Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.     

各态历经的地震动空间场的简化模拟

基于地震动空间场模拟中运用较广泛的原型谱表示法,给出了一种各态历经地震动空间场的模拟公式．首先给出原型谱表示法中体现任意两点间相关性的相位角的具体表达式,使其具有明确的物理意义,从而使得对复功率谱矩阵的Cholesky分解转化为对实数域内的相干函数矩阵的Cholesky分解,提高了合成效率．同时还在模拟公式中引入了双索引频率,以使得模拟公式具有均值与相关函数(自/互功率谱密度函数)的各态历经性,还对其各态历经性进行了理论上的证明,证明了当所模拟的各点地震动时间序列取一个周期时,其均值与相关函数的各态历经性．为进一步提高模拟效率,还给出了特定条件下,相干函数矩阵Cholesky分解后下三角矩阵中各元素的解析解,使得在合成中可以避免反复地在各频率下对相干函数矩阵进行Cholesky分解,从而实现了对模拟模型的简化．最后,给出一个简单的模拟实例,对改进前后模拟的地震动场进行比较,以说明改进后公式的模拟效果．     

低能电子束散射模拟在邻近效应修正中的应用

文章运用Monte Carlo方法模拟具有高斯分布特征的低能入射电子束斑在PMMA-村底中的复杂散射过程，分别得到了电子束在抗蚀剂中的穿透深度和能量沉积分布圈，并利用模拟结果进行邻近效应的修正．得到修正后的剂量数据文件。结果表明：采用修正后的剂量曝光，光刺胶中的能量沉积比较均匀．曝光分辨率有较大幅度的提高。该研究将对低能电子束曝光技术的定量研究和邻近效应修正技术的探索具有较高的理论指导意义。