On the statistical mechanics of distributed seismicity

Abstract

In order to understand the underlying physics of distributed seismicity better we have considered a 2-D array of slider blocks connected by springs and interacting via static friction with a surface. There is no driving plate in this model. The time evolution of the system is found from numerical simulations in a cellular automata formulation. Energy is conserved and is the single control parameter. The distribution of energies in the springs is found to obey a modified Maxwell-Boltzmann statistics. It is found that the number-size statistics of clusters of unstable sliding blocks is identical to those in percolation clusters in the site-to-site percolation model. There is a well-defined critical point when unstable blocks become connected across the array. It has been previously suggested that distributed seismicity in a seismic zone is the percolation backbone of a 3-D percolation cluster. The fact that low-level seismicity satisfies the Gutenberg-Richter frequency-magnitude relation and is nearly constant in time also suggests that this background seismicity is similar to thermally induced noise.