Time Frequency Localization of Earthquake Record by Continuous Wavelet Transforms
Wavelet analysis is a new mathematical method and has been increasingly applied in engineering in recent years. Unlike Fourier transform, this method is particularly appropriate for non stationary processes. Exceptional localization can be allowed using wavelet transform, both in time and frequency domains. Wavelet transform has been rarely used in earthquake engineering. A preliminary study of continuous wavelet transforms (CWTs) was conducted in this paper. As a rather novel technique, CWT application has generated enormous interest in recent years. It has been successfully employed in many fields, including the theories of communication and ordinary, partial differential equations, signal and image processing, and numerical analysis. As evidenced, exceptional localizations of time frequency domains have become possible through CWTs. In this paper, CWT capability of providing a full time frequency representation of an earthquake record was demonstrated. The Morlet mother wavelet was utilized to calculate the time frequency localization of the desired earthquake records. In this method, the time series of the earthquake records, which were broken in a wave flume, demonstrated the ability of the wavelet transform technique in detecting the complex variabilities of signals in the time frequency domain. In this investigation, various spectral representations resulting from the CWTs were discussed and their applications for earthquake records were shown.