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Plane-wave depth migration was done in wavenumber-frequency domain in this paper. The acoustic wave equation was replaced by the coupledfirst order in depth system of equations, the formula was derived, by which the wave field was continued downward. Rcconstruction was done every depth step with the imaging conditions, accurate migration could be attained. In the extrapolating formula, function ex was approximated by a series consisting of Chebyshev expansion, which converges exponcntially, so it could adap... Plane-wave depth migration was done in wavenumber-frequency domain in this paper. The acoustic wave equation was replaced by the coupledfirst order in depth system of equations, the formula was derived, by which the wave field was continued downward. Rcconstruction was done every depth step with the imaging conditions, accurate migration could be attained. In the extrapolating formula, function ex was approximated by a series consisting of Chebyshev expansion, which converges exponcntially, so it could adap laterally variable velocity structure and keep high auuracy. 在空间一频率域内进行平面波深度偏移。将声波方程化为常微分方程组,得到波场延拓公式并由此将波场逐层下推,根据平面波的成像原理逐层进行成像处理,可得到精度很高的偏移结果。递推公式中的函数ey选用Chebyshev多项式构成的快速收敛级数进行逼近,以适应横向速度变化且保持很高的精度。 Increasing attention is paid to prestack depth migration in view of its irnportanceto complicatedustructure image. Papers of depth migration increase yearly. Many ollcorporations or research groups have been developing a lot of practical softwares fordepth migration. The development of depth migration is described to advance the research on Chian ls depth migration technique. 叠前深度偏移作为复杂构造成像的手段日益受到重视。近年来,有关于深度偏移的文章逐年增多,许多国外石油公司或研究小组相继推出了许多实用深度偏移软件。本文的目的在于通过论述深度偏移技术的发展概况,促进我国关于这一技术的研究工作。 Without taking aceount of the lateral variation of velocities, time migration may cause stratigraphie images to deviate from their correct underground positions. Starting from the 45° depth migration cquation, we introduce a parameter called Mirectional derivativeu and incorporate tht refraction effect term caused by lateral velocity variation into the directional derivative so as to make the depth migration be formally consistent with the corresponding time migration. In this way,depth migration is achicvable... Without taking aceount of the lateral variation of velocities, time migration may cause stratigraphie images to deviate from their correct underground positions. Starting from the 45° depth migration cquation, we introduce a parameter called Mirectional derivativeu and incorporate tht refraction effect term caused by lateral velocity variation into the directional derivative so as to make the depth migration be formally consistent with the corresponding time migration. In this way,depth migration is achicvable with the current application module after a slight modification,i. e. increasing the part of non-integer nodes for interpolation. The efficiency in both computation and programming is thus improved. The results frorn numerical trial show that this method is reliable and effective. 时间偏移由于忽略了速度的横向变化而导致成像偏离正确位置。作者从45°深度偏移方程出发,引出方向导数,并将速度横向变化所引起的折射效应项纳入此方向导数内,使所构造的深度偏移方法在形式上与相应的时间偏移方法一致。因此,只需对目前生产中应用的时间偏移模块略作修改,即增加非整数节点插值部分,就可实现深度偏移。这样不仅节省了计算工作量,提高了计算效率,而且也缩短了编程的时间。数值试验结果表明,方法是可靠有效的。
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