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Mathematical Theory of Seismic Activity and Its Specific Cases: Gutenberg-Richter Law, Omori Law, Roll-Off Effect,
Roumen Borisov1, Nikolay K Vitanov1
1Institute of Mechanics, Bulgarian Academy of Sciences, Academician Georgi Bonchev Street, Block 4, 1113 Sofia, Bulgaria.
Abstract:
We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg-Richter relationship and the Omori law. These laws are valid for earthquakes that happen in a single cluster of sources of seismic activity. Further, we discuss the distribution of earthquakes for several clusters containing sources of seismic activity. This distribution contains, as a specific case, a version of the negative binomial distribution. We show that at least a part of the roll-off effect connected to the parameter b of the Gutenberg- Richter law occurs because one records earthquakes that happen in more than one cluster of sources of seismic activity.
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