多步法快速射线追踪与圆台型高精度走时外插计算

Multistep fast ray tracing and high accuracy traveltime extrapolation with truncated cone

为更好地适应复杂构造的地震偏移成像,本文提出了一套快速射线追踪算法和一种高精度的走时外插计算方法.采用线性多步法的预测-校正公式求解射线追踪方程组,与传统的四阶Runge-Kutta法相比,提高了计算效率.在网格节点上的走时计算中,应用一种基于圆台的外插方法,该方法以射线的方向为轴确定圆台,将轴上的走时外插到圆台内的网格节点上.与传统的矩形体外插方法相比,圆台走时外插方法提高了计算精度,且具有更好的稳定性.另外,该方法利用稀疏分布的射线即可获得高精度的走时表,节省计算量,对复杂构造的偏移成像非常有利,尤其是三维偏移.最后通过逆散射偏移成像算例,验证了算法的有效性和适用性.

In order to better adapt to seismic migration imaging of complex structures, this paper proposes a fast ray tracing algorithm and a high accuracy traveltime calculation method. In the proposed ray tracing approach, the predictor-corrector formula of linear multistep method is used to solve ray tracing equations, which improves the computational efficiency compared with classical fourth-order Runge-Kutta method. In the processing of calculating traveltimes at grids, we define a truncated cone (TC) which takes the ray direction as the axis, and extrapolate the traveltimes on the axis to the grids inside the TC. The presented extrapolation method with TC improves the computing accuracy, and shows higher stability in contrast to the traditional extrapolation method with a cubic box. Furthermore, this extrapolation method can obtain high-accuracy traveltime table even if sparsely distributed rays is applied, which effectively saves the computing time and is well beneficial for imaging complex structures, especially for 3D migration. Finally, we numerically validate our method by inverse scattering migration.