Models of the geomagnetic field on the territory of the Republic of Macedonia

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Models of the geomagnetic field on the territory
of the Republic of Macedonia

• S. Panovska(1), T. Delipetrov(2), M.
  Delipetrov(2), B. Delipetrov(1)
  
• University Goce Delcev
  Stip
  
• (1) Faculty of computer science
• (2) Faculty of mining, geology and
  polytechnics
  
• Republic of Macedonia

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• Various models of the geomagnetic field on the
  territory of Macedonia
  
• Theoretical basis of the models
• Ground and satellite data used for the models
• Correlation of the models

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Geomagnetic potential
a6371,2 km
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?errestrial measurement - The first three measu
rements were done in 2002 on Mt. Galicica, Mt.
Plackovica and Ponikva. - For covering of all ter
ritory of Republic of Macedonia, in 2003 net of
15 repeat stations was made and this net was
measured in 2004 also.
Location of the repeat stations in Macedonia
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Satellite measurements of magnetic field
SAC-C
CHAMP
ØRSTED
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SELECTION OF SATELLITE DATA
Selection of data was done for CHAOS (CHAMP,
Oersted ? SAC-C) model of the Earth magnetic
field, made from satellite data.
- Oersted scalar and vector data between March
2000 and December 2005, - CHAMP vector and scalar
data between August 2000 and December 2005,
- SAC-C scalar data between January 2001 and
December 2004.

• All data are selected according to quiet
  geomagnetic conditions
  
• - For all latitudes the Dst-index does not
  changed by more than 2 nT/h (dDst/dt).
  
• - At nonpolar latitudes (equatorwards of 60o
  dipole latitude) Kp 2o has to be fulfilled.
  
• - Only data from dark regions (sun 10o below
  horizon) were used, to reduce contributions from
  ionospheric currents.
  
• - Vector data have been taken for dipole
  latitudes equatorwards of 60o, to avoid the
  disturbing effect of field-aligned currents,
  which only influence the vector components but
  not field intensity.
• - Geomagnetic field modeling is done using vector
  data that are both calibrated and aligned.
  
• Decimation of satellite data

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Location of the scalar (?) satellite data used in
SCHA
Location of the vector (?) satellite data used
in SCHA
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SCHA model of geomagnetic field of the Balkan
Peninsula with central position of the Republic
of Macedonia
SCHA model of geomagnetic field of the Balkan
Peninsula with attention to the Republic of
Macedonia was made according to the three
component measurements of the net of repeat
stations in the Republic of Macedonia from 2002
to 2004, as well as the selected data from the
satellite measurements of Oersted, CHAMP ?
SAC-C. Derived model shows X, Y, Z and F compone
nt of the main magnetic field for the epochs
2000.0 to 2007.0. The model is for development of
the magnetic potential in spherical harmonics of
the spherical cap with half angle of 8?.
Because of the small territory of the Republic
of Macedonia, model of spherical harmonical
analyses is made for half angle of 8o of the
spherical cap, in order to cover the most
important harmonics (the smallest degree is close
to 12 with maximal spatial index K 2). The
final model has total of 27 coefficients
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After the testing, parameters which define the
best model with fitting the input data and their
spatial and time behaviour are ? 2, L 1,
covering the period between 2000.0 2007.0. The
referent epoch is 2003.5.
Number of data used in SCHA model
RMS values of SCHA and IGRF models (nT)
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Maps of X (up left), Y (up right), Z (down l
eft) and F (down right) components of the SCHA
model in nT for the epoch 2003.5 at sea level
(GMT)
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Polynomial analysis of the geomagnetic field on
the territory of the Republic of Macedonia

Coefficients of normal magnetic field for epoch
2003.5 on the territory of the Republic of Maced
onia on sea level
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Maps of X (up left), Y (up right), T (down left)
and I (down right) components
of the normal field for the epoch 2003.5 at sea
level (2 order polynomial)
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Correlation of the models
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Statistical analysis of differences between the
models IGRF, SCHA and polynomial model with meas
ured data of T, D, I for epoch 2003.5
Average value of sample
Standard error
Variance
Standard deviation
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• Conclusion
• Mathematical modeling of Earth magnetic field
  gives effective way for calculation of components
  of geomagnetic field every time and every where
  on the Earth.
• Model of the spherical analyses make better
  fitting of the X, Y, Z and T components on the
  Earth with respect to IGRF model for about 10 .
  
• From analysed models, SCHA and polynomial, the
  most representative for the magnetic field of the
  territory of the Republic of Macedonia is
  polynomial model.
• It is planed to make improved model with the new
  data get from the measurements of the net of the
  repeat stations in 2007.