全波动方程有限差分法倾角时差校正
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摘要
首先从倾角时差极正（DMO）微笑响应方程出发，导出了共偏移距地震剖面DMO波动方程，在浮动坐标系中，该方程化为一个只与炮检距有关而与速度无关的二阶偏微分方程，用时间步长上的分裂方法对此方程进行分裂，获得了以地面观测波场为这值，最大记录时间波场为初值的波动方程波场外推法DMO的定解问题.由于时间步长上的分裂方法没有任何近似，所以理论上讲能适应任何倾角反射波的成像，同时由于采用浮动坐标变换，波场只需延拓到t＝τ，处即可以成像，这样和其他波场外推法DMO相比计算量也减少了一半.最后给出了此方法子波响应的计算结果并就计算精度做了定性分析
The common offset dip moveout(DMO) equation is derived in the paper based on DMO smile response curve. In the floating coordinate, the DMO equation is changed into a two order partial differential equation. Because we solve the DMO equation by time splitting algorithm, so the reflections with any dips can be theoretically focused well, meanwhile, the calculation is reduced by a hall as comped with other wavefield continuahon DMO methods. In the end, it gives DMO wavelet responses and qualitative analysis of the calculation accuracy of our method.
The common offset dip moveout(DMO) equation is derived in the paper based on DMO smile response curve. In the floating coordinate, the DMO equation is changed into a two order partial differential equation. Because we solve the DMO equation by time splitting algorithm, so the reflections with any dips can be theoretically focused well, meanwhile, the calculation is reduced by a hall as comped with other wavefield continuahon DMO methods. In the end, it gives DMO wavelet responses and qualitative analysis of the calculation accuracy of our method.
引文
1Judson D R,schultz P S,Sherwood J W C.Equalizing the stacking velocities of dipping events via DEVILISH. in: Society of Exploration Geophysicists, ed. Technical Program Expanded Abstracts with Authors'Biographies, Society of Exploration Geophysicists Intemational Exposition&Forty-eighth Annual Meeting. Oklahoma: Society of Exploration Geophysicists, 1978. 200～201
2Boondi G, Loinger E, Rocca F. Offset continuation of seismic section. Geophysical Prospecting, 1982. 30:813～8283Yilmaz O,Claerbout J F. Prestack partial migration. Geophysics,1980,45:1753～1779
4Hale D. Dip moveout by Fourier transform. Geophysics,1984,49:741～757
5Liner C L.Bom theory of wave-equation dip moveout. Geophysics, 1991,56:182～189
6Deregowski S M, Rocca F. Geometrical optics and wave theory of contant offset sections in layered media. Geophysical Prospecting,1981,29:384～406
7Fowler P. Velocity independent imaging of seismic reflection. In: Society of Exploration Geophysicists, ed. Technical Program Expanded Abstractswith Authors’ Biographies,Society of Exploration Geophysicists Intemational Exposition & Fifty- forth Annual Meeting oklahoma:Society of Exploration Geophysicists, 1984 322～325
8张关泉.用波场转换进行倾角校正地球物理学报,1992,35:77～85
9耿建华,马在田.快速DMO算法石油地球物理勘探,1994,29:462～467
10马在田.P-SV反射转换波的倾角时差校正(DM)方法研究地球物理学报,1996,39:243～250
11Ronen J. Wave-equation trace interpolation. Geophysics, 1987, 52:973～984
12GegJianhua,Ma Zajtian;Wang Yong. 3-D DMO Algorithm in F-K domain and application. Chinese Joumal of Geophysics, 1995, 38:125～130
13Claerbout J F.Imaging of the earth's interior. New York: Blackwell Scientific Publication, 1985
14Berkhout A J.Steep dip finite difference migration Geophysical Prospecting, 1979, 27: 196～213
15Stolt R H. Migration by Fourier transform. Geophysics,1978, 43:23～48
16马在田地震成像技术北京:石油工业出版社,1989.87～120
17张关泉.利用低阶偏微分方程组的大倾角差分偏移.地球物理学报,1986,29:273～282
18贺振华,王才经,李建朝,等反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989.31～87
2Boondi G, Loinger E, Rocca F. Offset continuation of seismic section. Geophysical Prospecting, 1982. 30:813～8283Yilmaz O,Claerbout J F. Prestack partial migration. Geophysics,1980,45:1753～1779
4Hale D. Dip moveout by Fourier transform. Geophysics,1984,49:741～757
5Liner C L.Bom theory of wave-equation dip moveout. Geophysics, 1991,56:182～189
6Deregowski S M, Rocca F. Geometrical optics and wave theory of contant offset sections in layered media. Geophysical Prospecting,1981,29:384～406
7Fowler P. Velocity independent imaging of seismic reflection. In: Society of Exploration Geophysicists, ed. Technical Program Expanded Abstractswith Authors’ Biographies,Society of Exploration Geophysicists Intemational Exposition & Fifty- forth Annual Meeting oklahoma:Society of Exploration Geophysicists, 1984 322～325
8张关泉.用波场转换进行倾角校正地球物理学报,1992,35:77～85
9耿建华,马在田.快速DMO算法石油地球物理勘探,1994,29:462～467
10马在田.P-SV反射转换波的倾角时差校正(DM)方法研究地球物理学报,1996,39:243～250
11Ronen J. Wave-equation trace interpolation. Geophysics, 1987, 52:973～984
12GegJianhua,Ma Zajtian;Wang Yong. 3-D DMO Algorithm in F-K domain and application. Chinese Joumal of Geophysics, 1995, 38:125～130
13Claerbout J F.Imaging of the earth's interior. New York: Blackwell Scientific Publication, 1985
14Berkhout A J.Steep dip finite difference migration Geophysical Prospecting, 1979, 27: 196～213
15Stolt R H. Migration by Fourier transform. Geophysics,1978, 43:23～48
16马在田地震成像技术北京:石油工业出版社,1989.87～120
17张关泉.利用低阶偏微分方程组的大倾角差分偏移.地球物理学报,1986,29:273～282
18贺振华,王才经,李建朝,等反射地震资料偏移处理与反演方法.重庆:重庆大学出版社,1989.31～87
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