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.