横向线性变速介质中的共炮检距波场延拓
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摘要
对横向变速介质中振幅保真的共炮检距波场延拓方法进行了研究．在横向线性变速条件下，通过引入新的偏微分方程，给出了该介质中振幅保真的波场延拓方程．这一波场延拓方程是均匀介质中振幅保真延拓方程在横向线性变速介质中的推广．首先由线性变速介质中地震波射线的走时函数，证明了该延拓方程的运动学等价方程对横向线性变速介质中的所有炮检距和各种反射层倾角都适用．然后，通过对模型数据的计算并与传统的ＤＭＯ方法比较，证明了这一波场延拓方程能很好地保持波前的振幅特性，特别是能保持焦散点的波前的特性．
The amplitude preserving common offset continuation methods in lateral variedvelocity media are studied in this paper. An amplitude preserving kinematicallyequivalent offset continuation (OC) equation is proposed for lateral linearly variedvelocity media. A partial differential equation is introduced to be theamplitude-preserving OC operator, which can be regard as an extension of theamplitude preserving OC operator from constant velocity to lateral velocity media.Consequently, with the traveltime function in linearly varied velocity media,we haveproved that its kinematically equivalent equation is valid for all offsets and reflectordips. In addition, from the result of calculation on synthetic gathers and comparisonwith traditional DMO methods, we can conclude that the equation also preserves theamplitude of cross events in the OC process.
The amplitude preserving common offset continuation methods in lateral variedvelocity media are studied in this paper. An amplitude preserving kinematicallyequivalent offset continuation (OC) equation is proposed for lateral linearly variedvelocity media. A partial differential equation is introduced to be theamplitude-preserving OC operator, which can be regard as an extension of theamplitude preserving OC operator from constant velocity to lateral velocity media.Consequently, with the traveltime function in linearly varied velocity media,we haveproved that its kinematically equivalent equation is valid for all offsets and reflectordips. In addition, from the result of calculation on synthetic gathers and comparisonwith traditional DMO methods, we can conclude that the equation also preserves theamplitude of cross events in the OC process.
引文
1 Deregowsky S M. What is the DMO? First Break 1986, 14:6-24
2 Bolondi G, Loinger E, Rocca E Offset continuation of seismic sections. Geophysical Prospecting, 1982, 30:813-828
3 Bolondi G, Loinner E, Rocca F Offset continuation in theory and practice, Geophysical Prospecting, 1984,32: 1045-1073
4 Hale D.Dip-moveout by Fonder transform. Geophysics, 1984, 49:741-757
5 Goldin S V, Fomel S B. True-amplitude DMO. Russian Geology and Geophysics, 1995, 35: 131-145
6 Fomel S F. Amplitude preserving offset continuation in theory-Part I: The offset continuation equation,1994,SEP-84: 1-18
7 Popovici A M. Migration to zero-offset in variable velocity media [Ph. D Thesis] Stanford: StanfordUniversity, 1995
8 LIU Hong, YIN Xing-Yao, LI You-Ming. The offset continuation in complex media 67th Ann. SEG meeting,1997. 1901-1904
9 Hubral P, Tygel K Zien H. Three-dimension true-amplitude zero-offset migration. Geophysics, 1991, 56:18-26
10 Perroud R Hubral P. Common-reflection-point stacking in laterally inhomogeneous media. The 66th Ann.SEG meeting, 1996, 496-498
11刘洪,罗明秋,李幼铭等.共反射点轨迹 Hamilton方法.地球物理学报, 1999,(待发表)LIU HOng, LUO Ming-Qiu, LI You-Ming. Hamilion method in describing common reflection point trajectory.Chinese J Geophys. (in Chinese), 1999, (in Press)
12 Clearbout J. Multidimensional recursive filters via a helix with application to velocity estimation and 3-Dmigration. The 68th Ann. SEG meeting, 1998, 1995-1998
13 Rickett J, Clearbout J, Fomel S. Implicit 3-D depth migration by wavefield extrapolation with heliealboundary conditions. The 68th Ann. SEG meeting, 1998, 1124-1127
2 Bolondi G, Loinger E, Rocca E Offset continuation of seismic sections. Geophysical Prospecting, 1982, 30:813-828
3 Bolondi G, Loinner E, Rocca F Offset continuation in theory and practice, Geophysical Prospecting, 1984,32: 1045-1073
4 Hale D.Dip-moveout by Fonder transform. Geophysics, 1984, 49:741-757
5 Goldin S V, Fomel S B. True-amplitude DMO. Russian Geology and Geophysics, 1995, 35: 131-145
6 Fomel S F. Amplitude preserving offset continuation in theory-Part I: The offset continuation equation,1994,SEP-84: 1-18
7 Popovici A M. Migration to zero-offset in variable velocity media [Ph. D Thesis] Stanford: StanfordUniversity, 1995
8 LIU Hong, YIN Xing-Yao, LI You-Ming. The offset continuation in complex media 67th Ann. SEG meeting,1997. 1901-1904
9 Hubral P, Tygel K Zien H. Three-dimension true-amplitude zero-offset migration. Geophysics, 1991, 56:18-26
10 Perroud R Hubral P. Common-reflection-point stacking in laterally inhomogeneous media. The 66th Ann.SEG meeting, 1996, 496-498
11刘洪,罗明秋,李幼铭等.共反射点轨迹 Hamilton方法.地球物理学报, 1999,(待发表)LIU HOng, LUO Ming-Qiu, LI You-Ming. Hamilion method in describing common reflection point trajectory.Chinese J Geophys. (in Chinese), 1999, (in Press)
12 Clearbout J. Multidimensional recursive filters via a helix with application to velocity estimation and 3-Dmigration. The 68th Ann. SEG meeting, 1998, 1995-1998
13 Rickett J, Clearbout J, Fomel S. Implicit 3-D depth migration by wavefield extrapolation with heliealboundary conditions. The 68th Ann. SEG meeting, 1998, 1124-1127
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