最优化辛格式广义离散奇异核褶积微分算子地震波场模拟

将波动方程变换至Hamilton体系,构造了一种新的保结构算法,即最优化辛格式广义褶积微分算子(OSGCD). 在时间离散上,首先引入了Lie算子设计二级二阶辛格式,基于最小误差原理得到了优化的辛格式. 在空间离散上,引入广义离散奇异核褶积微分算子计算空间微分,提出了一种有效方法优化GCD并得到了稳定的算子系数. 针对本文发展的新方法,给出了OSGCD稳定性条件. 在数值实验中,将OSGCD与多种方法比较,从精度和计算效率两方面分析了OSGCD的计算优势,计算结果也表明OSGCD长时程以及非均匀介质中地震波模拟亦具有较强能力.

Optimal symplectic scheme and generalized discrete convolutional differentiator for seismic wave modeling

In this paper, seismic wave equation is transformed into Hamiltonian system, and a new symplectic numerical scheme is developed, which is so called optimal symplectic algorithm and generalized discrete convolutional differentiator(OSGCD). For temporal discretization, OSGCD introduces Lie operators to construct second-order and two stage symplectic scheme and adopts optimal symplectic scheme based on minimum error principle. For the spatial derivative, OSGCD employs generalized discrete convolution differentiator to approximate the spatial differential operators and uses derivative approximation to obtain stable operator coefficients. We obtain the stability condition for 2D case. In numerical experiments, OSGCD is compared with different methods and it has advantages in both accuracy and efficiency. OSGCD also has the ability for modeling long-term seismic wave propagation and modeling seismic wave in heterogeneous media.