Hierarchical model for distributed seismicity

A cellular automata model for the interaction between seismic faults in an extended region is presented. Faults are represented by boxes formed by a different number of sites and located in the nodes of a fractal tree. Both the distribution of box sizes and the interaction between them is assumed to be hierarchical. Load particles are randomly added to the system, simulating the action of external tectonic forces. These particles fill the sites of the boxes progressively. When a box is full it topples, some of the particles are redistributed to other boxes and some of them are lost. A box relaxation simulates the occurrence of an earthquake in the region. The particle redistributions mostly occur upwards (to larger faults) and downwards (to smaller faults) in the hierarchy producing new relaxations. A simple and efficient bookkeeping of the information allows the running of systems with more than fifty million faults. This model is consistent with the definition of magnitude, i.e., earthquakes of magnitude m take place in boxes with a number of sites ten times bigger than those boxes responsible for earthquakes with a magnitude m-1 which are placed in the immediate lower level of the hierarchy. The three parameters of the model have a geometrical nature: the height or number of levels of the fractal tree, the coordination of the tree and the ratio of areas between boxes in two consecutive levels. Besides reproducing several seismicity properties and regularities, this model is used to test the performance of some precursory patterns.

Earthquake size-frequency statistics in a forest-fire model of individual faults

The earthquake size-frequency distribution of individual seismic faults commonly differs from the Gutenberg-Richter law of regional seismicity by the presence of an excess of large earthquakes. Here we present a cellular automaton of the forest-fire model type that is able to reproduce several size-frequency distributions depending on the number and location of asperities on the fault plane. The model describes a fault plane as a two-dimensional array of cells where each cell can be either a normal site or a trigger site. Earthquakes start on trigger sites. Asperities appear as the dual entities of the trigger sites. We study the effect that the number and distribution of asperities (the dual of the set of trigger sites), the earthquake rate, and the aspect ratio of the fault have on the size-frequency distribution. Size-frequency distributions have been grouped into subcritical, critical, and supercritical, and the relationship between the model parameters and these three kinds of distributions is presented in the form of phase maps for each of the five asperity types tested. We also study the connection between the model parameters and the aperiodicity of the large earthquakes. For this purpose the concept of aperiodicity spectrum is introduced. The aperiodicity in the recurrence of the large earthquakes in a fault shows an interesting variability that can be potentially useful for prediction purposes.