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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.
Based on the prestack reflection ellipse equation, we derive the prestack migration equation of the co-offset seismic section based on the wave theory. Then we convert this equation to the floating coordinate in the reference velocity field to obtain the prestack depth migration equation . In order to solve the ill-posed problem of wavefront continuation imaging caused by the second derivative of depth in the prestack diffraction equation, a high order approximation equation of the diffraction equation is obtained by using the method of low order partial differential equations , And the difference scheme for calculating the diffraction equation and the refractive index equation is given. Finally, the seismic data in a carbonate rock area are tested and processed with this program.