ABSTRACT The staggered grid finite difference (SGFD) method has been widely utilised in seismic forward modelling. The accuracy of forward modelling results has a great influence on the results of subsequent seismic imaging and seismic inversion. Numerical dispersion is one of the inherent problems in the SGFD method. To suppress dispersion, we here introduce the truncated window function method, which can get optimised finite difference operators after truncating spatial convolution series of the pseudo-spectral method. The empirical criteria of window functions are the main lobe width that should be as narrow as possible and the side lobe attenuation should be as large as possible. According to these criteria, we propose the combined window function method based on the Gaussian window and Hanning window. The result of the amplitude spectrum response shows that the new combined window has narrower main lobe and greater side lobe attenuation, which results in higher accuracy in numerical simulations with SGFD operators. Numerical tests also illustrate the effectiveness of this new method.

中文翻译：

---

基于组合窗函数的优化交错网格有限差分算子

摘要 交错网格有限差分（SGFD）方法已广泛应用于地震正演建模。正演模拟结果的准确性对后续地震成像和地震反演的结果有很大影响。数值色散是 SGFD 方法的固有问题之一。为了抑制色散，我们在此引入截断窗函数法，它可以在截断伪谱法的空间卷积级数后得到优化的有限差分算子。窗函数的经验准则是主瓣宽度尽可能窄，旁瓣衰减尽可能大。根据这些标准，我们提出了基于高斯窗和汉宁窗的组合窗函数方法。幅度谱响应结果表明，新的组合窗口具有更窄的主瓣和更大的旁瓣衰减，从而在使用 SGFD 算子的数值模拟中具有更高的精度。数值试验也说明了这种新方法的有效性。