基于保辛算法的声波叠前逆时偏移

叠前逆时偏移是目前成像精度最高的地震偏移方法之一,其实现过程中的一个重要步骤是数值求解全波方程,所以快速有效求解全波方程的数值算法对逆时偏移至关重要. 四阶近似解析辛可分Runge-Kutta (NSPRK) 方法是近年发展的一种具有高效率、高精度的数值求解波动方程的保辛差分方法, 能在粗网格条件下有效压制数值频散, 从而提高计算效率, 节省计算机内存需求量. 本文利用四阶NSPRK方法构造的基本思想,发展了具有六阶空间精度的NSPRK方法,并对新的六阶NSPRK方法进行了详细的稳定性和数值频散分析,以及计算效率比较和波场模拟. 同时将该方法用于声波叠前逆时偏移中, 得到一种时间上保辛、空间具有六阶精度、低数值频散、可应用大步长进行波场延拓并能长时计算的叠前逆时偏移方法,对Sigsbee2B模型进行了偏移成像, 并和四阶NSPRK方法、传统的六阶差分方法、四阶Lax-Wendroff correction (LWC) 方法进行了对比. 数值结果表明, 基于六阶NSPRK方法的叠前逆时偏移能得到更好的成像结果, 是一种优于四阶NSPRK方法、传统的六阶差分方法、四阶LWC叠前逆时偏移的方法, 尤其是在粗网格情况下具有更明显的优越性.

Acoustic prestack reverse time migration based on the symplectic method

Prestack reverse time migration (RTM) is currently one of the most accurate seismic migration imaging methods. An important step of its implementation is to solve the full-wave equation, so the numerical algorithm of solving the full wave equation quickly and effectively is crucial for reverse-time migration. The nearly analytic symplectic partitioned Runge-Kutta (NSPRK) method is a high-efficiency and high-precision numerical symplectic difference method developed in recent years, which can effectively suppress the numerical dispersion when a coarse grid is used. So it can increase computation efficiency and save computer memory demand. In this article, we develop a sixth-order NSPRK method based on the fourth-order NSPRK method, analyze the stability and numerical dispersion of the new sixth-order NSPRK method, compare its calculation efficiency and conduct wave field simulation. Then we apply it to the acoustic prestack reverse time migration, obtaining a sixth-order symplectic prestack reverse time migration method with low numerical dispersion, which can be applied to wavefield extrapolation with large steps and compute in long time. We get migration images of the Sigsbee2B model, and compare them to the fourth-order NSPRK method, the sixth-order conventional finite difference method, and the fourth-order Lax-Wendroff correction method (LWC). Numerical results show that the method based on the NSPRK prestack reverse time migration can get better imaging results than the fourth-order NSPRK method, the sixth-order conventional finite difference method, and the fourth-order LWC prestack reverse time migration method, especially in the case of coarse meshes.