Determination of Seismic Design Parameters: A Stochastic Approach

A model of release of the seismic energy in an earthquake is developed by assuming that a seismic event is created by the progressive rupture of small coherent patches over the entire rupture surface. The motion at the site created by the rupture of a patch is analytically found by using a dislocation model where the fault plane is assumed to be a geometrical discontinuity across which there exists a sudden discontinuity in the displacement vector. The characteristics of the dislocation are represented by a ramp function. The solution is limited in the present case to body S-waves generated by the small patch sources.

Since the motion parameter is obtained as the Fourier Transform of the acceleration, in the complex domain, the effect of the rupture of the entire fault is obtained by superimposing the effect of all the individual patches with the proper phasing.

The model developed here is a three-dimensional model. It accounts not only for the directivity effects due to the relative position of the site with regard to the fault trace, but also for the dipping of the fault plane and the non horizontal direction of the average propagation of the rupture. In order to generate a realistic earthquake motion, the source parameters are taken as random variables with a given probability distribution. The propagation of the rupture in the fault plane is modeled by a random-walk type process. For use in seismic risk analysis, the uncertainty in the geometry of the system is also recognized (uncertainty in the location and orientation of the fault plane). A Monte Carlo simulation technique provides the statistics.