Advanced Wireless Communications Research Center, University of Electro-Communications (UEC), Chofu, Tokyo, Japan
Hayakawa Institute of Seismo Electromagnetics, Co. Ltd., UEC Incubation Center, Chofu, Tokyo, Japan
Earthquake Analysis Laboratory, Information Systems, Inc., Minato-ku, Tokyo, Japan
Corresponding author: M. Hayakawa, Advanced Wireless Communications Research Center, University of Electro-Communications (UEC), 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan. (firstname.lastname@example.org)
 The ULF/ELF short-term electromagnetic precursor is discovered for the disastrous Japan earthquake (EQ) occurred on 11 March 2011. This analysis is based on the records measured by search coil magnetometers located at Nakatsugawa (geographic coordinates; 35.42°N, 137.55°E), Shinojima (34.67°N, 137.01°E), and Izu (34.64°N, 137.01°E) of the Chubu University network. The data of these magnetometers are extensively used to analyze the ULF/ELF seismo-atmospheric radiation. It is then found that the ULF/ELF atmospheric radio emission is reliably detected on 6 March before the main shock on 11 March, probably as a precursory signature of the EQ. Further confirmation on its seismic origin was provided by the observational fact that the azimuths of the radiation source from all observation sites coincide approximately with the region of the forthcoming EQ.
 Extensive previous works during the last few decades have suggested that electromagnetic precursors do appear prior to an earthquake (EQ) [e.g., Hayakawa and Molchanov, 2002; Pulinets and Boyarchuk, 2004; Molchanov and Hayakawa, 2008; Hayakawa, 2009, 2012], and different kinds of electromagnetic precursors have been discovered; the first category is characterized by the direct radiation from the EQ hypocenter (or epicenter) in a different frequency range (from DC, ULF to VHF or even higher), and the second category is the indirect effect of an EQ; i.e., generation of atmospheric or ionospheric perturbations due to preseismic effects.
 It is unnecessary to say that any statistical study is of essential importance to obtain the correlation between any electromagnetic precursor and EQs. Ionospheric perturbations both in the lowest part (D/E layer) and in the upper F region are recently found to be statistically correlated with EQs [e.g., Liu, 2009; Hayakawa et al., 2010]. Parallel with those statistical studies on the correlation based on the long-term observation data, case studies are still very important to elucidate the presence of electromagnetic precursors of EQs. We can list several huge EQs for case studies, including the Spitak EQ, Loma-Prieta EQ, Kobe EQ, Sumatra EQ, etc. [e.g., Molchanov and Hayakawa, 2008], but we cannot avoid the latest Japanese EQ; that is, the 11 March 2011 Japan EQ with magnitude (M) 9.0. Unfortunately, it seems that there are not so many precursors to this EQ [Hayakawa et al., 2012b, 2013a, 2013b] probably because this EQ happened in the sea, whereas there were observed different kinds of precursors for the 1995 disastrous Kobe EQ [Nagao et al., 2002].
 In this paper we pay attention again to this huge 2011 Japan EQ, and we will report on one additional electromagnetic phenomenon in the ULF/ELF frequency range. Here we define the ULF range by the frequency below 3 Hz or so, while the ELF is in a range from ~ 3Hz to 3 kHz. In the ULF range, there is known the presence of lithospheric ULF radiation before major EQs including the 1988 Spitak EQ [Kopytenko et al., 1993; Molchanov et al., 1992], the 1989 Loma Prieta EQ [Fraser-Smith et al., 1990], and the 1993 Guam EQ [Hayakawa et al., 1996]. Later, ULF studies have been summarized in Hattori , Hayakawa et al. , Molchanov and Hayakawa , and Hayakawa et al. . Though we know that there have been published few papers criticizing those papers [e.g., Campbell, 2009].
 The aim of the present study is to test the forecasting ability of methods based on seismo-atmospheric ULF/ELF radiation in the conditions of strong artificial interferences and extreme seismic activity. The point is that our conclusion about reliability of this phenomenon for forecasting an EQ was obtained in Kamchatka in the presence of very low industrial interferences and EQs with magnitude not exceeding 7. That is, it was established that this phenomenon occurs 1–5 days (3 days on average) before a sharp beginning of seismic activity. So it allows us to provide us with the short-term prediction of the date of a forthcoming EQ. Moreover, the position of the source of this radiation roughly coincided with the epicenter of the forthcoming EQ. This last property gives a possibility to determine its position in the case of multipoint measurements. Such multipoint measurements are being carried out at three observatories located south-west of the epicenter of Tohoku EQ occurred on 11 March 2011 with magnitude M = 9. These measurements cover a rather long interval around its date and therefore provide us with more reliable results. This paper is devoted to the analysis of these data.
2 Observation System and Observation Network
 The geomagnetic data used in this paper have been obtained by the Chubu University ULF/ELF network which consists of three observatories; Shinojima (abbreviated as SHI; geographic coordinates, 34.67°N, 137.01°E), Nakatsugawa (NAK, 35.42°N, 137.55°E), and Izu (IZU, 34.64°N, 138.85°E) [Hata et al., 2010; Hayakawa et al., 2011]. Figure 1 illustrates the relative locations of three ULF/ELF observatories and the epicenter of the 2011 Japan EQ (11 March 2011, the biggest orange circle). Also, we have plotted, in Figure 1, one representative observatory of Kakioka (KAK) belonging to Japan Meterological Agency, and some other foreshocks (09 March 2011) and aftershocks (11 March 2011).
 At each observatory, we measure the magnetic field changes (H, D, and Z components) by means of three orthogonal magnetometers in the frequency range of 0.1 – 24 Hz. The magnetometer is an induction coil sensor, and the receiver attained a high sensitivity of about 0.05 at the frequency of 10 Hz. All the sensors are manufactured so as to have identical characteristics of amplitude and phase. The details of the equipment are described in Hata et al. . The data observed at each observatory are regularly sent to the master station in Chubu University (at Kasugai).
3 Data Analysis
 Horizontal components of magnetic field are digitized at the sampling frequency of 100 Hz with the use of the 16 bit data acquisition system (DAS) and those data are stored on a hard disk. Those data are transmitted to the master station of Chubu University at Kasugai (near Nagoya) through a telephone line or an internet.
 In this paper we describe the procedure of ULF/ELF magnetic field analysis in order to detect any seismo-atmospheric electromagnetic radiation and to determine the azimuth of its source.
 However, the preliminary routine data processing was applied before the main analysis. That is, this process includes substituting the interpolated data for short (several points) data gaps leading to some errors in DAS, band-pass filtration by means of four-order Butterworth filter with cutoff frequencies 0.1 and 24 Hz. Two-directional filtration was applied to prevent a time shift of data.
4 Seismo-Atmospheric ULF/ELF Electromagnetic Radiation and Signal Processing Methods
 As is given in our first paper by Schekotov et al. , seismo-atmospheric radiation in the ULF/ELF frequency band seems to provide us with a possibility of predicting an EQ; that is, not only predicting the occurrence time of a forthcoming EQ but also predicting the direction to its source of radiation (or its epicentral position).
 Some later works [Schekotov et al., 2008; Molchanov and Hayakawa, 2008; Hayakawa et al., 2012a; Schekotov and Molchanov, 2012] have indicated that the direction of radiation source is coincident approximately with the position of the epicenter of a future EQ.
 In the following, we describe how to detect seismo-atmospheric ULF/ELF radiation and then how to determine the direction of arrival of the radiation.
4.1 Direction Finding
 We determine the direction of the source of seismo-atmospheric ULF/ELF radiation as being perpendicular to the main axis of polarization ellipse. We denote by θ the angle between the main axis of the polarization axis and the D (EW) - component axis, and its tangent is given by the following equation [Fowler et al., 1967].
 Here Ah, Ad and ϕh, ϕd are instantaneous amplitudes and phases of the field component signals. h refers to the NS component of magnetic field, while d, the EW component. They are computed from appropriate complex signals which are, in turn, obtained from the real signals (Uh and Ud) by means of the Hilbert transform. The last ones are extracted from the recorded signals with narrowband filtration. The point is that equation (1) is true only for quasi-monochromatic signals, and the frequency range of 9–10 Hz was used to estimate the direction of arrival in this paper.
 The angle θ in an interval [−π/2, π/2] is totally determined by equation (1) and by the signs of the numerator and denominator of the right-hand side of equation (1). This angle is connected with the azimuth angle (α) of the radiation source.
 It is determined in the interval of [3π/2, π/2]. These same data α were added in the interval [π/2, 3π/2] to provide the determination of α in the whole interval of [0, 2π]. The value of α(i) for i satisfied the following conditions.
were used to obtain the azimuth distribution. The notation < > on the right of equation (3) means the average value of horizontal magnetic field. Here i is an index of discrete values of the signal which obey equation (3). And we adopt K = 5 which determines the minimal signal-to-noise ratio. The last condition of sufficient signal-to-noise ratio is of essential importance to provide the required accuracy of direction finding.
4.2 Detection of the Radiation
 In our first paper by Schekotov et al. , we have proposed a new parameter ∆S in order to detect seismo-atmospheric radiation, which is given by,
 The numerator contains the ratio of two horizontal spectral components Phh (NS component of magnetic field) and Pdd (EW component). The denominator is the root mean square (rms) of the deviation of the signal ellipticity. The expression of β is given by the following equation.
 Here Im means imaginary part. Because Schekotov et al.  have compared different parameters, and have found an enhancement in the spectral ratio of Phh/Pdd and a reduction in the polarization ellipticity before an EQ, and the parameter introduced by equation (4) is proved to be most sensitive and reproducible to seismic shock. The ellipticity or the ratio of minor axis to major axis is defined by tan β. The sense of polarization is characterized by the sign of β; when β > 0, the polarization is right hand (RH), and β < 0 means the left-hand (LH) polarization. The linear polarization is expressed by β = 0 [Fowler et al., 1967].
 The field component power spectral densities, Phh, Pdd and their cross-power spectral densities Phd, Pdh were calculated by using Fourier transforms with frequency resolution of about 0.1 Hz. Spectral components in a frequency range from 0.1 to 24 Hz were taken into account in this paper. They were averaged over 1 Hz intervals such as 0.1–1, 1.1–2, ……, 23.1–24 Hz, so that we have 24 spectral components in the present analysis.
 A success in the application of this parameter ∆S was partly due to a random fact that a majority of nearly EQs took place east of our Karymshiro, Kamchatka, Russia [Schekotov et al., 2007]. In a more general case with the rotation of axes by some angle, we can find a maximum of ∆S in which its radial component will be directed to the source of radiation. The radial Prr and tangential Ptt field components should be taken instead of Pdd and Phh.
where φi is the angle of rotation (φi = 0, Δφ, ⋅ ⋅ ⋅, (i − 1)Δφ, ⋅ ⋅ ⋅, (180∘ − Δφ)), Δφ is a step of rotation angle (30˚ in our case), and < > t in equation (6) means the averaging over nighttime of our interest. Ptt and Prr are the tangential and radial component power spectral densities of the field, calculated from the elements of coherency matrix by means of the following transformation,
where Re in equation (7) means real part. Here we repeat the physical significance of equations (4) and (6), which consists in using two characteristics of the signal to improve the detection of seismogenic ULF/ELF radio emissions. The meaning of the numerator in equation (6) consists in obtaining the maximum ratio of signal components for a given direction of the source. A small deviation of the signal ellipticity results in a decrease of the denominator in the presence of the signal. Both of these factors might lead to a growth of ∆S in the presence of the signal and consequently facilitate its detection.
5 Observational Results of Seismo-Atmospheric ULF/ELF Radiation
 Figure 2 illustrates the result of the spectrum ∆S(f) at a particular station of Nakatsugawa during a period from 4 to 9 March 2011, covering the date of the huge foreshock on 9 March. First, we look at the results in the top rectangular panel. The top panel indicates the local seismicity index (KLS), which is given by Molchanov and Hayakawa ,
where M is the EQ magnitude and R, the epicentral distance (in km). In the top panel of Figure 2, there is one day of higher KLS: a foreshock on 9 March (Ms = 7.3) (9 March 11 in Figure 1). In the analysis, we have used only the local nighttime data in the JST from 0.5 to 5.0 h (total duration of 4.5 h) where we expect the minimum local noise. The middle rectangular panel illustrates the temporal evolution of frequency spectrum of ∆S(f), in which stronger intensity is indicated with darker black. We can find that on 6 March, there is a remarkable enhancement of ∆S at the frequency of 9–10 Hz. This result is illustrated on the bottom rectangular panel where the temporal evolution of ∆S in this frequency range is shown.
 Here we comment on the effect of magnetic storms on the behavior of ∆S. Although this point was already discussed in our previous papers [Hayakawa et al., 2013a, 2013b], we repeat only the essential point here. Though the temporal evolution of Dst index as a measure of geomagnetic activity is not shown here, we know that the time of a minor magnetic storm is not coincident with our peak in ∆S and also the value of Dst is close to null on 6 March when ∆S is maximal [Hayakawa et al., 2013a, 2013b], so that our peak of ∆S is very likely to be seismogenic.
 Figure 3 illustrates an example of frequency spectra of quiet background (0.5–5.0 h LT) in the relevant frequency range at our three observatories (NAK, SHI, and IZU). Especially, the data from two observatories at NAK and SHI are found to exhibit two peaks at about 8 Hz and 14 Hz, which are apparently the effect of Schumann resonances [e.g., Nickolaenko and Hayakawa, 2002], and the frequency spectra at these observatories are relatively stable. On the other hand, the frequency spectrum at IZU is found to include many impulsive or quasi-harmonic artificial signals, probably due to the human activity. This is the reason why we will have rather bad results at IZU in the following.
 Figure 4 is the comparison of ∆S at the three observatories of NAK, SHI, and IZU during a much longer period of 1 February to 14 March 2011. It is found from this figure that the combined characteristic of the field, ∆S at all three observatories exhibits sharp maxima on the same day of 6 March, which is 3 days before the 9 March first strong foreshock and 5 days before the 11 March huge EQ. The peak at Nakatsugawa (NAK) is conspicuously enhanced because of lower electromagnetic noise there. While, the sharp peak on 6 March is still very remarkable at Shinojima (SHI). The electromagnetic noise environment at the third station of Izu is not so good enough (as seen in Figure 3) that we expect a lot of fluctuations in the variation of ∆S. As the conclusion, ULF/ELF radiation detected by means of ∆S appeared 3 days before the first foreshock, which is indicative of the beginning of seismic activity. This is in agreement with the conclusions of our previous studies and gives us a possibility to estimate the time of a forthcoming EQ. The aim of the present study is also to determine azimuthal distributions of the radiation. The procedure of their calculation was described in the subsection 4.1. An example of their presentation is shown on the round panels of Figure 2. The distribution of α is represented by an angle histogram, which is a polar plot (as in the bottom circular panels of Figure 2) showing the distribution of α values. Each group in each polar plot is shown as one bin, and each polar plot shows α (i) in 36 angle bins. The length of each lobe in the histogram and its degree of darkness is proportional to the number of elements in α(i) that fall within a bin. Examples of daily plots on 3 days (6 March, 7 March, and 8 March) are given in the bottom three panels of Figure 2. A summary of azimuthal distributions of ULF/ELF radiation for the last 5 days of observations is shown by a degree of blackness on the ring which is placed on the top right panel of Figure 2. Its most dark sectors are found to roughly coincide with the azimuths of probable forthcoming EQs. Their limits or probable error are shown by dashed lines which cross the point of observation.
 The azimuthal distribution of ULF/ELF radiation recorded on 6 March when the seismogenic ULF/ELF is strongest is shown on the map of our interest in Figure 5. The size of lobes and degree of blackness as well as in Figure 2 are proportional to the pulse flux density of ULF/ELF radiation. There are shown positions of observatories (NAK, SHI, IZU) and EQs with M > 7 occurred from 6 March to 11 March, and the magnitude and depth of EQs are represented by size and color of circles. Despite a long scattering of seismic disturbance, the maximum of azimuthal distributions are found to be roughly directed to the epicenter of the EQ.
 The temporal evolutions of azimuthal distributions of ULF/ELF radiation observed at NAK, SHI, and IZU during the period of 5–11 March 2011 are shown on seven circle panels of Figure 6. On the circular edge of each figure, we have a ring on which the degree of blackness reflects the total azimuthal distribution of 5 previous days of observations. Maxima of azimuthal distributions on 6 March and 10 March are found to coincide with the direction of the seismic disturbance caused by the Tohoku EQ. On this same day, we observe a sharp onset of radiation in the first case on 6 March. In the second case, the radiation happened after the foreshock on 9 March, but just before the main shock on 11 March. The last case is observed only in azimuthal distributions. Both of these cases are observed simultaneously on all sites. However, the azimuthal distributions of ULF/ELF radiation on other days are found to be different, which is possibly due to the effect of different local interferences.
6 Conclusion and Discussion
 By using the ULF/ELF data in a frequency range of 0.1–24 Hz observed by the Chubu University network, we have examined whether there is observed any ULF/ELF precursor to the 11 March 2011 EQ. The following facts have emerged from the present analysis.
 The combined characteristic of the magnetic field ∆S is again proved to be extremely useful in finding out seismo-atmospheric ULF/ELF radiation.
 The temporal evolution of ∆S is found to be peaked on 6 March, which happened 3 days before the first foreshock which is indicative of the beginning of seismic activity.
 The frequency of the maximum ∆S(f) is observed in the vicinity of the first Schumann resonance.
 The azimuthal distribution of ULF/ELF radio emission is found to be coincident approximately with the position of the main shock region.
 Consequently, we can come to the conclusion that the ULF/ELF radio emission is highly likely to be a precursor to the 11 March 2011 huge EQ.
 There have been performed some other attempts to find precursors to this EQ. It is known that seismogenic ULF emissions of lithospheric origin are dominating at the frequency of around a few hundreths of Hertz [e.g., Hayakawa et al., 2007, 2011], but unfortunately these frequencies are out of our receiver range. The similar works have already been published by means of the ULF data at other stations, which are not concerned with the emission, but the reduction in amplitude [Schekotov et al., 2006, 2013; Hayakawa et al., 2013a]. That is, the depression of ULF emission intensity has been observed on 5 and 6 March, several days before the EQ [Schekotov et al., 2013; Hayakawa et al., 2013a], which is interpreted in terms of seismo-ionospheric effect as studied with subionospheric VLF perturbations [Hayakawa et al., 2012b, 2013a, 2013b]. Next, the electromagnetic field in a higher frequency range (0.1 – 30 kHz) has been examined by Cohen and Marshall , who have indicated that there has been no evident precursory electromagnetic effect in this VLF range. Finally, it may be concluded that there are only scarce reports on electromagnetic precursors to the 2011 Japan EQ, which is probably due to the fact that this EQ happened in the sea. Because there have been observed a variety of electromagnetic phenomena before the disastrous Kobe EQ in 1995 (see the summary by Nagao et al. ). This asymmetry of land and sea EQs in the abundance of electromagnetic phenomena in association with EQs would be of essential importance in elucidating the generation of ULF/ELF atmospheric radiation, the lithosphere-atmosphere-ionosphere coupling [e.g., Molchanov and Hayakawa, 2008].
 The authors are grateful to Chubu University for its support to the ULF/ELF observations at three stations.