Abstract
The difference of seismic waves observed on piers at both ends of a long span bridge or at locations along an underground pipe often becomes a critical factor and is taken into consideration for aseismic design of such structures. The characteristics of the effect of the difference may be described by a coherence function which represents the dependency of two time series, and it is calculated from the power and cross-spectral density functions. However, in its estimation, it is often smoothed in the frequency domain. In this paper, the effects of the smoothing on the coherence function estimate are analyzed quantitatively, in the case that a time delay is observed between the two records or that they are statistically independent. Then, a modified method of calculating coherence function estimates is proposed.
