Usage of wavelet analysis for the detection of
seismogenic ULF emissions
L. Alperovich
Dept. of Geophysics & Planetary Sciences, Ramat-Aviv, 69978 Tel-Aviv University, Israel
V. Zheludev
School of Computer Sciences, Tel-Aviv University, 69978 Tel Aviv, Israel
M. Hayakawa
Department of Electronic Engineering, The University of Electro-Communications, Chofu, Tokyo, Japan
Abstract. Wavelet analysis have been applied to the high resolution magnetic ULF data in a seismoactive region in
order to determine whether there is an evidence of ULF electromagnetic emissions that precede or accompany an
earthquake. We have developed an algorithm specially adapted to the single-station wavelet detection of geomagnetic
events. For this purpose we constructed the wavelet based magnetic signatures of certain earthquakes. Namely, we
used the distribution of energies among blocks consisting of coefficients of wavelet packet transforms. Then we
found an evidence on the presence of short period seismogenic pulses associated with a strong earthquake (M=6.2) on
March 26, 1997 in Kushu, Japan. A comparison of extracted geomagnetic variations at two observatories located in its
epicentral zone has indicated that the seismogenic geomagnetic disturbances occurred 6-7 hours prior to the
earthquake.
1. Introduction
The problem of search for geophysical precursors of different nature (seismic, magnetic,
electric, etc.) has some inherent peculiarities which put this one into a range of exclusively
complicated problems of signal processing. In fact, when we try to extract signals initiated by
the earthquake preparation processes from data available, priory information on assumed time
instant of generation of the signals as well as on their intensity, is negligible. Moreover,
usually almost nothing is known on the characteristic frequency range, the signal should be
sought within. And, finally, the question of the shape of the signal remains fully open.
The principal aim of this work is to develop an improved technique for detection of the ULF
range (f<10Hz) electromagnetic emissions prior to or associated with an earthquake.
Extensive efforts have been made in recent years to improve the knowledge of the ULF
electromagnetic fields associated to an earthquake.
Successful attempts were performed by a number of researchers using single-observatory
measurement or regular network observation and network measurement specially matched for
this purpose. Typically, investigations based on the single point observations are focused on
finding an intensive signal, which exceeds essentially the background noise perturbations
caused by ionospheric and magnetospheric sources.
It has recently been found strong earthquake ULF precursors signals (Kopytenko et al., 1990;
Fraser-Smith et al., 1990; Bernardi et al., 1991; Molchanov et al., 1992; Hayakawa et al.,
1996; Merzer and Klemperer, 1997). The results by these authors are based on the ULF
magnetic field measurements for the two large earthquakes (Spitak and Loma Prieta).
Molchanov et al. (1992) have compared the ULF characteristics for these earthquakes and
have found many similarities between these two earthquakes.
However, weak perturbations remain unidentified, and there were attempts to find efficient
strategy to resolve this issue. Hayakawa et al. (1996) have proposed to use a comparison
between the ULF wave activity and ΣKp to distinguish space geomagnetic pulsations and
non-space emissions.
In addition, to be saved from space produced ULF noise, there were suggested to use
polarization of magnetic disturbances in the vertical plane. In the most cases, vertical
component (Z) of the variations in the middle and low latitude is defined by local
geoelectrical inhomogeneities. It means, that on the average ratio of Z to the horizontal
component (H) should be a constant independent on time. The ratio Z/H=0 for the
homogeneous earth and normally incident plane wave. Deviation this ratio from 0 could be an
indication on appearance of the ULF variations caused by an underground source. Indeed, it
has been demonstrated by Hayakawa et al. (1996) and Kopytenko et al. (1999, 2001) the
most prominent feature of the ULF variation associated with an earthquake and with duration
from several minutes to several hours is their high polarization ratio (Z/H>1). It was shown
also that there is an increasing of the Z/H ratio before a strong earthquake takes place, and
after the earthquake the ratio decreases.
Despite much progress achieved recently in searching of the ULF earthquake precursory
signatures (e.g. Seismo Electromagnetics, 2001), there are significant unanswered questions
associated primarily with weak imperceptible signals. One of the key questions is: How to
construct a formal procedure to distinguish seismogenic electromagnetic signal from the
magnetospheric oscillations. The most reliable way to address this problem is to construct
somehow ULF magnetic ‘portraits’ before and after an earthquake and investigate whether
distinction exists between them.
2. Outline of the algorithm
We undertake an examination of the half-year high-resolution 3-component magnetic
recordings (1 second sampling rate) taken at the geomagnetic observatory Kagoshima
(geographic coordinates; 31.50N, 130.70E) (Yumoto et al. 1992) to determine if there are any
distinguishing magnetic variations that could have an earthquake origin. During this period, 6
earthquakes of magnitude M  4.6 occurred in radius 300km (see Tabl. 1). On March 26 and
May 13 two strong took place. We used data of World Data Center A for Seismology
(National Earthquake Information Center (http://neic.usgs.gov/epic).
Table 1.
Year
1997
1997
1997
1997
1997
1997
Month
01
03
04
04
04
05
Day
11
26
02
02
05
13
Time
055023
083147
193322
214730
042451
053830
Lat.
31.63
31.92
31.82
33.36
31.96
31.82
Long.
131.54
130.43
130.09
132.22
130.43
130.28
Depth
52
10
10
45
33
33
Magnitude
4.9
5.9
5.0
4.6
4.8
5.8
We assume that the magnetic variations generated by earthquakes differ somehow from the
usual oscillations caused by extraterrestrial sources. We also believe that there are some
common properties to all seismogenic signals that were recorded during the analyzed interval.
First, these signals are quasi-periodic in the sense that there exist some dominating
frequencies in each signal, but these frequencies may vary with the location of seismic source.
However, for the close sources these variations are confined in narrow frequency bands.
So, we have conjectured that the distribution of the energy (or some energy-like parameters)
of signals belonging to some class over different areas of the frequency domain may provide a
reliable characteristic signature for this class. We focus in this paper on the separation of two
classes of geomagnetic signals namely of space and tectonic origins.
2
We develop a special mathematical procedure based on the wavelet technique and suggest an
approach based on the identification of wavelet signatures of the observed field during ‘quiet’
and seismic active periods preceding an earthquake.
2.1. Wavelet analysis
By now the wavelet transform are widespread and have been described comprehensively in
the literature (see e.g. Mallat, 1998). Therefore, we restrict ourselves to mention only relevant
facts that are necessary to understand the construction of the algorithm. The basic assumption
justifying an application of wavelet analysis is that the essential structure of a signal analyzed
consists of not a large number of various waveforms. The best way to reveal this structure is
representation of the signal by a set of basic elements containing waveforms coherent to the
signal. For structures of the signal coherent to the basis, large coefficients are attributed to a
few basic waveforms, whereas we expect small coefficients for the noise and structures
incoherent to all basic waveforms.
Wavelet analysis provides a rich library of waveforms available and fast, computationally
efficient procedures of representation of signals and of selection of relevant waveforms.
Wavelets are a family of functions ranging from functions of arbitrary smoothness to fractal
ones. A few examples of wavelets are plotted in Fig.1.
Wavelet analysis begins by choosing a specific family of wavelets to work with. The family
is specified by a scaling function and a wavelet, and these generate a basis by translation and
dilation. This is an issue of an extraordinary computational efficiency of WA. Basic concepts
of the wavelet analysis are given in Appendix I.
2.2. Formulation of the approach
The basic assumption is that the general signature of the geomagnetic field in the given region
could be obtained as a combination of energies inherent in a small set of most essential blocks
of the wavelet packet decompositions of the recorded signals. We assume a remarkable
disturbance of this configuration before and during the event of earthquake.
Two intrinsically interesting classification/detection problems based on geomagnetic
information are the problems of classification of geomagnetic signals emitted by processes of
preparing of an earthquake and the detection of the presence of the quake caused signal via
analysis of its wavelet signature against the existing database. A crucial factor in having a
successful classification is to construct signatures built from characteristic features that enable
to discriminate among recorded classes.
Multiscale wavelet analysis provides a promising methodology for this purpose. In the final
phase of the process, in order to identify the earthquake signatures of the predetermined
classes of signals, we used conventional classifiers such as: Linear Discriminant Analysis
(LDA) (Saito and Coifman, 1995) and Classification and Regression Trees (CART) (Breiman,
1993). Saito and Coifman (1997) applied the algorithm LDA to classification of some
geological phenomena.
From a set of signals with known membership we selected a few blocks of coefficients of the
wavelet packet transform (WPT) that discriminate efficiently between the given classes of
signals. Then, we applied the WPT to the signal to be classified (Averbuch et al., 2001). We
used as its characteristic features the energies contained in the selected blocks of the
coefficients of WPT. Finally, we submitted the extracted features to one of the abovementioned classical classifiers. The classifier, being appropriately trained beforehand, decides
which class this signal belongs to.
3
2.3. Algorithm
The algorithm is centered on two basic issues:
 Selection of the discriminant blocks of the wavelet packet coefficients;
 Discrimination among the signals.
We used the WPT based on Spline and Coiflet wavelet transforms. These transforms reduce
the overlapping among the frequency bands associated with different decomposition blocks.
We treated our problem as a two-class classification problem where one class comprised
signals recorded at ‘quiet’ time intervals. To the second class we attributed signals recorded
during earthquakes. Initially, we gathered as many recordings as possible for each class. We
prepare from each selected recording, which belongs to a certain class, a number of
overlapping slices, shifted with respect to each other. These groups of slices form the training
set for the search of discriminant blocks.
Each slice was subjected to the WPT. The energies of each block of coefficients were
calculated. As a result we obtained, to some extent, the distribution of the ‘energies’ of the
slice over various frequency bands. The whole frequency range is divided by S=2L –1
subintervals (blocks) where L is the number of decomposition levels.
The ``energies'' of each block are calculated in accordance to the chosen measure. An Scomponent energy vector presents the energy of a slice. As a result we obtain, to some extent,
the distribution of the ‘energies’ of the chosen slice over various frequency bands of widths
from N F / 2 to N F / m , where N F is Nyquist frequency. In our case
N Nyquist  0.5samplefrequency  f max  0.5Hz
The whole frequency range is divided by 2L subintervals (blocks). So the maximal frequency
fblock of the block of the block of number Nblock is
f block 
N block  f max
.
2N
Figure 2 demonstrates a subdivision scheme of the whole frequency range for L=7 to allow us
to go to finer resolution of the wavelet packet transform.
The energy is presented by an energy vector Eil of length 2 L 1  1. The energy vectors along
the training set of the class are averaged. The average energy map E l indicates how the
distribution of the ‘energies’ among various block of the decomposition and frequency bands,
respectively, is taking place within the whole class C l .
We performed the wavelet packet analysis presenting 27 days with rather strong earthquakes
(M>4.0) (Class C1) within a radius of 500 km from the observatory (depth 0-50 km) and 27
quiet days (Class C2). Top (C1) and middle (C2) panels of Figure 3 display the energy maps
for two classes for L=8 decomposition levels. Heights of the bars indicate the normalized
energy of each of the 513 decomposition blocks. The difference between two maps (low panel
of the Fig.3) provides some insight into the problem. The differences for most blocks are
nearly zero which means that they are of no use for the discrimination except a few blocks
with large values in their differences. As a result of the operations described above, we find a
relatively small set of decomposition blocks for which the distribution of energies amongst
them characterizes the classes to be distinguished.
2.4. Preparation of the reference set
We have chosen a number of recordings that belong to the classes to be distinguished from
which we form the reference set. After the decomposition, we calculate only the energies of
4
the blocks that are selected before. We do the same for both classes. The reference sets are
used for the construction of the classification tree, and as pattern sets for LDA. We are now in
a position to classify test signals.
3. Analysis of results
We have conducted two series of experiments: (1) Classification of signals emitted by
earthquakes; and (2) Discrimination between signal generated by earthquakes and the
background.
We have processed the signals using the scheme explained above. The recording is processed
with sliding overlapped windows of size n=1024. The window was shifted along the signal
with a step of s=128 samples. Each window is processed by the WPT up to the 8th levels. As
a result we have selected various sets of discriminant blocks. To improve the comprehension
of the training phase, we have used not only the component recordings (H, D, Z), but also
their combinations such as the variations of horizontal orientation angle and inclination.
During the training phase we have employed differences between the data of a chosen quake
day and of a day in the same month with the same Kp index to diminish an influence of the
magnetic activity and daylight conditions.
The top picture of Figure 4 illustrates the classification rate for the variations of Z-component.
Signals of Class C 1 (‘disturbed’ days) are January 17, 15:32, M=5.2 and 15:53, M=5.9; March
26, M=5.6; May 13, M=5.6. For the selection of discriminant blocks we have used
geomagnetic recordings around the times of 27 earthquakes with M>4.0 appearing at
distances up to 500km from the Kagoshima observatory. We have used Spline6 WPT up to
the 8th level. CART classifier made decision on every 0.5-hour fragment of a signal. Each *
in the picture corresponds to a single 0.5-hour interval of class C l . Its height, h l , may range
from 0 to 1 and reflects the probability of incorrect addressing the fragment to the class C l .
So, if h l  0 , then the signal S l is completely classified. If 0  h  0.5 then the probability of
correct answer prevails over that of wrong and the signal is classified. The closer h l gets to 0
the more reliable the answer. If hl  0.5 is non-classified. Finally, if 0.5  h l  1 then the
signal is misclassified.
As it is seen from the upper panel of Figure 4, within the time interval 0.5-1.5 hours before
and 2 hours after the January 17 earthquake almost all the signals from the classes C1 and C2
are classified correctly. We can also find that there is weak separation of signals between the
two March 26 quakes. Beyond the January quake the classification for March and May seems
to fail.
The results of next experiment are displayed in Figure 5. The signals are decomposed using
the Spline6 WPT up to the 7th level. We employed as the training signals magnetograms
recorded on March 25-27, 1997 (class C 1 ) and on March 9-11 (class C 2 ). We submitted the
following signals to classification: the signals of the C 1 class are May 12-14, 1997 (an
earthquake with M=5.6 on May 13). Its epicenter located almost at the same point as the
epicenter of the March 26 earthquake. For the signals of C 2 class we chose January 1,
February 1 and March 1. For decision we used both classifiers: Classification and Regression
Tree (CART) and Linear Discriminant Analysis (LDA). The result of LDA classification is
presented in Figure 5. Upper panel corresponds to the disturbed period and the bottom to the
quiet period. We can notice that classification rate for the signals of class C 2 is less than 0.5
in general; that is, both classifiers (though the result by CART is not shown) classify correctly
quiet magnetograms. At the same time a majority of C 1 signals are misclassified. One can see
from the figure that the classification procedure reliably separates observed magnetic field
5
into two classes only for the two isolated recordings, namely before 1 day (May 12) and 4
hours before the earthquake. There the substantial fraction of signals are classified well (LDA
classifier).
Common features are found to appear in the geomagnetic field preceding both March 26 and
May 13 earthquakes. The anomalies occupy a wide range of periods (from 10s to 250s).
Narrowing of the interval and excluding low frequency bands degrade classification.
Performed numerical experiment indicates that some irregularity disturbed the energy
signature of geomagnetic variations recorded closely (around 20km) to the epicenter of the
earthquake.
As the next stage we have constructed training set for C 1 class including new time intervals
corresponding to the moments of earthquakes taken from different distances. Results of
classification did not change till the radius up to 300km from the Kagoshima observatory
when we have included 6 3-day intervals containing 5 additional earthquakes. Further
increase in radius leads to degradation of the classification.
The localization of the geomagnetic signature we have discovered does not indicate directly
the locality of generated signals because a signal can sometime spread away from the source
over large distances. During this propagation the energetic portrait, distinctive relationship
between the energies within different levels and blocks can be lost, and an emitted signal
behaves as though it forgot anything about the source.
The wavelet analysis of simultaneous magnetic records at Kagoshima and Kanoya located
practically in the epicentre zone and spaced 20 km apart, revealed two successive pulses of
the same shape with 3.2 min and 6.8 min time delay, respectively, 6-7 hours prior to the
March 26 earthquake (Figure 6). The distance between the two observation points is about 25
km, and hence the horizontal wave velocities of the pulses are 8 km/min and 4km/min. Figure
4 also shows that the intensity of the pulses is strongly dependent on the distance. The pulses
manifest themselves predominantly in the H-component. Taking into account the relative
location of the observation points and the epicentre of the first quake, one can see that the
wave propagated from the epicentre via Kagoshima to Kanoya with strong longitudinal
magnetic component. As it follows from the Figure 4, attenuation rate  is 0.1km-1.
However, the direct comparisons of recordings preceding another earthquake with the
epicentre at the same place (Kyushu, M=6.2, May 13, 1997) have not demonstrated any such
simultaneous visible anomalies. The reason why the pulses were not observed during the
second earthquake though it occurred in the same place may be due to their distinct depths.
Hypocentre of the March 26 quake was at a depth of 10 km, and the May 13 at 33 km. Due to
the proximity to the ground surface, the signal of the March quake should be of high intensity.
Setting aside the question about the generation of such impulses (Gershenzon and Gokhberg,
1994; Molchanov and Hayakawa, 1998) the availability or lack of the simultaneous magnetic
pulses can be in principle explained not only by the remoteness of sources from ground
observer, but also the ground conductivity and propagation conditions. For the second quake,
the source is located in the high conductive layer surrounded by the low conductive medium.
While, the situation of the first earthquake is a low conductive waveguide with high
conductive walls (Vanyan, 1997). An electromagnetic wave can propagate here as a
‘diffusive’ wave with low velocity and high damping.
Acknowledgements. The geomagnetic data of Kagoshima observatory were kindly provided
by Prof. K. Yumoto and the members of the 2100 MM team. We are grateful to them and the
members of the 210o magnetic meridian team who contributed to the successful operation of
the station [Yumoto K. et al., 1992]
6
Appendix I.
Haar wavelets
To highlight basic concepts of WA, we use the simplest of wavelets -- the Haar ones -and
make some simplifying assumptions. In particular, we assume that a signal f(t) is given in
the interval [0,1] and we have at hand the samples in
N=2J equidistant points:
f k  f k / N , k  0,1,, N  1, 1, J - is any natural number. We will say in this case that
the signal f(t) is given at the J- scale. The starting point in construction of a wavelet scheme
is definition of the scaling function at the J- scale. In the Haar case it is simply the stripfunction:
as 0  t  N
else
1
0
 J t   N 
The normalizing multiplier
N is inserted to guarantee
  
1
J 2
 1.
0
Provided the sampling grid is reasonably fine, the signal f(t)
approximately by a step-function fJ(t):
N 1
can be represented
k


N
N

k 0
For further use we rewrite this approximate signal as follows:
f t   f
J
t    f k
2 J 1
f
J
t    y kJ  J  t 

k 0
k

N
1
 J t 
where
y kJ 
1
N
fk
(1)
Since
2
if m  n
0
k  J m


t



t

dt

,





0  N   N 
if m  n
1
we may write the following integral expressions for the coefficients:
1
J
k 1 / N

ylk 
f
J
t    J  t 
k/N

k
 dt
N
(2)
The entire set of the coefficients y kJ contains, of course, the whole structural information on
the signal f J t  . However, events of different nature and time scales are stirred in this signal
and can hardly be extracted, especially short-living and low-magnitude ones. To separate
these events and to follow their behavior in time is the goal of wavelet analysis. It is carried
out along with the following scheme.
Let us pass to the lower scales. At the (J-1) scale the scaling function becomes two times
wider:
 J 1 t  
N 1

2 0
as 0  t  2 / N
else
For representation of the signal we will use the shifts of  J 1 t  with two times longer step
2/N. The number of such shifts is N/2.
We introduce now the so-called Haar wavelet:
7
as 0  t  2 / N
1
N
 1
2
0
 J 1 t  
as 1 / N  t  2 / N
else
t  into the sum of two signals:
f J t   f J 1 t   w J 1 t 
Now we are in a position to decompose the signal f
J
(3)
where
f
J 1
N / 2 1
t   
k 0
w J 1 t  
 2k 
y kJ 1 J 1  t   ,
N

N / 2 1

k 0
(4)
 2k 
z kJ 1 J 1  t 
.
N

(5)
Similarly to (2), the coefficients are:
y
J 1
k
2  k 1 / N


f
J
t    J 1  t  2k  dt ,

2k / N
z
J 1
k

2  k 1 / N
J
 f t  
J 1
2k / N
N
(6)
 2k 
t 
 dt
N

Point out that, on the one hand,
 J 1 t  
1
2
t
2
J ,
i.e. the scaling function  t  is a dilation of  J t  . On the other hand, the following (twoscale relation) holds which is fundamental in wavelet analysis:
J 1
 J 1 t  
1  J
1 

  t    J  t   
2
 N 
For further reference we rewrite this relation in a more abstract form denoting h0  h1  1
p


 J 1 t   H J t    hk  J  t 
l 0
l 
,
N
p  1.
2.
(7)
As for the wavelet  J 1 t  , it can be written as the difference:
 J 1 t  
1  J
1 

 t    J  t   
2
 N 
The inverse formulas are readily seen:
1
1
(8)
y 2Jk 
y kJ 1  z kJ 1 ,
y 2Jk 1 
y kJ 1  z kJ 1
2
2
A proper interpretation of these simple formulas could be helpful to clear the basics of WA.
The structure of the first addend f J 1 t  structure in (3) is quite similar to that of the original
signal f J t  . Indeed, just as f J t  it is a linear combination of shifts of the scaling function.




The difference is that the scaling function  J 1 t  , is two times wider than  J t  . Any
coefficient y kJ 1 is an average of two adjacent coefficients of the original representation (see
(8)). Therefore we may characterize f
J 1
t  as a smoothed version of the signal
f
J
t  .
8
The second addend w J 1 t  in (3) is more meaningful. It provides details, which complement
the smoothed version f J 1 t  to the whole signal f J t  . It is a combination of the sharp
wavelets  J 1 t  2k / N  of extra short duration. The set of coefficients z kJ 1 in (5) is a result
of testing the signal f J t  for the presence of such wavelets. In accordance with (6), the
coefficient z kJ 1 indicates how much the wavelet  J 1 t  2k / N  is correlated with the signal
f. A coefficient z kJ 1 is the difference of two adjacent coefficients of the original
representation (see (8)). Hence, it differs significantly from zero only if the fragment of the
signal f located at ( 2k / N , 2k  2 / N  ) has a recognizable jump.
By this means at the first step of wavelet transform of the signal f J t  , we succeeded in
extraction of abrupt changes of the shortest duration in the signal. In search for more
extended in time local perturbations we put the smoothed signal f J 1 t  to the same
decomposition procedure as the original one with replacement J to J-1. It is the sum:
f
J 1
t  
f
J 2
t   w J 2 t  .
(9)
We have just passed into the scale J-2. The duration of the corresponding scaling function
 J 2 and the wavelet  J  2 has been doubled again as well as the length of their shifts.
Iterating the procedure m times, we come to the following multiscale representation of the
signal:
f
J
t   w J 1 t   w J 2 t     w J m t   f J m t 
Here f J m t  is a smoothed one to the coarsest (J-m) -scale version of f
of wavelet decomposition is depicted schematically in the Fig.2(a).
( 10 )
J
t  . The process
Actually, wavelet analysis of the signal f J t  in its most limited sense is accomplished at that
moment. Equation (11) yields decomposition of the signal into the sum of the trend f J m t  ,
and the components w J l t , 1  l  m, related to events of various time scales. So, the
addend w J 1 t  comprises events of shortest duration whereas w J m t  represents most
extended ones. The number m of iterations is arbitrary but not exceeding J, of course. Usually,
one chooses this parameter accordingly to the problem under investigation.
Coifman et al. (1992) suggested so-called Wavelet Packet Analysis (WPA) to enrich
remarkably the library of available testing forms without going, actually, beyond techniques
described above. The central idea of the WPA is to analyze not only approximations but also
details. At a certain scale the signal is given as a combination of shifts of all basic waveforms
associated with this scale. Schematically the wavelet packet transform is depicted in Fig. 2(b).
References
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9
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10
Figures captions:
Figure 1 Several different families of wavelets. The number next to the wavelet name
represents the number of vanishing moments. ‘D’ is Daubechies and ‘C’ is Coiflet wavelets.
Figure 2. Seven level of subdivision scheme for frequency band on different levels L and
block numbers Nblock. In the example L=7. On the left a diagram showing designation of
blocks are indicated as minimal frequency on the respect level.
Figure 3. Energy map for 8 decomposition levels of a twoclass problem (top picture. Energy
difference of of classC1 (27 quakes, radius 500km, depth 0-50 km) and class C2 (seismic
‘quiet’ days). The length of a slice is n=1024 samples.
Figure 4. The results of training and classification. The following parameters were used:
Spline6 wavelets; CART classifiers and every 0.5hour design were making. The signals were
decomposed up to the 8th level. As the training signals, we took recordings of 27 days
(‘disturbed’ days, class C1) corresponding to the days with earthquakes in radius 500 km for
0.5 year and 27 ‘quiet’ days of class C2. The signals of the C1 class were January 17 (M=5.6,
05:38UT), March 26 (M=5.6, 05:38UT) and May 13, 1997 (M=5.6, 05:38UT). Distances
from observation point to epicenters and depths of seismic sources are shown on the top
panel. For the signals of C2 class we choose 27 days from 0.5-year recordings. We used all
blocks. For decision we used Classification and Regression TREE (CART) classifiers –
bottom panel. Upper picture in the panel corresponds to the C1 class and bottom to the C2
class.
Figure 5. The following parameters were used for training and classification: Spline6
wavelets; CART and LDA classifiers and every 1hour design were made. The signals were
decomposed up to the 7th level. Recordings of March 25-27 (‘disturbed’ days, class C1) and
March 9-11 (‘quite’ days, class C2) are training signals. Signals of the C1 class submitted to
classification were May 12-14, 1997 (M=5.6, May 13, 05:38). Signals of C2 class were
January 1, February 1 and March 1. In the results presented in the left pictures, there were
used 1:2, 4:6 blocks and in the right picture all blocks. Upper picture in each panel
corresponds to the C1 class and bottom to the C2 class.
Figure 5. LDA classifier and every 0.5hour design were made. The signals were decomposed
by Spline6 wavelets; up to the 7th level. Recordings of March 25-27 (‘disturbed’ days, class
C1) and March 9-11 (‘quite’ days, class C2) are training signals. Signals of the C1 class
submitted to classification were May 12-14, 1997 Upper picture corresponds to the C1 class
and bottom to the C2 class. Signals of C2 class were January 1, February 1 and March 1.
There were used for classification 1st, 2nd, 4th, 5th and 6th wavelet blocks.
Figure 6: Two sequence pulses observed simultaneously by Kagoshima and Kanoya
observatory. The time delay between the first pulses fixed by the both observatories is 3.2
min, and for the second pulses is 6.8 min. The distance between the two observation points is
about 25 km. Thus, the horizontal velocities are 8km/min and 4km/min.
Figure 7. Three level diagram of wavelet transform (WT) (a) and Wavelet Packet Transform
(WPT) (b). ‘A’ with numbers is a low frequency Approximation on the corresponding level
and ‘D’ are the high frequency Details on this level. Reconstructed signal s ' in WT is
s ' =A3+D3+D2+D1 and
s ' =AAA3+DAA3+ADA3+DDA3+AAD3+AAD3+DAD3+ADD3+DDD3 in the WPT.
11
Figure 1.
12
Figure 2.
N=7
f min 
f max  0.5Hz
L=1
2
1
f min  f max / 2
f max
Nblock
2N
f max  0.5Hz
L=2
f min  f max / 4
3
4
5
6
f max  0.5Hz
L=3
7
f min  f max / 8
8
9
10
11
12
13
14
f max  0.5Hz
L=4
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
f min  f max / 16
f max  0.5Hz
L=7
f min  f max / 128
f max  0.5Hz
13
Figure 3.
14
Figure 4.
15
Figure 5.
16
Figure 6.
Kanoya
Kanoya
-0.022
-0.02
-0.023
-0.022
-0.024
-0.024
-0.025
-0.026
-0.026
-0.028
0.9
0.95
1
1.9
Kagoshima
1.95
2
2.05
2.1
Kagoshima
0.05
0
-0.01
0
-0.02
-0.03
-0.05
-0.04
-0.05
-0.1
-0.06
0.9
0.95
1
1.9
2
2.1
17
Figure 7.
S
A1
A2
A3
D1
D2
D3
(a)
S
A1
AA2
AAA3
DAA3
D1
DA2
ADA3
AD2
DDA3
AAD3
DAD3
DD2
ADD3
DDD3
(b)
18