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

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

doi:10.3390/e22050583

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

Entropy (Basel). 2020 May 21;22(5):583. doi: 10.3390/e22050583.

Authors

Nicholas V Sarlis^{1

2}, Efthimios S Skordas^{1

2}, Stavros-Richard G Christopoulos^{2

3}, Panayiotis A Varotsos^{1

2}

Affiliations

¹ Section of Condensed Matter Physics, Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, 157 84 Zografos, Greece.
² Solid Earth Physics Institute, Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, 157 84 Zografos, Greece.
³ Faculty of Engineering, Environment and Computing, Coventry University, Priory Street, Coventry CV1 5FB, UK.

Abstract

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.

Keywords: ROC; entropy; entropy change under time reversal; natural time analysis; order parameter of seismicity.