台湾集集地震近断层强震地面运动加速度时程的随机特性

The Randomness of Near Fault Acceleration Time History of the 1999 Chi-Chi, Taiwan, China, Earthquake

将强震地面运动加速度时程看作随机过程,选取台湾集集地震的30组近断层加速度时程为样本,研究其相关特性。3方向集系上的自相关矩阵和互相关矩阵表明3方向的加速度时程均为非平稳随机过程,并且相关系数的分布是随机的,这种随机相关性是无法用确定性的数学模型来模拟的。为此,又研究了样本函数的相关特性,即随机过程样本函数的相关函数,结果发现在随机过程的相关函数中包含有明显的随机函数分量,即相关函数仍为一随机过程,我们称这样的随机过程为超随机过程,本文建立了超随机过程相关函数的数学模型。本文的研究表明近断层强地面运动为一复杂的随机过程,对其相关特性的研究应当包括相关系数(性)的大小和相关系数(性)的随机分布两个方面。

The 1999 Chi-Chi, Taiwan, China earthquake (Mw = 7. 6) supplied us unprecedented recordings of near fault round motions and made it possible to study the randomness of near fault ground motions. In this paper, the acceleration history of every component is regarded as a random process. The recordings of 30 near-fault stations with certain qualification are used as assembly of the three random processes respectively. The autocorrelation and cross-correlation matrixes of assembly and correlation function of sample functions are studied. We find that the correlation matrixes of acceleration random process comprise a random component. Such kind of correlation could not be simulated by deterministic mathematical expression. Then the correlation function of the stationarized sample functions of acceleration random process is studied. We found that its autocorrelation function is still a random process, which could be divided into two parts, a deterministic process and a random process. A mathematic model of the autocorrelation function is constructed in this article. Considering the high randomness of the correlation-functions of near fault accelerations, the strong earthquake near fault ground motion is named as the super random process in this article. To study the random characteristics of acceleration time history, the autocorrelation function of cross-correlation function of three components are studied at the end of this paper.