On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis

Abstract

Natural time analysis has led to the introduction of an order parameter for seismicity when considering earthquakes as critical phenomena. The study of the fluctuations of this order parameter has shown that its variability exhibits minima before strong earthquakes. In this paper, we evaluate the statistical significance of such minima by using the recent method of event coincidence analysis. Our study includes the variability minima identified before major earthquakes in Japan and Eastern Mediterranean as well as in global seismicity.

Natural Time Analysis: The Area under the Receiver Operating Characteristic Curve of the Order Parameter Fluctuations Minima Preceding Major Earthquakes

“…It is characterized outstanding when AUC is more than 0.9 [ 51 ], which is of course the present case of since the AUC computed here is around 0.95. This result corroborates with the fact that the statistical significance of the precursory nature of has been shown by two other independent procedures, in particular Monte Carlo calculations in Reference [ 43 ] and ECA in Reference [ 44 ].…”

“…Using Monte Carlo calculations, Sarlis et al [ 43 ] showed that the probability to achieve the above results by chance is of the order of (we shall return to this point later). This conclusion was also recently strengthened by Christopoulos et al [ 44 ] using the event coincidence analysis (ECA) [ 45 ]. It is the scope of the present paper to investigate the diagnostic accuracy of the precursory minima before major EQs in Japan during 1984–2011 by employing the area under the receiver operating characteristic (ROC) [ 46 ] curve (AUC), which is a very recent technique for judging the quality of binary predictions.…”

“…First, only the minima of the order parameter fluctuations defined in Equation ( 4 ), but not the minima of (as claimed in Reference [ 78 ]), are of precursory nature [ 30 , 43 , 44 ].…”

Natural Time Analysis of Seismicity within the Mexican Flat Slab before the M7.1 Earthquake on 19 September 2017

“…Natural time analysis is based on a new definition of time introduced in Reference [ 22 ] (see Preface and Chapter 2 of Reference [ 21 ] and in particular its Section 2.1 and Section 2.2 , as well as Reference [ 31 ]) and has been found of usefulness [ 21 ] to uncover important features hidden in complex systems time series spanning various disciplines from cardiology [ 25 , 32 , 33 ] to seismology (including laboratory fracture experiments under well controlled conditions) [ 3 , 4 , 5 , 6 , 34 , 35 , 36 , 37 , 38 ] and from atmospheric sciences [ 39 , 40 ] to complex networks [ 41 ], and civil engineering [ 42 ].…”

“…In this analysis, the elapsed time between consecutive events is ignored, but preserving the occurrence order and their energy Q k . For seismic catalogues , where the moment magnitude [ 43 ] M is used [ 37 , 38 , 44 ]. In natural time we study the evolution of the pair ( , ) or alternatively ( , ) where is the normalized energy for the k -th event.…”