Evidence of self organization in great Sumatra earthquake recurrence times: Implications for coupling of tidal forcing and tectonic stress accumulation

We analyzed inter- event time series of earthquake activities (M≥ 5) of Sumatra region spanning over 1973 to 2009 using techniques of nonlinear dynamics. The earthquake data were taken from the USGS catalogue centered on latitude 3.240N and longitude 95.825E. As a first step, in our analyses we computed the rank order statistics which revealed mixed response of earthquake dynamics indicating distinct breaks in slope of the rank order. This suggests that earthquake dynamics in this region is partly unstable and partly "self-organized" with a random tail. Comparison of return maps of the earthquakes inter- event time series with those representing random, stochastic and chaotic processes shows a quasi-deterministic behavior of earthquake genesis in the region. We further assessed the dimensionality of earthquake-generating mechanisms using a nonlinear predictor technique on two dimensional phase portrait constructed by recurrence time series. The nonlinear forecasting analysis suggests that the earthquake processes in the Sumatra region evolve on a non-random low-dimensional chaotic plane. Further, "K2" Entropy revealed a coherent structure indicating the deterministic dynamical pattern. This analysis is consistent with "self-organized" processes which could be explained invoking earth's internal dynamics, where, impulsively derived interdependencies cascades through the stress generated by tectonic plate movement. Our results, however, do not preclude the role of coupling of the above self-organized system with tidal forcing. Evidence for such a coupling in this region exists as 'triggering force". Keywords: Sumatra Earthquakes, Quasi-deterministic, Stochastic, Chaotic, Self-organized, K2 entropy, Phase portrait.