Skopje and Sofia 2005 Earthquake and Geomagnetic data and the Geomagnetic

Quake as Imminent Reliable Earthquake’s Precursor

S. Cht. Mavrodiev1, L. Pekevski2, T. Jimseladze3

1Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,

Sofia, Bulgaria

2 Seismological Observatory, Faculty of Natural Sciences and Mathematics, Skopje,

Macedonia

3 Institute of Geophysics, Georgian Academy of Sciences, Tbilisi, Georgia

Correspondence to: S.Cht.Mavrodiev (mavrodi@inrne.bas.bg)

Abstract.

The imminent regional “when” earthquake’s predictions are based on the correlation between

geomagnetic quakes and the incoming minimum (or maximum) of tidal gravitational

potential. The geomagnetic quake is defined as a jump of day mean value of geomagnetic

field one minute standard deviation measured at least 2.5 times per second. The probability

time window for the incoming earthquake or earthquakes is approximately ± 1 day for the

tidal minimum and for the maximum- ± 2 days. The statistic evidence for reliability of the

geomagnetic precursor is based on the distributions of the time difference between occurred

and predicted earthquakes for the period 2002- 2005 for Sofia region and 2004- 2005 for

Skopje region which lean to the Gaussian behaviour with increasing of the statistic. The

predicted earthquake is identified by the maximum of the function proportional to the density

of the earthquake radiated energy in the monitoring point. The analytical size of this function

as well as one minute time scale for calculating the geomagnetic quake signal was established

by Dubna inverse problem method.

The project for complex regional NETWORK for earthquake prediction by using the reliable

precursors will be proposed in near future. The Project is based on the temporary data

1

acquisition system for preliminary archiving, testing, visualizing and analyzing the data with

aim to prepare regional daily risk estimations.

1 Introduction The problem of “when, where and how” earthquake prediction can not be solved only on

the basis of seismic and geodetic data (Aki, 1995; Pakiser and Shedlock, 1995; Geller et al.,

1997, Main, 1999a, b; Ludwin, 2001).

The possible tidal trigging of the earthquakes has been investigated for a long period of

time (Knopoff, 1964; Tamrazyan, 1967; 1968; Ryabl at al., 1968; Shlien, 1972; Molher, 1980;

Sounau et al., 1982; , Burton, 1986; Shirley, 1988; Bragin, 1999).

The including of additional information in the precursors monitoring, for example, the

analysis of under, on and above Erath surface electromagnetic field variations can define

reliable earthquake precursor and to estimate the most probable time of incoming earthquake.

Sea for example some results and analysis in papers: Hayakawa et all,1999, Eftaxias, 2001;

Hayakawa, Molchanov, 2002; Varotsos et all, 2002, 2003; Dudkin et al, 2003; Telesca et all,

2004; Contoyiannis et all, 2005; Karamanos et al, 2005,

The simultaneous analysis of more accurate space and time measuring set for the Earth’s

crust condition parameters, the including in the monitoring of the electromagnetic fields

measurements under, on and over the Earth surface, the temperature distribution and other

possible precursors and their analysis the basis of nonlinear inverse problem methods can be

promising for the study and solving the “when, where and how” earthquake’s prediction

problem.

In the papers (Mavrodiev, Thanassoulas, 2001; Mavrodiev, 2002 a, b, 2003 a, b, c;

Mavrodiev, 2004) was presented some progress for establishing the geomagnetic filed

variations as regional earthquake precursor. The approach is based on the understanding that

earthquake processes have a complex origin. Without creating of adequate physical model of

the Earth existence, the gravitational and electromagnetic interactions, which ensure the

stability of the Sun system and its planets for a long time, the earthquake prediction problem

can not be solved in reliable way. The earthquake part of the model have to be repeated in the

infinity way “theory- experiment- theory” using nonlinear inverse problem methods looking

for the correlations between fields in dynamically changed space and time scales. Of course,

every approximate model (see for example Varotsos, 1984, a, b, Varotsos et al, 2006;

2

Thanassoulas, 1991; Thanassoulas et al., 2001a, b; Eftaxias at all, 2006, Duma, 2006) which

has some experimental evidence has to be included in the analysis. The adequate physical

understanding of the correlations between electromagnetic precursors, tidal extremums and

incoming earthquake is connected with the progress of the adequate Earth’s magnetism theory

as well as the quantum mechanical understanding of the processes in the earthquake source

volume before and in the time of earthquake.

The achievement of the Earth’s surface tidal potential modeling, which includes the ocean

and atmosphere tidal influences, is an essential part of the research. In this sense the

comparison of the Earth tides analysis programs (Dierks and Neumeyer, ws) for the

ANALYZE from the ETERNA-package, version 3.30 (Wenzel, 1996 a, b), program

BAYTAP-G in the version from 15.11.1999 (Tamura, 1991), Program VAV (version from

April 2002) of Venedikov et al, 2001, 2003 is very useful.

The role of geomagnetic variations as precursor can be explained by the hypothesis that

during the time before the earthquakes, with the strain, deformation or displacement changes

in the crust there arise in some interval of density changing the chemical phase shift which

leads to an electrical charge shift. The preliminary Fourier analysis of geomagnetic field gives

the time period of alteration in minute scale. Such specific geomagnetic variation we call

geomagnetic quake. The last years results from laboratory modelling of earthquake processes

in increasing stress condition at least qualitatively support the quantum mechanic phase shift

explanation for mechanism generating the electromagnetic effects before earthquake and

others electromagnetic phenomena in the time of earthquake (Freund et al, 2002; St-Laurent

et al, 2006, Vallianatos et all, 2003, 2006)

The future epicentre coordinates have to be estimated from at least 3 points of measuring

the geomagnetic vector, using the inverse problem methods, applied for the estimation the

coordinates of the volume, where the phase shift arrived in the framework of its time window.

For example the first work hypothesis can be that the main part of geomagnetic quake is

generated from the vertical Earth Surface- Ionosphere electrical current. Sea also the results of

papers (Vallianatos, Tzanis, 2003 ; Duma, Ruzhin, 2003, Duma, 2006 ) and citations there.

In the case of incoming big earthquake (magnitude > 5 - 6) the changes of vertical

electropotential distribution, the Earth’s temperature, the infrared Earth’s radiation, the

behaviour of debit, chemistry and radioactivity of water sources, the dynamics and

temperature of under waters, the atmosphere conditions (earthquakes clouds, ionosphere

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radioemitions, and etc.), the charge density of the Earth radiation belt, have to be dramatically

changed near the epicentre area- see for example papers … .

The achievements of tidal potential modeling of the Earth’s surface, including ocean and

atmosphere tidal influences, multi- component correlation analysis and nonlinear inverse

problem methods in fluids dynamics and electrodynamics are crucial for every single step of

the constructing of the mathematical and physical models.

In paper (Mavrodiev, 2004) the geomagnetic quake was defined as a jump of day mean

value of signal function Sig:

Sig = Σm=1,M σHm/M, δSig = Σm=1,M δσHm/M, (1)

where σΗm is the standard deviation (its error δσΗ m ) of geomagnetic field component Hm:

σΗ m = sqrt Σι=1,Ν (Ηι−Η m )2/Ν, δσΗ m = sqrt Σι=1,Ν (δΗι−δΗ m )2/Ν,

Hm is one minute averaged value of geomagnetic vector projection Hi, measured 2.4 times per

second:

Η m = Σι=1,Ν Ηι/Ν, δΗ m = Σι=1,Ν δΗι/Ν,

M=1440 (the minutes per day), and samples per minute are N=144.

The geomagnetic vector projection Hi is measured with relative accuracy less or equal to 1

nT by a fluxgate, feedback based device of rather original and simple, but powerful

construction. (know-how of JINR, Dubna, Boris Vasiliev, 1998, private communication). It is

used with 2.4 samples per second. Due to technical reasons the sensor was oriented under the

Horizon in a manner that the measured value of Hi is less than 20 000 nT.

The predicted earthquake is identified by the maximum of the function proportional to the

density of the earthquake radiated energy in the monitoring point. The analytical size of this

function is

SChtM = 10Ml / (D+Depth +Distance)2, (2)

where the distances are in hundred km, fit parameter D = 40 km and Ml is Richter magnitude.

Thus, if we have a jump of signal function Sig and its error δSig is such that satisfy

numerically the next condition (3):

SigToday – SigYesterday > (δSigToday + δSigYesterday) / 2, (3)

4

in the next tidal exstremum time the function SChtM will has a local maximum value. The

earthquake for which the function SChtM has a maximum can be interpreted as predicted

earthquake.

The probability time window for the incoming earthquake or earthquakes is approximately

± 1 day for the tidal minimum and for the maximum- ± 2 days.

The analytical size of the function SChtM as well as one minute time period for calculating

the unique signal for geomagnetic quake which is reliable earthquake precursor was

established by Dubna inverse problem method (Dubna Papers). One could say that this

method is algoritmization of “probe- error” researching of hidden dependences for some time

or space series of experimental data.

In the case of vector geomagnetic monitoring one have to calculate the minute standard

deviation as a geometrical sum of standard deviations of tree geomagnetic vector components:

σΗ m = sqrt ( σΗ m x2 + σΗ m y2 + σΗ m z2) .

The Skopje Seismological Observatory triaxial fluxgate magnetometer is FGE model,

Danish Meteorological Institute, with year sensors drift less then a few nT and temperature

coefficient less or equal to 0.25 nT/C0. The magnetometer is used in variometer mode with

resolution 0.2 nT, 10 samples/sec.

The statistic evidence for the reliability of geomagnetic precursor is based on the

distribution of the time difference between occurred and predicted earthquakes. The

geomagnetic and earthquake monitoring for Sofia (2002- 2005) and Skopje region (2004-

2005) demonstrates that both distributions lean to the Gaussian behaviour with increasing of

the statistic.

One can say that the data support the evidence that the geomagnetic quake is reliable

imminent precursor for incoming earthquake or earthquakes in the region- “when” regional

earthquake prediction.

The distance sensibility of the approach can not be estimated uniquely on the basis of one

point geomagnetic monitoring or, as in our case, by two but different magnetometers. One of

the reasons is that the tidal behaviour is almost the same for distances till 1000 km in parallel

direction for time scale one day.

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The solving of distance sensibility problem can be performed on the basis of at least tree

stationary and one mobile devices for vector geomagnetic field measuring which fulfil the

INTERMAGNET standards but with at least 10 samples per second. The data acquisition

system has to include the almost real time frequency analysis (Fourier analysis) for

establishing the characteristics of geomagnetic quake.

Eq data

There was analyzed earthquakes data in region with latitude (370, 410) and longitude

(150, 310) for 2005, reported in USGS, NEIC: earthquake search results, Catalog- PDE,

magnitude range from 3.0 to 9.0, data selection- historical & preliminary data- 705

earthquakes. The next map illustrates the region and data (source

http://www.iris.edu/quakes/eventsrch.htm :

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There are reported 2007 data for 705 earthquakes because IRIS catalogue contains all types of

measured for one earthquake magnitudes.

The next Figures 1, 2, 3 illustrate the distributions of earthquake’s magnitudes, depth and the

difference between tidal extremum date and time of occurred earthquakes with magnitude

grater then 3.

Fig.1. The magnitude distribution

Fig.2. The earthquake’s depth distribution

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Fig. 3. The distribution of time difference between tidal extremum date and time of occurred

earthquakes with magnitude grater then 3

Analysis

The next two Tables contains the monitoring data for Skopje and Sofia and its analysis,

described above, which illustrate that the geomagnetic quake is regional reliable earthquake

precursor. The columns are the number of signal before the incoming tidal extremum data,

information for the tidal minimum (1) or maximum (2), the data of tidal extremum, the time

of occurred earthquake, latitude [degree], longitude [degree], depth [km], magnitude, type of

magnitude, station, distance from monitoring point [100 km], value of function (2) [J/km2],

the difference between the date of tidal exstremum and the time of occurred earthquake

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[day]. The table consist a data for the earthquake with magnitude grater then 3 and with

energy “density” grater then 200.

In Skopje table the number of empty sells in Signal time column is 8 for 5 tidal extremums.

The reasons for lost predictions are the device or communication problems.

Skopje

Number

of

signals

Tidal min,

max

Signal

Time

Tidal min, max

time

Eq time Lat Lon Dept

[km]

Mag Type Station Distance

[100 km]

SChtM Time

difference

[Day]

2 1 12/30/2004 1/2/2005 12:00 12/30/2004 7:35 39.1 22.3 98 4.4 MD PDG 3.18 1207 3.18

2 1 12/30/2004 1/2/2005 12:00 1/2/2005 1:24 41.1 20.2 10 3.5 MD ATH 1.36 911 0.44

2 2 1/4/2005 1/9/2005 12:00 1/10/2005 23:48 37 27.8 15 5.5 Mw HRV 7.7 4646 -1.49

2 2 1/4/2005 1/9/2005 12:00 1/10/2005 23:50 37 27.9 10 5 mb GS 7.77 1461 -1.49

2 1 1/11/2005 1/16/2005 12:00 1/16/2005 3:21 40.1 19.7 24 3.8 MD ATH 2.49 644 0.36

1 2 1/17/2005 1/23/2005 12:00 1/26/2005 15:04 37.6 22 15 4 ML ATH 4.79 350 -3.13

4 1 1/29/2005 1/31/2005 12:00 1/31/2005 1:05 37.5 20.2 31 5.7 Mw GS 4.99 15434 0.45

2 2/6/2005 12:00 2/5/2005 22:04 39.1 20.6 5 4.1 mb GS 3.18 953 0.58

4 1 2/7/2005 2/14/2005 12:00 2/12/2005 12:13 39.9 19.7 0 4.6 ML ATH 2.65 4278 1.99

4 1 2/7/2005 2/14/2005 12:00 2/14/2005 0:44 41.9 23 10 3.6 MD ATH 1.29 1242 0.47

2 2 2/16/2005 2/21/2005 12:00 2/19/2005 11:49 38.7 20.7 5 3.7 MD ATH 3.67 295 2.01

2 1 2/25/2005 2/28/2005 12:00 3/3/2005 2:43 40.8 20.9 18 3.2 MD ATH 1.38 414 -2.61

1 2 3/5/2005 3/6/2005 12:00 3/3/2005 7:19 45.6 26.7 113 4.5 mb GS 5.85 580 3.2

1 2 3/5/2005 3/6/2005 12:00 3/10/2005 0:57 41.4 19.2 36 3.6 MD ATH 1.94 546 -3.54

2 1 3/6/2005 3/15/2005 12:00 3/11/2005 11:05 42.4 19.9 10 4.5 ML CSEM 1.37 9056 4.04

1 2 3/16/2005 3/18/2005 12:00 3/19/2005 3:26 41.3 22.4 13 3.5 MD ATH 0.99 1364 -0.64

1 1 3/21/2005 3/22/2005 12:00 3/22/2005 18:30 39.8 19.9 12 4.1 ML ATH 2.71 1210 -0.27

4 2 3/24/2005 4/1/2005 12:00 4/3/2005 21:34 41.1 20.8 20 3.3 MD ATH 1.09 695 -2.4

1 1 4/4/2005 4/5/2005 12:00 4/5/2005 20:49 40.6 23.8 24 3.4 MD ATH 2.46 261 -0.37

1 1 4/4/2005 4/5/2005 12:00 4/6/2005 1:26 40.6 23.7 21 3.4 MD ATH 2.42 274 -0.56

1 2 4/5/2005 4/11/2005 12:00 4/10/2005 13:37 39.2 21.6 23 3.9 MD ATH 3.02 598 0.93

1 2 4/5/2005 4/11/2005 12:00 4/13/2005 18:52 41.5 22.7 24 3.5 MD ATH 1.15 988 -2.29

1 1 4/11/2005 4/19/2005 12:00 4/20/2005 7:52 40.8 22.9 24 4.1 ML ATH 1.71 2280 -0.83

3 2 4/20/2005 4/27/2005 12:00 4/26/2005 21:20 41.9 20.9 10 3 ML SKO 0.49 1025 0.61

2 1 4/30/2005 5/3/2005 12:00 5/5/2005 3:22 41.1 20.3 10 3.2 MD ATH 1.31 484 -1.64

3 2 5/4/2005 5/9/2005 12:00 5/8/2005 21:20 40.8 20.2 10 3.7 MD ATH 1.67 1064 0.61

3 2 5/6/2005 5/9/2005 12:00 5/11/2005 10:05 39.4 20.6 19 4.1 mb GS 2.86 1056 -1.92

1 1 5/11/2005 5/17/2005 12:00 5/14/2005 1:53 45.7 26.4 148 5.2 Mw HRV 5.8 2687 3.42

1 1 5/11/2005 5/17/2005 12:00 5/19/2005 23:19 42.7 19 22 4.6 ML ZAMG 2.24 4883 -2.47

1 2 5/23/2005 5/25/2005 12:00 5/24/2005 5:50 37.6 20.9 18 4.2 MD ATH 4.85 538 1.26

2 1 5/28/2005 5/31/2005 12:00 5/29/2005 8:55 38.3 22.7 104 5 MD PDG 4.2 3142 2.13

2 1 5/28/2005 5/31/2005 12:00 5/30/2005 19:51 41.3 21.1 12 3.6 MD ATH 0.78 2350 0.67

1 2 6/4/2005 6/7/2005 12:00 6/5/2005 23:40 40.1 19.4 26 3.5 MD ATH 2.61 296 1.51

1 2 6/4/2005 6/7/2005 12:00 6/7/2005 9:09 40.1 19.7 33 3.7 MD ATH 2.46 493 0.12

2 1 6/12/2005 6/15/2005 12:00 6/11/2005 3:38 40.6 19.6 5 4.4 ML ATH 2.13 3784 4.35

2 1 6/15/2005 6/15/2005 12:00 6/17/2005 5:33 41.9 19.7 11 3.8 ML PDG 1.46 1633 -1.73

3 2 6/16/2005 6/22/2005 12:00 6/18/2005 15:16 45.7 26.7 138 4.8 mb GS 5.96 1052 3.86

3 2 6/16/2005 6/22/2005 12:00 6/18/2005 16:13 38.9 21.2 25 4.4 ML PDG 3.4 1528 3.82

2 1 6/25/2005 6/28/2005 12:00 6/30/2005 19:44 41.9 20.4 6 3.5 ML PDG 0.85 1835 -2.32

1 2 7/1/2005 7/5/2005 12:00 7/3/2005 23:44 42.7 17.4 5 4.5 mb GS 3.45 2076 1.51

1 2 7/1/2005 7/5/2005 12:00 7/4/2005 4:30 42 21.5 16 3.1 ML SKO 0.1 2891 1.31

3 1 7/9/2005 7/13/2005 12:00 7/10/2005 13:10 42.4 19.8 4 5.5 ML CSEM 1.44 89006 2.95

3 2 7/16/2005 7/20/2005 12:00 7/20/2005 19:08 42.4 19.8 10 3.1 ML PDG 1.47 325 -0.3

3 2 7/17/2005 7/20/2005 12:00 7/21/2005 1:33 39.8 20.4 25 3.5 MD ATH 2.51 317 -0.56

9

2 1 7/24/2005 7/27/2005 12:00 7/25/2005 2:34 41.9 21.9 10 4 MD ATH 0.37 13064 2.39

2 1 7/24/2005 7/27/2005 12:00 7/30/2005 3:50 41.8 21.9 15 3.5 MD ATH 0.37 3739 -2.66

2 2 8/28/2005 8/3/2005 12:00 8/1/2005 10:42 41.8 21.9 15 3.5 MD ATH 0.37 3739 2.05

2 2 8/28/2005 8/3/2005 12:00 8/4/2005 5:47 39 23.4 4 4.4 mb GS 3.66 1492 -0.74

1 1 8/6/2005 8/11/2005 12:00 8/12/2005 18:53 40.2 19.2 13 4.2 MD ATH 2.64 1578 -1.29

3 2 8/13/2005 8/17/2005 12:00 8/14/2005 0:46 40 24.3 28 3.8 ML ATH 3.15 430 3.47

3 2 8/17/2005 8/17/2005 12:00 8/19/2005 18:34 44.9 25.3 10 3.9 ML BUC 4.57 309 -2.27

1 1 8/20/2005 8/24/2005 12:00 8/24/2005 3:06 39.7 25.6 29 4.7 ML ATH 4.26 2045 0.37

2 2 8/24/2005 8/31/2005 12:00 8/30/2005 17:39 39.1 27.9 16 4.2 ML ISK 6.26 340 0.76

2 1 9/1/2005 9/8/2005 12:00 9/5/2005 14:23 45.8 26.8 98 4.9 MD IRSA 6.1 1418 2.9

2 1 9/2/2005 9/8/2005 12:00 9/8/2005 16:35 45.5 26.4 139 4.8 MD IRSA 5.64 1143 -0.19

2 1 9/2/2005 9/8/2005 12:00 9/10/2005 9:58 41.4 21 18 3.4 MD ATH 0.7 1544 -1.92

3 2 9/8/2005 9/14/2005 12:00 9/12/2005 19:08 40.7 23.4 24 4.3 ML ATH 2.08 2689 1.7

3 2 9/8/2005 9/14/2005 12:00 9/12/2005 19:26 40.7 23.4 19 4 ML ATH 2.1 1384 1.69

3 2 9/10/2005 9/14/2005 12:00 9/15/2005 3:30 39.7 21 14 4.1 mb GS 2.49 1372 -0.65

1 1 9/15/2005 9/15/2005 12:00 9/16/2005 1:52 39.6 24 10 3.5 ML THE 3.38 211 -0.58

1 2 9/16/2005 9/16/2005 12:00 9/16/2005 8:08 38.1 20.3 10 4.8 ML PDG 4.35 2679 0.16

1 2 9/16/2005 9/16/2005 12:00 9/17/2005 18:43 41.3 20 1 4.1 ML THE 1.41 3821 -1.28

1 1 9/21/2005 12:00 9/19/2005 22:17 38 20.2 15 4.7 ML THE 4.42 2029 1.57

1 1 9/21/2005 12:00 9/20/2005 13:14 38.2 20.3 15 4 mb GS 4.26 432 0.95

1 1 9/21/2005 12:00 9/21/2005 6:09 39.4 20.5 5 4 ML ATH 2.9 889 0.24

1 2 9/22/2005 12:00 9/22/2005 8:23 40.1 21.8 5 3.2 MD ATH 2.05 254 0.15

1 2 9/22/2005 12:00 9/24/2005 7:23 40 21.1 5 3.3 MD ATH 2.15 296 -1.81

3 1 9/24/2005 9/28/2005 12:00 9/27/2005 0:25 43.2 18.2 19 5.1 ML BUC 2.99 9825 1.48

4 2 10/4/2005 10/10/2005 12:00 10/9/2005 7:12 40.7 23.4 0 3.9 ML THE 2.09 1279 1.2

1 1 10/13/2005 12:00 10/16/2005 7:01 41.6 22.7 7 3.5 MD ATH 1.06 1346 -2.79

1 2 10/14/2005 10/19/2005 12:00 10/17/2005 5:45 38.1 26.5 8 5.7 ML ISK 6.02 11879 2.26

1 2 10/14/2005 10/19/2005 12:00 10/17/2005 9:46 38.2 26.5 10 5.8 Mw GS 5.96 15121 2.09

1 2 10/14/2005 10/19/2005 12:00 10/18/2005 15:26 37.6 20.9 14 5.6 Mw HRV 4.79 14026 0.86

1 2 10/14/2005 10/19/2005 12:00 10/20/2005 21:40 38.2 26.8 10 5.9 Mw GS 6.15 17941 -1.4

4 1 10/22/2005 10/27/2005 12:00 10/25/2005 23:23 40.7 22.7 10 3.4 ML THE 1.75 495 1.53

4 1 10/27/2005 10/27/2005 12:00 10/29/2005 14:48 38.1 26.6 14 4.5 ML ISK 6.12 712 -2.12

2 2 10/31/2005 11/4/2005 12:00 11/1/2005 19:53 41.1 20.4 0 4.4 ML SKO 1.25 9241 2.67

2 2 10/31/2005 11/4/2005 12:00 11/1/2005 19:53 41.1 20.4 0 4.2 ML SKO 1.25 5831 2.67

1 1 11/10/2005 12:00 11/10/2005 8:56 40.5 21.9 16 3.7 MD ATH 1.59 1083 0.13

1 2 11/14/2005 11/16/2005 12:00 11/15/2005 5:51 40.2 25.4 27 4.4 ML THE 3.79 1263 1.26

3 1 11/18/2005 11/25/2005 12:00 11/20/2005 21:24 43.2 21.1 11 4 mb GS 1.51 2450 4.61

3 1 11/19/2005 11/25/2005 12:00 11/26/2005 20:05 43.8 21.8 25 4 mb GS 2.15 1272 -1.34

3 2 11/29/2005 12/2/2005 12:00 12/3/2005 7:49 45.9 27.3 30 4.7 MD IRSA 6.4 994 -0.83

3 2 11/30/2005 12/2/2005 12:00 12/4/2005 4:13 40.3 20.7 13 4.2 ML ATH 1.88 2738 -1.68

1 1 12/9/2005 12/9/2005 12:00 12/10/2005 3:20 41.9 20.1 11 3.4 ML PDG 1.09 979 -0.64

3 2 12/11/2005 12/15/2005 12:00 12/13/2005 12:14 45.8 26.8 144 5.2 MD IRSA 6.06 2540 1.99

3 2 12/11/2005 12/15/2005 12:00 12/14/2005 10:35 45.7 26.7 130 5 UK BUC 5.93 1718 1.06

3 1 12/23/2005 12/23/2005 12:00 12/26/2005 5:53 41.3 20 2 4.2 ML PDG 1.38 4918 -2.75

3 2 12/29/2005 12/31/2005 12:00 1/2/2006 3:41 37.8 20 19 4 ML ATH 4.69 359 -1.65

The next Table contains the monitoring data for Sofia and its analysis, described above, which

illustrate that the geomagnetic quake is regional reliable earthquake precursor. The number of

empty sells in Signal time column is 11 for 8 tidal extremums. The reasons for lost

predictions was only the device problems.

10

Sofia

Numb

er of

signals

Tidal min,

max

Signal date Tidal min, max

time

Eq time Lat Lon Dept

[km]

Mag Type Station Distance

[100

km]

SChtM Time

difference

[Day]

1 12/27/2004 1/2/2005 12:00 1/2/2005 1:24 41.1 20.21 10 3.5 MD ATH 2.89 276 0.44

1 12/27/2004 1/2/2005 12:00 1/3/2005 21:44 37.64 23.33 123 4.5 mb GS 5.28 662 -1.41

1 2 1/4/2005 1/9/2005 12:00 1/10/2005 23:48 37.02 27.8 15 5.5 Mw HRV 7.13 5358 -1.49

2 1 1/10/2005 1/16/2005 12:00 1/13/2005 11:00 39.12 27.73 10 4.3 ML ATH 5.25 604 3.04

2 1/17/2005 1/23/2005 12:00 1/20/2005 23:27 38.66 27.14 17 4 ML ISK 5.3 290 2.52

2 2 1/21/2005 1/23/2005 12:00 1/26/2005 15:04 37.62 22.02 15 4 ML ATH 5.4 282 -3.13

1 1/27/2005 1/31/2005 12:00 1/31/2005 1:05 37.53 20.16 31 5.7 Mw GS 6 11125 0.45

2 -- 2/6/2005 12:00 2/5/2005 22:04 39.11 20.64 5 4.1 mb GS 4.25 570 0.58

1 2/14/2005 2/14/2005 12:00 2/14/2005 0:44 41.9 23 10 3.6 MD ATH 0.58 3425 0.47

3 2/14/2005 2/14/2005 12:00 2/14/2005 4:04 41.95 23.08 17 3.6 d Sof 0.51 3440 0.33

1 2 2/16/2005 2/21/2005 12:00 2/25/2005 13:05 42.99 26.64 7 3.8 ML BUC 2.86 568 -4.05

1 2/22/2005 2/28/2005 12:00 3/3/2005 7:19 45.55 26.71 113 4.5 mb GS 4.48 876 -2.8

2 -- 3/6/2005 12:00 3/10/2005 1:21 42.4 21.76 16 3.5 d Sof 1.21 1012 -3.56

4 1 3/3/2005 3/15/2005 12:00 3/11/2005 11:05 42.39 19.91 10 4.5 ML CSEM 2.73 3038 4.04

1 3/11/2005 3/15/2005 12:00 3/16/2005 22:11 41.98 23.25 8 3.1 d Sof 0.46 1434 -1.42

1 3/21/2005 3/22/2005 12:00 3/21/2005 3:17 41.41 22.72 23 3.3 MD ATH 1.17 616 1.36

2 3/28/2005 4/1/2005 12:00 4/4/2005 18:59 45.38 26.48 115 4.2 UK BUC 4.22 476 -3.29

1 4/4/2005 4/5/2005 12:00 4/6/2005 1:26 40.58 23.73 21 3.4 MD ATH 2.05 354 -0.56

2 1 4/12/2005 4/19/2005 12:00 4/20/2005 7:52 40.83 22.9 24 4.1 ML ATH 1.76 2192 -0.83

2 4/22/2005 4/27/2005 12:00 4/26/2005 23:13 39.3 21.14 26 4.1 MD ATH 3.86 617 0.53

1 5/29/2005 5/3/2005 12:00 5/2/2005 21:31 40.18 24.35 2 3.6 Md Sof 2.63 428 0.6

2 5/9/2005 5/9/2005 12:00 5/11/2005 10:05 39.41 20.62 19 4.1 mb GS 3.97 605 -1.92

2 5/9/2005 5/9/2005 12:00 5/11/2005 10:20 39.41 20.66 0 3.9 ML THE 3.95 419 -1.93

1 5/11/2005 5/17/2005 12:00 5/14/2005 1:53 45.68 26.44 148 5.2 Mw HRV 4.46 3938 3.42

1 5/13/2005 5/17/2005 12:00 5/19/2005 23:20 42.36 21.72 2 4 Md Sof 1.24 3622 -2.47

2 5/20/2005 5/25/2005 12:00 5/22/2005 23:07 41.76 23.06 17 3.2 MD ATH 0.72 959 2.54

2 5/20/2005 5/25/2005 12:00 5/24/2005 5:50 37.57 20.88 18 4.2 MD ATH 5.72 399 1.26

2 5/25/2005 5/31/2005 12:00 5/29/2005 8:55 38.26 22.73 104 5 MD PDG 4.61 2732 2.13

3 1 5/26/2005 5/31/2005 12:00 5/30/2005 19:51 41.27 21.05 12 3.6 MD ATH 2.19 540 0.67

2 2 6/1/2005 6/7/2005 12:00 6/7/2005 9:09 40.14 19.68 33 3.7 MD ATH 3.88 236 0.12

2 6/6/2005 6/7/2005 12:00 6/11/2005 3:38 40.58 19.61 5 4.4 ML ATH 3.62 1513 -3.65

1 6/11/2005 6/15/2005 12:00 6/18/2005 15:16 45.71 26.69 138 4.8 mb GS 4.61 1546 -3.14

1 6/11/2005 6/15/2005 12:00 6/18/2005 16:13 38.85 21.24 25 4.4 ML PDG 4.28 1034 -3.18

2 6/20/2005 6/22/2005 12:00 6/21/2005 23:06 37.18 20.79 18 4.3 ML ATH 6.15 440 0.54

2 6/20/2005 6/22/2005 12:00 6/23/2005 22:44 37.76 26.7 19 4.3 ML THE 5.93 469 -1.45

3 1 6/24/2005 6/28/2005 12:00 6/30/2005 19:44 41.88 20.41 6 3.5 ML PDG 2.39 388 -2.32

2 6/29/2005 7/5/2005 12:00 7/3/2005 23:44 42.68 17.37 5 4.5 mb GS 4.81 1143 1.51

2 7/1/2005 7/5/2005 12:00 7/7/2005 1:40 41.69 23.19 16 3.4 MD ATH 0.78 1399 -1.57

1 7/11/2005 7/13/2005 12:00 7/10/2005 13:10 42.39 19.81 4 5.5 ML CSEM 2.81 29967 2.95

1 7/22/2005 7/27/2005 12:00 7/25/2005 2:34 41.87 21.89 10 4 MD ATH 1.25 3272 2.39

4 1 7/22/2005 7/27/2005 12:00 7/25/2005 4:38 37.37 21.01 26 4.7 mb GS 5.89 1167 2.31

1 7/22/2005 7/27/2005 12:00 7/25/2005 13:43 41.99 21.93 42 3.6 MD ATH 1.16 1015 1.93

1 7/22/2005 7/27/2005 12:00 7/28/2005 14:38 40.83 20.24 9 4.1 mb GS 3.03 1015 -1.11

1 7/25/2005 7/27/2005 12:00 7/29/2005 1:58 41.88 22.03 10 3.5 MD ATH 1.14 1173 -1.58

11

2 7/31/2005 8/3/2005 12:00 8/4/2005 5:47 38.97 23.4 4 4.4 mb GS 3.8 1395 -0.74

2 8/1/2005 8/3/2005 12:00 8/4/2005 7:50 41.93 23.08 8 3.3 Md Sof 0.53 1966 -0.83

1 8/5/2005 8/11/2005 12:00 8/12/2005 18:53 40.24 19.2 13 4.2 MD ATH 4.13 731 -1.29

2 8/14/2005 8/17/2005 12:00 8/18/2005 17:42 41.64 24 12 3.2 MD ATH 1.05 645 -1.24

1 8/19/2005 8/24/2005 12:00 8/24/2005 3:06 39.68 25.56 29 4.7 ML ATH 3.59 2737 0.37

1 2 8/30/2005 8/30/2005 12:00 8/30/2005 17:39 39.14 27.9 16 4.2 ML ISK 5.34 456 -0.24

1 1 9/1/2005 9/8/2005 12:00 9/5/2005 14:23 45.82 26.79 98 4.9 MD IRSA 4.75 2113 2.9

1 9/1/2005 9/8/2005 12:00 9/8/2005 16:35 45.53 26.36 139 4.8 MD IRSA 4.29 1705 -0.19

1 2 9/13/2005 9/14/2005 12:00 9/12/2005 19:08 40.72 23.37 24 4.3 ML ATH 1.86 3192 1.7

1 -- 9/15/2005 12:00 9/15/2005 3:30 39.7 20.96 14 4.1 mb GS 3.55 754 0.35

2 -- 9/16/2005 12:00 9/16/2005 8:08 38.1 20.25 10 4.8 ML PDG 5.4 1814 0.16

1 -- 9/21/2005 12:00 9/19/2005 22:17 38.04 20.24 15 4.7 ML THE 5.46 1387 1.57

2 -- 9/22/2005 12:00 9/21/2005 6:09 39.4 20.48 5 4 ML ATH 4.05 494 1.24

1 -- 9/28/2005 12:00 9/27/2005 0:25 43.15 18.2 19 5.1 ML BUC 4.19 5509 1.48

2 9/29/2005 10/10/2005 12:00 10/9/2005 7:12 40.72 23.36 8 4 Md Sof 1.86 1826 1.2

1 1 10/13/2005 10/13/2005 12:00 10/13/2005 6:42 40.96 24.31 0 3.2 MD ATH 1.82 320 0.22

1 10/13/2005 10/13/2005 12:00 10/16/2005 7:01 41.64 22.67 7 3.5 MD ATH 0.95 1558 -2.79

1 2 10/17/2005 10/19/2005 12:00 10/17/2005 5:45 38.13 26.5 8 5.7 ML ISK 5.49 14080 2.26

2 10/17/2005 10/19/2005 12:00 10/17/2005 9:46 38.2 26.5 10 5.8 Mw GS 5.42 18013 2.09

2 10/17/2005 10/19/2005 12:00 10/18/2005 15:26 37.62 20.92 14 5.6 Mw HRV 5.65 10373 0.86

2 10/17/2005 10/19/2005 12:00 10/20/2005 21:40 38.15 26.75 10 5.9 Mw GS 5.58 21507 -1.4

1 10/24/2005 10/27/2005 12:00 10/31/2005 5:26 38.16 26.58 8 4.8 ML ISK 5.49 1769 -3.73

2 -- 11/5/2005 12:00 11/1/2005 19:53 41.1 20.4 0 4.4 ML SKO 2.75 2529 3.67

2 -- 11/5/2005 12:00 11/7/2005 16:37 41.7 23.3 5 3.3 MD ATH 0.77 1341 -2.19

1 -- 11/10/2005 12:00 11/11/2005 7:24 40.31 25.29 17 3.9 MD ATH 2.88 667 -0.81

2 11/14/2005 11/16/2005 12:00 11/15/2005 5:51 40.22 25.37 27 4.4 ML THE 3 1864 1.26

1 11/21/2005 11/25/2005 12:00 11/26/2005 20:05 43.83 21.8 25 4 mb GS 1.98 1450 -1.34

2 -- 12/2/2005 12:00 12/3/2005 7:49 45.85 27.27 30 4.7 MD IRSA 5.01 1535 -0.83

3 1 12/5/2005 12/9/2005 12:00 12/7/2005 19:11 40.12 24.09 7 3.5 ML THE 2.62 330 1.7

1 12/5/2005 12/9/2005 12:00 12/10/2005 3:20 41.9 20.12 11 3.4 ML PDG 2.62 256 -0.64

1 12/8/2005 12/15/2005 12:00 12/13/2005 12:14 45.74 26.62 132 4.9 mb GS 4.6 1988 1.99

2 2 12/12/2005 12/15/2005 12:00 12/14/2005 10:35 45.69 26.66 130 5 UK BUC 4.58 2539 1.06

3 1 12/19/2005 12/23/2005 12:00 12/19/2005 17:48 39.12 20.88 18 4.6 mb GS 4.14 1788 3.76

1 12/19/2005 12/23/2005 12:00 12/24/2005 0:14 39.01 23.33 23 4.3 ML ATH 3.76 1036 -0.51

1 12/22/2005 12/23/2005 12:00 12/24/2005 3:56 38.81 27.74 16 4.6 ML ISK 5.5 1082 -0.66

1 12/23/2005 12/23/2005 12:00 12/26/2005 5:53 41.3 20 2 4.2 ML PDG 2.94 1406 -2.75

1 2 12/28/2005 12/30/2005 12:00 1/2/2006 3:41 37.84 19.99 19 4 ML ATH 5.76 248 -2.65

In the next Fig.4 up to down the daily and hour behaviour of the tidal potential,

earthquake’s energy “density” SChtM, magnitude, distance from Sofia (vertical lines from the

magnitude) and function Sig are presented as they are published in the directory “Every day

monitoring” of the website “Earthquake prediction using reliable earthquake precursors-

http://theo.inrne.bas.bg/~mavrodi/” for the period October- November, 2005. As is it seen that

12

after fulfilling the condition (3) in the next tidal extremum there is occurring event in the

region, which is identifying by the maximum of function (3).

For convenience to test the predictions in the website directory “Monthly monitoring” are

presented the functions Hm, its daily averaged value and Sig- Fig. 5.

Fig.4. The reliability of the time window prediction for incoming earthquake October-

December, 2005, Sofia region.

Fig.5. The “monthly monitoring” figure- October, 2005, Sofia region.

In the next Fig.6 up to down the daily behaviour of geomagnetic vector components,

the daily and hour behaviour of the tidal potential, earthquake’s energy density SChtM,

13

magnitude, distance from Skopje and function Sig are presented as they are published in the

directory “Every day monitoring” of the website “Earthquake prediction using reliable

earthquake precursors- http://theo.inrne.bas.bg/~mavrodi/” for the period October- November,

2005. As is it seen that after fulfilling the condition (3) in the next tidal extremum there is

occurring event in the region, which is identifying by the maximum of function (3).

For convenience to test the predictions in the directory “Monthly monitoring” are

presented the functions Hm, its daily averaged value and Sig- Fig. 7.

.

Fig.6. The reliability of the time window prediction for incoming earthquake- June- October,

2005, Skopje.

Fig.7. The “monthly monitoring” figure- October, 2005, Skopje.

14

The next Fig.8. present the distribution of the difference between predicted tidal exstremum

data and the date of occurred earthquakes in the region identified as predicted from the

condition for local time maximum of function SChtM:

Fig.8.

The comparison of time distributions presented in Fig.3 for all occurred in the region

earthquakes and in Fig. 8. for Skopje and Sofia as well as its Chi2 and wide is in support the

geomagnetic quake is reliable time precursor for impending earthquake or earthquakes in the

region.

The next Fig.9. present the time distribution for all occurred earthquakes in the region

earthquake with conditions SChtM>200 and magnitude >3.

Fig.9.

15

The next Fig.10. present the SChtM and magnitude distribution for all occurred in the region

earthquake as function of distance from the monitoring point with SChtM>200 and magnitude

>3.

Fig.10.

The comparison of the distributions in Fig.10. and Fig.11. can give some presentation for

distance and magnitude sensibility of the geomagnetic approach.

Fig.11.

One have to stress that the solving the problem of distance and magnitude sensibility of the

geomagnetic approach using the inverse methods can be performed uniquely on the basis of at

least triangle (100- 200 km) stationary geomagnetic monitoring set plus one mobile.

16

The next Fig.12. present the comparison of the numbers of all and predicted earthquakes for

Sofia and Skopje. It is seen that all occurred earthquakes with magnitude grater then 5 was

predicted.

Fig.12.

The next Fig.13. present the map graphic for earthquakes with magnitude grater then 5

predicted simultaneously from Skopje and Sofia measurements.

Fig.13.

The confirmation of one geomagnetic component Sofia data from the vector Skopje results

for reliability time window earthquake prediction can be consider as a first step for solution of

17

“when, where and how” earthquake prediction at level “when”. It is obvious that the occurred

in the predicted time period earthquake with maximum value of function SChtM (proportional

to the Richter energy density in the monitoring point) is the predicted earthquake. But some

times there are more then one geomagnetic signals in one day or some in different days. It is

not possible to perform unique interpretation and to choose the predicted earthquakes between

some of them with less values of energy density. The solution of this problem can be given by

the analysis of the vector geomagnetic monitoring data in at least 3 points, which will permit

to start solving the inverse problem for estimation the coordinates of geomagnetic quake

source as function of geomagnetic quake. The numbering of powers of freedom for estimation

the epicenter, depth, magnitude and intensity (maximum values of accelerator vector and its

dangerous frequencies) and the number of possible earthquake precursors show that the

nonlinear system of inverse problem will be overdeterminated.

Thus, the first prove, that in the framework of such complex approach, the “when, where

and how” earthquake prediction problem can be solve will be the “when, where” prediction

on the basis of at least 3 points for electromagnetic real time monitoring is essential. If the

statistic estimation will be successful for a long enough period of time (6-12 months) and the

established correlations are confirmed by the adequate physical model solutions, one could

say that the earthquake prediction problem is under solving using the electromagnetic quake

precursor.

Experimentally, the first attempts for estimation of the future epicenter can be performed

on the basis of isolines distribution of geomagnetic quake and electropotential data set as well

as by using the VAN and radio data.

Theoretically, the simplest model for starting to solve the inverse problem is to estimate

the coordinates of vertical Earth surface – Ionosphere electrical current which is generated by

the geomagnetic quake. Such type of modeling has to be performed step by step by including

the volume of solid state phase shifts and frequency characteristics like function of stress,

depth and geology.

The posteriori analysis for England, Alaska, India, Kamchatka, Hokkaido regions on the

basis of second vector Intermagnet data [INTERMAGNET, WS], also confirm the reliability

of geomagnetic quake as imminent earthquake precursors (Mavrodiev 2003 a, b, 2004).

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3. Conclusion

The correlations between the local geomagnetic quake and incoming earthquakes, which

occur in the time window defined from tidal minimum (± 1 day) or maximum (± 2 days) of

the Earth tidal gravitational potential are tested statistically. The distribution of the time

difference between predicted and occurred events is going to be Gaussian with the increasing

of the statistics.

This result can be interpreted as first reliable approach for solving the “when” earthquakes

prediction problem using the geomagnetic data.

Acknowledgement: Thanks to Cht. S. Mavrodiev and I. Angelov for technical support. The

financial support from Bulgarian Scientific Fund (contract BM-9/2005) is highly appreciated

from moral point of view.

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