Fluctuations of the entropy change under time reversal: Further investigations on identifying the occurrence time of an impending major earthquake

A procedure has been developed in a previous publication (Skordas E. S. et al., EPL, 128 (2019) 49001) for the identification of the occurrence time of the Tohoku earthquake of magnitude M = 9.0 that occurred in Japan on 11 March 2011 based on natural time analysis of seismicity. Using the complexity measure that quantifies the fluctuations of the entropy change ΔS of seismicity under time reversal, we show here that, in the longer scales, the complexity measure of the entire Japanese region starts increasing from 22 December 2010 (the date at which ΔS is minimized) reaching a maximum close to the appearance of a Seismic Electric Signals activity (evidenced from the recording of anomalous magnetic field variations on the z-component) in the beginning of January 2011; then it gradually diminishes until just before the mega earthquake. On the other hand, around two days before its occurrence, the complexity measure in the candidate epicentral area exhibits an abrupt increase. This difference reveals, well in advance, that the M7.3 earthquake on 9 March 2011 was a foreshock. Copyright c © EPLA, 2020 Introduction. – It is widely accepted [1–3] that earthquakes (EQs), which exhibit complex correlations in time, space and magnitude (M) (e.g., [4–11]), can be considered as critical phenomena, since the observed EQ scaling laws [12] indicate the existence of phenomena closely associated with the proximity of the system to a critical point. The order parameter of seismicity is the quantity by which one can identify the approach of the dynamical system to a critical point. The introduction of such a parameter for the case of seismicity, labeled hereafter κ1, became possible after the suggestion of a new procedure for the analysis of complex time series, termed natural time analysis, which was introduced in the beginning of the 2000s (e.g., see ref. [13]) and is summarized in the next section. The Tohoku mega earthquake of magnitude 9.0 that occurred in Japan on 11 March 2011 devastated the Pacific side of northern Honshu with a huge tsunami causing more than 20000 victims and serious damage to the Fukushima nuclear plant. It is the largest magnitude event recorded in Japan and seismologists were shocked because it was not even considered possible that it might happen in the East Japan subduction zone. This mega earthquake was preceded by a M7.3 foreshock that occurred almost two days before. Upon the occurrence of this M7.3 EQ, seismologists could not identify that this was foreshock of a significantly larger EQ, which would be of paramount importance for practical purposes. It is one of the main goals of this paper to investigate whether such an identification was possible by means of the fluctuations of the entropy change ΔS under time reversal (i.e., upon reversing the direction of the time arrow). We clarify that the concept of entropy S in natural time defined below is applicable to deterministic as well as stochastic processes. It is a dynamic entropy depending on the sequential order of events and is fundamentally different [14,15] from other entropies. The quantity ΔS is a measure that may serve for the identification of when the system approaches the critical