678—686
29．马在田．当前反射地震学研究中的问题浅析，地球物理学进展，1994，9(1)：84—89
30．马在田．地震成像技术——有限差分偏移．北京：石油工业出版社，1989
31．马在田等编著．计算地球物理学概论．上海：同济大学出版社，1997
32．钱伟长 主编．奇异摄动理论及其在力学中的应用．北京：科学出版社，1981
33．宋海斌，张关泉．层状介质弹性参数反演问题研究综述．地球物理学进展．1998，13(4)：67—78
34．王辉，何兵寿．应用T—A双重拟合法进行多次波压制．物探化探计算技术，1999，21(1)：9—13
35．王妙月．我国地震勘探研究进展．地球物理学报，1997，40(增刊)：257—265
36．王忠仁，何樵登．叠前共炮点道集的奇性反演研究．地球物理学报，1998，41(增刊)：326—336
37．王守东，刘家琦，黄文虎．二维声波方程速度反演的一种方法．地球物理学报，1995，38(6)：833—839
38．吴律．在时间域中的大倾角波动方程偏移．地球物理学报，1980，23(23)
39．吴律．层析基础及其在井间地震中的应用．北京：石油工业出版社，1997
40．谢干权，李建华．解三维方程逆散射势问题的新特征迭代法．中国科学(A辑)，1988，17(4)：359—656
41．杨文采．地球物理反演和地震层析成像．北京：地质出版社，1989
42．杨文采．非线性波动方程地震反演的方法原理及问题．地球物理学进展，1992，7(7)：9—19
43．杨文采．波动方程的逆散射与迭代线性化反演．石油物探，1995，34(3)：114—121
44．杨文采．非线性地震反演方法的补充及比较．石油物探，1995，34(4)：109—116
45．杨文采．地震波反演的BG—逆散射方法．地球物理学报，1995，38(3)：358—366
46．尹峰，王俊生，最大熵时域逆散射层析成像的研究．地球物理学报，1994，37(5)：673—681
47．俞寿朋．高分辨率地震勘探．北京：石油工业出版社，1994
48．张关泉，侯唯健．三维叠后差分偏移的因子分解法．地球物理学报，1996，39(3)：382—391
49．张关泉．一维声波方程的反演问题．中国科学(A辑)，1988，17(7)：707—721
50．张钋，李幼铭，刘洪．几类叠前深度偏移方法的研究现状．地球物理学进展，2000，15(2)：30—39
51．郑继明，周宗放，杨春德．基于小波变换的信号奇异性检测．重庆邮电学院学报，1998，10(1)：8—12
52．钟森．反射地震记录的多尺度边缘检测．石油地球物理勘探，1998，33(1)：61—65
53．朱文浩，钟伟芳．三维弹性波场的线性化逆散射问题．华中理工大学学报，1994，22(9)：71—75
54．朱文浩，陈柏鸿，钟伟芳．地表反射弹性波多参数反演．石油物探，1997，36(1)：28—35
55．朱文浩，戴辉，钟伟芳．半空间反射弹性波多参数线性化逆散射．应用数学和力学，2000，21(10)：1081—1086
56. Andrew E. Yagle, Bernard C. Levy, Layer-stripping solutions of multidimensional inverse scattering problems. J. Math. Phys., 1986, 27(6): 1701—1710
57. Antoine Guitton, Guillaume Cambois, Multiple elimination using a pattern-recognition technique. The Leading Edge, 1999, 18(1): 92—98
58．Berkhout J．著，马在田，张叔伦译．地震偏移．北京：石油工业出版社，1983
59. Berkhout J., M. P. de Graaff, The inverse scattering problem in terms of multiple elimination and seismic migration, 1982, Annual Meeting Abstracts, Society Of Exploration Geophysicists, Session:S9.1
60. Berkhout J., Multiple removedbased on the feedback model. The Leading Edge, 1999, 18(1): 127—131
61. Berkhout J., Verschuur D. J., Estimation of multiple scattering by iterative inversion, part Ⅰ:
Theoretical considerations. Geophysics, 1997, 62(5): 1586—1595.
62. Berkhout J., Verschuur D. J., Estimation of multiple scattering by iterative inversion, part Ⅱ: Practical aspects and examples. Geophysics, 1997, 62(5): 1596—1611.
63. Beylkin G., Imaging of discontinuities in the inverse scattering problem by inversion of a csusal generalized Radon transform. J. Math. Phys., 1985,26(1): 99—108
64. Bleistein N., Cohen J. K., and John W. Stockwell, Jr., Mathematics of Multi-dimensional Seismic Imaging, Migration, and Inversion. Springer Verlag, New York, 1996
65. Bleistein N., On the imaging of reflectors in the earth. Geophysics, 1987, 52(7): 931—942
66. Bleistein N., Cohen J. K., Hagin E G., Two and one-half domension Born inversion with an arbitrary reference. Geophysics, 1987,52(1): 26—36
67. Bleistein N., Cohen J. K., Hagin F. G., Computional and asymptotic of velocity inversion. Geophysics, 1985, 50(8): 1253—1265
68. Bleistein N., Cohen J. K., The velocity inversion problem—Present status, new direction, Geophysics, 1982, 47(11): 1497—1511
69. Bleistein N., Gray S. H., An extension of the Born inversion method to a depth dependent reference profile. Geophysical Prospecting, 1985, 33(8): 999—1022
70. Bleistein N., Two-and-one-half dimensional in-plane wave propagation. Geophysical Prospecting, 1986, 34(6): 686—703
71. Bleistein N., Mathematical methods for wave phenomena. Academic Press, Inc., 1984
72. Chert Y. M., Liu J. Q., A numerical algorithm for solving inverse problems of two-dimensional wave equation. J. Comp. Phys., 1983, 50(1): 193—208
73．Chadan K．，Sabatier P．C．著，张天元译．量子散射理论的逆问题．北京：科学出版社，1989
74．Claerbout J．著，许云译．地震成像理论及方法．北京：石油工业出版社，1991
75．Claerbout J．著，陈玉等译．地球物理数据处理基础．北京：石油化学工业出版社，1979
76. Clayton R. W., Stolt R. H., A Born-WKBJ inversion method for acoustic reflection data. Geophysics, 1981, 46(8): 1559—1567
77. Coen S., Velocity, density profiles of a layered acoustic medium from common source-point data. Geophysics, 1982, 47(6):, 898—905
78. Cohen J. K., Hagin F. G., Velocity inversion using a stratified reference. Geophysics, 1985, 50(11): 1689—1700
79. Cohen J. K., Bleistein N., Three-dimensional Born inversion with an arbitrary referece, Geophysics, 1986, 51(8): 1552—1558
80. Cohen J. K., Bleistein N., Velocity inversion procedure for acoustic waves. Geophysics, 1979, 44(6): 1077—1087
81. De Hoop. Asymptotic inversion: multi pathing and caustics. 1998, 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts: 1534—1537
82. Dong Wenjie, Emanue M. J., Bording P., et al, A computer implementation of 2.5D common-shot inversion. Geophysics, 1991, 56(9): 1384—1394
83. Douglas J. Foster, Charles C. Mosher, Suppression of multiple reflections using the Radom transform. Geophysics, 1992, 57(3): 386—395
84. Eaton D. W., Weak elastic-wave scattering from massive sulfide orebodies. Geophysics, 1999, 64(1): 289—299
85．Gaust Nolet编，冯锐等译．地震层析技术．北京：地质出版社，1991
86. Gazdag J., Wave-equation migration with the phase shift method. Geophysics. 1978, 43(6): 1342—1352
87. Gazdag J., Sguazzero P., Migration of seismic data by phase shift plus interpolation. Geophysical Prospecting. 1984, 49(1): 124—131
88. Guitton, G. Cambois, Multiple elimination using a patteron-recognition technique. The Leading Edge, 1999, 18(1): 92—98
89. Hagin F. G., Cohen J. K., Refinement to the linear velocity inversion theory. Geophysics, 1984, 49(2): 112—118
90. Han B., Two prestack converted-wave migration algorithms for vertical transverse isotropy. 2000, CWP Project Review, Center for Wave Phenomena, Colorado School of Mines, CWP-344
91. Hill N. R., Gaussian beam migration. Geophysics, 1990, 55(11): 1416—1428
92. Houston L. M., Multiple suppression using a local coherence filter. Geophysics, 1998,63(2): 652—659
93. Howard M. S., Inverse scattering for a layered acoustic medium using the first-order equations of motion. Geophysics, 1983, 48(2): 163—170.
94. Huang Lian-Jie, Fehler M. C., Wu Ru-Shan, Extended local Born Fourier migration method. Geophysics, 1999, 64(5): 1524—1534
95. Ikelle L. T., Using even terms of the scattering series for deghosting and multiple attenuation of ocean-bottom cable data. Geophysics, 1999, 64(2): 579—592
96. Jost R., Walte K., Construction of a potential from a pahase shift. Physical Review. 1952, 87(6): 977—991
97. Kessinger W., Extended split-step Fourier migration. 1992, 62nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts: 917—920
98. Kristensson G., Krueger R. J., Direct and inverse scattering in the time domain for a dissipative wave equation.I.Scattering operators. J. Math. Phys., 1986, 27(6): 1667—1682
99. Kristensson G., Krueger R. J., Direct and inverse scattering in the time domain for a dissipative wave equation. Ⅱ.Simultaneous reconstruvtion of disspation and phase velocity profiles. J. Math. Phys., 1986, 27(6): 1683—1693
100. Landa E., Belfer I. and Keydar S., A new method for multiple attenuation in the parabolic t-p domain. 1997, Annual Meeting Abstracts, Society Of Exploration Geophysicists: 1402—1405
101. Lee M., Mason L., Jacek G. M., Split-step Fourier shot-record migration with deconvolution imaging. Geophysics, 1991, 56(11): 1768—1793
102. Li Z., Compensating finite-defference errors in 3D migration and modeling. Geophysics, 1991, 56(10): 1650—1660
103. Lokshtanov D., Multiple suppression by single channel and multi-channel deconvolution in the tua-p domain. 1995, The 65th Annual International Meeting, SEG Expanded abstracts: 1428
104. Lokshtanov D., Multiple suppression by data-consistent deconvolution. The Leading Edge, 1999, 18(1): 115—119
105. Lu Guochun, Bjφrn Ursin, Jan Lutro, Model-based removal of water-layer multiple reflection. Geophysics, 1999, 64(6): 1816—1827
106. Matson K. H., The relationship between scattering theory and the primaries and multiples of reflection seismic data. Journal of Seismic Exploration, 1996, No.5: 63—78
107. Matson K. H., Weglein A. B., Removal of elastic interface multiples from land and ocean bottom data using inverse scattering. 1996, Annual Meeting Abstracts, Society Of Exploration Geophysicists: 1526—1530.
108. Matson K. H., An inverses scattering series method for attenuating elastic multiples from multicomponent land ocean bottom seismic data. Ph.D. Theory, 1997, The University of British Columbia.
109. Miller D., Oristaglio M., Beylkin G., A new slant on seismic imaging migration and integral geometry. Geophysics, 1987, 52(7): 931—942
110. Moses H. E., Calculation of the scattering potential from reflection coefficients. Physical Review. 1955, 102(2): 559—567
111. M. Nieto-Vesperinas, Innverse scattering problems: A study in terms of the zeros of entire functions. J. Math. Phys., 25(6): 2109—2115
112. Newton R. G., Inverse scattering: Ⅰ. One dimension. J. Math. Phys., 1980, 21(3): 493—505
113. Newton R. G., Inverse scattering: Ⅱ. Three dimensions. J. Math. Phys., 1980, 21(7): 1698—1715
114. Newton R. G., Inverse scattering: Ⅱ. Three dimensions, continued. J. Math. Phys., 1981, 22(10): 2191—2200
115. Newton R. G., Inverse scattering by a local impurity in a periodic potential in one dimension. J. Math. Phys., 1983, 24(8): 2152—2162
116. Norton J., Itertive seismic inversion, Geophys. J., 1988, 94: 457—468
117. Pratt R. G., Worthington M. H., The application of diffraction tomography to cross-hole seismic data. Geophysics, 1988, 53(5): 1284—1294
118. Prosser R. T., Formal solution of inverse scattering problems: Ⅰ. J. Math. Phys., 1969, 10(8): 1819—1822
119. Prosser R. T., Formal solution of inverse scattering problems: Ⅱ. J. Math. Phys., 1976, 17(11): 1775—1779
120. Prosser R. T., Formal solution of inverse scattering problems, Ⅲ. J. Math. Phys., 1980, 21(11): 2648—2653
121. Prosser R. T., Formal solution of inverse scattering problems, Ⅳ: Error estimates. J. Math. Phys., 1982, 23(11): 2127—2130
122. Schneider W. A., Integral formulation for migration in two and three dimensions. Geophysics, 1978, 43(1): 49—76
123. Stolt R. H., Migration by Fourier transform. Geophysics, 1978, 43(1): 23—48
124. Tarantola, Inversion of seismic reflection data in the acoustic approximation. Geophysics, 1984, 49(6): 1259—1266
125．Taylor J．R．著，耿天明，温源淇译．散射理论——非相对论性碰撞的量子理论．北京：科学出版社，1987
126. Thorson J. R., Velocity Stack and Slant Stack Stochastic Inversion. Geophysics, 1995, 60(12): 2727—2741
127. Tuncay Aktosun, Martin Klaus, Comelis van der Mee, Scattering and inverse scattering in one-dimensional nonhomogeneous media. J. Math. Phys., 1992, 33(5): 1717—1744
128. Weglein A. B., Gasparotto F. A., Carvalho P. M., Stolt R. H., An inverse-scattering series method for attenuating multiple in seismic reflection data. Geophysics, 1997, 62(6): 1975—1989
129. Weglein A. B., Multiple attenuation: an overview of recent advances. The Leading Edge, 1999, 18(1): 40—44
130. Weglein A. B., How can the inverse-scattering method really predict and subtract all multiples from a multidimensional earth with absolutely no subsurface information? The Leading Edge, 18(1): 132—136
131. Weglein A. B., Carvalho E M., Stolt R. H., Nonlinear inverse scattering for multiple suppression: Application to real data. part Ⅰ. 1992, Annual Meeting Abstracts, Society Of Exploration Geophysicists: 1093—1095.
132. Wiggins J. W., Multiple attenuation by explicit wave extrapolation to an interpreted horizon. The Leading Edge, 1999, 18(1): 48—54
133. Wiggins J. W., Using the parabolic Radon transform as a moveout filter. The 52th Annual
Meeting of the EAEG in Copenhagen.
134. Wiggins J. W., Kirchhoff integral extrapolation and migration of nonplanar data. Geophysics, 1984, 49(8): 1239—1248
135. Wolfgang Friederich, Propagation of seismic shear and surface wave in a laterally heterogeneous mantle by multiple forward scatting. Geophysical Journal International, 1999, 136(1): 180—204
136. Yoshio Murai, Teruo Yamashita, Multiple scattering of SH wave by imperfectly bonded interfaces with inhomogeneous strengths. Geophysical Journal International, 1998, 134(3): 677—688
137. Zhenyue Liu, N. Bleistein, Migration velocity analysis. Theory and an iterative algorithm. Geophysics, 1995, 60(1): 142—153
138. Zhou, B. and S. A. Greenhalgh, Wave-equation extrapolation-based multiple attenuation: 2-D filtering in the f-k domain. Geophysics, 1994, 59(9): 1377—1391
139. Zhou Binzhong, Stewart Greenhalgh, 1996, Multiple suppression by 2D filtering in the parabolic τ-p domain: a wave-equation-based method. Geophysical Prospecting, 44(5): 375—401
140. Zhu J., Lines L., Comparison of Kirchhoff and reverse-time migration methods with applications to prestack depth imaging of complex structures. Geophysics, 1998, 63(4): 1166—1176
2．陈生昌，曹景忠，马在田．基于拟线性Born近似的叠前深度偏移方法．地球物理学报，2001，44(5)：704—709
3．陈小宏，牟永光．二维地震资料波动方程非线性反演．地球物理学报，1996，39(3)：401—408
4．陈祖权．最佳加权叠加．海上油气，1982，No．2
5．陈祖传．多次波剩余时差分析法．北京：石油工业出版社，1997
6．大港油田科技丛书编委会．地震勘探资料处理和解释技术．北京：石油工业出版社，1999
7．丁科，宋守根等．层状介质模型散射波场的研究．中南工业大学学报，2001，32(6)：555—558
8．丁科，宋守根．逆散射序列的研究．中国地球物理学会年刊(2001)(中国地球物理学会 编)．云南科技出版社，2001：348
9．董泽斌，吴良元．地震资料数据处理．北京：石油工业出版社，1992
10．段虞荣，郑继明，段绍光．小波分析在油气田地球物理勘探中的应用．重庆大学学报(自然科学版)，1996，19(6)：44—53
11．范祯祥，郑仙种．变背景速度2.5维反散射技术在地震勘探中的应用问题．地球物理学报，1995，38(增刊1)：112—122
12．顾德淦 主编．摄动方法及其在某些力学问题中的应用．北京：高等教育出版社，1993
13．何樵登主编．地震勘探原理与方法．北京：地质出版社，1986
14．黄联捷，杨文采．参考波速线性变化时声波方程逆散射反演．地球物理学报，1991，34(1)：89—98
15．黄联捷，杨文采．声波方程逆散射反演的近似方法．地球物理学报，1991，34(5)：626—634
16．李庆春，朱光明．基于小波变换的薄层地震信号奇点的检测．地震学报，2000，22(1)：54—58
17．李世雄，林其彭，叶雅菊．沿曲线族的Radon变换．地球物理学报，1990，33(专辑Ⅱ)：81—88
18．李世雄．一维波动方程的奇性反演与小波．地球物理学报，1995，38(1)：93—104
19．刘洪，李幼铭，吴如山．三维散射算子及其在逆散射中的应用．地球物理学进展，1994，9(2)：54—83
20．刘继军，王元明．层状不均匀介质的一维地球模型物性参数反演．高校应用数学学报，1994，9(A辑Ⅱ)：109—117
21．刘继军．2.5维介质Born近似波速反演唯一性．应用数学学报，1998，21(1)：66—73
22．刘继军，王元明．一类双曲反问题的逼近算法及收敛性．数学物理学报，1997，17(2)：134—144
23．栾文贵．我国地球物理反演问题研究的某些进展．地球物理学报，1990，33(5)：501—508
24．栾文贵．关于一维弹性波动方程的反问题．地球物理学报，1990，33(专辑Ⅱ)：39—53
25．陆基孟 主编．地震勘探原理(上、下)．北京：石油大学出版社，2001
26．陆振球，谭春虎，薛强，陶智勇．普遍声逆散射微扰论与形式参数展开法．南开大学学报(自然科学版)，1999，32(3)：75—82
27．马在田．高阶方程偏移的分裂算法．地球物理学报，1983，31(5)：678—686
28．马在田．标量波动方程全倾角有限差分偏移．地球物理学报，1988，39(5)：678—686
29．马在田．当前反射地震学研究中的问题浅析，地球物理学进展，1994，9(1)：84—89
30．马在田．地震成像技术——有限差分偏移．北京：石油工业出版社，1989
31．马在田等编著．计算地球物理学概论．上海：同济大学出版社，1997
32．钱伟长 主编．奇异摄动理论及其在力学中的应用．北京：科学出版社，1981
33．宋海斌，张关泉．层状介质弹性参数反演问题研究综述．地球物理学进展．1998，13(4)：67—78
34．王辉，何兵寿．应用T—A双重拟合法进行多次波压制．物探化探计算技术，1999，21(1)：9—13
35．王妙月．我国地震勘探研究进展．地球物理学报，1997，40(增刊)：257—265
36．王忠仁，何樵登．叠前共炮点道集的奇性反演研究．地球物理学报，1998，41(增刊)：326—336
37．王守东，刘家琦，黄文虎．二维声波方程速度反演的一种方法．地球物理学报，1995，38(6)：833—839
38．吴律．在时间域中的大倾角波动方程偏移．地球物理学报，1980，23(23)
39．吴律．层析基础及其在井间地震中的应用．北京：石油工业出版社，1997
40．谢干权，李建华．解三维方程逆散射势问题的新特征迭代法．中国科学(A辑)，1988，17(4)：359—656
41．杨文采．地球物理反演和地震层析成像．北京：地质出版社，1989
42．杨文采．非线性波动方程地震反演的方法原理及问题．地球物理学进展，1992，7(7)：9—19
43．杨文采．波动方程的逆散射与迭代线性化反演．石油物探，1995，34(3)：114—121
44．杨文采．非线性地震反演方法的补充及比较．石油物探，1995，34(4)：109—116
45．杨文采．地震波反演的BG—逆散射方法．地球物理学报，1995，38(3)：358—366
46．尹峰，王俊生，最大熵时域逆散射层析成像的研究．地球物理学报，1994，37(5)：673—681
47．俞寿朋．高分辨率地震勘探．北京：石油工业出版社，1994
48．张关泉，侯唯健．三维叠后差分偏移的因子分解法．地球物理学报，1996，39(3)：382—391
49．张关泉．一维声波方程的反演问题．中国科学(A辑)，1988，17(7)：707—721
50．张钋，李幼铭，刘洪．几类叠前深度偏移方法的研究现状．地球物理学进展，2000，15(2)：30—39
51．郑继明，周宗放，杨春德．基于小波变换的信号奇异性检测．重庆邮电学院学报，1998，10(1)：8—12
52．钟森．反射地震记录的多尺度边缘检测．石油地球物理勘探，1998，33(1)：61—65
53．朱文浩，钟伟芳．三维弹性波场的线性化逆散射问题．华中理工大学学报，1994，22(9)：71—75
54．朱文浩，陈柏鸿，钟伟芳．地表反射弹性波多参数反演．石油物探，1997，36(1)：28—35
55．朱文浩，戴辉，钟伟芳．半空间反射弹性波多参数线性化逆散射．应用数学和力学，2000，21(10)：1081—1086
56. Andrew E. Yagle, Bernard C. Levy, Layer-stripping solutions of multidimensional inverse scattering problems. J. Math. Phys., 1986, 27(6): 1701—1710
57. Antoine Guitton, Guillaume Cambois, Multiple elimination using a pattern-recognition technique. The Leading Edge, 1999, 18(1): 92—98
58．Berkhout J．著，马在田，张叔伦译．地震偏移．北京：石油工业出版社，1983
59. Berkhout J., M. P. de Graaff, The inverse scattering problem in terms of multiple elimination and seismic migration, 1982, Annual Meeting Abstracts, Society Of Exploration Geophysicists, Session:S9.1
60. Berkhout J., Multiple removedbased on the feedback model. The Leading Edge, 1999, 18(1): 127—131
61. Berkhout J., Verschuur D. J., Estimation of multiple scattering by iterative inversion, part Ⅰ:
Theoretical considerations. Geophysics, 1997, 62(5): 1586—1595.
62. Berkhout J., Verschuur D. J., Estimation of multiple scattering by iterative inversion, part Ⅱ: Practical aspects and examples. Geophysics, 1997, 62(5): 1596—1611.
63. Beylkin G., Imaging of discontinuities in the inverse scattering problem by inversion of a csusal generalized Radon transform. J. Math. Phys., 1985,26(1): 99—108
64. Bleistein N., Cohen J. K., and John W. Stockwell, Jr., Mathematics of Multi-dimensional Seismic Imaging, Migration, and Inversion. Springer Verlag, New York, 1996
65. Bleistein N., On the imaging of reflectors in the earth. Geophysics, 1987, 52(7): 931—942
66. Bleistein N., Cohen J. K., Hagin E G., Two and one-half domension Born inversion with an arbitrary reference. Geophysics, 1987,52(1): 26—36
67. Bleistein N., Cohen J. K., Hagin F. G., Computional and asymptotic of velocity inversion. Geophysics, 1985, 50(8): 1253—1265
68. Bleistein N., Cohen J. K., The velocity inversion problem—Present status, new direction, Geophysics, 1982, 47(11): 1497—1511
69. Bleistein N., Gray S. H., An extension of the Born inversion method to a depth dependent reference profile. Geophysical Prospecting, 1985, 33(8): 999—1022
70. Bleistein N., Two-and-one-half dimensional in-plane wave propagation. Geophysical Prospecting, 1986, 34(6): 686—703
71. Bleistein N., Mathematical methods for wave phenomena. Academic Press, Inc., 1984
72. Chert Y. M., Liu J. Q., A numerical algorithm for solving inverse problems of two-dimensional wave equation. J. Comp. Phys., 1983, 50(1): 193—208
73．Chadan K．，Sabatier P．C．著，张天元译．量子散射理论的逆问题．北京：科学出版社，1989
74．Claerbout J．著，许云译．地震成像理论及方法．北京：石油工业出版社，1991
75．Claerbout J．著，陈玉等译．地球物理数据处理基础．北京：石油化学工业出版社，1979
76. Clayton R. W., Stolt R. H., A Born-WKBJ inversion method for acoustic reflection data. Geophysics, 1981, 46(8): 1559—1567
77. Coen S., Velocity, density profiles of a layered acoustic medium from common source-point data. Geophysics, 1982, 47(6):, 898—905
78. Cohen J. K., Hagin F. G., Velocity inversion using a stratified reference. Geophysics, 1985, 50(11): 1689—1700
79. Cohen J. K., Bleistein N., Three-dimensional Born inversion with an arbitrary referece, Geophysics, 1986, 51(8): 1552—1558
80. Cohen J. K., Bleistein N., Velocity inversion procedure for acoustic waves. Geophysics, 1979, 44(6): 1077—1087
81. De Hoop. Asymptotic inversion: multi pathing and caustics. 1998, 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts: 1534—1537
82. Dong Wenjie, Emanue M. J., Bording P., et al, A computer implementation of 2.5D common-shot inversion. Geophysics, 1991, 56(9): 1384—1394
83. Douglas J. Foster, Charles C. Mosher, Suppression of multiple reflections using the Radom transform. Geophysics, 1992, 57(3): 386—395
84. Eaton D. W., Weak elastic-wave scattering from massive sulfide orebodies. Geophysics, 1999, 64(1): 289—299
85．Gaust Nolet编，冯锐等译．地震层析技术．北京：地质出版社，1991
86. Gazdag J., Wave-equation migration with the phase shift method. Geophysics. 1978, 43(6): 1342—1352
87. Gazdag J., Sguazzero P., Migration of seismic data by phase shift plus interpolation. Geophysical Prospecting. 1984, 49(1): 124—131
88. Guitton, G. Cambois, Multiple elimination using a patteron-recognition technique. The Leading Edge, 1999, 18(1): 92—98
89. Hagin F. G., Cohen J. K., Refinement to the linear velocity inversion theory. Geophysics, 1984, 49(2): 112—118
90. Han B., Two prestack converted-wave migration algorithms for vertical transverse isotropy. 2000, CWP Project Review, Center for Wave Phenomena, Colorado School of Mines, CWP-344
91. Hill N. R., Gaussian beam migration. Geophysics, 1990, 55(11): 1416—1428
92. Houston L. M., Multiple suppression using a local coherence filter. Geophysics, 1998,63(2): 652—659
93. Howard M. S., Inverse scattering for a layered acoustic medium using the first-order equations of motion. Geophysics, 1983, 48(2): 163—170.
94. Huang Lian-Jie, Fehler M. C., Wu Ru-Shan, Extended local Born Fourier migration method. Geophysics, 1999, 64(5): 1524—1534
95. Ikelle L. T., Using even terms of the scattering series for deghosting and multiple attenuation of ocean-bottom cable data. Geophysics, 1999, 64(2): 579—592
96. Jost R., Walte K., Construction of a potential from a pahase shift. Physical Review. 1952, 87(6): 977—991
97. Kessinger W., Extended split-step Fourier migration. 1992, 62nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts: 917—920
98. Kristensson G., Krueger R. J., Direct and inverse scattering in the time domain for a dissipative wave equation.I.Scattering operators. J. Math. Phys., 1986, 27(6): 1667—1682
99. Kristensson G., Krueger R. J., Direct and inverse scattering in the time domain for a dissipative wave equation. Ⅱ.Simultaneous reconstruvtion of disspation and phase velocity profiles. J. Math. Phys., 1986, 27(6): 1683—1693
100. Landa E., Belfer I. and Keydar S., A new method for multiple attenuation in the parabolic t-p domain. 1997, Annual Meeting Abstracts, Society Of Exploration Geophysicists: 1402—1405
101. Lee M., Mason L., Jacek G. M., Split-step Fourier shot-record migration with deconvolution imaging. Geophysics, 1991, 56(11): 1768—1793
102. Li Z., Compensating finite-defference errors in 3D migration and modeling. Geophysics, 1991, 56(10): 1650—1660
103. Lokshtanov D., Multiple suppression by single channel and multi-channel deconvolution in the tua-p domain. 1995, The 65th Annual International Meeting, SEG Expanded abstracts: 1428
104. Lokshtanov D., Multiple suppression by data-consistent deconvolution. The Leading Edge, 1999, 18(1): 115—119
105. Lu Guochun, Bjφrn Ursin, Jan Lutro, Model-based removal of water-layer multiple reflection. Geophysics, 1999, 64(6): 1816—1827
106. Matson K. H., The relationship between scattering theory and the primaries and multiples of reflection seismic data. Journal of Seismic Exploration, 1996, No.5: 63—78
107. Matson K. H., Weglein A. B., Removal of elastic interface multiples from land and ocean bottom data using inverse scattering. 1996, Annual Meeting Abstracts, Society Of Exploration Geophysicists: 1526—1530.
108. Matson K. H., An inverses scattering series method for attenuating elastic multiples from multicomponent land ocean bottom seismic data. Ph.D. Theory, 1997, The University of British Columbia.
109. Miller D., Oristaglio M., Beylkin G., A new slant on seismic imaging migration and integral geometry. Geophysics, 1987, 52(7): 931—942
110. Moses H. E., Calculation of the scattering potential from reflection coefficients. Physical Review. 1955, 102(2): 559—567
111. M. Nieto-Vesperinas, Innverse scattering problems: A study in terms of the zeros of entire functions. J. Math. Phys., 25(6): 2109—2115
112. Newton R. G., Inverse scattering: Ⅰ. One dimension. J. Math. Phys., 1980, 21(3): 493—505
113. Newton R. G., Inverse scattering: Ⅱ. Three dimensions. J. Math. Phys., 1980, 21(7): 1698—1715
114. Newton R. G., Inverse scattering: Ⅱ. Three dimensions, continued. J. Math. Phys., 1981, 22(10): 2191—2200
115. Newton R. G., Inverse scattering by a local impurity in a periodic potential in one dimension. J. Math. Phys., 1983, 24(8): 2152—2162
116. Norton J., Itertive seismic inversion, Geophys. J., 1988, 94: 457—468
117. Pratt R. G., Worthington M. H., The application of diffraction tomography to cross-hole seismic data. Geophysics, 1988, 53(5): 1284—1294
118. Prosser R. T., Formal solution of inverse scattering problems: Ⅰ. J. Math. Phys., 1969, 10(8): 1819—1822
119. Prosser R. T., Formal solution of inverse scattering problems: Ⅱ. J. Math. Phys., 1976, 17(11): 1775—1779
120. Prosser R. T., Formal solution of inverse scattering problems, Ⅲ. J. Math. Phys., 1980, 21(11): 2648—2653
121. Prosser R. T., Formal solution of inverse scattering problems, Ⅳ: Error estimates. J. Math. Phys., 1982, 23(11): 2127—2130
122. Schneider W. A., Integral formulation for migration in two and three dimensions. Geophysics, 1978, 43(1): 49—76
123. Stolt R. H., Migration by Fourier transform. Geophysics, 1978, 43(1): 23—48
124. Tarantola, Inversion of seismic reflection data in the acoustic approximation. Geophysics, 1984, 49(6): 1259—1266
125．Taylor J．R．著，耿天明，温源淇译．散射理论——非相对论性碰撞的量子理论．北京：科学出版社，1987
126. Thorson J. R., Velocity Stack and Slant Stack Stochastic Inversion. Geophysics, 1995, 60(12): 2727—2741
127. Tuncay Aktosun, Martin Klaus, Comelis van der Mee, Scattering and inverse scattering in one-dimensional nonhomogeneous media. J. Math. Phys., 1992, 33(5): 1717—1744
128. Weglein A. B., Gasparotto F. A., Carvalho P. M., Stolt R. H., An inverse-scattering series method for attenuating multiple in seismic reflection data. Geophysics, 1997, 62(6): 1975—1989
129. Weglein A. B., Multiple attenuation: an overview of recent advances. The Leading Edge, 1999, 18(1): 40—44
130. Weglein A. B., How can the inverse-scattering method really predict and subtract all multiples from a multidimensional earth with absolutely no subsurface information? The Leading Edge, 18(1): 132—136
131. Weglein A. B., Carvalho E M., Stolt R. H., Nonlinear inverse scattering for multiple suppression: Application to real data. part Ⅰ. 1992, Annual Meeting Abstracts, Society Of Exploration Geophysicists: 1093—1095.
132. Wiggins J. W., Multiple attenuation by explicit wave extrapolation to an interpreted horizon. The Leading Edge, 1999, 18(1): 48—54
133. Wiggins J. W., Using the parabolic Radon transform as a moveout filter. The 52th Annual
Meeting of the EAEG in Copenhagen.
134. Wiggins J. W., Kirchhoff integral extrapolation and migration of nonplanar data. Geophysics, 1984, 49(8): 1239—1248
135. Wolfgang Friederich, Propagation of seismic shear and surface wave in a laterally heterogeneous mantle by multiple forward scatting. Geophysical Journal International, 1999, 136(1): 180—204
136. Yoshio Murai, Teruo Yamashita, Multiple scattering of SH wave by imperfectly bonded interfaces with inhomogeneous strengths. Geophysical Journal International, 1998, 134(3): 677—688
137. Zhenyue Liu, N. Bleistein, Migration velocity analysis. Theory and an iterative algorithm. Geophysics, 1995, 60(1): 142—153
138. Zhou, B. and S. A. Greenhalgh, Wave-equation extrapolation-based multiple attenuation: 2-D filtering in the f-k domain. Geophysics, 1994, 59(9): 1377—1391
139. Zhou Binzhong, Stewart Greenhalgh, 1996, Multiple suppression by 2D filtering in the parabolic τ-p domain: a wave-equation-based method. Geophysical Prospecting, 44(5): 375—401
140. Zhu J., Lines L., Comparison of Kirchhoff and reverse-time migration methods with applications to prestack depth imaging of complex structures. Geophysics, 1998, 63(4): 1166—1176