Panorama of Fractals and Their Uses


The Gutenberg-Richter Law is an empirical relation
log(N) = -b⋅m + a
between the magnitude m and the number N of earthquakes of magnitude exceeding m.
Straightforward calculations (pgs 178-179 of Turcotte) convert this to a power law.
N = B⋅r-2b
where the length of the fault break is r = √A and A is the area of the fault break. Then 2b = D, the dimension of seismic activity for the region from which the data were collected.
For example, the graph below (inspired by page 179 of Turcotte) illustrates the number N of earthquakes per year of magnitude exceeding m in southern California for the period 1932-1972. The circle represents the expected rate of great earthquakes in southern California. The data predict about one per century.