The low-frequency microseismic oscillations and their correlation with the processes occurring in the hydrosphere and atmosphere of the Earth, which are the major sources of microseismic energy, are a common subject of research in geophysics [1-4]. It is however evident that the variations in the structure of the microseismic background may also reflect the changes in the properties of the Earth’s crust, which is the medium where the microseismic signals propagate. These changes in the parameters of microseisms in relation to Japan mega-earthquake 11 of March 2011, are the subject of the present paper.

This paper presents results of analysis of properties of low-frequency seismic noise on the basis of more than 15 years of continuous observations, from the beginning of 1997 up to the middle of May 2012, at F-net (Japan) broad-band seismic stations including more than one year after the mega-earthquake 11 of March 2011. In previous papers an analysis of the multifractal parameters of low-frequency microseismic noise allowed us to hypothesize, in as early as 2008, that Japanese Islands were approaching a large seismic catastrophe, the signature of which was a statistically significant decrease in the support width of the multifractal singularity spectrum [5,6]. Subsequently, as new data became available and after some new statistics of microseismic noise were included in joint analysis, we obtained some new results, indicating the facts that the parameters of the microseismic background had been increasingly synchronized (the synchronization process was estimated to start in the middle of 2002) and that the seismic danger had permanently grown [7-10]. A cluster analysis of background parameters led us to conclude that in the middle of 2010 the islands of Japan entered a critically dangerous developmental phase of seismic process [8,11]. The prediction of the catastrophe, first in terms of approximate magnitude (middle of 2008) and then in terms of approximate time (middle of 2010), was documented in advance in a series of papers and in proceedings at international conferences [5-11] (the paper [11] was submitted at April of 2010). The whole experience of Great Japan earthquake prediction on the basis of seismic noise analysis was published in [12].

In this paper a maps of 4 low-frequency seismic noise statistics are plotted for different adjacent time fragments before the mega-earthquake 11 of March 2011 and after it. It is shown that all considered seismic noise parameters have prognostic properties and could extract seismically danger domains. According to results of data analysis after 11 of March 2012 it is shown that there is a danger for occurring the 2nd mega-earthquake at the region to the south direction from Tokyo. This danger was estimated in [13] using the singularity spectrum support width only.

It should be noticed that using of multifractal singularity spectrum support width has a rather long history in investigation of nonlinear systems behavior. Particularly the “loss of multifractality” i.e. decreasing of singularity spectrum support width, is a well known effect before the abrupt change of different system properties. Mainly this effect was investigated in biological and medicine systems [14-16], but in [15] it was shown that it has a rather universal character and is observed in physical systems as well. The analogy between effect of singularity spectrum support narrowing of seismic noise waveforms and the loss of multifractality in the behavior of other nonlinear systems [14-16] gave an impulse to the author to make a hypothesis about approaching Japanese island to seismic catastrophe [5].

For the analysis a vertical broadband seismic oscillations components with 1-second sampling time step (LHZ-records) from the broad-band seismic network F-net stations in Japan were downloaded from internet address http://www.fnet.bosai.go.jp starting from the beginning of 1997 up to 15 of May 2012 (more than one year after seismic catastrophe). The whole list of F-net seismic stations includes 83 positions. We considered the stations which are located northward from 30˚N and, thereby excluding the data from six solitary stations located on remote small islands. The locations of 77 stations which were chosen for analysis are indicated in Figure 1 with epicenters of 2 the strongest earthquakes which occurred during observations: near Hokkaido at 25 of September 2003 with magnitude 8.3 and Tohoku mega-earthquake at 11 of March 2011 with magnitude 9.0. In this paper the seismic data were analyzed after transforming them to sampling time step 1 minute by calculating mean values within adjacent time windows of the length 60 sec. Thus, the minimum period of seismic

noise variations for the analysis equals 2 minutes.

The seismic records from each stations after coming to 1 minute sampling time step were split into adjacent time fragments of the length 1 day (1440 samples) and for each fragment parameters, , and were calculated. Thus, time series of these 4 values with sampling time step 1 day were obtained from each of 77 seismic stations which are presented at the Figure 1.

Having the values of, , and from all seismic stations it is possible to create maps of spatial distribution of these seismic noise statistics. For this purpose let us consider the regular grid of the size 30 × 30 nodes covering the rectangular domain with latitudes between 30˚N and 46˚N and longitudes between 128˚E and 148˚E (see Figure 1). For each node of this grid the daily values of, , and are corresponded which are calculated as median for the values of five nearest to the node seismic stations. This simple procedure provides the sequence of daily maps of all parameters. The averaged maps are created by averaging daily maps for all days between 2 given dates. Taking into account that almost all stations of the F-net are placed at large Japanese islands these map in the ocean regions have the less significance than at islands of course. But we had to work with those data which we have at our disposal. The method of nearest neighbors which is used in this paper provides a rather natural extrapolation of the used values into domains which have no points of observations.

Figures 2 and 3 present averaged maps of, , and for 3 adjacent time fragments: from the beginning of 1997 up to 25 of September 2003, the day of earthquake with magnitude 8.3 near Hokkaido; from 26 of September 2003 up to 10 of March 2011, the day before Tohoku mega-earthquake 11 of March with magnitude 9.0 and from 14 of March 2011 up to 15 of April 2011. Three days, 11, 12 and 13 of March 2011 are excluded from the analysis because during these days a lot of seismic station of F-net were not working properly after seismic shock of 11 of March 2011.

The Figures 2(a') and (b') show that plotting averaged maps of spatial distribution of singularity spectrum support width could extract the place of future catastrophe as the regions with relatively low values of. Figure 2(a') presents a map where the area of relatively low could be noticed which includes the place of future mega-earthquake and it is not split into North and South parts. At the Figure 2(b') we can see that after the event 25 of September 2003 this area was split into North and South parts and the North part turned to be the area of aftershocks of Great Japan earthquake of 11 of March 2011 whereas the South part remains to be the region of relatively low values of singularity spectrum support width before and after 11 of March 2011 (Figure 2(c')). According to interpretation of regions with low values of as the seismically dangerous ones we could propose a hypothesis that during Tohoku earthquake only a half of accumulated seismic energy was dropped and that the above written South region (the north part of Philippine plate, Nankai Through) will be the area of future mega-earthquake with magnitude 8.5 - 9.0. The estimate of magnitude follows from the size of the area of low values (Figure 2(c')) which approximately equals to the area of Tohoku earthquake aftershocks.

The Figures 2(a″)-(c″) show that linear predictability index is a some kind of “antipode” to the parameter and almost everything what was written above about properties of could be repeated for with changing “minimum” to “maximum”: relatively maximum values of linear predictability index extract seismically danger domain before the earthquake.

The Figure 3 presents averaged maps for waveletbased statistics and. Smoothness index is defined as integer but after operations of taken median values among 5 nearest to the node stations for mapping it becomes fractional. It could be noticed that these statistics are rather similar to linear predictability index and they are “antipodes” to the parameter: they extract the region of future earthquake by their relatively high values. The minimum normalized entropy seems even be the most “clean” statistics in comparison with all others: it has no essential maximum values anywhere except the region of Tohoku earthquake and the region of the proposed future earthquake to the south direction from Tokyo. The results presented at the Figures 2 and 3 are remarkable by the fact that 4 statistics which are absolutely different by their construction extract the same regions as seismically danger.

The Figure 4 presents the graphic of daily mean values of smoothness index computed for all stations. This graphic is interesting by the explicit positive trend of seismic noise smoothness which started at the beginning of 2003 and was continuing till the beginning of 2010 when the mean smoothness attains maximum value. After that a time interval of large mean variability began which include the time moment of Tohoku earthquake and this peculiarity is continuing till now. Maybe when the SI variability became less and mean value became high then it will be a precursor of the next megaearthquake?

Plotting the maps of different properties of low-frequency seismic noise within moving time window could present a new method of dynamic seismic hazard estimate.

It gives a possibility to inspect the origin and evolution of the “spots of danger”. Analysis of seismic noise at Japan islands from broad-band seismic network F-net gave a possibility for prediction of Great Japan earthquake of 11 of March 2011. The prediction was published in a number of scientific papers and abstracts at international conferences in advance of the seismic catastrophe. According to the analysis of seismic noise after 11 of March of 2011 the next mega-earthquake with magnitude 8.5 - 9.0 could occur at the region of Nankai Trough.

Just because the experience of using these statistics is very short it is rather hard now to make an order: which parameters are the most “prognostic” and which are the less ones. After comparing maps at the Figures 2 and 3 it seems that singularity spectrum support width (Figure 2(a')-(c')) and normalized entropy (Figure 3(a″)-(c″)) have “the most strong power” to extract dangerous regions. For more reliable conclusion these methods should be tested in other seismically active regions where a rather dense broad-band seismic networks exist, for instance in California.

The probable physical interpretation of the precursory effects which are presented at this paper could be the following. Hierarchical self-similar block structure of the Earth’s crust [22,23] has a consequence of existence of a lot of blocks with different sized (scales) which are at different stages of their consolidation from their constitutive parts (block of less sizes). In dependence on the state of consolidation and on the range of the block within Earth’s crust structure hierarchy the transfer and resonance properties of the block are different. A great variety of consolidated block sizes follows a large multifractal singularity spectrum support width of low-frequency seismic noise which is generated as a result of seismic waves propagation from atmosphere and oceanic sources through hierarchical block medium consisting of blocks with different transfer and resonance properties.

Seismic noise is a multifractal random process because the hierarchical medium (consisting of consolidated blocks of different ranges) of seismic waves propagation is multifractal. What happens before the strong earthquake? In order that strong earthquake could occur it is necessary the existence of a consolidated crust block of large size—otherwise the energy could not be accumulated and will be dissipated in a large number of small earthquakes. The existence of the large consolidated block of Earth’s crust means the loss of variety of transfer and resonance properties of the medium (it becomes more uniform). The loss of variety of medium properties follows the loss of multifractality, i.e. the decreasing of. Thus, if the mean value of is decreasing it is an indicator of consolidation of large block of the Earth’s crust and increasing of seismic danger.

The consolidation of small blocks into the large one before the strong earthquake has a consequence that mutual movements of small blocks canceled. It means that the low-frequency seismic noise does not include now high amplitude variations which are connected with these mutual movements. The absence of high amplitude variations (“low-frequency spikes”) follows the high value of entropy of squared wavelet coefficients distribution. For the same reason the noise became more smooth and more predictable.

This work was supported by the Russian Foundation for Basic Research (project no. 12-05-00146) and Russian Ministry of Science (project no. 11.519.11.5024). The author is grateful to National Institute for Earth Science and Disaster Prevention (NIED), Japan, for providing free access to the source of broadband seismic noise waveforms registered at the F-net stations.