Abstract
A theoretical relation between the characteristic periods and peak values of strong ground motions is derived based on random-vibration theory. The relation, summarized as a simple form of theorem, is analogous to the one between period and amplitude of a harmonic motion. The theorem leads to the bounded prediction of central periods whose upper and lower limit values are dependent only on peak acceleration, peak velocity and peak displacement. Following the confirmation of its validity in comparison with observed strong-motion records, the theorem is further expanded to theoretically scale acceleration, velocity and displacement spectra in seismic source area.
