2015 Volume 91 Issue 1 Pages 25-30
The criticality of ULF (Ultra-low-frequency) magnetic variations is investigated for the 2011 March 11 Tohoku earthquake (EQ) by natural time analysis. For this attempt, some ULF parameters were considered: (1) Fh (horizontal magnetic field), (2) Fz (vertical magnetic field), and (3) Dh (inverse of horizontal magnetic field). The first two parameters refer to the ULF radiation, while the last parameter refers to another ULF effect of ionospheric signature. Nighttime (L.T. = 3 am ± 2 hours) data at Kakioka (KAK) were used, and the power of each quantity at a particular frequency band of 0.03–0.05 Hz was averaged for nighttime hours. The analysis results indicate that Fh fulfilled all criticality conditions on March 3–5, 2011, and that the additional parameter, Dh reached also a criticality on March 6 or 7. In conclusion, criticality has reached in the pre-EQ fracture region a few days to one week before the main shock of the Tohoku EQ.
Based on extensive studies during the last few decades it is generally accepted nowadays that electromagnetic phenomena appear prior to an earthquake (EQ).1)–4) Using the amplitude data of VLF/LF (very low frequency/low frequency) transmitter signals propagating in the Earth-ionosphere waveguide during the 7-year observation, Hayakawa et al. (2010)5) established a significant statistical correlation between the perturbations in the lower ionosphere and EQs. Perturbations in the upper ionospheric F region observed as changes in foF2 (critical frequency of F2 layer) were also confirmed to be correlated with EQs based on long-term data.6)
Compared with these ionospheric phenomena, the number of reports is not so abundant for ULF (ultra low frequency) electromagnetic emissions, even though they were found promising for short-term EQ prediction.7)–10) Seismogenic ULF electromagnetic waves are usually “emission or radiation” from the lithosphere as observed as intensification of ULF magnetic power.7)–10) Whereas a new phenomenon in ULF magnetic field changes is vice versa, the depression (or a decrease) in the amplitude of ULF downgoing waves of magnetospheric origin.11)
In addition to the above, there is another direction of signal processing based on the concept of critical evolution or self-organized criticality. There are a few possible methods along this line: One is fractal analysis,12) and the other is “natural time” analysis introduced by Varotsos,4) which has been applied to time series data of a point process like SES events.13),14) This paper is an attempt to apply the natural time method to our ULF geomagnetic data observed in Japan, especially during a period of a few months before the 2011 Tohoku EQ.
The ULF data were obtained from the World Data Center (WDC) for Geomagnetism, Kyoto. The data from this WDC are provided in the format of IAGA (International Association of Geomagnetism and Aeronomy) 2000, in which the magnetic field is represented by four components: Horizontal (H), declination (D), vertical (Z), and total field (F).
We use ULF data from three magnetic observatories belonging to JMA (Japan Meteorological Agency): Memambetsu (MMB) (geographic coordinates: at 43°54′36′′N, 144°11′19′′E), Kakioka (KAK) (at 36°13′56′′N, 140°11′11′′E), and Kanoya (KNY) (at 31°25′27′′N, 130°52′48′′E) as shown by black diamonds in Fig. 1. The sampling frequency of magnetometers at these stations is 1 Hz. Positions and magnitudes of EQs with Mw > 7 and with depth smaller than 100 km are also shown by circles in the same figure. We have used seismic data from the ANSS (Advanced National Seismic System) Worldwide Earthquake Catalog. The main shock of the Tohoku EQ took place at 14:46:18 JST (UTC+9h) on March 11, 2011 with its epicenter at the geographic coordinates (38°06′N, 142°52′E) as shown in Fig. 1. The magnitude was Mw = 9 and the depth was about 20 km. This EQ is a very typical oceanic EQ of the plate subduction type. The distance of each magnetic observatory from the EQ epicenter is 640 km for MMB, 300 km for KAK, and 1,300 km for KNY, respectively.
Relative location of three ULF observations (KAK, MMB and KNY by black triangles) and most powerful (MW > 7) and shallow (depth smaller than 100 km) EQs shown by circles which occurred from December 1, 2010 to May 31, 2011. Our target EQ took place on March 11, 2011. The center of the circle is the EQ epicenter and its color indicates the depth.
The concept of “natural time” is suitable for time series data of point processes, including seismicity and DC geoelectric potential. On the other hand, ULF variations are not a point process, but they are continuous in nature, so that we have to think of what kind of ULF parameters should be used for the natural time analysis.
In the following, we present the results only from KAK which is closest to the EQ epicenter, because our preliminary studies indicated no significant unusual phenomena at other stations. We take, as the first step, the following procedure on ULF magnetic data to be used for the natural time analysis. To avoid industrial interference, we use ULF data only during nighttime (LT = 3 h a.m. ± 2 hours). After performing spectral analysis on the raw ULF data and choosing a particular frequency range of 0.03–0.05 Hz (for which we have observed clear effects in ULF15)), we average the squared amplitude during this nighttime interval to obtain one datum per day.15)
The following ULF parameters are generated to characterize the ULF magnetic data.
Figure 2 illustrates temporal evolutions of some physical parameters: (from top to bottom) geomagnetic (Dst index) and seismic (Kls index) activities, Fh, Fz, Pz/h, Dh, and ULF depression (δDep) as discussed in Ref. 15, all in the same frequency range of 0.03–0.05 Hz. The index Kls is a function of EQ magnitude and epicentral distance.3) As was already shown,15),17) a significant peak in depression (δDep) on March 6 was observed as a precursor to the 2011 Tohoku EQ. Our glance at the temporal evolution of Fh, suggests an enhancement in the beginning (1st) of March, but we are not sure whether this is a real precursor to the EQ or not. This enhancement in Fh looks to be correlated with a decrease in Dst index. It will be shown that this kind of uncertainty can be investigated with the use of natural time analysis.
Top panel: Temporal evolution of geomagnetic (Dst) (unit is given on the right ordinate) and seismic (Kls) (unit is given on the left ordinate) activities. 2nd and 3rd panels: root-mean-squares of the horizontal (Fh) and vertical (Fz) magnetic fields in the frequency band 0.03–0.05 Hz (in arbitrary unit (au)), and the 4th panel, Pz/h (ratio of vertical and horizontal components). The 5th and bottom panels refer to the temporal evolutions of the inverse of the horizontal component (Dh) (in arbitrary unit (au)), and the normalized depression δDep as discussed in Ref. 15.
The transformation of a time-series of “events” from the conventional time domain to natural time domain is performed by ignoring the time interval between events and retaining only its normalized order of occurrence. So the kth event corresponds to a natural time χk = k/N, where N is the total number of successive events. The “energy” Qk of each event is also retained. Then the time series (χk, Qk) is studied. A system is considered to approach criticality when the parameter $\kappa _{1} = \sum\nolimits_{k = 1}^{N}p_{k} \chi _{k}^{2} - (\sum\nolimits_{k = 1}^{N}p_{k} \chi _{k})^{2}$ ($p_{k} = Q_{k}/\sum\nolimits_{n = 1}^{N}Q_{n} $ is the energy of kth event normalized by the total energy) converges to κ1 = 0.070 and at the same time both the entropy in natural time, $S_{nt} = \sum\nolimits_{k = 1}^{N}p_{k} \chi _{k}\ln \chi _{k} - (\sum\nolimits_{k = 1}^{N}p_{k} \chi _{k})\ln (\sum\nolimits_{k = 1}^{N}p_{k} \chi _{k})$ and the entropy under time reversal, Snt−, satisfy the condition Snt, Snt− < Su = (ln 2/2) − 1/4, where Su stands for the entropy of a “uniform” distribution in natural time.18)
The criticality is considered truly achieved when the following three conditions are also satisfied:18) (i) The “average” distance ⟨D⟩ between the curves of normalized power spectra Π(ϕ) of the evolving seismicity and the theoretical estimation of Π(ϕ) for κ1 = 0.070 is smaller than 10−2, (ii) the parameter κ1 approaches κ1 = 0.070 “by descending from above”, and (iii) since the underlying process is expected to be self-similar, the time of criticality does not change by varying the magnitude threshold. It may be worth mentioning that these criticality conditions, including κ1 = 0.070, were not derived theoretically but empirically from computing κ1 values for well-known phenomena and actual data of seismicity in Greece.18)
The natural time analysis starts from 5 January 2011, following the findings of Skordas and Sarlis (2014).19) We consider each daily value which is above a certain threshold as an event. So in our ULF cases (Fh, Fz, and Dh), the “energy” of kth event Qk is considered to be equal to each one of above quantities. Starting from 5 January 2011, all the parameters (κ1, Snt, Snt−, ⟨D⟩ in Section 4) are calculated for the time-series rescaled in the natural time domain each time a new event is added. Although the selection of thresholds is arbitrary, if criticality conditions are met in close dates for more than one of the considered threshold values, then this is considered to be an indication of the validity of performed analysis.
Results of natural time analysis for different ULF parameters are presented below.
Figure 3 illustrates an example of the natural time analysis results for Fh for a particular threshold. The four critical parameters κ1, Snt, Snt− and ⟨D⟩ are calculated each time a new event is included in the analysis, so their evolution is seen as a function of date of new event occurrence. We found that the process was self-similar because the time of criticality did not change by changing the threshold. Then Fh fulfilled all criticality conditions around the date of March 3, 4, or 5, 2011.
The corresponding figures for Fz are not shown, because Fz did not exhibit any criticality condition.
Figure 4 is again just one example of the results of natural time analysis for the parameter Dh for a particular threshold. We confirmed that the date of criticality did not change by changing the threshold, and so it seems that Dh reaches a critical condition around March 6 or 7, 2011.
Natural time analysis of the ULF electromagnetic emission quantity Fh for the time period of 05 January through 11 March 2011: Variations of the natural time analysis parameters (κ1, Snt, Snt−, and ⟨D⟩) for a particular threshold.
Natural time analysis of the ULF electromagnetic emission quantity Dh for the time period from 05 January to 11 March 2011: Variations of the natural time analysis parameters for a particular threshold.
A question naturally arising is whether the analyzed parameters were observables of a process taking place in the Earth’s crust system or any other process that could influence magnetic field variations such as magnetic storms. In Fig. 2 we find two relatively small (−50 nT) storms on March 1 and March 11 (unfortunately this latter is masked by the plot of EQs in Fig. 2). These two magnetic storms occurred not on the same dates as the dates of criticality indicated by the natural time analysis of ULF parameters (March 3, 4, or 5 for Fh, March 6, 7 for Dh).
This paper is the first attempt to analyze criticality in ULF magnetic fields by means of natural time method. The results of the natural time analysis can be summarized as follows.
First, we discuss the lithospheric aspect of the ULF parameters, Fh, and Fz. It is not clear why we have detected criticality only in Fh, but not in Fz. Tentatively, we consider as follows. The 2011 Tohoku EQ was the most powerful EQ ever recorded to have hit Japan, and Hirose et al. (2011)20) reported that the hypocentral region of this EQ is extended from offshore Iwate prefecture to offshore Ibaraki prefecture, with a length of 500 km and a width of 200 km. From the huge area of the rupture region, it may not be unreasonable to consider that the corresponding pre-fracture region is also very wide, even extending to our ULF observation point of KAK. Whatever the mechanism of electrification in the source region, dynamic processes in association with pre-EQ microfracture can lead to the generation of current systems.21),22) Our finding of the criticality at KAK only in Fh, but not in Fz, may be explained by the relative position of the current source and observatory. When using the method as used in Kawate et al. (1998),23) we can infer that the source current, at least, responsible for the seismogenic ULF radiation observed at KAK, might have been located in an area relatively close to KAK, for example, offshore Ibaraki prefecture.
Next we move on to the ionospheric ULF phenomena. Criticality was observed on March 6 and 7 in the temporal evolution of critical parameters for Dh, which is in agreement with the conclusion of Schekotov et al. (2013).15) They found a depression in ULF magnetic field intensity on the ground (as shown in the bottom panel of Fig. 2), which may be satisfactorily interpreted in terms of an enhanced absorption of downgoing Alfvén waves through the perturbed lower ionosphere.17) It seems that the pre-EQ criticality has taken place in a wide area of the lithosphere, and the criticality is also recognized in the lower ionosphere with a small time difference of one day or so. The area of lower ionospheric perturbation as sensed by the ULF magnetic field depression is found to be much wider15),17) than such a localized area (radius less than 100 km) for the lithospheric ULF radiation observed at KAK. So the information on ionospheric perturbations derived from Dh is likely to reflect the criticality taking place on March 6 and 7 in the lithosphere over a wider area of the rupture region in the Pacific ocean. The difference in criticality dates for Fh and Dh is probably due to slightly different dates for criticality at a relatively localized region near KAK and at a much wider pre-EQ fracture region.
We would like to express our sincere thanks to the unknown two referees and Prof. S. Uyeda for their valuable comments.
