A SELF-CONSISTENT DESCRIPTION OF RUPTURES IN AN ELASTIC MEDIUM - AN APPLICATION TO EARTHQUAKES

We present a general self-consistent procedure using lattice Green's f unctions to find the stress redistribution due to multiple ruptures in a discrete elastic medium. We use this method to study a dipole versi on of the quasi-static crack-propagation model for earthquakes propose d by Chen et al. Unlike the earlier treatment we do not assume that ru ptures occur independently. We obtain the stresses self-consistently a nd this changes the scaling behaviours of the frequency-size (seismic moment, energy) distribution. We make a careful comparison of our resu lts with recent analysis of seismological data.