方向导数法三维 P-R 分裂偏移

Three-dimensional P-R splitting migration using directional derivative method.

本文提出一种新的三维波动方程 P-R 分裂偏移方法,即方向导数法三维 P-R 分裂偏移方法。该方法在 Clearbout 浮动时间坐标中采用一种特殊的平行四边形网格及其相应的差分格式,来逼近三维波动方程中关于τ和 t 的二阶偏导数项(即方向导数项),而不事先对三维波动方向作任何近似,最后可得到一个与15°三维 P-R 分裂偏移在形式上完全相同的三维差分方程。这种方法在所有方位角上都具有波场全倾角归位特性,具有计算量与15°三维 P-R 分裂偏移方法相当,克服了15°三维 P-R 分裂偏移方法只适应地层倾角较小的缺点和45°旋转坐标系下全倾角三维 P-R 分裂偏移方法计算量较大的缺点,从而更具有应用价值。

The paper describes a new three-dimensional wave equation P-R splitting migra- tion-three-dimensional P-R splitting migration using directional derivative.In this method,a special parallelogram grid and the corresponding difference scheme in Clear- bout's floating time coordinate system are used to approximate the second order partial derivatives of the equation with respect to τ and t (directional derivatives),without any prior approximation of three-dimensional wave direction.Finally,we can obtain a three-dimensional difference equation that is formally similar to the equation for 15° P- R sphtting migration.This method is more practical than others because it can achieve all-dip migration of full waves at all azimuths,only needs the calculation equivalent to that for 15°three-dimensional P-R splitting migration,and avoids the troubles that 15° three-dimensional P-R splitting migration is only applicable to small dip formations and that all dip three-dimensional P-R migration in 45° rotational coordinate system needs more calculation.