Dear Navid, 

it is well-known that real earthquake ground motion contains several frequencies, which from other perspective means that infinite sinusoidal curves are required to be added to obtain a resultant earthquake ground motion time history. However, there are only few frequencies (of the sinusoids) which actually contribute largely in the development of the resultant time history; an information that can be obtained from the Fourier spectrum of the motion.

Obviously, some earthquake ground motions are broad-band activities, i.e. they contain contribution from several sinusoids. On the other hand, some other earthquake ground motions are narrow-banded activities, i.e. they contain predominantly limited number of sinusoids contributing in the resultant motion. If one sees several peaks in the fast Fourier transform (FFT) spectrum corresponding to a large number of frequencies for an earthquake ground motion, it can be categorized as a broad-band activity. Contrary, if one sees very few peaks in the FFT spectrum corresponding to a limited number of frequencies for an earthquake ground motion, it can be categorized as a narrow-band activity. If you would like to assess contributions of the frequencies contained in an earthquake ground motion, apart from the FFT spectral amplitude, you may look in to the Power Spectral Density Function (PSDF).

Of course, the frequency (Hz) content is inverse to the time periods! Generally, when we study a response spectrum for an earthquake ground motion, it is plotted against time period (s) and contains several peaks and valleys. From such response spectrum also we observe the predominant time periods to which the spectral acceleration are quite high. Thereby, the structures, with their natural time periods matching to these time periods corresponding to the larger peaks in the spectral acceleration curves, are more vulnerable to that particular earthquake ground motion. The smoothed earthquake response spectrum is merely a representation of spectra of several earthquake ground motions.

These two spectra: (a) FFT spectrum and (b) response spectra for an earthquake are different representations altogether.

Hope this description helps to clarify. Good luck.

With best regards,

Vasant Matsagar.

Everything written above is ok. In my opinion one has to focus on FFT.

Obtaining the predominant frequency of an earthquake it is not an easy task. There are numerous predominant frequency and not only one. The most important methods are Fast Fourier Transform (FFT), Power Spectral Density, Terzband spectra and response spectra.

It depends on your intended use of the 'predominant period'. In my experience, the parameter is used rarely in practice. While it does indicate a single maximum peak on the spectrum, there are other local peaks as mentioned above, whether one is addressing the response spectrum or the Fourier amplitude spectrum. Design response spectra developed from modern codes have a broad plateau defining the peak acceleration. The peak acceleration on design spectra is constant between two frequencies. Call the two periods corresponding to those frequencies, To and Ts. This plateau typically widens as the supporting subsurface profile becomes softer. Perhaps a more meaningful representation of frequency content might be the period range, To to Ts at a given site. Finally, there is no discrepancy between the definition given by SeismoSignal and that given by Kramer.