Modelling earthquake ground motions by stochastic method

The prediction of earthquake ground motions in accordance with recorded observations from past events is the core business of engineering seismology. An attenuation model presents values of parameters characterising the intensities and properties of ground motions estimated of projected earthquake scenarios (which are expressed in terms of magnitude and distance). Empirical attenuation models are developed from regression analysis of recorded strong motion accelerograms. In situations where strong motion data are scarce the database of records has to cover a very large area which may be an entire continent (eg. Ambrasey model for Europe) or a large part of a continent (eg. Toro model for Central & Eastern North America) in order that the size of the database has statistical significance (Toro et al., 1997; Ambrasey, 1995). Thus, attenuation modelling based on regression analysis of instrumental data is problematic when applied to regions of low and moderate seismicity. This is because of insufficient representative data that has been collected and made available for model development purposes. An alternative approach to attenuation modelling is use of theoretical models. Unlike an empirical model, a theoretical model only makes use of recorded data to help ascertain values of parameters in the model rather than to determine trends from scratch by regression of data. Thus, much less ground motion data is required for the modelling. Data that is available could be used to verify the accuracies of estimates made by the theoretical model. Ground motion simulations by classical wave theory provides comprehensive description of the earthquake ground motions but information that is available would typically not be sufficient as input to the simulations. The heuristic source model of Brune (1970) which defines the frequency content of seismic waves radiated from a point source is much simpler. The model has only three parameters: seismic moment, distance and the stress parameter. Combining this point source model with a number of filter functions which represent modification effects of the wave travel path and the site provides estimates for the Fourier amplitude spectrum of the motion generated by the earthquake on the ground surface. The source model (of Brune) in combination with the various filter functions are collectively known as the seismological model (Boore, 1983). Subsequent research by Atkinson and others provides support for the proposition that simulations from a well calibrated point source model are reasonably consistent with those from the more realistic finite fault models.