The interpretation of the b and the b 0 values and its implications on the regional deformation of the crust

Summary After reviewing the model and the interpretation of the negative power laws which represent the statistical distributions of the linear dimension of faults l and of the stress drops p of the earthquakes, it is seen that the γ coefficient of the law log M 0 =ω+γ M increases with M for smaller M. It is verified that the parameters l and p of California earthquakes are independent and also it is suggested that one may consider a fractal dimension of earthquakes associated with p. It is shown how these statistical distributions may allow distribution of slips in the seismic regions to be inferred where all the slips occur approximately in the same horizontal direction. From the density distribution of the length of the faults it is found that in California 50 per cent of the regional displacement is due to the faults with linear lengths larger than 63 per cent of the maximum linear length of the faults. Similar results are obtained using the seismic moment M 0 or the magnitude M instead of l ; in these cases, however, the density distribution of p is also needed for the exact computation of the displacement. Assuming that in California the regional displacement has been 5 cm yr −1 , as measured with ground observations and space techniques, it is tentatively estimated that the displacement due to earthquakes with M 0 larger than 10 27.1 , may be as large as 4.2 cm yr −1 and that a cumulative displacement of at least 170 cm, due to earthquakes with M 0 larger than 10 27.1 , may have not been released since the great 1906 San Francisco earthquake. It is finally discussed how the variation in the density distribution of stress drops may be a precursor to earthquakes.