A hierarchical model for earthquake generation on coupled segments of a transform fault

Models for earthquake generation employing high-dimensional cellular automata reproduce realistic event sequences which conform to the Gutenberg-Richter relation. These models allow individual degrees of freedom to many small areal increments of a fault face. Simple, low-dimensional spring-block models with as few as two blocks have been shown, however, to explain neatly the coupling between adjacent segments of transform faults which has been observed in the stratigraphic record. The comparative usefulness of these dynamically distinct models may be assessed by elucidating the number of degrees of freedom which are required to reproduce the complexity of a real earthquake catalogue.

In this study the dimensionality of earthquake generating mechanisms is assessed by non-linear predictability analysis (from the literature of non-linear dynamical systems theory) on phase portraits constructed from time and magnitude data from a standard earthquake catalogue, a high-dimensional cellular automaton and a low-dimensional double-block model. The results show that complete earthquake populations are best described by complex, high-dimensional dynamics.

Considerations of the structure of the frequency-magnitude distributions of real earthquake populations and the evidence for coupling between active fault sections across seismic gaps indicate, however, that such dynamics may not explain many important features of natural seismicity. A hierarchical model is therefore proposed. In this model there is an explicit change in the generating dynamics with magnitude; a high-dimensional cellular automaton being responsible for the production of low-energy events and a low-dimensional, double-block mechanism representing the dynamics of events in which an entire fault face slips. The magnitude dependence of the dimensionality and b value, which is predicted from this model, is observed in a real earthquake catalogue. Coupling across a seismic gap is also a fundamental consequence of the model.

These dynamics may be appropriate for modelling seismicity on a section of a transform fault which includes more than one active segment.