地震速度分析方法综述
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摘要
地震波速度参数贯穿于地震数据采集、处理和解释的整个过程,是地震勘探中最重要的参数之一。主要对叠加速度分析、偏移速度分析和速度层析反演三大类典型的速度分析方法的基本原理、发展及应用条件等作简要的回顾与介绍。在复杂地质构造及低信噪比资料情况下,提高速度分析的精度和计算效率是当前及未来研究的重点。
Seismic velocity is one of the most important parameters in seismic exploration,because it is used in the whole course of seismic exploration,including seismic data acquisition,pro- cessing and interpretation.This paper reviewed the theory,de- velopment and applications of 3 typical velocity analysis tech- nologies,stack velocity analysis,migration velocity analysis and tomographic inversion.To cope with complex geology and low S/N data,it will be the focus of research to improve the computation precision and efficiency of velocity analysis at present and in the future.
Seismic velocity is one of the most important parameters in seismic exploration,because it is used in the whole course of seismic exploration,including seismic data acquisition,pro- cessing and interpretation.This paper reviewed the theory,de- velopment and applications of 3 typical velocity analysis tech- nologies,stack velocity analysis,migration velocity analysis and tomographic inversion.To cope with complex geology and low S/N data,it will be the focus of research to improve the computation precision and efficiency of velocity analysis at present and in the future.
引文
1辛可锋，王华忠，马在田．一种高精度的偏移速度分析方法——广义屏偏移加Born反演[J]．勘探地球物理进展，2002，25(3)：20～26
2叶勇，郑雄．偏移速度分析技术新进展[J]．勘探地球物理进展，2003，26(2)：136～142
3朱海龙，崔远红．速度分析和层析成像[J]．勘探地球物理进展，2003，B6(5—6)：433～438
4 Garotta R,Michon D.Continuous analysis of the velocity function and of the normal-moveout corrections[J].Geophysical Prospecting,1967,15(4):584～597
5 Cook E E,Taner M T.Velocity spectra and their use in stratigraphic and lithologic differentiation[J].Geophysical Prospecting,1969,17(4):433～448
6 Hale D.Dip moveout by Fourier transform[J].Geophysics,1984,49(6):741～757
7 Forel D,Gardner G H F.A three-dimensional perspective on two-dimensional dip moveout[J].Geophysics,1988,53(5):604～610
8 Taner M,Koehler F.Velocity spectra-digital computer derivation applications of velocity functions[J].Geophysics,1969,34(6):859～881.
9 Al-Chalabi M.Series approximation in velocity and traveltime computation[J].Geophysical Prospecting,1973,21(4):783～795
10 Causse E,Haugen G,Rommel B.Large offset approximation to seismic reflection traveltimes[J].Geophysical Prospecting,2000,48(4):763～778
11 Sun C,Martinez R.Amplitude preserving 3D pre-stack Kirchhoff time migration for V(z) and VTI media[J].Expanded Abstracts of the 72~(nd) Annual Internat SEG Meeting,2002,1 224～1 227
12 Taner M,Al-Chalabi M.A new travel time estimation method for horizontal strata[J].Expanded Abstracts of the 75~(th)Annual Internat SEG Meeting,2005,2 273～2 276
13 Doherty S M,Claerbout J F.Structure independent velocity estimation[J].Geophysics,1976,41(5):850～881
14 Yilmaz O,Chambers R.Migration velocity analysis by wavefield extrapolation[J].Geophysics,1984,49(10):1 664～1 674
15 Faye J P,Jeannot J P,Denelle E.Prestack migration velocities from depth focusing analysis[J].Expanded Abstracts of the 56~(th)Annual Internat SECT Meeting,1986,438～440
16 Audebert F.Migrated focus panel:focusing analysis reconciled with prestack depth migration[J].Expanded Abstracts of the 63~(rd)Annual Internat SEG Meeting,1993,961～964
17 MacKay S,Abma R.Imaging and velocity estimation with depth-focusing analysis[J].Geophysics,1992,57(12):1 608～1 622
18 MacKay S,Abma R.Depth-focusing analysis using a wavefront-curvature criterion[J].Geophysics,1993,58(8):1 148～1 156
19 Lafond C F,Levander A R.Migration moveout analysis and depth focusing[J].Geophysics,1993,58(1):91～100
20 Wang B,Pann K,Malloy J.Macro velocity model estimation through model-based globally-optimized depth focusing analysis[J].Expanded Abstracts of the 57~(th) EAGE Conference and Exhibition,1995,038
21 Wang B,Pann K.Model-based interpretation of focusing panels for depth focusing analysis[J].Expanded Abstracts of the 68~(th)Annual Internat SEG Meeting,1998,1 596～1 599
22 Berkhout A J,Rietveld W E.Determination of macro models for prestack migration:Part 1,Estimation of macro velocities[J].Expanded Abstracts of the 64~(th)Annual Internat SEG Meeting,1994,1 330～1 333
23 Kabir M M N,Verschuur D J.Migration velocity analysis using the common focus point technology[J].Expanded Abstracts of the 66~(th)Annual Internat SEG Meeting,1996,407～410
24 Kabir M M N,Verschuur D J.Velocity estimation of the complex subsurface using the common focus point technology[J].Expanded Abstracts of the 67~(th)Annual Internat SECT Meeting,1997,1 822～1 825
25 Berkhout A J.Pushing the limits of seismic imaging,PartⅠ:Prestack migration in terms of double focusing[J].Geophysics,1997,62(3):937～953
26 Berkhout A J.Pushing the limits of seismic imaging,PartⅡ:Integration of prestack migration,velocity esti-marion,and AVO analysis[J].Geophysics,1997b,62(3):954～969
27 Cox B E,Verschuur D J.Data-driven tomographic inversion of focusing operators[J].Expanded Abstracts of the 71~(st) Annual Internat SEG Meeting,2001,722～725
28 Cox B E,Winthaegen P,Verschuur D.Combined CFP based global and local velocity analysis applied to North Sea data[J].Expanded Abstracts of the 73~(rd) Annual Internat SEG Meeting,2003,2 164～2 167
29 de Rijzen M,Verschuur D.3D focusing operator estimation using sparse data[J].Expanded Abstracts of the 74~(th)Annual Internat SEG Meeting,2 048～2 051
30王成祥，张关泉，刘超颖等．速度模型反演的CFP方法[J]．石油地球物理勘探，2003，38(2)：139～146
31刘超颖，王成祥，赵波等．CFP层速度扫描建模方法[J]．石油物探，2003，42(3)：294～297
32辛可锋，王华忠，马在田等．CFP道集交互速度分析[J]．石油地球物理勘探，2005．40(4)：386～390
33 Al-Yahya K.Velocity analysis by iterative profile migration[J].Geophysics,1989,54(6):718～729
34 Liu Z,Bleistein N.Velocity analysis by residual moveout[J].Expanded Abstracts of the 62~(nd) Annual Internat SEG Meeting,1992,1 034～1 036
35 Meng Z,Bleistein N,Wyatt K D.3D Analytical migration velocity analysisⅠ:Two-step velocity estimation by reflector-normal update[J].Expanded Abstracts of the 69~(th) Annual Internat SEG Meeting,1999,1 727～1 730
36李振春，王华忠，马在田．共中心点道集偏移速度分析[J]．石油物探，2000，39(1)：20～26
37崔兴福，张关泉，何忠泉．双平方根算子波场延拓道集速度分析[J]．石油物探，2004，43(1)：16～19
38张文生，宋海斌，崔兴福．双平方根算子波场外推叠前偏移速度分析[J]．石油物探，2004，43(4)：313～318
39 Jiao J,Stoffa P,Sen M,et al.Residual migration velocity analysis in the plane-wave domain[J].Expanded Abstracts of the 70~(th) Annual Internat SEG Meeting,2000,942～945
40 Biondi B,Sava P.Wave equation migration velocity analysis[J].Expanded Abstracts of the 69~(th) Annual Internat SEG Meeting,1999,1 723～1 726
41 Clapp R,Biondi B.Tau domain migration velocity analysis using angle CRP gathers and geologic constraints[J].Expanded Abstracts of the 60~(th) Annual Internat SEG Meeting,2000,926～929
42 Mosher C C,Jin S,Foste D J.Migration velocity analysis using common angle image gathers[J],Expanded Abstracts of the 71~(st) Annual Internat SEG Meeting,2001,889～892
43 Liu W,Popovici A,Bevc D,et al.3D migration velocity analysis for common image gathers in the reflection an-gle domain[J].Expanded Abstracts of the 71~(st) Annual Internat SEG Meeting,2001,885～888
44 Liu Z,Bleistein N.Velocity analysis by perturbation[J].Expanded Abstracts of the 64~(th) Annual Internat SEG Meeting,1994,1 191～1 194
45 Liu Z,Bleistein N.Migration velocity analysis:Theory and an iterative algorithm[J].Geophysics,1995,60(1):142～153
46 Lee W,Zhang L.Residual shot profile migration[J].Geophysics,1992,57(6):815～822
47 Biondi B,Tisserant T.Angle-domain common-image gathers for wave-equation velocity analysis[J].Geophysical Prospecting,2004,52(6):575～591
48 Biondi B,Symes W.Angle-domain common-image gathers for migration velocity analysis by wavefieldcontinuation imaging[J].Geophyisics,2004,69(5):1 283～1 298
49 Reshef M,Rüger A.Influence of structural dip on interval velocity analysis[J].Expanded Abstracts of the 75~(th) Annual Internat SEG Meeting,2005,2 245～2 248
50 Bednar J,Thorson J,Vinson L.Residual tomographic updating[J].Expanded Abstracts of the 69~(th) Annual Internat SEG Meeting,1999,1 251～1 254
51李振春，姚云霞，马在田等．波动方程法共成像点道集偏移速度建模[J]．地球物理学报，2003，46(1)：86～93
52 Trier J,Symes W W.Upwind finite-difference calculation of seismic traveltimes[J].Expanded Abstracts of the 60~(th) Annual Internat SEG Meeting,1990,1 000～1 003
53 Kosloff D,Sherwood J,Koren Z,et al.Velocity and interface depth determination by tomography of depth migrated gathers[J].Geophysics,1996,61(5):1 511～1 523
54 Chauris H,Noble M,Lambare G,et al.Migration velocity analysis form locally coherent events in 2-D laterally heterogeneous media,Part 1:Theoretical aspects[J].Geophysics,2002,67(4):1 202～1 212
55 Chauris H,Noble M,Lambare G,et al.Migration velocity analysis form locally coherent events in 2-D laterally heterogeneous media,Part 2:Appiication on synthetic and real data[J].Geophysics,2002,67(4):1 213～1 224
56 Docherty P,Silva R,Singh S,et al.Migration velocity analysis using a genetic algorithm[J].Geophysical Prospecting,1997,45(5):865～878
57 Jin S,Beydoun W.2D multiscale non-linear velocity estimation[J].Geophysical Prospecting,2000,48(1):163～180
58 Bois P,La Porte M,Lavergne M,et al.Well-to-well seismic measurements[J].Geophysics,1972,37(3):471～480
59 Dines K A,Lytle R J.Computerized geophysical tomography[J].Proc IEEE,1979,67(7):1 065～1 073
60 Anderson D L,Dziewonski A M.Seismic tomography,Scientific American[J].GEOL 453/653,1984,60～68
61 Daily W.Underground oil-shale retort monitoring using geotomography[J].Geophysics,1984,49(10):1 701～1 707
62 Somerstein S F,Berg M,Chang D,et al.Radio-frequency geotomography for remotely probing the interiors of operating mini-sized and commercial-sized oilshale retorts[J].Geophysics,1984,49(8):1 288～1 300
63 Bishop T,Bube K,Cutler R,et al.Tomographic determination of velocity and depth in laterally varying media[J].Geophyisics,1985,50(6):903～922
64 Ivansson S.A study of methods for tomographic velocity estimation in the presence of low-velocity zones[J].Geophysics,1985,50(6):969～988
65 Williamson P R.Tomographic inversion in reflection seismology[J].Geophysical Journal International,1990,100(1):255～274
66 Williamson P R,Worthington M H.Resolution limits in ray tomography due to wave behavior:Numerical experiments[J].Geophysics,1993,58(5) :727～735
67 Stork C.Reflection tomography in the postmigrated domain[J].Geophysics,1992,57(5):680～692
68 Berkhout A J.Multidimensional linearized inversion and seismic migration[J].Geophysics,1984,49(11):1 881～1 895
69 Devaney A J.Geophysical diffraction tomography[J].IEEE Trans Geoscience and Remote Sensing,1984,GE-22(1):3～13
70 Levy B,Esmersoy C.Variable background born inversion by wavefield back propagation[J].SIAM J Appl Math,1988,48(4):952～972
71 Luo Y,Schuster G T.Wave equation traveltime inversion[J].Expanded Abstracts of the 60~(th) Annual Internat SEG Meeting,1990,1 207～1 210
72 Symes W W,Carazzone J J.Velocity inversion by differential semblance optimization[J].Geophysics,1991,56(5):654～663
73 Symes W W.High frequency asymptotics,dierential semblance,and velocity estimation[J].Expanded Abstracts of the 68~(th) Annual Internat SECT Meeting,1998,1 616～1 619
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75 Riabinkin L A.Fundamentals of resolving power of Controlled Directional Reception(CDR)of seismic waves[M].Tulsa:Society of Exploration Geophysicists,1957.36～60
76 Sword C H.Tomographic determination of interval velocities from reflection seismic data:The method of controlled directional reception:[Dissertation][D].USA:Stanford University,1987
77 Billette F,Lambare G.Velocity macro-modei estimation from seismic reflection data by stereotomography[J].Geophysical Journal International,1998,135(2):671～690
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80 Chalard E,Podvin P,Le Begat S,et al.3D Stereotomographic inversion on a real dataset[J].Expanded Abstracts of the 72~(nd) Annual Internat SEG Meeting,2002,946～948
81 Billette F,Le Begat S,Podvin P,et al.Practical aspects and applications of 2D Stereotomography[J].Geophysics,2003,68(3):1 008～1 021
82 Lambare G,Alerne R,Baina R,et ai.Stereotomography:a fast approach for velocity macromodel estimation[J].Expanded Abstracts of the 73~(rd) Annual Internat SEG Meeting,2003,2 076～2 079
83 Lambare G,Alerini M.Podvin P.Stereotomographic picking in practice[J].Expanded Abstracts of the 74~(th)Annual Internat SEG Meeting,2004,2 347～2 350
84 Tarantola A.Linearized inversion of seismic reflection data[J].Geophysical Prospecnng,1984,32(6):998～1 015
85 Tarantola A.A strategy for nonlinear elastic inversion of seismic reflection data[J].Expanded Abstracts of the 56~(th) Annual lnternat SEG Meeting.1986,527～530
2叶勇，郑雄．偏移速度分析技术新进展[J]．勘探地球物理进展，2003，26(2)：136～142
3朱海龙，崔远红．速度分析和层析成像[J]．勘探地球物理进展，2003，B6(5—6)：433～438
4 Garotta R,Michon D.Continuous analysis of the velocity function and of the normal-moveout corrections[J].Geophysical Prospecting,1967,15(4):584～597
5 Cook E E,Taner M T.Velocity spectra and their use in stratigraphic and lithologic differentiation[J].Geophysical Prospecting,1969,17(4):433～448
6 Hale D.Dip moveout by Fourier transform[J].Geophysics,1984,49(6):741～757
7 Forel D,Gardner G H F.A three-dimensional perspective on two-dimensional dip moveout[J].Geophysics,1988,53(5):604～610
8 Taner M,Koehler F.Velocity spectra-digital computer derivation applications of velocity functions[J].Geophysics,1969,34(6):859～881.
9 Al-Chalabi M.Series approximation in velocity and traveltime computation[J].Geophysical Prospecting,1973,21(4):783～795
10 Causse E,Haugen G,Rommel B.Large offset approximation to seismic reflection traveltimes[J].Geophysical Prospecting,2000,48(4):763～778
11 Sun C,Martinez R.Amplitude preserving 3D pre-stack Kirchhoff time migration for V(z) and VTI media[J].Expanded Abstracts of the 72~(nd) Annual Internat SEG Meeting,2002,1 224～1 227
12 Taner M,Al-Chalabi M.A new travel time estimation method for horizontal strata[J].Expanded Abstracts of the 75~(th)Annual Internat SEG Meeting,2005,2 273～2 276
13 Doherty S M,Claerbout J F.Structure independent velocity estimation[J].Geophysics,1976,41(5):850～881
14 Yilmaz O,Chambers R.Migration velocity analysis by wavefield extrapolation[J].Geophysics,1984,49(10):1 664～1 674
15 Faye J P,Jeannot J P,Denelle E.Prestack migration velocities from depth focusing analysis[J].Expanded Abstracts of the 56~(th)Annual Internat SECT Meeting,1986,438～440
16 Audebert F.Migrated focus panel:focusing analysis reconciled with prestack depth migration[J].Expanded Abstracts of the 63~(rd)Annual Internat SEG Meeting,1993,961～964
17 MacKay S,Abma R.Imaging and velocity estimation with depth-focusing analysis[J].Geophysics,1992,57(12):1 608～1 622
18 MacKay S,Abma R.Depth-focusing analysis using a wavefront-curvature criterion[J].Geophysics,1993,58(8):1 148～1 156
19 Lafond C F,Levander A R.Migration moveout analysis and depth focusing[J].Geophysics,1993,58(1):91～100
20 Wang B,Pann K,Malloy J.Macro velocity model estimation through model-based globally-optimized depth focusing analysis[J].Expanded Abstracts of the 57~(th) EAGE Conference and Exhibition,1995,038
21 Wang B,Pann K.Model-based interpretation of focusing panels for depth focusing analysis[J].Expanded Abstracts of the 68~(th)Annual Internat SEG Meeting,1998,1 596～1 599
22 Berkhout A J,Rietveld W E.Determination of macro models for prestack migration:Part 1,Estimation of macro velocities[J].Expanded Abstracts of the 64~(th)Annual Internat SEG Meeting,1994,1 330～1 333
23 Kabir M M N,Verschuur D J.Migration velocity analysis using the common focus point technology[J].Expanded Abstracts of the 66~(th)Annual Internat SEG Meeting,1996,407～410
24 Kabir M M N,Verschuur D J.Velocity estimation of the complex subsurface using the common focus point technology[J].Expanded Abstracts of the 67~(th)Annual Internat SECT Meeting,1997,1 822～1 825
25 Berkhout A J.Pushing the limits of seismic imaging,PartⅠ:Prestack migration in terms of double focusing[J].Geophysics,1997,62(3):937～953
26 Berkhout A J.Pushing the limits of seismic imaging,PartⅡ:Integration of prestack migration,velocity esti-marion,and AVO analysis[J].Geophysics,1997b,62(3):954～969
27 Cox B E,Verschuur D J.Data-driven tomographic inversion of focusing operators[J].Expanded Abstracts of the 71~(st) Annual Internat SEG Meeting,2001,722～725
28 Cox B E,Winthaegen P,Verschuur D.Combined CFP based global and local velocity analysis applied to North Sea data[J].Expanded Abstracts of the 73~(rd) Annual Internat SEG Meeting,2003,2 164～2 167
29 de Rijzen M,Verschuur D.3D focusing operator estimation using sparse data[J].Expanded Abstracts of the 74~(th)Annual Internat SEG Meeting,2 048～2 051
30王成祥，张关泉，刘超颖等．速度模型反演的CFP方法[J]．石油地球物理勘探，2003，38(2)：139～146
31刘超颖，王成祥，赵波等．CFP层速度扫描建模方法[J]．石油物探，2003，42(3)：294～297
32辛可锋，王华忠，马在田等．CFP道集交互速度分析[J]．石油地球物理勘探，2005．40(4)：386～390
33 Al-Yahya K.Velocity analysis by iterative profile migration[J].Geophysics,1989,54(6):718～729
34 Liu Z,Bleistein N.Velocity analysis by residual moveout[J].Expanded Abstracts of the 62~(nd) Annual Internat SEG Meeting,1992,1 034～1 036
35 Meng Z,Bleistein N,Wyatt K D.3D Analytical migration velocity analysisⅠ:Two-step velocity estimation by reflector-normal update[J].Expanded Abstracts of the 69~(th) Annual Internat SEG Meeting,1999,1 727～1 730
36李振春，王华忠，马在田．共中心点道集偏移速度分析[J]．石油物探，2000，39(1)：20～26
37崔兴福，张关泉，何忠泉．双平方根算子波场延拓道集速度分析[J]．石油物探，2004，43(1)：16～19
38张文生，宋海斌，崔兴福．双平方根算子波场外推叠前偏移速度分析[J]．石油物探，2004，43(4)：313～318
39 Jiao J,Stoffa P,Sen M,et al.Residual migration velocity analysis in the plane-wave domain[J].Expanded Abstracts of the 70~(th) Annual Internat SEG Meeting,2000,942～945
40 Biondi B,Sava P.Wave equation migration velocity analysis[J].Expanded Abstracts of the 69~(th) Annual Internat SEG Meeting,1999,1 723～1 726
41 Clapp R,Biondi B.Tau domain migration velocity analysis using angle CRP gathers and geologic constraints[J].Expanded Abstracts of the 60~(th) Annual Internat SEG Meeting,2000,926～929
42 Mosher C C,Jin S,Foste D J.Migration velocity analysis using common angle image gathers[J],Expanded Abstracts of the 71~(st) Annual Internat SEG Meeting,2001,889～892
43 Liu W,Popovici A,Bevc D,et al.3D migration velocity analysis for common image gathers in the reflection an-gle domain[J].Expanded Abstracts of the 71~(st) Annual Internat SEG Meeting,2001,885～888
44 Liu Z,Bleistein N.Velocity analysis by perturbation[J].Expanded Abstracts of the 64~(th) Annual Internat SEG Meeting,1994,1 191～1 194
45 Liu Z,Bleistein N.Migration velocity analysis:Theory and an iterative algorithm[J].Geophysics,1995,60(1):142～153
46 Lee W,Zhang L.Residual shot profile migration[J].Geophysics,1992,57(6):815～822
47 Biondi B,Tisserant T.Angle-domain common-image gathers for wave-equation velocity analysis[J].Geophysical Prospecting,2004,52(6):575～591
48 Biondi B,Symes W.Angle-domain common-image gathers for migration velocity analysis by wavefieldcontinuation imaging[J].Geophyisics,2004,69(5):1 283～1 298
49 Reshef M,Rüger A.Influence of structural dip on interval velocity analysis[J].Expanded Abstracts of the 75~(th) Annual Internat SEG Meeting,2005,2 245～2 248
50 Bednar J,Thorson J,Vinson L.Residual tomographic updating[J].Expanded Abstracts of the 69~(th) Annual Internat SEG Meeting,1999,1 251～1 254
51李振春，姚云霞，马在田等．波动方程法共成像点道集偏移速度建模[J]．地球物理学报，2003，46(1)：86～93
52 Trier J,Symes W W.Upwind finite-difference calculation of seismic traveltimes[J].Expanded Abstracts of the 60~(th) Annual Internat SEG Meeting,1990,1 000～1 003
53 Kosloff D,Sherwood J,Koren Z,et al.Velocity and interface depth determination by tomography of depth migrated gathers[J].Geophysics,1996,61(5):1 511～1 523
54 Chauris H,Noble M,Lambare G,et al.Migration velocity analysis form locally coherent events in 2-D laterally heterogeneous media,Part 1:Theoretical aspects[J].Geophysics,2002,67(4):1 202～1 212
55 Chauris H,Noble M,Lambare G,et al.Migration velocity analysis form locally coherent events in 2-D laterally heterogeneous media,Part 2:Appiication on synthetic and real data[J].Geophysics,2002,67(4):1 213～1 224
56 Docherty P,Silva R,Singh S,et al.Migration velocity analysis using a genetic algorithm[J].Geophysical Prospecting,1997,45(5):865～878
57 Jin S,Beydoun W.2D multiscale non-linear velocity estimation[J].Geophysical Prospecting,2000,48(1):163～180
58 Bois P,La Porte M,Lavergne M,et al.Well-to-well seismic measurements[J].Geophysics,1972,37(3):471～480
59 Dines K A,Lytle R J.Computerized geophysical tomography[J].Proc IEEE,1979,67(7):1 065～1 073
60 Anderson D L,Dziewonski A M.Seismic tomography,Scientific American[J].GEOL 453/653,1984,60～68
61 Daily W.Underground oil-shale retort monitoring using geotomography[J].Geophysics,1984,49(10):1 701～1 707
62 Somerstein S F,Berg M,Chang D,et al.Radio-frequency geotomography for remotely probing the interiors of operating mini-sized and commercial-sized oilshale retorts[J].Geophysics,1984,49(8):1 288～1 300
63 Bishop T,Bube K,Cutler R,et al.Tomographic determination of velocity and depth in laterally varying media[J].Geophyisics,1985,50(6):903～922
64 Ivansson S.A study of methods for tomographic velocity estimation in the presence of low-velocity zones[J].Geophysics,1985,50(6):969～988
65 Williamson P R.Tomographic inversion in reflection seismology[J].Geophysical Journal International,1990,100(1):255～274
66 Williamson P R,Worthington M H.Resolution limits in ray tomography due to wave behavior:Numerical experiments[J].Geophysics,1993,58(5) :727～735
67 Stork C.Reflection tomography in the postmigrated domain[J].Geophysics,1992,57(5):680～692
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