Scale invariance for a heterogeneous fault model

A very simple model of fault fracturing is presented. The fault is envisaged as a series of faultlets whose area is randomly distributed and whose strength have a Gaussian distribution. Faultlet slip occurs when the loading stress reaches its strength. Large earthquakes are generated by coalescence of smaller cracks. Theb value of the Gutenberg-Richter frequency magnitude relation is then calculated. Ab equal to 1 (scale invariance) is obtained only for events with magnitudeM greater than 3. At lower magnitude the number of events decreases with decreasing magnitude. A similar result can be explained by the experimental observation of an anomalous scaling law of real earthquakes. Here the suggestion is advanced that a similar observation could be interpreted by a multifractal approach.