中文摘要：

早期的褶积微分算子法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l6阶有限差分相当。粘弹性波动方程更真实地描述了实际地下介质中弹性波的传播规律及其波场特征。本文以二维粘弹性波动方程为例,推导了粘弹性介质波动方程的离散格式,用迭积微分算子法实现了粘弹性介质的地震波场正演模拟,并对其波传播特征进行了分析。计算结果表明该算法能正确模拟粘弹性介质中的地震波,正确地反映粘弹性介质中波场的传播规律。

英文摘要：

Early convolutional differentiators are all based on the Fourier transformation,their precision is a little higher than that of four-order finite difference.For improving the precision and efficiency of seismic modeling,a new modeling approach（Convolutional Forsyte Polynomial Differentiator Method,CFPD）is developed in this paper 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.Viscous-elastic wave equation can better explain wave phenomena of the true earth media.This paper applies the CFPD method to model 2-D viscous-elastic seismic wave field for the first time,and further derives the first-order velocity-stress discreate equations for viscous-elastic media.The numerical results show that the algorithm can bring reliable outcomes with high precision and fast speed,and viscous-elastic modeling is much efficient.