A preliminary study on the randomness of response spectra of the 1999 Chi-Chi, Taiwan, Earthquake

The Chi-Chi earthquake supplied us unprecedented information on near-fault ground motions and made it possible to study the randomness of near-fault g round motions in assembly. From the viewpoint of random function, response spectra of 30 stations under similar conditions are used as the samples of three random functions. The mean value functions, autocorrelation, and cros s-correlation matrixes of response spectra are studied. According to this s tudy, the response spectra of three components are all the nonstationary fu nctions. The spectra characteristics of two horizontal components are simil ar in statistical meaning, but there are certain differences in randomness. There are considerable differences between randomness of response spectra of vertical component and horizontal components. It can be seen that during the period range from 0.1 to 4 sec, which is the most commonly investigate d period range in engineering practice, the autocorrelation and cross-corre lation matrixes of response spectra of two horizontal components have rough ly diamond-like shapes; however, it is not the case for the autocorrelation matrixes of vertical component and cross-correlation matrixes of vertical to horizontal components, which are irregular in general. In this article, a primary mathematic model is established to simulate the autocorrelation m atrixes and cross-correlation matrixes of response spectra of two horizonta l components, which paves a way for further study in the randomness of resp onse spectra.