Stochastic characterization of earthquakes through their response spectrum

If earthquakes are modelled by a stochastic process, it is possible to interpret the associated response spectrum in terms of the statistics of extreme values of oscillator response to the process. For a stationary earthquake model this interpretation leads to a relationship between the power spectral density function of the process and the response spectrum. This relationship is examined in this paper and forms the basis for two methods presented to obtain the power spectrum of the earthquake process from its response spectrum. One of these methods is approximate but leads to an explicit representation of the power spectral density function in terms of the response spectrum. The other method is exact wherein an iterative scheme for the solution of the problem is established. An example problem is solved to illustrate the use of the two methods and it is shown that for small values of damping, the approximate derivation yields a fairly accurate solution.