Fractal characterization of an earthquake sequence

The generalized fractal dimensions for the distribution of interoccurrence time and the relation of cumulative frequency versus interoccurrence time of earthquakes are studied. The data set used is a complete one consisting of M 6 earthquakes occurring in the north-south seismic belt of mainland China during the 1900–1990 period. The log-log plot of Cq(t) versus t, where Cq(t) is the generalized correlation integral and t is the interoccurrence time in years between two events, is constructed. Result shows that a linear portion for t < tc = 50.1 years can be delineated. However, the pattern of data points bends and becomes flat at t = tc. The value of Dq at positive q is estimated from the slope value of the regression line to fit the linear portion of the data points for t < tc. The obtained Dq−q relation monotonically decreases with increasing q. The log-log plot of N versus T, where N is the cumulative frequency and T is the interoccurrence time in days between two events, shows two different patterns separating at Tc = 316.2 days. For T > Tc, the data points follow a linear distribution with a slope value of about −1.65 ± 0.11; in other words, N relates to N in a power-law form of N T−1.65. While for T < Tc, the data points follow a line with a very small slope value. Consequently, it is concluded that the earthquake sequence shows multifractality.