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

Nicholas V Sarlis,Panayiotis A Varotsos,Efthimios S Skordas,Stavros-Richard G Christopoulos

doi:10.3390/e22050583

Nicholas V Sarlis, Panayiotis A Varotsos + Show 2 more

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It has been reported that major earthquakes are preceded by Seismic Electric Signals (SES). Observations show that in the natural time analysis of an earthquake (EQ) catalog, an SES activity starts when the fluctuations of the order parameter of seismicity exhibit a minimum. Fifteen distinct minima—observed simultaneously at two different natural time scales and deeper than a certain threshold—are found on analyzing the seismicity of Japan from 1 January 1984 to 11 March 2011 (the time of the M9 Tohoku EQ occurrence) 1 to 3 months before large EQs. Six (out of 15) of these minima preceded all shallow EQs of magnitude 7.6 or larger, while nine are followed by smaller EQs. The latter false positives can be excluded by a proper procedure (J. Geophys. Res. Space Physics 2014, 119, 9192–9206) that considers aspects of EQ networks based on similar activity patterns. These results are studied here by means of the receiver operating characteristics (ROC) technique by focusing on the area under the ROC curve (AUC). If this area, which is currently considered an effective way to summarize the overall diagnostic accuracy of a test, has the value 1, it corresponds to a perfectly accurate test. Here, we find that the AUC is around 0.95 which is evaluated as outstanding.

Highlights

Earthquakes (EQs) exhibit complex correlations in time, space and magnitude, e.g., [1,2,3,4,5,6,7,8,9,10].The observed EQ scaling laws point to [11,12,13] the existence of phenomena closely associated with the proximity of the system to a critical point
Other minima below the threshold (i.e., β 200,min ≤ 0.295) that have not been marked by red circles or green squares, did not obey any of the following criteria: β 200 and β 300 should appear simultaneously with a ratio β 300,min /β 200,min in the range 0.95 to 1.08
We vary the value of the shallowest β 200,min from 0.295 down to 0.157 and we obtain the receiver operating characteristics (ROC) depicted by the red solid line which has area under the ROC curve (AUC)=0.951

Summary

Introduction

The observed EQ scaling laws point to [11,12,13] the existence of phenomena closely associated with the proximity of the system to a critical point (the mainshock is the new phase [13,14]) In this frame, the order parameter κ1 of seismicity is the quantity by means of which one can identify the approach of the dynamical system to the critical point. The order parameter κ1 of seismicity is the quantity by means of which one can identify the approach of the dynamical system to the critical point Such a parameter has been introduced [15] upon analyzing the seismicity, in a new time domain, termed natural time [13,14,16,17,18] (see below) which has found useful applications in diverse fields [13,19,20]. This analysis unveils hidden properties in time series of complex systems [13] and has recently been used by Turcotte and coworkers as basis of a new methodology to estimate the current seismic risk level [21,22,23,24,25,26,27,28].

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