The 2009 L'Aquila (Central Italy) seismic sequence as a chaotic process

Abstract In this paper we demonstrate that the seismic sequence of foreshocks culminating with the recent M w  = 6.3 main shock on April 6, 2009 in L'Aquila (Central Italy) evolved as a chaotic process. To do this, we apply a nonlinear retrospective prediction to this seismic sequence and look at the temporal behaviour of the error between predicted and actual occurrence of the main shock when gradually increasing parts of the sequence are considered. This is a generalisation of the typical nonlinear approach which is quite powerful to detect chaos in relatively short time series. The method of prediction is based on the Accelerated Strain Release (ASR) analysis in time and on the nonlinear forecasting approach in a reconstructed phase space. We find that i) the temporal decay of the prediction error is consistent with an exponential function with a time constant τ of about 10 days and ii) at around 6 days before the main shock, ASR analysis is quite powerful for anticipating the time of occurrence with an uncertainty of about a day. Due to its retrospective characteristics, the latter result could be affected by changes on some a-priori parameters used in the application of the ASR technique. However, we consider these findings, together with those obtained from the phase-space analysis, to be strong evidence that the studied sequence of foreshocks was produced by a physical process dominated by a significant chaotic component characterised by a K -entropy = 1/ τ of about 0.1 day −1 . This result could have important implications for the predictability of the possible main shock for those seismic sequences showing analogous nonlinear chaotic properties.