最优化广义离散Shannon奇异核褶积微分算子地震波场模拟

Optimal generalized Shannon singular kernel convolution differentiator in seismic wavefield modeling

本文运用广义离散Shannon奇异核褶积微分算子(GDSCD)计算波动方程的空间导数,推导了一阶和二阶GDSCD的具体形式,并提出了系数优化方法,即在频率域逼近平面波的真实导数,得到不同半径和采样下限的最优权系数。通过计算滤波响应分析算子精度,与多种数值方法进行了对比。模型试算结果表明,本文构造的最优化GDSCD方法模拟地震波具有高精度、高效率的特点。

In this paper,we present an optimal generalized Shannon singular kernel convolution differentiator for solving seismic wave equation.Using generalized Shannon singular kernel convolution differentiator(GDSCD),the first and second order convolution differentiators are derived.Then an efficient method is developed to optimize the coefficients of the convolution differentiator.Many groups of optimal coefficients are obtained for various operator length and sampling rate per shortest wavelength.Compared with various numerical methods,the operator accuracy is discussed through filter response.Our results from model tests show that this new method has high accuracy and efficiency in seismic modeling.