Nonlinear theory and tests of earthquake recurrence times

Abstract

We develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in (Saichev and Sornette, 2007), which describes the distribution of inter-event times in the framework of a general model of earthquake clustering with long memory. Detailed comparisons between the linear and nonlinear versions of the theory and direct synthetic catalogs show that the nonlinear theory provides an excellent fit to the synthetic catalogs, while there are significant biases resulting from the use of the linear approximation. We then address the suggestions proposed by some authors to use the empirical distribution of inter-event times to obtain a better determination of the so-called clustering parameter. Our theory and tests against synthetic and empirical catalogs find a rather dramatic lack of power for the distribution of inter-event times to distinguish between quite different sets of parameters, casting doubt on the usefulness of this statistics for the specific purpose of identifying the clustering parameter.

31 pages including 11 figures

References in corpus (4)

• "Universal" Distribution of Inter-Earthquake Times Explained
• Theory of Earthquake Recurrence Times
• Apparent Clustering and Apparent Background Earthquakes Biased by Undetected Seismicity
• Universal Earthquake-Occurrence Jumps, Correlations with Time, and Anomalous Diffusion

Cited by in corpus (6)

• Return interval distribution of extreme events and long term memory
• Multiple-Time Scaling and Universal Behavior of the Earthquake Interevent Time Distribution
• Statistical Physics Approaches to Seismicity
• Estimation of the Hawkes Process With Renewal Immigration Using the EM Algorithm
• Statistics of seismic cluster durations
• Asymmetry in earthquake interevent time intervals