A theoretical study has been made to derive the energy spectrum of random-pulse time-series. Since the pulse width corresponds to a rupture time of a random fault patch, the random time-series approximates short-period seismic radiation from the heterogeneous faultings. Assuming exponentially decaying pulses, a parameter S is introduced as the inverse of pulse relaxation times. Energy spectra of the random time series are expressed by a Lorentzian-like spectrum of 1/(ω²+S²) with a weighting function P(S), where ω is angular frequency. Cases that P(S) represents the probability density for Gaussian, uniform, and power-law distributions are studied. It is found that the power-law distributions are related to the probability density distribution specified by the Cantor set. Spectra converge respective constant values at the low frequency end, whereas in high frequencies they show the ω^-2 decay. The energy spectrum for the Gaussian is described by the Lorentzian with a spectral corner frequency of the mean value of S. Linear and quadratic power-law distributions of S suggest the Lorentzian-like energy spectra. Fractal spectrum is obtained from the uniform distribution and distributions specified by the Cantor set, showing the 1/f and 1/f^1+δ spectra, where f is the frequency and δ is a small fractional number between 0 and 1. The fractional power of spectral decay is related to the variance of the probability distribuition.

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