基于广义旋转法双九点格式标量波方程数值模拟

前人虽然基于传统旋转法提出了四阶精度最优17点差分格式，用于提高频率域地震波场数值模拟精度，但其仅适用于等网格间距的情形.这大大限制了该格式的使用范围.为了进一步提高17点有限差分格式的数值精度并将其推广到矩形网格，本文基于二阶精度有限差分算子利用广义旋转法提出了双九点格式，由于其差分格点与前人17点格式在分布上一样，所以也可称为二阶精度最优17点格式，但由差分格式构造原理上来讲，称其为双九点格式更妥.前人四阶精度17点格式仅为本文等网格间距情形时的特殊情况，本文方法单位波长网格点数仅需要2.2个即可.本文格式在继承传统旋转法良好几何旋转性质的同时，拥有平均导数方法适用于矩形网格的特点，和平均导数法所得的广义17点格式相比，本文格式数值精度更高，数值频散抑制性能和差分算子对称性更好.同时，本文双九点格式方法和思想对于后人借助传统九点格式的构造方法将其扩展到17点格式求解各类波动方程具有十分重要的意义.

Optimal double 9-point scheme scale wave equation simulation based on the generalized rotation method

Based on the conventional rotation method, a classical optimal 17-point scheme has been proposed to improve the accuracy of wave equation modeling in the frequency domain. However, this scheme just can be applied to the square grid, which seriously limits its application. What's more, its accuracy is not the best. To extend this method to a rectangle grid and obtain the best accuracy, this paper proposes a new 17-point scheme based on the generalized rotation method, which can also be a called the double nine-point scheme, while the traditional 17-point scheme is just a special case of this new method. It has a higher accuracy than the average-derivative 17-point scheme. What is the most important is that the idea we construct the double nine-point scheme in this paper can help us extend the arbitrarily nine-point scheme to a double nine-point scheme to solve all kinds of equations and then obtain higher accuracy in the frequency domain.