基于旋转交错网格和FCT技术的高精度数值模拟

High-precision Numerical Simulation on Rotating Staggered Grid and FCT Technology

地震波波动方程正演模拟技术是地震学和地震勘探的重要基础,是当前地球物理勘探学界的一个重要研究领域。在非均匀介质中,常规交错网格需要对弹性模量插值,当弹性模量变化较大时,计算不稳定,旋转交错网格有限差分将密度和弹性模量定义在相同网格点,不需要进行插值处理,提高了计算稳定性。有限差分在小网格条件下进行正演模拟时,占用内存大,计算效率低;在大网格条件下,提高效率的同时降低了数值模拟精度,产生较为严重的数值频散。通量校正传输法(FCT)可以压制粗网格情况下造成的有限差分数值频散问题。为了提高数值模拟精度、计算效率和稳定性,首次将旋转交错网格有限差分数值模拟与通量传输校正技术相结合,通过对旋转交错网格有限差分求解得到的速度进行漫射与反漫射处理,降低截断误差的累计达到提高精度的目的。

A forward modeling model of seismic wave equation is an important foundation of seismology and seismic exploration,as is a currently-important research field of geophysical exploration. In inhomogeneous medium,the conventional staggered grid will need elastic modulus of interpolation when the elastic modulus change is bigger.When computing is not stable,the rotating staggered grid in finite difference method of defines the density and elastic modulus is at the same grid point. It does not need interpolation processing to improve the computational stability. The flux correction method（ FCT） can suppress the finite difference numerical dispersion caused by the coarse mesh. In order to improve the accuracy,including efficiency and stability of numerical simulation,the finite difference method of rotational staggered grid and flux correction technique are combined for the first time. Through the diffusion and anti diffusion of the velocity from rotated staggered grids,we find the cumulative error of truncation error is reduced to improve the accuracy.