中文摘要：

本文详细论述了功率谱与功率谱密度、平方和SS与平方平均值MS的适用范围及物理意义，比较深入地分析了平稳和非平稳加速度时间历程的统计特征，通过引入时域包线获取特定相位的方法，考虑了非平稳特性。本文基于非平稳时间历程，在不考虑频率非平稳性的基础上，提出了设计地震动三要素：（1）平方和SS；（2）归一化自相关函数或其对应的功率谱；（3）地震动时域包线．本文提出了在设计地震动合成中考虑超随机特性的实用方法。并指出地震动的超随机特性（即归一化功率谱的锯齿状波动部分，或归一化自相关函数的随机噪声部分）与相位的随机性是地震动随机特性的两个重要方面。本文将地震动的统计分析直接建立在非平稳时间历程的基础之上，从而避开了要对地震动进行平稳化处理的困难。这样提取出的地震动统计特征完全是以真实地震动记录为基础的。应用这些统计特征，可模拟出符合统计要求的基于非平稳时间历程的设计地震动。最后本文还讨论了工程上常用的将反应谱近似转换为功率谱的转换式的一些缺陷。

英文摘要：

This paper deliberately discusses the physical meanings and the applicability of power spectra and power spectra density, sum of squares and mean of squares, and analyzes the statistical characteristics of stationary and non-stationary acceleration time history. The non-stationarity of ground motion is considered through introducing the time-domain envelope and acquiring phase characteristics. Based on the non-stationary time history, three elements of design ground motion are proposed, i.e. , the sum of squares （ SS）, the norm autocorrelation function or its corresponding power spectra, and the time-domain envelope. Moreover, this paper proposes a practical approach to consider the super-randomness in design ground motion synthesis and indicates that both the super-randomness （the zigzag fluctuation over power spectra or random noise superposed on the auto correlation function） and the phase randomness are essential random characteristics. In this paper the statistical characteristics of ground motion are directly based on the non-stationary time history and then the difficulties of turning ground motions into stationary vibrating signals in analysis are avoided. As a result, the extracted statistical features of ground motion may be fully based on the real and original data of ground motion recordings. Utilizing these statistical features, we can simulate the design ground motion founded on the theories of non-stationary time history. Finally, the paper also point out some flaws in the popularly used formula for approximately transforming the response spectra into power spectra.