# Presentation: 528053

## 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**

##  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

## a=6371,2 km 

- a=6371,2 km

## Тerrestrial measurement

- - The first three measurements were done in 2002 on Mt. Galicica, Mt. Plackovica and Ponikva.
- - For covering of all territory 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

## ØRSTED

| Satellite | Inclination | Altitude range | Launch | Instruments |
| --- | --- | --- | --- | --- |
| Ørsted | 96.5о | 630 – 860 km | 02.1999 | CSC flux-gate magnetometer, 
Overhauser magnetometer, 
Star imager (SIM), 
GPS Turbo-Rogue, 
Detector of particles |
| CHAMP | 87о | 350 – 450 km | 07.2000 | Overhauser magnetometer, 
Acceleratormeter, 
GPS receiver, 
Star sensor,  
Laser reflector |
| SAC-C | 98.2о | 700 km | 11.2000 | Scalar helium magnetometer, 
GPS Turbo-Rogue |

**ØRSTED**

**CHAMP**

**SAC-C**

**Satellite measurements of magnetic field**

## 	Selection of data was done for CHAOS (CHAMP, Oersted и 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****.**

**SELECTION OF SATELLITE DATA**

**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 60****o**** dipole latitude) *****Kp *****≤ 2o has to be fulfilled. **
**- Only data from dark regions (sun 10****o**** below horizon) were used, to reduce contributions from ionospheric currents. **
**-  Vector data have been taken for dipole latitudes equatorwards of ±60****o****, 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**

## Location of the scalar (▲) satellite data used in SCHA 

- Location of the scalar (▲) satellite data used in SCHA

-  Location of the vector (♦) satellite data used in SCHA

## 	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 и SAC-C.

- 	Derived model shows X, Y, Z and F component 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 8о.
- 	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:

**SCHA model of geomagnetic field of the Balkan Peninsula with central position of the Republic of Macedonia**

## Number of data used in SCHA model 

| Data for model | Repeat station data | Satellite data |  |
| --- | --- | --- | --- |
| SUM | 132 | Scalar | Vector |
|  |  | 40 | 129 |

- RMS values of SCHA and IGRF models (nT)

| Model | RMS X | RMS Y | RMS Z | RMS F |
| --- | --- | --- | --- | --- |
| IGRF (ground) | 57.1 | 82.7 | 77.1 | 71.9 |
| SCHA (ground) | 49.9 | 74.3 | 74.0 | 69.9 |

- After the testing, parameters which define the best model with fitting the input data and their spatial and time behaviour are К = 2, L = 1, covering the period between 2000.0 – 2007.0. The referent epoch is 2003.5.

## Maps of 

- Maps of
- X (up left),
- Y (up right),
- Z (down left) and
- F (down right)
- components of the SCHA model in nT for the epoch 2003.5 at sea level
- (GMT)

## 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 Macedonia on sea level

| Element | a1 | a2 | a3 | a4 | a5 | a6 |
| --- | --- | --- | --- | --- | --- | --- |
| T | 46565.19931 | 360.63040 | 88.63350 | 91.70045 | 34.32665 | 35.90337 |
| D | 3.208242 | 0.027133 | 0.090219 | -0.259889 | -0.065314 | -0.096687 |
| I | 58.298752 | 1.052109 | 0.076513 | 0.252788 | 0.032474 | -0.061213 |
| H | 24469.90417 | -539.60365 | -6.61295 | 138.77884 | -4.63379 | 58.59862 |
| X | 24431.35649 | -539.48468 | -8.67530 | -132.38872 | -2.99993 | 60.70491 |
| Y | 1370.029165 | -17.10737 | 38.06225 | -119.54230 | -29.11334 | -38.39349 |
| Z | 39617.69585 | 756.00120 | 108.22834 | 181.50537 | 43.05518 | 5.174464 |

## Maps of X (up left), Y (up right), T (down left) and I (down right) components 

- 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)

## Correlation of the models

| Тotal intensity Т (nT) |  |  | Inclination I (o) |  |  | Declination D (o) |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| m-igrf | m-scha | m-poly | m-igrf | m-scha | m-poly | m-igrf | m-scha | m-poly |
| -94.2 | -125.3 | -127.1 | 0.164 | 0.103 | 0.063 | -0.345 | -0.239 | -0.171 |
| 73.6 | 66.5 | 33.7 | -0.026 | -0.061 | -0.054 | -0.187 | -0.029 | 0.039 |
| 38.4 | 62.0 | 42.6 | 0.061 | 0.040 | -0.009 | -0.077 | -0.005 | -0.016 |
| -29.0 | 3.9 | -58.3 | 0.056 | 0.020 | -0.026 | -0.127 | -0.080 | -0.019 |
| -138.4 | -130.6 | -100.7 | -0.112 | -0.140 | -0.101 | 0.341 | 0.439 | 0.339 |
| 141.3 | 110.5 | 72.1 | 0.148 | 0.085 | 0.013 | -0.063 | 0.069 | 0.224 |
| 1.0 | -20.7 | -13.3 | 0.112 | 0.039 | 0.057 | -0.053 | -0.027 | -0.025 |
| -10.7 | 15.1 | 12.3 | 0.078 | 0.052 | 0.047 | -0.223 | -0.087 | -0.157 |
| -63.5 | -78.4 | -51.8 | -0.040 | -0.094 | -0.033 | -0.121 | 0.000 | -0.043 |
| 31.7 | 8.4 | 13.6 | 0.079 | 0.012 | 0.048 | -0.490 | -0.357 | -0.332 |
| 118.8 | 107.9 | 151.4 | 0.094 | 0.085 | 0.105 | -0.100 | -0.023 | -0.110 |
| -19.5 | -14.3 | -19.4 | -0.007 | -0.053 | -0.006 | 0.032 | 0.183 | 0.156 |
| -23.7 | -29.0 | -8.4 | 0.052 | 0.019 | 0.043 | -0.013 | 0.045 | -0.016 |
| 46.4 | 24.4 | 36.1 | -0.014 | -0.059 | -0.096 | 0.000 | 0.049 | 0.046 |
| 16.4 | -11.0 | 17.0 | 0.002 | -0.055 | -0.053 | 0.037 | 0.105 | 0.086 |

## Standard error: 

- and polynomial model with measured data of T, D, I for epoch 2003.5

|  | 2003.5 | MIN | MAX | Average value | Standard error | Variance | Standard deviation |
| --- | --- | --- | --- | --- | --- | --- | --- |
| Т | M-IGRF | -138.4 | 141.3 | 5.9 | 19.3 | 5559.5 | 74.6 |
|  | M-SCHA | -130.6 | 110.5 | -0.7 | 18.7 | 5251.3 | 72.5 |
|  | M-POLY | -127.1 | 151.4 | 6.3 | 17.7 | 4712.7 | 68.6 |
| D | M-IGRF | -0.490 | 0.341 | -0.092 | 0.048 | 0.035 | 0.186 |
|  | M-SCHA | -0.357 | 0.439 | 0.003 | 0.046 | 0.032 | 0.178 |
|  | M-POLY | -0.332 | 0.339 | 0.000 | 0.042 | 0.027 | 0.165 |
| I | M-IGRF | -0.112 | 0.164 | 0.043 | 0.019 | 0.006 | 0.075 |
|  | M-SCHA | -0.140 | 0.103 | 0.000 | 0.019 | 0.005 | 0.072 |
|  | M-POLY | -0.101 | 0.105 | 0.000 | 0.016 | 0.004 | 0.061 |

**Standard error: **

**Variance: **

**Standard deviation: **

**Average value of sample: **

## 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.