【摘要】 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.更多还原

【Abstract】 A simplified method for the simulation of ergodic spatially correlated seismic ground motions was proposed,based on the commonly used original spectral representation method.Firstly,the phase angles,to represent the correlation among ground motions, were given by explicit items with a clear physical.By using these explicit items,computational efficiency can be increased by changing the decomposition of complex cross-spectral matrix into the decomposition of real incoherence coefficient matrix.Double-indexing frequencies were introduced to simulate ergodic seismic ground motions,and the ergodic feature of the improved method was demonstrated theoretically.Subsequently,an explicit solution of the elements of the lower triangular matrix under Cholesky decomposition was given.By using this explicit solution,the improved method had been simplified,and the computational efficiency can be increased greatly,by avoiding repetitive Cholesky decomposition of cross-spectral matrix in every frequency step.At last,a numerical example was employed to illustrate the good character of the improved method.更多还原