<Emphasis Type="Italic">M</Emphasis><Subscript>W</Subscript>9 Tohoku earthquake in 2011 in Japan: precursors uncovered by natural time analysis

This paper reviews the precursory phenomena of the 2011 M _W9 Tohoku earthquake in Japan that emerge solely when we analyze the seismicity data in a new time domain termed natural time. If we do not consider this analysis, important precursory changes cannot be identified and hence are missed. Natural time analysis has the privilege that enables the introduction of an order parameter of seismicity. In this frame, we find that the fluctuations of this parameter exhibit an unprecedented characteristic change, i.e., an evident minimum, approximately two months before Tohoku earthquake, which strikingly is almost simultaneous with unique anomalous geomagnetic field variations recorded mainly on the z component. This is consistent with our finding that such a characteristic change in seismicity appears when a seismic electric signal (SES) activity of the VAN method (from the initials of Varotsos, Alexopoulos, Nomicos) initiates, and provides a direct confirmation of the physical interconnection between SES and seismicity.     

Seismic electric signals in seismic prone areas

The Varotsos-Alexopoulos-Nomicos(VAN) method of short-term earthquake prediction was introduced in the 1980s. The VAN method enables estimation of the epicenter, magnitude and occurrence time of an impending earthquake by observing transient changes of the electric field of the Earth termed seismic electric signals(SES). Here, we present a few examples of SES observed in various earthquake prone areas worldwide.     

Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection

A new passive seismic response control device has been developed, fabricated, and tested by the authors and shown to be capable of producing negative stiffness via a purely mechanical mechanism, thus representing a new generation of seismic protection devices. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (the desired relationship being that the product of restoring force and displacement is nonnegative), when implemented in parallel with a structure having positive stiffness, the combined system appears to have substantially reduced stiffness while remaining stable. Thus, there is an ‘apparent weakening and softening’ of the structure that results in reduced forces and increased displacements (where the weakening and softening is of a non‐damaging nature in that it occurs in a seismic protection device rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the negative stiffness device. The combination of negative stiffness and passive damping provides a large degree of control over the expected performance of the structure. In this paper, a numerical study is presented on the performance of a seismically isolated highway bridge model that is subjected to various strong earthquake ground motions. The Negative Stiffness Devices (NSDs) are described along with their hysteretic behavior as obtained from a series of cyclic tests wherein the tests were conducted using a modified design of the NSDs (modified for testing within the bridge model). Using the results from the cyclic tests, numerical simulations of the seismic response of the isolated bridge model were conducted for various configurations (with/without negative stiffness devices and/or viscous dampers). The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. This assessment was conducted as part of a NEES (Network for Earthquake Engineering Simulation) project which included shaking table tests of a quarter‐scale highway bridge model. Copyright © 2014 John Wiley & Sons, Ltd.     

On the Motivation and Foundation of Natural Time Analysis: Useful Remarks

Since its introduction in 2001, natural time analysis has been applied to diverse fields with remarkable results. Its validity has not been doubted by any publication to date. Here, we indicate that frequently asked questions on the motivation and the foundation of natural time analysis are directly answered if one takes into account the following two key points that we have considered as widely accepted when natural time analysis was proposed: first, the aspects on the energy of a system forwarded by Max Planck in his Treatise on Thermodynamics; second, the theorem on the characteristic functions of probability distributions which Gauss called Ein Schönes Theorem der Wahrscheinlichkeitsrechnung (beautiful theorem of probability calculus). The case of the time series of earthquakes and of the precursory Seismic Electric Signals are discussed as typical examples.     

Identifying the occurrence time of an impending mainshock:a very recent case

The procedure by means of which the occurrence time of an impending mainshock can be identified by analyzing in natural time the seismicity in the candidate area subsequent to the recording of a precursory seismic electric signals(SES) activity is reviewed. Here, we report the application of this procedure to an MW5.4 mainshock that occurred in Greece on 17 November 2014. This mainshock(which is pretty rare since it is the strongest in that area for more than half a century) was preceded by an SES activity recorded on 27 July 2014, and the results of the natural time analysis reveal that the system approached the critical point(mainshock occurrence) early in the morning on 15 November 2014.     

Magnetic field near the outcrop of an almost horizontal conductive sheet

The magnetic field components are studied near the outcrop of an almost horizontal (elongated) conductive sheet when an electric dipole lies far away from the outcrop but close to the sheet. The results have been applied to the case of the transmission of seismic electric signals (SES) by considering the current aspects on the orientation of the maximum principal stress with respect to the fault. Assuming that the latter orientation coincides with that of the emitting dipole source, it seems likely that the SES are accompanied by magnetic field variations with prominent B_Z component. These variations become detectable near the outcrop only for strong earthquakes (with M6.5) at epicentral distances of the order of 100 km.     

Additional evidence on some relationship between Seismic Electric Signals (SES) and earthquake focal mechanism

Investigating the period 1983–1994 for western Greece, a possible correlation between the selectivity characteristics of the SES (seismic electric signals of the VAN method) and earthquake parameters has been reported by Uyeda et al. [Uyeda, S., Al-Damegh, K.S., Dologlou, E., Nagao, T., 1999. Some relationship between VAN seismic electric signals (SES) and earthquake parameters, Tectonophysics, 304, 41–55.]. They found that the earthquake source mechanism changed from largely strike-slip type to thrust type at the end of 1987, and this coincided with a shift in the SES sensitive site from Pirgos (PIR) to Ioannina (IOA) VAN station. Here, we report the results for the period January 1, 2002–July 25, 2004, during which the SES sensitive site of PIR became again active, after a 10-year period of “quiescence”. This activation was followed by strike slip earthquakes (on August 14, 2003 and March 17, 2004 with magnitude 6.4 and 6.5, respectively) in the Hellenic arc, which provides additional evidence on the correlation reported by Uyeda et al. The SES activities recorded at PIR have been discriminated from “artificial” noise by employing the natural time-domain analysis introduced recently.     

A tentative model for the explanation of Båth law using the order parameter of seismicity in natural time

Using the order parameter of seismicity defined in natural time, we suggest a simple model for the explanation of Båth law, according to which a mainshock differs in magnitude from its largest aftershock by approximately 1.2 regardless of the mainshock magnitude. In addition, the validity of Båth law is studied in the Global Centroid Moment Tensor catalogue by using two different aftershock definitions. It is found that the mean of this difference, when considering all the pairs mainshock-largest aftershock, does not markedly differ from 1.2 and the corresponding distributions do not depend on the mainshock’s magnitude threshold in a statistically significant manner. Finally, the analysis of the cumulative distribution functions provides evidence in favour of the proposed model.     

Statistical Significance of Minimum of the Order Parameter Fluctuations of Seismicity Before Major Earthquakes in Japan

In a previous publication, the seismicity of Japan from 1 January 1984 to 11 March 2011 (the time of the \(M9\) Tohoku earthquake occurrence) has been analyzed in a time domain called natural time \(\chi.\) The order parameter of seismicity in this time domain is the variance of \(\chi\) weighted for normalized energy of each earthquake. It was found that the fluctuations of the order parameter of seismicity exhibit 15 distinct minima—deeper than a certain threshold—1 to around 3 months before the occurrence of large earthquakes that occurred in Japan during 1984–2011. Six (out of 15) of these minima were followed by all the shallow earthquakes of magnitude 7.6 or larger during the whole period studied. Here, we show that the probability to achieve the latter result by chance is of the order of \(10^{-5}\). This conclusion is strengthened by employing also the receiver operating characteristics technique.