A model for the shape of the fourier amplitude spectrum of acceleration at high frequencies

At high frequencies f the spectrum of S-wave accelerations is characterized by a trend of exponential decay, e^−πkf. In our study, the spectral decay parameter k shows little variation at a single station for multiple earthquakes at the same distances, but it increases gradually as the epicentral distance increases. For multiple recordings of the San Fernando earthquake, k increases slowly with distance, and k is systematically smaller for sites on rock than for sites on alluvium. Under the assumption that the Fourier spectrum of acceleration at the source is constant above the corner frequency (an ω⁻² source model), the exponential decay is consistent with an attenuation model in which Q increases rapidly with depth in the shallow crustal layers.