错格实数傅里叶变换微分算子及其在非均匀介质波动传播研究中的应用

提出一种新的数值微分运算方法，即错格实数傅里叶变换微 分法. 该方法的运算速度 比错格复数傅里叶变换数值微分解法快0.33倍；因为该微分算法在整个微分运算过程中保留 了奈奎斯特分量，使得它比普通分格的实数傅里叶变换数值微分算法的精度高，稳定性好. 将该方法和Cagniard De Hoop解析法在求解半无限空间地震波动的问题中进行比较，结果 表明，新微分法的精度和解析方法的精度相同. 在非均匀介质中的地震波传播数值模拟的结 果表明，该方法是一种研究非均匀介质中地震波传播问题的有效的数值微分方法.

STAGGERED GRID REAL VALUE FFT DIFFERENTIATION OPERATOR AND ITS APPLICATION ON WAVE PROPAGATION SIMULATION IN THE HETEROGENEOUS MEDIUM

A new fast differentiation operator，“staggered grid real value FFT d ifferentiation operator”，is proposed in this paper. The method is one third fa ster on average than the traditional differentiation method by using the complex FFT differentiation，and is very efficient in economy. Furthermore，the new met hod has higher accuracy and higher stability than the traditional grid real FFT method because the Nyquist component is remained throughout calculation procedur e.The validity of staggered grid real value FFT differentiation operator is confir med by comparing with the analytic Cagniard De Hoop method in the half space SH problem. The new operation is applied to simulate seismic wave propagation in i nhomogeneous medium，and the results show that the staggered grid real value FFT differentiation operator for the pseudospectral method is valid for the seismic wave simulation in the heterogeneous medium.