In this paper, the evolutionary (time varying) power spectra of seismic accelerograms are estimated using the recently proposed method of separation. The procedure is based on a number of sample functions of the non-stationary random process characterizing the seismic event. These sample functions are artificial accelerograms as well as natural ground motion records. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time-frequency localization. However, it requires at least approximate spectral separability of the input samples to achieve satisfactory accuracy. The estimated evolutionary spectra are found to be in good agreement with those of the input samples in an average sense and can be used to generate artificial accelerograms compatible with specific ground motion records.