On the statistical mechanics of distributed seismicity

SUMMARY 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 GutenbergRichter frequency-magnitude relation and is nearly constant in time also suggests that this background seismicity is similar to thermally induced noise.

[1]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[2]  Ian G. Main,et al.  Statistical physics, seismogenesis, and seismic hazard , 1996 .

[3]  Newman,et al.  log-periodic behavior of a hierarchical failure model with applications to precursory seismic activation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Klein,et al.  Boltzmann Fluctuations in Numerical Simulations of Nonequilibrium Lattice Threshold Systems. , 1995, Physical review letters.

[5]  M. Sahimi,et al.  Fractal analysis of three‐dimensional spatial distributions of earthquakes with a percolation interpretation , 1995 .

[6]  M. Basta,et al.  An introduction to percolation , 1994 .

[7]  Bruce E. Shaw,et al.  Dynamics of earthquake faults , 1993, adap-org/9307001.

[8]  D. Turcotte,et al.  A cellular-automata, slider-block model for earthquakes II. Demonstration of self-organized criticality for a 2-D system , 1992 .

[9]  D. Turcotte.  Fractals and Chaos in Geology and Geophysics , 1992 .

[10]  Donald L. Turcotte,et al.  Are earthquakes an example of deterministic chaos , 1990 .

[11]  Carlson,et al.  Mechanical model of an earthquake fault. , 1989, Physical review. A, General physics.

[12]  P. Bak,et al.  Earthquakes as a self‐organized critical phenomenon , 1989 .

[13]  Wu,et al.  Scaling and universality in avalanches. , 1989, Physical review. A, General physics.

[14]  Keisuke Ito,et al.  Fractal structure of spatial distribution of microfracturing in rock , 1987 .

[15]  L. Knopoff,et al.  Model and theoretical seismicity , 1967 .

[16]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[17]  D. Turcotte.  Self-organized criticality , 1999 .

[18]  D. J. Wallace,et al.  Critical point phenomena: universal physics at large length scales , 1993 .

[19]  Sidney R. Nagel,et al.  Instabilities in a sandpile , 1992 .