DELIPETREV_correctedOK_Layout 6 ANNALS OF GEOPHYSICS, 56, 3, 2013, R0327; doi:10.4401/ag-5311 R0327 New geomagnetic measurements in the Republic of Macedonia Marjan Delipetrev1,*, Nenad Novkovski2, Todor Delipetrov1 1 University of Goce Delcev, Faculty of Natural and Technical Sciences, Stip, Republic of Macedonia 2 University of St. Cyril and Methodius, Faculty of Natural Science and Mathematics, Institute of Physics, Skopje, Republic of Macedonia ABSTRACT This study presents measurements of the geomagnetic field of the Re- public of Macedonia, performed through a network of newly defined re- peat stations. The measurements of these elements were in the intervals of 3.378° ≤ DD ≤ 3.983°, 57.276° ≤ I ≤ 59.005°, and 46 235 nT ≤ F ≤ 46903 nT. The geomagnetic data were processed and the results of the ob- served elements of the geomagnetic field on the repeat stations are pre- sented. Additional data processing was performed to calculate the reduced values of the intensive elements of the field at the level of H500 a.s.l.. Based on these data, new maps of the geomagnetic field of the Republic of Macedonia are developed, together with the polynomial model of the elements of the geomagnetic field for the 2010.0 epoch. 1. Introduction The territory of the Republic of Macedonia occu- pies the central part of the Balkans Peninsula, with an area of 25,713 km2. The terrain is mountainous due to highly active neotectonic processes. These processes have formed uplift blocks, with crests to 2,600 m a.s.l. and blocks of sinking depressions that mainly spread east to west [Arsovski 1997]. The geomagnetic investigations can be divided into three periods. The first period began in the 19th century and finished in 1945. Scientists from mainly Eu- ropean countries were engaged in infrequent special ex- peditions to investigate the geomagnetic field in the Balkans, which included investigations in the territory of the present-day Republic of Macedonia. The second period was from 1945 to 1991, when Macedonia was a constitutional part of Yugoslavia, and the third period began after the declaration of independence in 1991. The geomagnetic observations for the territory of the Republic of Macedonia up to 1990 were carried out by teams of scientists from the Geomagnetic Obser- vatory Grocka (Republic of Serbia). To continue mon- itoring and to obtain new data for the geomagnetic field of Macedonia, Panovska and Delipetrov [2006] de- veloped the appropriate maps and models for the given epochs. In 2002, the first measurements of the geo- magnetic field for the locations of Plackovica, Ponikva and Galicica were initiated, with the help of the Royal Meteorological Institute Geomagnetic Observatory in Dourbes (Belgium). This report presents the results from the terrestrial measurements and data processing, and the newly developed maps and the polynomial model of the geomagnetic field of Macedonia. 2. The repeat station network The geomagnetic field in a given area is measured for a network of repeat stations, often at five-year inter- vals. Based on these measurements, the raw geomag- netic data are collected and processed, which produces models and maps of the geomagnetic field elements. A team from the Faculty of Natural Sciences, ‘Goce Delcev’ University (Stip, Republic of Macedonia) conducted investigations to define the repeat station network in the Republic of Macedonia. The repeat sta- tion networks of 16 countries were investigated, with the mean distance between stations of 230 km, which varied from 53 km to 415 km. In the process of defining the repeat station net- work, geomagnetic measurements were performed for every point in four directions (north, south, east, west) at intervals of 1 m at a distance of 10 m. The International Association of Geomagnetism and Aeronomy guidance states that the maximum gradient of the magnetic field for repeat stations should not exceed 50 nT in a radius of 10 m. The selected repeat stations in Macedonia have a gradient below 1 nT [Rasson and Delipetrov 2006]. Based on these investigations and the characteris- tics of Macedonia, a network of 15 repeat stations was defined (Figure 1, Table 1). The minimum distance be- Article history Received July 13, 2011; accepted March 22, 2013. Subject classification: Geomagnetic survey, Geomagnetic field, Repeat station, Measurements. tween the repeat stations is 26.1 km, with a maximum distance of 201.3 km, and a mean distance of 98.6 km. The lowest repeat station is Nikolic, at an altitude of 300 m a.s.l., while the highest is Galicica, at 1,684 m a.s.l. 3. Normal geomagnetic field maps The first field measurements for the definition of the repeat station network were carried out in 2002- 2003 with the instruments from the geomagnetic ob- servatory in Dourbes (Belgium), with the help of Jean Rasson. The second series of geomagnetic field meas- urements was carried out in 2007-2009 for the newly es- tablished repeat station network (Table 1). The repeat station measurements in 2007-2009 were performed with the instruments of the ‘Goce Del- cev’ University. The instruments used were a LEMI 203 DIM sensor, a Geometrics G 856 proton magnetome- ter, and a Trimble global positioning system (GPS). During the field observations, the declination D, inclination I, and total field vector F were measured. As there is no geomagnetic observatory available in the Republic of Macedonia, a time-series from the Panagjuriste Observatory (Bulgaria) was used. This ob- servatory was selected due to its proximity, as it is 225 km away, with coordinates: latitude, 42.52°N; longi- tude, 24.18°E; altitude: 556 m a.s.l. The time-series data was used to reduce the results of the 2010.0 epoch, and to calculate the mean yearly changes in the geomag- netic field. The measurements for the 2010.0 epoch are given in Table 2 and illustrated in Figures 2-4.Using the data from Tables 1 and 2, a reduction of the intensive measurements was made to the level h = 500 m a.s.l. (Table 3). For any intensive field element with a value E [e.g., De Santis et al. 2003] at a height h, the correction DE for computing its value for h = 500 m is expressed as: (1) where R = 6,371.2 km is the Earth mean radius. Table 3 shows the corrections and reduced values for F500, H500 and Z500. Using the software SURFER 9 and the data from Tables 2 and 3, the maps of the elements for the normal geomagnetic field were created (Figures 2-4). The declination (D) in the observed area varies from 3.378° for the repeat station Galicica, to 3.983° for station Slivnica. The mean declination from the ob- DELIPETREV ET AL. 2 Repeat station Geographic latitude (°:min:sec) Geographic longitude (°:min:sec) Altitude (m) Bajlovce 42:13:16 21:55:17 592 Crna skala 41:59:41 22:47:28 833 Egri 41:23:15 21:57:06 626 Galicica 40:57:56 21:26:54 1684 Island Gradot 40:57:23 20:48:51 317 Luke 42:20:39 22:16:29 1180 Mavrovo 41:42:58 20:43:38 1418 Nikolic 41:15:54 22:44:36 300 Plackovica 41:47:41 22:18:13 677 Ponikca 42:01:35 22:21:29 1618 Prilep Lake 41:24:11 21:36:32 870 Slivnica 41:37:38 21:11:36 1252 St. Marija Precesna 41:36:54 22:51:46 837 Tetovo 41:59:09 21:04:46 522 Vodno 41:58:40 21:24:57 569 Figure 1. Map of the repeat stations in the Republic of Macedonia. Table 1. GPS coordinates of the repeat stations. E R h Eh R Rh3 3 D = + = 3 served data is Dsr = 3.628°. The means of the geomag- netic fields are calculated using an arithmetic mean. Analysis of the declination field shows that for the ob- served territory, the most extreme value is in the central southern part, near the measuring station of Island Gradot. The field is quiet in the west and northwest parts of the country. The observations show that the inclination varies from 57.276° for Galicica to 59.005° for Luke station. The mean inclination (I) is Isr = 58.125°. The inclina- tion field compared to the declination is more homog- enous and relatively quiet. There is a slight twisting of the isolines in the central-southern part. The measured points for the total field vector (F) vary from 46,235 nT for Luke to 46,903 nT for the repeat station Crna Skala. The mean total field vector is Fsr = 46,532 nT. The west- ern part of the field, as the western-Macedonia part, has a quiet field. Again, there is a twisting of the iso- NEW GEOMAGNETIC MEASUREMENTS IN THE REPUBLIC OF MACEDONIA Station D (°) I (°) F (nT) H (nT) X (nT) Y (nT) Z (nT) Bajlovce 3.507 58.850 46675 24144 24099 1477 39945 Crna Skala 3.769 58.244 46903 24685 24632 1623 39881 Egri 3.465 57.367 46330 24984 24938 1510 39016 Galicica 3.378 57.276 46271 25014 24970 1474 38927 Island Gradot 3.946 57.667 46327 24777 24719 1685 39144 Luke 3.737 59.005 46235 23809 23759 1552 39633 Mavrovo 3.466 58.122 46451 24531 24486 1483 39445 Nikolic 3.499 57.823 46493 24759 24713 1511 39352 Plackovica 3.698 58.217 46575 24531 24480 1582 39591 Ponikva 3.721 58.603 46750 24355 24304 1581 39905 Prilep Lake 3.509 57.854 46567 24777 24731 1517 39428 Slivnica 3.983 58.166 46607 24583 24524 1708 39596 St. Marija Precesna 3.533 58.039 46453 24590 24543 1515 39411 Tetovo 3.617 58.346 46683 24499 24450 1546 39738 Vodno 3.597 58.298 46671 24526 24477 1539 39707 Station DF500 (nT) DH500 (nT) DZ50 (nT) F500 (nT) H500 (nT) Z500 (nT) Bajlovce 2.0219 1.0459 1.7201 46677.02 24145.05 39708.72 Crna skala 7.3540 3.8704 6.2530 46910.35 24688.87 39887.25 Egri 2.7487 1.4823 2.3148 46332.75 24985.48 39018.31 Galicica 25.7917 13.9429 21.6981 46296.79 25027.94 38948.70 Island Gradot -3.9921 -2.1351 -3.3731 46323.01 24774.86 39140.63 Luke 14.8024 7.6226 12.6888 46249.80 23816.62 39645.69 Mavrovo 20.0759 10.6022 17.0479 46471.08 24541.60 39462.05 Nikolic -4.3786 -2.3317 -3.7060 46488.62 24756.67 39348.29 Plackovica 3.8816 2.0444 3.2996 46578.88 24533.04 39594.30 Ponikca 24.6064 12.8190 21.0036 46774.61 24367.82 39926.01 Prilep Lake 8.1125 4.3164 6.8688 46575.11 24781.32 39434.87 Slivnica 16.5013 8.7037 14.0190 46623.50 24591.70 39610.02 St. Marija Precesna 7.3709 3.9018 6.2535 46460.27 24593.90 39417.25 Tetovo 0.4836 0.2538 0.4116 46683.48 24499.25 39738.41 Vodno 1.5163 0.7968 1.2901 46672.52 24536.80 39708.29 Table 2. Reduced measurements for the epoch 2010.5. D, declination; I, Inclination; T, Total intensity; H, Horizontal component; X, East component; Y, North component; Z, vertical component. Table 3. Corrections and reduced values for the intensive field elements at h = 500 m a.s.l. lines in the central-southern part. The maps presented here (Figures 2-4) show that the largest deformations in the field occur in the cen- tral part and the eastern Macedonia zone. The geomagnetic field on the Earth surface can be present as the vector sum of many different components: (2) where, is the field of the homogenous magnetized Earth, or the field of a dipole magnet, is the field from the magnetic objects in the deeper parts of the Earth, known as the nondipole or field of continents, is the field created by the magnetization of the upper parts of the Earth crust, known as the anom- alous field, is the field related to external phenom- ena with respect to the Earth surface, and is the field of variations. With the measurement procedure performed and the processing of the collected data, components and can be eliminated. The anomalous field can be represented as a sum of two components: (3) where, is the regional anomalous field for the ob- served territory, which is caused by the influence of the magnetic layers and the deeper parts of the Earth crust, and which is manifest over larger areas, is the local anomalous field for the observed territory. This field re- sults from the magnetic media (rock, ore deposits) near the Earth surface, which influences a relatively small area. Separation of the local and anomalous fields de- pends on the size of the area investigated. The method- ology and the observations of the geomagnetic field allow the elimination of the anomalous component of local character, . The Italian Geomagnetic Reference Field models represent the geomagnetic field generated in the core, or the component (T0) and the nondipole field (Tm), or the sum of these two. The referent model for an investigated territory (state) is given by: (4) The influence of the regional component presents specific geomagnetic features for the explored area that create differences from the global geomagnetic models of the Earth. For a more precise definition of the re- gional geomagnetic field, observations on a denser net- work of repeat stations should be made. 4. Model of the normal geomagnetic field of the Re- public of Macedonia Today, two methods of modeling geomagnetic fields have been defined: one that uses spherical har- monic analysis, and the other, polynomial analysis. Studies show that for areas with <15° spatial angle, polynomial analysis is an effective method [De Santis et al. 1999]. Given the size of the territory of the Repub- DELIPETREV ET AL. 4 Figure 4. Map of total field vector F for the 2010.0 epoch. Figure 3. Map of the inclination I for the 2010.0 epoch.Figure 2. Map of the declination D for the 2010.0 epoch. T T T T T T0 a d= + + + +m e T T Ta = + aa r I T T T TNM = + + am0 r T0 Tm Ta Ta Te Te Td Td Ta r Ta r Ta I 5 lic of Macedonia, the polynomial model is appropriate. To calculate the coefficients of the polynomial model, the method of least squares is used. The geo- magnetic field for a given territory can be expressed as: where, E(D{,Dm) is a normal field of the point with co- ordinates {1 and m1, {1 and m1 are the geographic lati- tude and longitude of the point, respectively, {0 and m0 are the geographic latitude and longitude of the point, respectively, in respect of which the measurements are reduced. For the Republic of Macedonia, the central point is for {0 = 41.50° and m0 = 22°. Then, D{ = {1 − − {0 is the difference in the geographic latitudes, in minutes, Dm = m1 − m0 is the difference in the geo- graphic longitudes, in minutes, and ai is the coefficient for the corresponding differences in nT/min; i.e., min/min. Usually, the differences in the latitude and longitude are calculated in terms of the coordinates of the geomagnetic observatory located in that territory. The normal field of the territory of Macedonia is calculated according to the measurements of absolute values for the total intensity (F), declination (D) and in- clination (I) for the period from 2007-2009 for the 15 network stations. The values for the other components of the geomagnetic field are derived from these (Table 1). Calculate coefficients or polynomial model from the absolute measurements for 2010.0 epoch is given in (Table 4). 5. Conclusions This report presents the measurements of the ge- omagnetic field of the Republic of Macedonia. The ge- omagnetic field observations were carried out for the newly developed repeat station network in 2007-2009. The data gathered was processed and the maps of the geomagnetic field elements are produced here. With the reduction in H500 a.s.l., the influence of the relief was minimized in relation to the regional magnetic com- ponent presented. The data are used to create the poly- nomial model of the elements of the geomagnetic field for the 2010.0 epoch. The model is a second-degree poly- nomial in longitude and latitude and consists of obser- vations of six coefficients for each magnetic element. The measurements given in this report are a con- tinuation of the observations on the geomagnetic field in the Republic of Macedonia that was started after 2000. The geomagnetic model can be used for further studies and analysis of the geomagnetic field of this area. Acknowledgements. The authors would like to thank Dr Jean Rasson, Royal Meteorological Institute Geomagnetic Obser- vatory, Dourbes, Belgium, for help with the recording in 2002- 2003, the University of Goce Delcev, for support from the Tempus Project Geomagnetic measurements and quality standards, and the Panagjuriste Observatory, Bulgaria, for the geomagnetic observa- tory time-series. References Arsovski, M. (1997). Tectonics of Macedonia, Faculty of Geology and Mining, Stip (Republic of Macedo- nia), 18-25. De Santis, A., J.M. Torta and F.J. Lowes (1999). Spheri- cal cap harmonics revisited and their relationship to ordinary spherical harmonics, Phys. Chem. Earth, Part A: Solid Earth Geod., 24 (11/12), 935-941. De Santis, A., L. Gaya-Piqué, G. Dominici, A. Meloni, J.M. Torta and R. Tozzi (2003). Italian Geomagnetic Reference Field (IGRF): update for 2000 and secular variation model up to 2005 by autoregressive fore- casting, Annals of Geophysics, 46 (3), 491-500. Delipetrov, T., and B. Paneva (2006). Geomagnetic field of the Republic of Macedonia, In: J.L. Rasson and T. Delipetrov (eds), Geomagnetics for aeronautical safety: a case study in and around the Balkans, Pro- ceedings of the NATO Advanced Research Work- shop (Ohrid, Republic of Macedonia, 16-20 May 2005), Springer, 15-42. Panovska, S., and T. Delipetrov (2006). Analysis of ge- omagnetic field data from measurements during 2003 in Macedonia, In: J.L. Rasson and T. Delipetrov NEW GEOMAGNETIC MEASUREMENTS IN THE REPUBLIC OF MACEDONIA Element Coefficient a0 a1 a2 a3 a4 a5 D (°) 3.6278 0.1176 -0.0386 0.0778 0.0154 -0.3455 I (°) 58.0876 -0.0367 -0.1578 0.1196 0.0928 -0.4256 T (nT) 46550 -24.4499 -172.2784 -20.5894 197.7838 -449.6354 H (nT) 24607 11.0723 17.1495 -95.3759 38.9003 57.7547 X (nT) 24558 7.9397 18.2187 -97.3217 37.0952 66.8624 Y (nT) 15560 46.6355 -15.9659 23.6280 13.3079 -145.0884 Z (nT) 39514 -36.4622 -217.0881 33.5642 210.5535 -567.0112 Table 4. Model for the 2010.0 epoch. ,E a a a a a a 2 3 4 2 5 2 6 1 $ $ $ $ $ { m { m { m { m D D D D D D D D + + + + + = +^ h (eds), Geomagnetics for aeronautical safety: a case study in and around the Balkans, Proceedings of the NATO Advanced Research Workshop (Ohrid, Re- public of Macedonia, 16-20 May 2005), Springer, 325-346. Rasson, J.L., and M. Delipetrov (2006). Repeat surveys of Macedonia, In: J.L. Rasson and T. Delipetrov (eds), Geomagnetics for aeronautical safety: a case study in and around the Balkans, Proceedings of the NATO Advanced Research Workshop (Ohrid, Republic of Macedonia, 16-20 May 2005), Springer, 97-114. *Corresponding author: Marjan Delipetrev, University of Goce Delcev, Faculty of Natural and Technical Sciences, Stip, Republic of Macedonia; email: marjan.delipetrev@ugd.edu.mk. © 2013 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved. DELIPETREV ET AL. 6 << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles false /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.3 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.1000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize false /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile (None) /AlwaysEmbed [ true /AndaleMono /Apple-Chancery /Arial-Black /Arial-BoldItalicMT /Arial-BoldMT /Arial-ItalicMT /ArialMT /CapitalsRegular /Charcoal /Chicago /ComicSansMS /ComicSansMS-Bold /Courier /Courier-Bold /CourierNewPS-BoldItalicMT /CourierNewPS-BoldMT /CourierNewPS-ItalicMT /CourierNewPSMT /GadgetRegular /Geneva /Georgia /Georgia-Bold /Georgia-BoldItalic /Georgia-Italic /Helvetica /Helvetica-Bold /HelveticaInserat-Roman /HoeflerText-Black /HoeflerText-BlackItalic /HoeflerText-Italic /HoeflerText-Ornaments /HoeflerText-Regular /Impact /Monaco /NewYork /Palatino-Bold /Palatino-BoldItalic /Palatino-Italic /Palatino-Roman /SandRegular /Skia-Regular /Symbol /TechnoRegular /TextileRegular /Times-Bold /Times-BoldItalic /Times-Italic /Times-Roman /TimesNewRomanPS-BoldItalicMT /TimesNewRomanPS-BoldMT /TimesNewRomanPS-ItalicMT /TimesNewRomanPSMT /Trebuchet-BoldItalic /TrebuchetMS /TrebuchetMS-Bold /TrebuchetMS-Italic /Verdana /Verdana-Bold /Verdana-BoldItalic /Verdana-Italic /Webdings ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 150 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.10000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.10000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.08250 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName (http://www.color.org) /PDFXTrapped /Unknown /CreateJDFFile false /SyntheticBoldness 1.000000 /Description << /ENU (Use these settings to create PDF documents with higher image resolution for high quality pre-press printing. The PDF documents can be opened with Acrobat and Reader 5.0 and later. These settings require font embedding.) /JPN /FRA /DEU /PTB /DAN /NLD /ESP /SUO /NOR /SVE /KOR /CHS /CHT /ITA >> >> setdistillerparams << /HWResolution [2400 2400] /PageSize [595.000 842.000] >> setpagedevice