Nonlinear theory and tests of earthquake recurrence times

TL;DR

This paper introduces a nonlinear model for earthquake recurrence times, demonstrating its superior fit to synthetic data and questioning the effectiveness of using inter-event time distributions to estimate clustering parameters.

Contribution

The authors develop an efficient numerical scheme for nonlinear integral equations describing earthquake inter-event times, improving over linear approximations and challenging existing methods for parameter estimation.

Findings

Nonlinear theory fits synthetic catalogs well

Linear approximation introduces significant biases

Inter-event time distribution has limited power to determine clustering parameters

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.