Exact computation of input‐energy spectra from Fourier amplitude spectra

Abstract

Abstract A theoretically exact relation is presented between the Fourier amplitude spectrum and the elastic input‐energy spectrum. This energy spectrum is computed from the Fourier acceleration amplitude spectrum and the real part of the relative velocity transfer function of the single‐degree‐of‐freedom elastic oscillator. Some accelerometric records collected worldwide are used to prove the solution. It is shown that the relation presented in this work opens the door for a better understanding of the relationship between the input‐energy spectrum and other seismological variables, such as magnitude and focal distance. Copyright © 2003 John Wiley & Sons, Ltd.