Wavelet Energy Spectrum for Time-Frequency Localization of Earthquake Energy

摘要

The authors recently developed a method for time-frequency signal analysis of earthquake records using Mexican hat wavelets. Ground motions in earthquakes are postulated as a sequence of simple penny-shaped ruptures at different locations along a fault line and occurring at different times. In this article, a wavelet energy spectrum is proposed for time-frequency localization of the earthquake input energy. The ground acceleration generated by a simple penny-shaped rupture is used as the basis to form the mother wavelet. The symmetric Mexican hat wavelet is chosen as the mother wavelet. The spectrum is presented pictorialiy in a two-dimensional, time-frequency domain. The proposed wavelet energy spectrum can be used to observe the evolution of the frequency contents of earthquake energy over time and distance of the site from the epicenter in a more accurate manner than the traditional time series (accelerogram) or frequency domain (Fourier amplitude spectrum) representation. It can be viewed as a microscope for looking into the time-frequency characteristics of earthquake acceleration records. The wavelet energy spectrum provides frequency evolution information to be used in the structural design process.