中文摘要：

早期的褶积微分算子都是基于正反傅立叶变换而实现的,其精度比四阶有限差分的精度稍高,本文将计算数学中的Forsyte广义正交多项式微分算子与褶积算子相结合,构建了一个新的快速、高精度褶积微分算子,其计算结果非常接近实验函数微分的精确值,精度与16阶有限差分的精度相当,远优于错格伪谱法的精确度.另外,2.5维数值模拟比二维模拟可以更真实地模拟三维介质的某个剖面的波场,并且2.5维地震波模拟的计算量比三维模拟的计算量及计算耗时要大大减少.本文利用基于Forsyte广义正交多项式褶积微分算子法计算2.5维非均匀介质地震波场,模拟结果表明,该算法的计算速度快,计算精度高,能够直观、高效地反映复杂介质中波场的传播规律,并且2.5维波场数值模拟具有更高的计算效率,是一种非常值得深入研究并广泛应用的方法.

英文摘要：

Early convolutional differentiators were all based on the Fourier transformation, their precision was a little higer than that of the four-order finite difference. For improving the precision and efficiency of seismic modeling, the authors develop a new modeling approach （Convolutional Forsyte Polynomial Differentiator Method） by using optimized convolutional operators for spatial differentiation and staggered-grid finite-difference for time differentiation in wave equation computation. The solution of this new method is much close to the exact value, and the precision is nearly equal to that of 16 order finite difference, and higher than that of the pseudospectral method. 2.5D modelling is more efficient than 3D modelling, and more effective to model the 3D seismic field than 2D modelling. This paper applies the convolutional Forsyte polynomial differentiator method to model 2.5D seismic waves field. The numerical results show that the algorithm can bring reliable outcomes with high precision and fast speed, and 2.5D modelling is much efficient and economical, and deserves more attentatlon, research and extensive application.