波动方程有限差分法叠前深度偏移
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摘要
从地震叠前反射椭圆方程出发，本文导出了基于波动理论的共偏移距地震剖面叠前偏移方程，然后对此方程进行参考速度场中的浮动坐标变换，获得了叠前深度偏移方程．为了解决叠前衍射方程中含有对深度的二阶导数引起波场延拓成像的不适定问题，文中采用低阶偏微分方程组近似描述全上行波的办法，得到了衍射方程的高阶近似方程，并给出了计算衍射方程和折射方程稳定的差分格式，最后用此方法编制的程序对某一碳酸岩地区的地震资料进行了试处理，效果良好．
Prestack depth migration is an effective way of imaging complex structures inside the earth. In the paper, it firstly derives common-offset prestack migration wave equation from the prestack reflection ellipse, then by the floating coordinate transform in the reference velocity field, gives prestack depth migration wave equations. When only known wavefields recorded on the surface, the prestack diffraction equation can not be solved because it has second derivative with respect to the term of depth. In order to solve the problem, we use the system of low-order partial differential equations to approximate to upgoing wave and obtain the high-order approximate equations, create the stationary difference scheme of the high-order approximation equation and the refraction. Finally we apply the technique to process the real data and obtain the sahsfactory seismic section.
Prestack depth migration is an effective way of imaging complex structures inside the earth. In the paper, it firstly derives common-offset prestack migration wave equation from the prestack reflection ellipse, then by the floating coordinate transform in the reference velocity field, gives prestack depth migration wave equations. When only known wavefields recorded on the surface, the prestack diffraction equation can not be solved because it has second derivative with respect to the term of depth. In order to solve the problem, we use the system of low-order partial differential equations to approximate to upgoing wave and obtain the high-order approximate equations, create the stationary difference scheme of the high-order approximation equation and the refraction. Finally we apply the technique to process the real data and obtain the sahsfactory seismic section.
引文
1Hubral P.Time migration-some ray theoretical aspects. Geophysics, 1977, 25(5):738-745 2 Larner K et al. Depth migration of imaged time sections. Geophysics, 1981, 46(5):734-750
3马在田.地震成像技术.北京:石油工业出版社,1989
4曹景忠.Hubral观测的解析证明.石油物探,1990,29(1):47-58
5范尚武,范敏波等.波动方程三维吸收边界分解与拟合深度偏移.地球物理学报,1996,39(4):533-543
6李志明.一种理想的二维波场深度延拓法.石油地球物理勘探,1990,25(5):517-538
7金胜汉,曹景忠,马在田等.可分裂的三维陡倾角深度偏移算法.地球物理学报,1996,39(4):544-549
8刘超颖.大倾角有限差分深度偏移.石油地球物理勘探,1992,27(5):695-705
9Deng Jian-hua,Ma Zai-tian, Huang Hai-gui. Imaging of echo data of submatine sedimentary beds layer-by-layer with acoustic wave equation refraction correction method. Chinese Journal of Acoustic, 1995, 14(3): 200-208
10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(3):273-282
11马在田.P-SV反射转换波的倾角时差校正(DMO)方法研究.地球物理学报,1996,39(2):244-250
12马在田.沦常炮检距地震剖面叠前们移方法.石油地球物理勘探,1990,25(2):127-136
13Claerbout J F. Imaging of the Earth's Interior,Blackwell: Scientific Publication.1985
14Stolt R H Migration by Fourier transforms. Geophysics, 1978, 43(1):23-48
15 Berkhout A J. Steep dip finite-difference migration. Geophysical Prospecting, 1979, 27(2):196-213
16马在田.高阶方程的分裂算法.地球物理学报,1983,26(4):377-388
17 Zhang Guan-quan, Zhang shu-lun, et al. A new algorithm for finite-difference migration of steep-dips.Geophysics,1988,53(1):167-175
18马在田.时移法高阶方程深度偏移.同济大学学报,1992,20(3):361-369
3马在田.地震成像技术.北京:石油工业出版社,1989
4曹景忠.Hubral观测的解析证明.石油物探,1990,29(1):47-58
5范尚武,范敏波等.波动方程三维吸收边界分解与拟合深度偏移.地球物理学报,1996,39(4):533-543
6李志明.一种理想的二维波场深度延拓法.石油地球物理勘探,1990,25(5):517-538
7金胜汉,曹景忠,马在田等.可分裂的三维陡倾角深度偏移算法.地球物理学报,1996,39(4):544-549
8刘超颖.大倾角有限差分深度偏移.石油地球物理勘探,1992,27(5):695-705
9Deng Jian-hua,Ma Zai-tian, Huang Hai-gui. Imaging of echo data of submatine sedimentary beds layer-by-layer with acoustic wave equation refraction correction method. Chinese Journal of Acoustic, 1995, 14(3): 200-208
10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(3):273-282
11马在田.P-SV反射转换波的倾角时差校正(DMO)方法研究.地球物理学报,1996,39(2):244-250
12马在田.沦常炮检距地震剖面叠前们移方法.石油地球物理勘探,1990,25(2):127-136
13Claerbout J F. Imaging of the Earth's Interior,Blackwell: Scientific Publication.1985
14Stolt R H Migration by Fourier transforms. Geophysics, 1978, 43(1):23-48
15 Berkhout A J. Steep dip finite-difference migration. Geophysical Prospecting, 1979, 27(2):196-213
16马在田.高阶方程的分裂算法.地球物理学报,1983,26(4):377-388
17 Zhang Guan-quan, Zhang shu-lun, et al. A new algorithm for finite-difference migration of steep-dips.Geophysics,1988,53(1):167-175
18马在田.时移法高阶方程深度偏移.同济大学学报,1992,20(3):361-369
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