Natural Time Analysis: The Area under the Receiver Operating Characteristic Curve of the Order Parameter Fluctuations Minima Preceding Major Earthquakes
Abstract
:1. Introduction
2. Receiver Operating Characteristics Technique
3. Data Analyzed
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
AUC | Area under the ROC curve |
ECA | Event coincidence analysis |
EQ | Earthquake |
JMA | Japan Meteorological Agency |
ROC | Receiver operating characteristic |
SES | Seismic electric signals |
References
- Telesca, L.; Lapenna, V.; Macchiato, M. Spatial variability of the time-correlated behaviour in Italian seismicity. Earth Planet. Sci. Lett. 2003, 212, 279–290. [Google Scholar] [CrossRef]
- Huang, Q. Seismicity changes prior to the Ms8.0 Wenchuan earthquake in Sichuan, China. Geophys. Res. Lett. 2008, 35, L23308. [Google Scholar] [CrossRef]
- Lennartz, S.; Livina, V.N.; Bunde, A.; Havlin, S. Long-term memory in earthquakes and the distribution of interoccurrence times. EPL 2008, 81, 69001. [Google Scholar] [CrossRef] [Green Version]
- Telesca, L. Analysis of Italian seismicity by using a non-extensive approach. Tectonophysics 2010, 494, 155–162. [Google Scholar] [CrossRef]
- Lennartz, S.; Bunde, A.; Turcotte, D.L. Modelling seismic catalogues by cascade models: Do we need long-term magnitude correlations? Geophys. J. Int. 2011, 184, 1214–1222. [Google Scholar] [CrossRef] [Green Version]
- Telesca, L.; Lovallo, M.; Amin Mohamed, A.E.E.; ElGabry, M.; El-hady, S.; Abou Elenean, K.M.; ElShafey Fat ElBary, R. Investigating the time-scaling behavior of the 2004–2010 seismicity of Aswan area (Egypt) by means of the Allan factor statistics and the detrended fluctuation analysis. Nat. Hazards Earth Syst. Sci. 2012, 12, 1267–1276. [Google Scholar] [CrossRef] [Green Version]
- Tiampo, K.F.; Shcherbakov, R. Seismicity-based earthquake forecasting techniques: Ten years of progress. Tectonophysics 2012, 522–523, 89–121. [Google Scholar] [CrossRef]
- Tenenbaum, J.N.; Havlin, S.; Stanley, H.E. Earthquake networks based on similar activity patterns. Phys. Rev. E 2012, 86, 046107. [Google Scholar] [CrossRef] [Green Version]
- Vallianatos, F.; Michas, G.; Papadakis, G. Non-extensive and natural time analysis of seismicity before the Mw6.4, October 12, 2013 earthquake in the South West segment of the Hellenic Arc. Physica A 2014, 414, 163–173. [Google Scholar] [CrossRef]
- Sarlis, N.V.; Skordas, E.S.; Mintzelas, A.; Papadopoulou, K.A. Micro-scale, mid-scale, and macro-scale in global seismicity identified by empirical mode decomposition and their multifractal characteristics. Sci. Rep. 2018, 8, 9206. [Google Scholar] [CrossRef]
- Carlson, J.M.; Langer, J.S.; Shaw, B.E. Dynamics of earthquake faults. Rev. Mod. Phys. 1994, 66, 657–670. [Google Scholar] [CrossRef]
- Holliday, J.R.; Rundle, J.B.; Turcotte, D.L.; Klein, W.; Tiampo, K.F.; Donnellan, A. Space-Time Clustering and Correlations of Major Earthquakes. Phys. Rev. Lett. 2006, 97, 238501. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Natural Time Analysis: The New View of Time. Precursory Seismic Electric Signals, Earthquakes and other Complex Time-Series; Springer: Berlin/Heidelberg, Germany, 2011. [Google Scholar] [CrossRef]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Spatio-Temporal complexity aspects on the interrelation between Seismic Electric Signals and Seismicity. Pract. Athens Acad. 2001, 76, 294–321. [Google Scholar]
- Varotsos, P.A.; Sarlis, N.V.; Tanaka, H.K.; Skordas, E.S. Similarity of fluctuations in correlated systems: The case of seismicity. Phys. Rev. E 2005, 72, 041103. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Long-range correlations in the electric signals that precede rupture. Phys. Rev. E 2002, 66, 011902. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Long-range correlations in the electric signals the precede rupture: Further investigations. Phys. Rev. E 2003, 67, 021109. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Attempt to distinguish electric signals of a dichotomous nature. Phys. Rev. E 2003, 68, 031106. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S.; Lazaridou, M.S. Identifying sudden cardiac death risk and specifying its occurrence time by analyzing electrocardiograms in natural time. Appl. Phys. Lett. 2007, 91, 064106. [Google Scholar] [CrossRef]
- Baldoumas, G.; Peschos, D.; Tatsis, G.; Chronopoulos, S.K.; Christofilakis, V.; Kostarakis, P.; Varotsos, P.; Sarlis, N.V.; Skordas, E.S.; Bechlioulis, A.; et al. A Prototype Photoplethysmography Electronic Device that Distinguishes Congestive Heart Failure from Healthy Individuals by Applying Natural Time Analysis. Electronics 2019, 8, 1288. [Google Scholar] [CrossRef] [Green Version]
- Rundle, J.B.; Turcotte, D.L.; Donnellan, A.; Grant Ludwig, L.; Luginbuhl, M.; Gong, G. Nowcasting earthquakes. Earth Space Sci. 2016, 3, 480–486. [Google Scholar] [CrossRef]
- Rundle, J.B.; Luginbuhl, M.; Giguere, A.; Turcotte, D.L. Natural Time, Nowcasting and the Physics of Earthquakes: Estimation of Seismic Risk to Global Megacities. Pure Appl. Geophys. 2018, 175, 647–660. [Google Scholar] [CrossRef] [Green Version]
- Luginbuhl, M.; Rundle, J.B.; Hawkins, A.; Turcotte, D.L. Nowcasting Earthquakes: A Comparison of Induced Earthquakes in Oklahoma and at the Geysers, California. Pure Appl. Geophys. 2018, 175, 49–65. [Google Scholar] [CrossRef]
- Luginbuhl, M.; Rundle, J.B.; Turcotte, D.L. Natural Time and Nowcasting Earthquakes: Are Large Global Earthquakes Temporally Clustered? Pure Appl. Geophys. 2018, 175, 661–670. [Google Scholar] [CrossRef]
- Luginbuhl, M.; Rundle, J.B.; Turcotte, D.L. Statistical physics models for aftershocks and induced seismicity. Phil. Trans. R. Soc. A 2018, 377, 20170397. [Google Scholar] [CrossRef] [Green Version]
- Luginbuhl, M.; Rundle, J.B.; Turcotte, D.L. Natural time and nowcasting induced seismicity at the Groningen gas field in the Netherlands. Geophys. J. Int. 2018, 215, 753–759. [Google Scholar] [CrossRef]
- Rundle, J.B.; Giguere, A.; Turcotte, D.L.; Crutchfield, J.P.; Donnellan, A. Global Seismic Nowcasting With Shannon Information Entropy. Earth Space Sci. 2019, 6, 191–197. [Google Scholar] [CrossRef] [Green Version]
- Rundle, J.B.; Luginbuhl, M.; Khapikova, P.; Turcotte, D.L.; Donnellan, A.; McKim, G. Nowcasting Great Global Earthquake and Tsunami Sources. Pure Appl. Geophys. 2019. [Google Scholar] [CrossRef]
- Kanamori, H. Quantification of Earthquakes. Nature 1978, 271, 411–414. [Google Scholar] [CrossRef]
- Sarlis, N.V.; Skordas, E.S.; Varotsos, P.A.; Nagao, T.; Kamogawa, M.; Tanaka, H.; Uyeda, S. Minimum of the order parameter fluctuations of seismicity before major earthquakes in Japan. Proc. Natl. Acad. Sci. USA 2013, 110, 13734–13738. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Study of the temporal correlations in the magnitude time series before major earthquakes in Japan. J. Geophys. Res. 2014, 119, 9192–9206. [Google Scholar] [CrossRef]
- Varotsos, P.; Sarlis, N.; Skordas, E. Scale-specific order parameter fluctuations of seismicity in natural time before mainshocks. EPL 2011, 96, 59002. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.; Alexopoulos, K. Physical Properties of the variations of the electric field of the Earth preceding earthquakes, I. Tectonophysics 1984, 110, 73–98. [Google Scholar] [CrossRef]
- Varotsos, P.; Alexopoulos, K.; Nomicos, K.; Lazaridou, M. Earthquake prediction and electric signals. Nature 1986, 322, 120. [Google Scholar] [CrossRef]
- Uyeda, S.; Kamogawa, M.; Tanaka, H. Analysis of electrical activity and seismicity in the natural time domain for the volcanic-seismic swarm activity in 2000 in the Izu Island region, Japan. J. Geophys. Res. 2009, 114, B02310. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.; Lazaridou, M. Latest aspects of earthquake prediction in Greece based on Seismic Electric Signals. Tectonophysics 1991, 188, 321–347. [Google Scholar] [CrossRef]
- Varotsos, P.; Alexopoulos, K.; Lazaridou, M. Latest aspects of earthquake prediction in Greece based on Seismic Electric Signals, II. Tectonophysics 1993, 224, 1–37. [Google Scholar] [CrossRef] [Green Version]
- Sarlis, N.V.; Skordas, E.S.; Lazaridou, M.S.; Varotsos, P.A. Investigation of seismicity after the initiation of a Seismic Electric Signal activity until the main shock. Proc. Jpn. Acad. Ser. B Phys. Biol. Sci. 2008, 84, 331–343. [Google Scholar] [CrossRef]
- Mintzelas, A.; Sarlis, N. Minima of the fluctuations of the order parameter of seismicity and earthquake networks based on similar activity patterns. Physica A 2019, 527, 121293. [Google Scholar] [CrossRef]
- Goldenfeld, N. Lectures on Phase Transitions and the Renormalization Group; CRC Press, Taylor & Francis Group: Boca Raton, FL, USA, 2018. [Google Scholar]
- Sarlis, N.V.; Skordas, E.S.; Varotsos, P.A.; Nagao, T.; Kamogawa, M.; Uyeda, S. Spatiotemporal variations of seismicity before major earthquakes in the Japanese area and their relation with the epicentral locations. Proc. Natl. Acad. Sci. USA 2015, 112, 986–989. [Google Scholar] [CrossRef] [Green Version]
- Sarlis, N.V.; Skordas, E.S.; Varotsos, P.A. A remarkable change of the entropy of seismicity in natural time under time reversal before the super-giant M9 Tohoku earthquake on 11 March 2011. EPL 2018, 124, 29001. [Google Scholar] [CrossRef]
- Sarlis, N.V.; Skordas, E.S.; Christopoulos, S.R.G.; Varotsos, P.A. Statistical Significance of Minimum of the Order Parameter Fluctuations of Seismicity Before Major Earthquakes in Japan. Pure Appl. Geophys. 2016, 173, 165–172. [Google Scholar] [CrossRef] [Green Version]
- Christopoulos, S.R.G.; Skordas, E.S.; Sarlis, N.V. On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis. Appl. Sci. 2020, 10, 662. [Google Scholar] [CrossRef] [Green Version]
- Donges, J.; Schleussner, C.F.; Siegmund, J.; Donner, R. Event coincidence analysis for quantifying statistical interrelationships between event time series. Eur. Phys. J. Spec. Top. 2016, 225, 471–487. [Google Scholar] [CrossRef] [Green Version]
- Fawcett, T. An introduction to ROC analysis. Pattern Recogn. Lett. 2006, 27, 861–874. [Google Scholar] [CrossRef]
- Ogata, Y. Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes. Research Memorandum (Technical Report). 1985, Volume 288. Available online: https://www.ism.ac.jp/editsec/resmemo-j.html (accessed on 19 May 2020).
- Ogata, Y. Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes. J. Am. Statist. Assoc. 1988, 83, 9–27. [Google Scholar] [CrossRef]
- Ogata, Y. Statistical model for standard seismicity and detection of anomalies by residual analysis. Tectonophysics 1989, 169, 159–174. [Google Scholar] [CrossRef] [Green Version]
- Ogata, Y.; Katsura, K.; Tsuruoka, H.; Hirata, N. High-resolution 3D earthquake forecasting beneath the greater Tokyo area. Earth Planets Space 2019, 71, 113. [Google Scholar] [CrossRef]
- Mandrekar, J.N. Receiver Operating Characteristic Curve in Diagnostic Test Assessment. J. Thorac. Oncol. 2010, 5, 1315–1316. [Google Scholar] [CrossRef] [Green Version]
- Lalkhen, A.G.; McCluskey, A. Clinical tests: Sensitivity and specificity. CEACCP 2008, 8, 221–223. [Google Scholar] [CrossRef] [Green Version]
- Hosmer, D.W.; Lemeshow, S. Applied Logistic Regression; John Wiley & Sons, Ltd.: New York, NY, USA, 2000. [Google Scholar] [CrossRef]
- Mason, S.J.; Graham, N.E. Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation. Quart. J. R. Meteor. Soc. 2002, 128, 2145–2166. [Google Scholar] [CrossRef]
- Sarlis, N.V.; Christopoulos, S.R.G. Visualization of the significance of Receiver Operating Characteristics based on confidence ellipses. Comput. Phys. Commun. 2014, 185, 1172–1176. [Google Scholar] [CrossRef] [Green Version]
- Dologlou, E. A three year continuous sample of officially documented predictions issued in Greece using the VAN method: 1987–1989. Tectonophysics 1993, 224, 189–202. [Google Scholar] [CrossRef]
- Sarlis, N.V. Statistical Significance of Earth’s Electric and Magnetic Field Variations Preceding Earthquakes in Greece and Japan Revisited. Entropy 2018, 20, 561. [Google Scholar] [CrossRef] [Green Version]
- Han, P.; Hattori, K.; Zhuang, J.; Chen, C.H.; Liu, J.Y.; Yoshida, S. Evaluation of ULF seismo-magnetic phenomena in Kakioka, Japan by using Molchan’s error diagram. Geophys. J. Int. 2017, 208, 482–490. [Google Scholar] [CrossRef]
- Kappler, K.; Schneider, D.; MacLean, L.; Bleier, T.; Lemon, J. An algorithmic framework for investigating the temporal relationship of magnetic field pulses and earthquakes applied to California. Comput. Geosci. 2019, 133, 104317. [Google Scholar] [CrossRef]
- Tanaka, H.K.; Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. A plausible universal behaviour of earthquakes in the natural time-domain. Proc. Jpn. Acad. Ser. B Phys. Biol. Sci. 2004, 80, 283–289. [Google Scholar] [CrossRef] [Green Version]
- Hanks, T.C.; Kanamori, H. A moment magnitude scale. J. Geophys. Res. 1979, 84, 2348–2350. [Google Scholar] [CrossRef]
- Nanjo, K.Z.; Ishibe, T.; Tsuruoka, H.; Schorlemmer, D.; Ishigaki, Y.; Hirata, N. Analysis of the Completeness Magnitude and Seismic Network Coverage of Japan. Seismol. Soc. Am. Bull. 2010, 100, 3261–3268. [Google Scholar] [CrossRef]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S.; Lazaridou, M.S. Seismic Electric Signals: An additional fact showing their physical interconnection with seismicity. Tectonophysics 2013, 589, 116–125. [Google Scholar] [CrossRef]
- Japan Meteorological Agency. Recent seismic activity in the Miyakejima and Niijima-Kozushima region, Japan -the largest earthquake swarm ever recorded-. Earth Planets Space 2000, 52, i–viii. [Google Scholar] [CrossRef] [Green Version]
- Uyeda, S.; Hayakawa, M.; Nagao, T.; Molchanov, O.; Hattori, K.; Orihara, Y.; Gotoh, K.; Akinaga, Y.; Tanaka, H. Electric and magnetic phenomena observed before the volcano-seismic activity in 2000 in the Izu Island Region, Japan. Proc. Natl. Acad. Sci. USA 2002, 99, 7352–7355. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Xu, G.; Han, P.; Huang, Q.; Hattori, K.; Febriani, F.; Yamaguchi, H. Anomalous behaviors of geomagnetic diurnal variations prior to the 2011 off the Pacific coast of Tohoku earthquake (Mw9.0). J. Asian Earth Sci. 2013, 77, 59–65. [Google Scholar] [CrossRef] [Green Version]
- Han, P.; Hattori, K.; Xu, G.; Ashida, R.; Chen, C.H.; Febriani, F.; Yamaguchi, H. Further investigations of geomagnetic diurnal variations associated with the 2011 off the Pacific coast of Tohoku earthquake (Mw 9.0). J. Asian Earth Sci. 2015, 114, 321–326. [Google Scholar] [CrossRef]
- Han, P.; Hattori, K.; Huang, Q.; Hirooka, S.; Yoshino, C. Spatiotemporal characteristics of the geomagnetic diurnal variation anomalies prior to the 2011 Tohoku earthquake (Mw 9.0) and the possible coupling of multiple pre-earthquake phenomena. J. Asian Earth Sci. 2016, 129, 13–21. [Google Scholar] [CrossRef]
- Olami, Z.; Feder, H.J.S.; Christensen, K. Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. Phys. Rev. Lett. 1992, 68, 1244–1247. [Google Scholar] [CrossRef] [Green Version]
- Ramos, O.; Altshuler, E.; Måløy, K.J. Quasiperiodic Events in an Earthquake Model. Phys. Rev. Lett. 2006, 96, 098501. [Google Scholar] [CrossRef] [Green Version]
- Sarlis, N.; Skordas, E.; Varotsos, P. The change of the entropy in natural time under time-reversal in the Olami-Feder-Christensen earthquake model. Tectonophysics 2011, 513, 49–53. [Google Scholar] [CrossRef]
- Skordas, E.S.; Sarlis, N.V.; Varotsos, P.A. Identifying the occurrence time of an impending major earthquake by means of the fluctuations of the entropy change under time reversal. EPL 2019, 128, 49001. [Google Scholar] [CrossRef]
- Varotsos, P.A.; Skordas, E.S.; Sarlis, N.V. Fluctuations of the entropy change under time reversal: Further investigations on identifying the occurrence time of an impending major earthquake. EPL 2020, 130, 29001. [Google Scholar] [CrossRef]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Phenomena preceding major earthquakes interconnected through a physical model. Ann. Geophys. 2019, 37, 315–324. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.A.; Sarlis, N.V.; Skordas, E.S. Natural time analysis: Important changes of the order parameter of seismicity preceding the 2011 M9 Tohoku earthquake in Japan. EPL 2019, 125, 69001. [Google Scholar] [CrossRef] [Green Version]
- Penrose, O.; Lebowitz, J.L.; Marro, J.; Kalos, M.H.; Sur, A. Growth of clusters in a first-order phase transition. J. Stat. Phys. 1978, 19, 243–267. [Google Scholar] [CrossRef]
- Lifshitz, I.; Slyozov, V. The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 1961, 19, 35–50. [Google Scholar] [CrossRef]
- Helman, D.S. Seismic electric signals (SES) and earthquakes: A review of an updated VAN method and competing hypotheses for SES generation and earthquake triggering. Phys. Earth Planet. Int. 2020, 302, 106484. [Google Scholar] [CrossRef] [Green Version]
- Varotsos, P.; Sarlis, N.; Lazaridou, M. Reply to “Rebuttal to Reply by Varotsos and Lazaridou: Towards plainly successful prediction,” by Paul W. Burton. Geophys. Res. Lett. 1996, 23, 1389–1390. [Google Scholar] [CrossRef]
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Sarlis, N.V.; Skordas, E.S.; Christopoulos, S.-R.G.; Varotsos, P.A. Natural Time Analysis: The Area under the Receiver Operating Characteristic Curve of the Order Parameter Fluctuations Minima Preceding Major Earthquakes. Entropy 2020, 22, 583. https://doi.org/10.3390/e22050583
Sarlis NV, Skordas ES, Christopoulos S-RG, Varotsos PA. Natural Time Analysis: The Area under the Receiver Operating Characteristic Curve of the Order Parameter Fluctuations Minima Preceding Major Earthquakes. Entropy. 2020; 22(5):583. https://doi.org/10.3390/e22050583
Chicago/Turabian StyleSarlis, Nicholas V., Efthimios S. Skordas, Stavros-Richard G. Christopoulos, and Panayiotis A. Varotsos. 2020. "Natural Time Analysis: The Area under the Receiver Operating Characteristic Curve of the Order Parameter Fluctuations Minima Preceding Major Earthquakes" Entropy 22, no. 5: 583. https://doi.org/10.3390/e22050583