错格傅里叶伪谱微分算子在波场模拟中的应用

本文在传统傅里叶微分矩阵的基础上，对原始微分算子进行改进，引入了错格微分算子的傅里叶伪谱方法．尽管该方法增加了一些计算量，但却极大地提高了计算精度和稳定性．而且，该方法将微分计算过程由传统的傅里叶变换转换为一般的矩阵矢量乘积，大大降低了微分求解过程的复杂程度．在均匀介质中，将错格伪谱微分算子计算的结果和解析解进行比较，结果表明本文算子几乎达到了解析解的精度．而在分层均匀介质中的实验结果同时显示，该方法精度高、稳定性好，是一种研究层状介质中地震波传播的有效数值方法．

The application of staggered-grid Fourier pseudospectral differentiation operator in wavefield modeling

Based on traditional Fourier differentiation matrix and some modifications of the original differentiation operator, this paper refers to a new kind of method——staggered-grid Fourier pseudospectral differentiation operator. The staggered-grid strategy proposed in this paper, though a little more time-consuming than the traditional method, greatly improves the accuracy and stability of the computing process. And the thought of converting the traditional fast Fourier transform into matrix vector multiplication, at the same time, reduces the complexity of the difference, which then makes them more easily to be treated. A comparison with the analytic result for vertical displacement in homogeneous medium demonstrates that the staggered-grid differentiation operator almost achieves as the same accuracy as the analytic method. The application of this method in homogeneous layered media also shows high accuracy and robust stability. These attractive properties of this method make it an effective modeling method for seismic wave propagation in homogeneous layered media.