The finite difference method is widely used in seismic wave numerical simulation, reverse time migration and full waveform inversion. However, the numerical dispersion problem seriously affects the results of seismic imaging and inversion. Based on this, we introduced cosine-combined window function (CCWF) used in harmonic analysis of the power system and compared the amplitude response and error properties with other window functions. Then, an optimised CCWF and a new weighting method are proposed, which results in finite-difference operators with not only large spectral coverage but also small precision error fluctuation. In this paper, the analysis shows the good stability of using finite difference operators. Finally, we perform numerical forward modelling, which denotes that our method is superior than other optimum methods. From an economic point of view, this method will effectively reduce the computation cost and improve efficiency.

有限差分法广泛应用于地震波数值模拟，逆时偏移和全波形反演中。但是，数值色散问题严重影响了地震成像和反演的结果。在此基础上，我们介绍了用于电力系统谐波分析的余弦组合窗函数（CCWF），并将幅度响应和误差特性与其他窗函数进行了比较。然后，提出了一种优化的CCWF和一种新的加权方法，该方法导致了有限差分算子不仅具有较大的频谱覆盖范围，而且具有较小的精度误差波动。在本文中，分析表明使用有限差分算子具有良好的稳定性。最后，我们进行数值正向建模，这表明我们的方法优于其他最优方法。