We quantify the correlation between earthquakes and use the same to
distinguish between relevant causally connected earthquakes. Our correlation
metric is a variation on the one introduced by Baiesi and Paczuski (2004). A
network of earthquakes is constructed, which is time ordered and with links
between the more correlated ones. Data pertaining to the California region has
been used in the study. Recurrences to earthquakes are identified employing
correlation thresholds to demarcate the most meaningful ones in each cluster.
The distribution of recurrence lengths and recurrence times are analyzed
subsequently to extract information about the complex dynamics. We find that
the unimodal feature of recurrence lengths helps to associate typical rupture
lengths with different magnitude earthquakes. The out-degree of the network
shows a hub structure rooted on the large magnitude earthquakes. In-degree
distribution is seen to be dependent on the density of events in the
neighborhood. Power laws are also obtained with recurrence time distribution
agreeing with the Omori law.Comment: 17 pages, 5 figure