一种基于全局优化的交错网格有限差分法

在地震波场数值模拟中， 交错网格有限差分技术得到了广泛的应用， 但是在弹性模量变化较大时， 通常会因插值而导致模拟误差增大. 旋转交错网格可以很好地克服这个缺点， 因而适合于各向异性介质正演模拟. 但是对于同样大小的网格单元， 旋转交错网格需要的步长比常规交错网格要大， 这会使梯度和散度算子的误差增大因而更易产生空间数值频散. 针对这些问题， 本文提出了旋转交错网格与紧致有限差分相结合的方法， 并基于模拟退火算法进行全局优化， 压制数值频散， 拓宽波数范围. 数值模拟结果表明， 此方法可以有效地压制数值频散， 且具有较高的模拟精度. 

A staggered grid finite difference method based on global optimization

Staggered grid finite difference techniques have been widely used in numerical simulation of seismic wave field， but the interpolation might enlarge the simulation errors when the elastic moduli change dramatically. Rotated staggered grid can overcome this drawback thus be more applicable for modeling the anisotropic media. However， for the grid cells with the same size， rotated staggered grid needs larger step than conventional staggered grid does， consequently， the gradient operator and divergence operator generate larger errors which are more likely to cause spatial numerical dispersion. Aiming at the above problems， a combination of rotated staggered grid and compact finite difference method is proposed， simultaneously， global optimization is preformed based on simulated annealing algorithm to suppress numerical dispersion and to broaden the range of wavenumber. Numerical simulation results show that this method can effectively suppress the numerical dispersion and exhibits high simulation accuracy at the same time.