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.