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This research presents one possible way for imminent prediction of earthquakes’ magnitude, depth and epicenter coordinates by solving the inverse problem using a data acquisition network system for monitoring, archiving and complex analysis of geophysical variables-precursors. Among many possible precursors the most reliable are the geoelectromagnetic field, the boreholes water level, radon earth-surface concentration, the local heat flow, ionosphere variables, low frequency atmosphere and Earth core waves. The title demonstrates that only geomagnetic data are used in this study. Within the framework of geomagnetic quake approach it is possible to perform an imminent regional seismic activity forecasting on the basis of simple analysis of geomagnetic data which use a new variable SChtM with dimension surface density of energy. Such analysis of Japan Memambetsu, Kakioka, Kanoya INTERMAGNET stations and NEIC earthquakes data, the hypothesis that the “predicted” earthquake is this with biggest value of the variable SChtM permits to formulate an inverse problem (overdetermined algebraic system) for precursor’s signals like a function of earthquake’s magnitude, depth and distance from a monitoring point. Thus, in the case of data acquisition network system existence, which includes monitoring of more than one reliable precursor variables in at least four points distributed within the area with a radius of up to 700 km, there will be enough algebraic equations for calculation of impending earthquake’s magnitude, depth and distance, solving the overdetermined algebraic system.

It is well known now that the “when, where and how” earthquake’s prediction problem cannot be solved by a only analyzing the earthquakes data base [

The role of the Sun-Moon Earth tides as possible earthquake’s trigger has been analyzed in [

The role of the atmospheric and ionosphere electromagnetic phenomena which can serve as earthquake’s precursors in the last time has been researched in many studies. Physical models of the observed phenomena were proposed in [

The heat released as earthquake’s precursor was researched in [

The variations of regional water-level reflect fast deformational cycles in lithosphere and may also serve as an earthquake’s precursor as one was demonstrated by G.S. Vartanyan [

The analysis of data for radon concentrations and its fluctuations in the atmosphere and ground-water has been demonstrated in many studies (see [

The research of the correlation between variations of geo-electromagnetic field and impending earthquakes has a long-time history [

A comparative analysis of the two measured values in time of geomagnetic field with the calculation of the standard deviation (dispersion) in the same subintervals-periods of time allowed offering geomagnetic quake as an earthquake precursor [

The calculation of the differences (DayDiff) between the times of the earthquakes occurred in the region around the monitoring point and the nearest time of tide extremes permit to build the distribution of DayDiff. It was established that this distribution is described well by Gauss curve with a certain width W_{all}.

Introducing a new variable

and the calculation of its value in the monitoring point permits to classify the earthquakes occurred in the monitoring region and in the time period around tide extremes time.

The distribution of DayDiff for earthquakes with the biggest value of _{pr}.

In the paper [_{all} = 4.46 +/− 0.22.

The distributions of DayDiff for earthquakes with the biggest

There is a simple intuitive physical explanation [

The increase of the strain before an earthquake is accompanied by electrochemical and electrokinetic effects which generate electrical currents in the epifocal volume;

These currents, which can be identified using the geomagnetic quake approach.

The earthquake’s preparing continues as follow:

The preliminary stage of an earthquake is accompanied by negative divergence of the energy due to increased dissipation of tidal waves;

The maximum of two time daily tides’ acceleration leads to the transformation of this non-equilibrium state to a new balance that is closer to bifurcation, which explains the role of tides as an earthquake’s trigger.

There is the hope that including the above described research of regional precursors in the common approach for solving the earthquake prediction problem (see the paper [

In Section 2 is describing the approach for forecasting of imminent regional seismic activity on the basis of Japan geomagnetic data and Sun-Moon Earth tide to de data. In Section 3 is demonstrated the reliability of geomagnetic quake approach for the regions (700 km) of Memambetsu, Kakioka, Kanoya stations. In Section 4 is presented the description of precursor signal as a function of earthquake’s magnitude, depth and distance. In Section 5 is presented the formulation of inverse problem for forecasting the magnitude, depth and epicenter coordinates of regional imminent earthquake

In Application 1, _{ChtM} [J/km^{2}], the distance from station [km], the difference between the predicted time and the time of occurred earthquake [day], the values of experimetal and model precursor signal and its difference (Expt―Th). Aplication 2 is presented the FORTRAN version of precursor signal function PrecSigTh (Mag, Depth, Distance).

In this paragraph the data acquisition system for archiving, visualization and analysis is presented [

The data used:

• The Japan INTERMAGNET geomagnetic stations MMB (Memambetsu, Lat 43.907˚N, Lon 144.193˚E, Altitude = 42 m), KAK (Kakioka, Lat 36.232˚N, Lon 140.186˚E, Altitude = 36 m) KNY (Kanoya, Lat 31.42˚N, Lon 130.88˚E, Altitude = 107 m) minute data (http://www.intermagnet.org/);

• The software for calculation of the daily and minute Earth tide behaviour [

• The Earth tide extremes (daily average maximum, minimum and inflexed point) as a trigger of earthquakes;

• The data for World A-indices, www.swpc.noaa.gov.

The geomagnetic signal is calculated as a simple function of relative standard deviations of the components of the geomagnetic vector. The precursor signal is the difference between today and yesterday’s geomagnetic signal corrected by the A- indices values. As the increase of precursor signal means increase of geomagnetic field variability, we call such positive leap a geomagnetic quake in analogy with an earthquake. The analysis of the correlation between the earthquakes occurred and the time of Sun- Moon Earth tide extremes on the basis of the variable earthquake’s surface energy density S_{ChtM} permits to forecast the imminent regional seismic activity. The calculation of the day differences (DayDiff) between the time of the earthquakes occurred and the time of the nearest Tide extreme permits to build the curve of DayDiff and its Gauss fit. The comparison of Gauss widths for all the earthquakes occurred and those with the biggest S_{ChtM} is basis for formulation the hypothesis for “predictable” earthquakes.

The simple mathematics for the calculation of the precursor signal, the software for illustrating the reliability of forecasting and its statistic estimation and the variables in

The Geomagnetic field components

where

The geomagnetic signal

The A indices are the Low, Medium and High indices, calculated by the NOAA, Space weather prediction center: www.swpc.noaa.gov. In this paper we use A_{low};

The variable

and

The indices of earthquake’s magnitude value are the distance in hundred km between the epicenter and the monitoring point.

The variable

The variable ^{2}] is the sum of the variable

The variable ^{2} per day] is the sum of the variable

One has to note that the explicit form of the variable

The variable Tide Minute [cm] is the module of tide vector calculated every 15 minutes;

The variable Tide Day [cm] is the diurnal mean value in time calculated in the analogy of mass center formulae in many bodies’ classical mechanics:

Note: For seconds and more samples per second, the generalization has to calculate geomagnetic field characteristics for every minute and correspondingly the values of

The positive value of the variable

As one can see from

In

The use of the above described analysis for a longer time period with calculation of distribution of day difference between the “predicted” earthquakes (earthquakes with the highest value

In the following

The values of divisions near to 100% for all the three stations confirm the reliability of the imminent regional seismic activity forecasting. The values of Gauss fit widths can be interpreted as a confirmation of our hypotesis about “predicted” earthquakes: the stronger the earthquake is, the higher is the probability that after the precursor signal it will occur in the region in the time period (+/− 1.97 days) around the time of the following Tide’s extreme.

Station | PrEqs S_{ChtM} Sum [J/km^{2}] | AllEqs S_{ChtM} Sum [J/km^{2}] | Pr/All % | Gauss fit width all [day] | Gauss fit width PrEqs [day] |
---|---|---|---|---|---|

MMB | 4.01E+12 | 4.11E+12 | 97.6 | 5.14+/−0.56 | 4.32+/−0.72 |

KAK | 1.48E+13 | 1.68E+13 | 88.1 | 4.89+/−0.60 | 3.75+/−0.37 |

KNY | 1.96E+10 | 1.98E+10 | 99.0 | 5.44+/−0.0 | 3.74+/−0.51 |

Upon analysing the data for predicted earthquakes presented in

where_{i},^{6}.

The accuracy of description of the experimet is presented in the following _{i}:

where

In this section we will present apossibility for solving the inverse problem for the parameters established for an incoming earthquake―the time period, magnitude, depth and epicenter coordinate.

If our hypotesis for predicted earthquake is true, itmeans that after a geomagnetic quake in the following tide extreme with anaccuracy equal to +/− 2 days al leas one earthquake in the region will occur.

From the previous section we know the explicit form of precursor signal depending on the magnitude, depth and coordinates of the epicenter―4 variables. It means that the number of unkonwn parameters N is

where G is the number of geomagnetic monitoring points.

But the number of equations is G, which means that with a Network for only one precursor it is not possible to solve the problem for calculation of Mag, Depth and Coordinates of an incoming earthquake.

The condition to have sufficient data for defining the overdetemined system of equations is:

where P is the number of precursors (Earth Geomagnetic field, Earth currents field, Borehole water level, Radon concentration, Soil temperature, Atmosphere and Earth core low frequency waves, Ionosphere variability).

which has a solution if P ³ 3 at G > 2.

In case this condition is respected, the first stage of research allows to estimate the epicenter coordinates using simple triangulation, the condition (9) is

with solution P > 2 and G >= 2.

Of course, one has to note that the proposed scheme will take place after the reliability test of earthquake’s precursors (mentioned in many papers) as Earth electric current, borehole water level, radon concentration, soil temperature, ionosphere behaviour, low frequences wave in the atmosphere and the Earth core will be performed.

The approach proposed for solving the problem of regional imminent “how, where and when” earthquake’s prediction does not except the commonly accepted investigations based on seismology, geology, geoelectroma- gnetism and JPS data.

The reliability test of the Earth currents, Borehole water level, Radon concentration, Atmosphere and the terrestrial low frequency waves as demonstrated in this paper geomagnetic quake reliability for forerecasting the regional seismic activity, after including them in a regional network, will give data for discovering the explicit forms of different precursor signal functions. After collecting enough statistics for a suffucient number of earhquakes occurred in the network region and solving the overdetermined systems defined from conditions (9) or (10), we will have data for estimating the prediction accuracy for earthquake’s time period, magnitude, depth and epifocal coordinates prediction accuracy.

I would like to thank my co-authors from BlackSeaHazNet FP7 IRSES (2011-2014) for cooperation and discussions, Boris Vasilev, JINR, Dubna for the one-component magnetometer, the mathematician and program- mer Lubomir Aleksandrov for his code REGN and discussions on the inverse problem methods, Oleg Molchanov and Alexey Sissakyan for many years of fruitful polemics, as well as my late Professor Vladimir Kadyshevsky, who taught me how to try to gradually understand the physics with analyzing the dynamics and kinemathics of the processes in different time, space and energy scales.

Special thanks to Lazo Pekevski, Ludwig Ries, Alexandr Vol and Arie Gilat for the help in the preparation of the paper.

Strachimir Cht.Mavrodiev, (2016) Imminent Earthquake Forecasting on the Basis of Japan INTERMAGNET Stations, NEIC, NOAA and Tide Code Data Analysis. Open Journal of Earthquake Research,05,62-78. doi: 10.4236/ojer.2016.51005

No | St1St2 | Date | Lat | Long | Depth | Mag | SChtM | Distance R | TimeDiff | PrecSignal | Th | Res | Def |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MM.DD.YYYY | km | J/km^{2} | 100 km | Day | (Expt-Th)/Expt | Expt-Th | |||||||

1 | KNYKAK | 7.20.2010 | 34.28 | 135.533 | 34.28 | 4.90 | 2.70E+06 | 6.13 | 2.25 | 8.81E+00 | 8.37E+00 | 0.05 | 0.44 |

2 | KAKKNY | 7.20.2010 | 34.28 | 135.533 | 34.28 | 4.90 | 4.20E+06 | 4.75 | 2.27 | 4.76E+00 | 5.24E+00 | −0.10 | −0.48 |

3 | KNYKAK | 1.1.2012 | 31.456 | 138.072 | 31.46 | 6.80 | 8.20E+08 | 6.96 | 0.18 | 8.00E+00 | 7.67E+00 | 0.04 | 0.33 |

4 | KAKKNY | 1.1.2012 | 31.456 | 138.072 | 31.46 | 6.80 | 1.10E+09 | 5.66 | 0.80 | 4.54E+00 | 5.03E+00 | −0.11 | −0.49 |

5 | KNYKAK | 4.12.2013 | 34.369 | 134.828 | 34.37 | 5.80 | 8.00E+07 | 5.75 | 2.42 | 2.26E+00 | 4.06E+00 | −0.80 | −1.80 |

6 | KAKKNY | 4.12.2013 | 34.369 | 134.828 | 34.37 | 5.80 | 9.30E+07 | 5.29 | 2.42 | 2.77E+00 | 3.34E+00 | −0.20 | −0.57 |

7 | MMBKAK | 6.27.2010 | 41.662 | 141.657 | 41.66 | 5.30 | 3.00E+07 | 3.25 | 2.44 | 4.22E+00 | 3.54E+00 | 0.16 | 0.68 |

8 | MMBKAK | 6.27.2010 | 41.662 | 141.657 | 41.66 | 5.30 | 3.00E+07 | 3.25 | 2.44 | 2.62E+00 | 3.54E+00 | −0.35 | −0.92 |

9 | MMBKAK | 7.4.2010 | 39.697 | 142.369 | 39.70 | 6.30 | 5.70E+08 | 4.93 | 1.41 | 5.50E+00 | 4.84E+00 | 0.12 | 0.66 |

10 | KAKMMB | 7.4.2010 | 39.697 | 142.369 | 39.70 | 6.30 | 7.20E+08 | 4.31 | 0.30 | 2.73E+00 | 5.30E+00 | −0.94 | −2.60 |

11 | MMBKAK | 8.10.2010 | 39.406 | 143.148 | 39.41 | 5.90 | 1.40E+08 | 5.09 | 0.79 | 4.45E+00 | 4.53E+00 | −0.02 | −0.08 |

12 | KAKMMB | 8.10.2010 | 39.406 | 143.148 | 39.41 | 5.90 | 1.80E+08 | 4.39 | 0.19 | 5.83E+00 | 4.68E+00 | 0.20 | 1.20 |

13 | MMBKAK | 9.1.2010 | 37.925 | 141.788 | 37.93 | 5.20 | 6.50E+06 | 6.96 | 1.81 | 1.45E+00 | 2.55E+00 | −0.76 | −1.10 |

14 | KAKMMB | 9.1.2010 | 37.925 | 141.788 | 37.93 | 5.20 | 3.90E+07 | 2.36 | 1.78 | 4.37E+00 | 4.11E+00 | 0.06 | 0.26 |

15 | MMBKAK | 12.6.2010 | 40.904 | 142.967 | 40.90 | 5.70 | 1.30E+08 | 3.49 | 0.79 | 5.67E+00 | 5.91E+00 | −0.04 | −0.24 |

16 | KAKMMB | 12.6.2010 | 40.904 | 142.967 | 40.90 | 5.70 | 5.50E+07 | 5.73 | 0.77 | 5.52E+00 | 4.36E+00 | 0.21 | 1.20 |

17 | MMBKAK | 6.8.2014 | 39.164 | 141.709 | 39.16 | 5.20 | 8.10E+06 | 5.67 | 2.70 | 4.34E+00 | 4.05E+00 | 0.07 | 0.29 |

18 | KAKMMB | 6.8.2014 | 39.164 | 141.709 | 39.16 | 5.20 | 1.70E+07 | 3.53 | 1.62 | 4.70E+00 | 5.53E+00 | −0.18 | −0.83 |

19 | MMBKAK | 3.11.2011 | 38.297 | 142.373 | 38.30 | 9.00 | 3.90E+12 | 6.43 | 0.29 | 5.94E+00 | 7.23E+00 | −0.22 | −1.30 |

20 | KAKMMB | 3.11.2011 | 38.297 | 142.373 | 38.30 | 9.00 | 1.50E+13 | 3.01 | 0.23 | 9.20E+00 | 8.05E+00 | 0.13 | 1.20 |

21 | MMBKAK | 5.5.2011 | 38.17 | 144.032 | 38.17 | 6.00 | 1.30E+08 | 6.39 | 0.18 | 4.20E+00 | 3.74E+00 | 0.11 | 0.46 |

22 | KAKMMB | 5.5.2011 | 38.17 | 144.032 | 38.17 | 6.00 | 3.10E+08 | 4.03 | 1.21 | 2.60E+00 | 2.69E+00 | −0.03 | −0.09 |

23 | MMBKAK | 6.22.2011 | 39.955 | 142.205 | 39.96 | 6.70 | 2.40E+09 | 4.70 | 0.65 | 4.55E+00 | 3.52E+00 | 0.23 | 1.00 |

24 | KAKMMB | 6.22.2011 | 39.955 | 142.205 | 39.96 | 6.70 | 2.60E+09 | 4.50 | 0.69 | 3.49E+00 | 3.64E+00 | −0.04 | −0.14 |

25 | MMBKAK | 10.1.2012 | 39.808 | 143.099 | 39.81 | 6.10 | 3.30E+08 | 4.65 | 1.39 | 2.65E+00 | 4.54E+00 | −0.71 | −1.90 |

26 | KAKMMB | 10.1.2012 | 39.808 | 143.099 | 39.81 | 6.10 | 3.20E+08 | 4.73 | 2.43 | 7.87E+00 | 4.51E+00 | 0.43 | 3.40 |

27 | MMBKAK | 10.25.2012 | 38.306 | 141.699 | 38.31 | 5.60 | 2.80E+07 | 6.58 | 1.98 | 5.73E+00 | 4.30E+00 | 0.25 | 1.40 |

28 | KAKMMB | 10.25.2012 | 38.306 | 141.699 | 38.31 | 5.60 | 1.20E+08 | 2.67 | 1.93 | 2.94E+00 | 4.23E+00 | −0.44 | −1.30 |

29 | MMBKAK | 12.7.2012 | 37.89 | 143.949 | 37.89 | 7.30 | 1.00E+10 | 6.70 | 0.94 | 5.38E+00 | 5.41E+00 | −0.01 | −0.03 |

30 | KAKMMB | 12.7.2012 | 37.89 | 143.949 | 37.89 | 7.30 | 2.70E+10 | 3.82 | 0.91 | 4.09E+00 | 4.10E+00 | 0.00 | −0.01 |

31 | MMBKAK | 7.10.2013 | 39.638 | 141.705 | 39.64 | 5.30 | 1.40E+07 | 5.18 | 1.78 | 2.01E+00 | 2.55E+00 | −0.27 | −0.54 |

32 | KAKMMB | 7.10.2013 | 39.638 | 141.705 | 39.64 | 5.30 | 2.00E+07 | 4.02 | 1.80 | 4.83E+00 | 3.08E+00 | 0.36 | 1.80 |

Function PrecSigTh (aMag, Depth, Distance)

IMPLICIT DOUBLE PRECISION (A-H, O-Z)

DIMENSION A (16)

DATA A/0.653118375493643180E+04, 0.239327649144353849E+02, −0.441055930229294688E+03, −0.190062527379474363E+04, &

−0.195894833103010524E+04, −0.514929656067517226E+04, −0.745560820661331309E+04, 0.421788002467532533E+04, &

0.420599862430744270E+04, 0.319880390225624069E+04, −0.583971362592100718E+01, 0.536940127973910677E+02, &

0.510487668346017074E+03, 0.287881656908347106E+00, −0.264988287827522662E+01, −0.614005144491253532E+02/

DepL = dlog(Depth); DisL = dlog(Distance)

Str1 = a(2)*aMag + a(3)*DepL + a(4)*DisL

Str2 = a(5)/aMag + a(6)/(DepL+1.d0) + a(7)/(DisL+1.d0)

Str3 = a(8)/aMag**2 + a(9)/(DepL+1.d0)**2 + a(10)/(DisL+1.d0)**2

Str4 = a(11)*aMag**2 + a(12)*DepL**2 + a(13)*DisL**2

Str5 = a(14)*aMag**3 + a(15)*DepL**3 + a(16)*DisL**3

PrecSigTh = (eexp(a(1) + Str1 + Str2 + Str3 + Str4 +Str5))

RETURN

END