Frequency-Size Distribution of Model Seismicity in a Statistical Mechanical Model of Earthquakes

The frequency-size distribution of model earthquakes in a one-dimensional Burridge-Knopoff spring-block model Phys. Rev. Lett. 22 (1989) 2632 is studied. Analytical approach is taken to avoid the limitations on the size of models and computation time in numerical calculations. By using the Hamiltonian of the spring-block system a concept of seismic phonon' is proposed which is similar to the concept of phonon in solid state physics. The result of the occurrence frequency of model earthquakes shows a distribution similar to the modified gamma distribution proposed by Main and Burton using information theory.