Panorama of Fractals and Their Uses

Earthquakes

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 = sqrt(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.