Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 2 3/4 1995 10.5194/npg-2-131-1995 http://www.nonlin-processes-geophys.net/2/131/1995/ http://www.nonlin-processes-geophys.net/2/131/1995/npg-2-131-1995.html http://www.nonlin-processes-geophys.net/2/131/1995/npg-2-131-1995.pdf 131 135 0000-00-00 Size-frequency relation of earthquakes in load-transfer models of fracture J. B. Gómez D. Iñiguez A. F. Pacheco Department of Geological Sciences, University College London, Gower Street, London WC1 6BT,U.K. Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain Using Monte Carlo simulations of the process of breaking in arrays of elements with load-transfer rules, we have obtained the size- frequency relation of the avalanches occurring in 1- and 2-dimensional stochastic fracture models. The resulting power-law behaviour resembles the Gutenberg-Richter law for the relation between the size (liberated energy) of earthquakes and their number frequency. The value of the power law exponent is calculated as a function of the degree of stress dissipation present in the model. The degree of dissipation is implemented in a straightforward and simple way by assuming that only a fraction of the stress is transferred in each breaking event. The models are robust with respect to the degree of dissipation and we observe a consistent power-law behaviour for a broad range of dissipation values, both in ID and 2D. The value of the power-law exponent is similar to the phenomenological <i>b</i>- value (0.8 <u>&lt;</u> b <u> &lt;</u> 1.1) for intermediate magnitude earthquakes.