Tesis 3112: This work presents an analytical method for calculating stochastic response spectra from seismological models. We have assumed that the stochastic characterization of seismic ground motion can be represented by the Fourier amplitude spectra of stationary or non-statioanry seismological models. The first part of the work presents a state of the art review of seismological models. A unified and general formulation is developed that incorporates the mechanics of the fault rupture process termed source models; the specific conditions of the prediction site; and the transformation of the seismic waves in their propagation from the source to the earth’s surface termed site seismological models. We carefully analyze several seismological stationary and non-stationary models that have been applied in various seismogenetic areas of the earth.

To calculate a stochastic response spectrum from a theoretical amplitude spectrum it is necessary to regard an	 earthquake as a non-stationary process. In the present work, we have chosen the Priestley evolutionary stochastic process, which consists of windowing an underlying stationary stochastic process using an amplitude modulation function termed intensity function. We then analyze the relationship between the seismological model and the underlying stationary process in order to obtain a coherent definition of the earthquake duration. Therefore, we define a new duration parameter termed the equivalent stationary duration because its definition is related to an equivalence criterion based on the Arias intensity concept between the underlying stationary process and the evolutionary process. Moreover, with the aim of developing a new method for the estimation of the intensity function of a single strong motion record we assume that the evolutionary process is uniformly modulated. The method is called USP method that stands Underlying Stationary Process because the intensity funcion is obtain by applying an iterative algorithm that force the underlying stationary record to be as much statioanry as possible. The method perfoms very well with different types of accelerograms and intensity functions.

The last step in the calculation of a stochastic response spectrum from non-stationary seismological models is the application of the random vibration theory. In particular, we determine the peak factor for the case of an evolutionary process that includes the evolution of energy and frequency content. Thus, we obtain stochastic response spectra related to a certain non-exceedance probability. This general method is very good; but the time calculation is considerable. Therefore, a simplified method is developed with a reasonable time calculation for practical purposes in Earthquake Engineering. This simplified method assumes that the underlying stationary process of the evolutionary process of the ground motion acceleration is white noise. Finally, once the non-stationary displacement response of the stochastic process of the linear oscillator is obtained, a new equivalent stationary process is computed. The most common expressions of the peak factor can then be directly applied for the case.

Finally, the method for computing stochastic response spectra is applied to a possible European earthquake and then compared with the corresponding design response spectrum of the seismic codes and empirical response spectra. Moreover, we carry out a parametric study of the influence of some seismological and oscillator parameters on the response spectrum magnitude, hypocentral distance, site effects, damping, etc. Thus, we determine the parameters that must be included in the formulation of a design response spectrum. The stochastic displacement response spectrum is also computed and compared with the corresponding design response spectrum of the seismic codes. This method has been shown to be a very powerful tool because we have obtained realistic response spectra and, in addition, some levels of structural performance can be defined through the non-exceedance probability.