Gravimetry and geoid modelling in Croatia–

an overview

Lorand Eotvos centenary

Matej Varga, Tomislav Basic

in Budapest, May 15th, 2019

Eotvos’s influence on gravity andmagnetic field research in Croatia

Szabo 2016

1

Artur Gavazzi- the pioneer of gravimetry in Croatia

Bio

� Split, 1861 - Zagreb, 1944� mainly physical geographer, but contributed to hidrology, meteorology, oceanography, geodesy� dean of the Faculty of Philosophy (Ljubljana)� member of several academies in Europe� wrote several books

Figure 1: prof. dr. Artur Franovic Gavazzi (Hanzek et al. 2012)

Figure 2: Constants of the Gavazzi’s variometer

Eotvos torsion balance

� supported and financed by Croatians: prof. dr. Karlo Gorjanovic-Kramberger, ban Pavao Rauch� built during 1909 and 1910� Hungarians worked on instrument: Ferdinand Suss (1848–1921), Dezso Pekar (1873–1953), Istvan Rybar (1886-1971)� for that time-period the most accurate Eotvos torsion balance instruments (∼ 1 E)

Measurements

� in 1911 and 1912 performed torsion balance measurements- one of the first gravity field measurements across Croatia� made topographic reductions� Gavazzi communicated intensively with Eotvos, e.g. ”Equations, by which we perform calculations were published, but Eotvos did

write to me some significant changes which simplified our calculations...”� in 2013 published results of 51 measurements of 37 different sites (Gavazzi 1913)

2

Artur Gavazzi- the pioneer of gravimetry in Croatia

Bio

� Split, 1861 - Zagreb, 1944� mainly physical geographer, but contributed to hidrology, meteorology, oceanography, geodesy� dean of the Faculty of Philosophy (Ljubljana)� member of several academies in Europe� wrote several books

Figure 1: prof. dr. Artur Franovic Gavazzi (Hanzek et al. 2012) Figure 2: Constants of the Gavazzi’s variometer

Eotvos torsion balance

� supported and financed by Croatians: prof. dr. Karlo Gorjanovic-Kramberger, ban Pavao Rauch� built during 1909 and 1910� Hungarians worked on instrument: Ferdinand Suss (1848–1921), Dezso Pekar (1873–1953), Istvan Rybar (1886-1971)� for that time-period the most accurate Eotvos torsion balance instruments (∼ 1 E)

Measurements

� in 1911 and 1912 performed torsion balance measurements- one of the first gravity field measurements across Croatia� made topographic reductions� Gavazzi communicated intensively with Eotvos, e.g. ”Equations, by which we perform calculations were published, but Eotvos did

write to me some significant changes which simplified our calculations...”� in 2013 published results of 51 measurements of 37 different sites (Gavazzi 1913)

2

Artur Gavazzi- the pioneer of gravimetry in Croatia

Bio

� Split, 1861 - Zagreb, 1944� mainly physical geographer, but contributed to hidrology, meteorology, oceanography, geodesy� dean of the Faculty of Philosophy (Ljubljana)� member of several academies in Europe� wrote several books

Figure 1: prof. dr. Artur Franovic Gavazzi (Hanzek et al. 2012) Figure 2: Constants of the Gavazzi’s variometer

Eotvos torsion balance

� supported and financed by Croatians: prof. dr. Karlo Gorjanovic-Kramberger, ban Pavao Rauch� built during 1909 and 1910� Hungarians worked on instrument: Ferdinand Suss (1848–1921), Dezso Pekar (1873–1953), Istvan Rybar (1886-1971)� for that time-period the most accurate Eotvos torsion balance instruments (∼ 1 E)

Measurements

� in 1911 and 1912 performed torsion balance measurements- one of the first gravity field measurements across Croatia� made topographic reductions� Gavazzi communicated intensively with Eotvos, e.g. ”Equations, by which we perform calculations were published, but Eotvos did

write to me some significant changes which simplified our calculations...”� in 2013 published results of 51 measurements of 37 different sites (Gavazzi 1913)

2

Boris Apsen- outstanding mathematician

Bio

� Moscow, 1894 - Split, 1980� immigrated from Russia to former Yugoslavia in 1921� in 1916 graduated law and economics� in 1931 graduated geodesy at the Faculty of Geodesy

� in 1942 obtained PhD degree with thesis Eotvos’ gravitational variometer and his theory and

application in higher geodesy

� the first doctor of geodetic sciences at the Technical Faculty (former) of University of

Zagreb

� worked as mathematics teacher on university and high-schools� wrote several books in (higher) mathematics which are still considered valuable source of

knowledge in faculty education in Croatia

Figure 3: Boris Apsen (Francula 2007)3

Torsion balance from the Faculty of Geodesy

Was used in research, industry and education during second half of the

20th century

Professors of physical geodesy:

� prof. dr. Nikola Cubranic, 1905-1989� prof. emer. dr. Stjepan Klak, 1920-2000� academic prof. dr. Kresimir Colic, 1938-2000

� prof. dr. Tomislav Basic

� since ∼2000 held in Technical Museum Nikola Tesla (Zagreb)

Figure 4: Schematic diagram of the horizontal variometer (large double balance Eotvos torsion balance) which was held on the Faculty ofGeodesy, Univ. of Zagreb

Compromise loss

4

Geomagnetic measurements in Croatia from the beginning of

the 20th century

”From 1902 to 1904, R. Eotvos measured all three rectangular components of

the geomagnetic field at Fruska gora and further to the north, but these data

were never released. Following gravity variation measurements during 1911 and

1912 in Srijem, Gavazzi calculated magnetic declination at 51 points using his

own and previous Eotvos data along with time variation registrations in Pula.”

(Brkic et al. 2003)

12 ° 14 °

16 ° 18 ° 20 °

42 °

43 °

44 °

45 °

46 °

47 °

48 °

Figure 5: Eotvos geomagnetic measurements from 1902 to 1904 5

Gravity field research in Croatia was strongly

influenced by Lorand Eotvos.

”I cannot finish writing this part of the book if I do not thank mr. prof. dr. baron Eotvos and

his associates dr. D. Pekar and dr. Stj. Rybar, who happily helped me on the Physical Institute

in Budapest.” (Gavazzi 1913)

5

Gravimetry, geoid modelling andgeomagnetism in Croatia– current

status

5

Study area

Figure 6: Topography of the Republic of Croatia

6

Croatian Fundamental Gravity Network

13 14 15 16 17 18 19 2042

43

44

45

46

47

RP101

RP210

RP215

RP258

RP363

RP389

RP391

RP402

RP5002

RP5004

RP5011

RP525

RP728

RP734

RPR13

HP0002

HP0006

HP0011

HP0017

HP0024HP0028

HP0033

HP0048

HP0055

HP0061

HP0066 HP0068 HP0076

HP0078HP0085

HP0088HP0096

HP0097 HP0115

HP0120

HP0124

HP0133

HP0140 HP0147 HP0153

HP0164HP0166HP0168

HP0184

HP0187

HP0191

HP0196HP0199HP0203HP0206

HP0252

HP0254

HP0258

HP0260

HP0261

HP0263

HP0267

HP0269

HP0277

HP0284

HP0286

HP0290

HP0293

HP0295

HP0301

HP0304

HP0305

HP0310

HP0312

HP0313

HP0316

HP0323

HP0329

HP0331

HP0333

HP0335

HP0341

HP0343

HP0355

HP0358

HP0360

HP0364

HP0380

HP0387

HP0397

HP0399

HP0410

HP0412

HP0415

HP0418

HP0420

HP0502

HP0506

HP0508HP0514

HP0527HP0532

HP0546

HP0548HP0550HP0552HP0555

HP0573HP0576

HP0581HP0584

HP0594

HP0603HP0605

HP0611

HP0621

HP0623

HP0630HP0632

HP0642

HP0651HP0656

HP0662

HP0669HP0671

HP0710

HP0716

HP0720

HP0729

HP0733

HP0741

HP0745

HP0758

HP0760

HP0764

HP0766

HP0774

HP0775

HP0782

HP0789

HP0790

HP0797 HP0804

HP0821

HP0828 HP0830

HP0843

HP0850HP0851

HP0857HP0858

HP0860

HP0869

HP0871

HP0906HP0909

HP0911

HP0917

HP0920

HP0929

HP0933

HP0937

HP0940

HP0942

HP0947

HP0953

HP0956

HP0959

HP0968

HP0970

GT101

GT102

GT103

GT104

GT105

GT106

GT107

GT108

GT109

GT110

GT111

GT112

GT113

GT114

GT115

GT116

GT117

GT118

GT119

GT120

GT121

GT122

GT123

GT124

GT125

GT126

GT127

GT128

GT129

GT130

GT131

GT132

GT133

GT134

GT135

GT136

AGT01

AGT02AGT03

AGT04

AGT05

AGT06

1st order gravity network2nd order gravity network

0. order gravity networkLEGEND

Figure 7: Stations of the Croatian Fundamental Gravity Network (Basic et al.2006, Markovinovic 2009)

Description

� gravity reference system: IGSN71� 0. order: 6 points (1996-2000)� 1st: 36 points (2003) + 23 points (2007-2009)� 2nd: 193 points (2010-2015), adjustment in progress� horizontal gravimetric calibration base, in progress

7

Gravity database

12 °

14 ° 16 ° 18 ° 20 °

42 °

43 °

44 °

45 °

46 °

47 °

48 °

Figure 8: Distribution of the points in the database

Description

� ∼ 28,000 points (∼1pt/18 km2)� measurements from 1970s to 1995� database was several times updated,

de-biased, cleaned� estimated accuracy: σpos = ±0.3 m,

σH = ±0.5m, σ∆g = 2 − 4 mGal

8

Maps of gravity anomalies- recent updates

(a) Map of free-air gravity anomalies (b) Map of gravimetric terrain corrections

(c) Map of complete Bouguer anomalies (d) Map of Airy-Heiskanen topo-isostatic anomalies 9

Quasi-geoid modelling in Croatia

Stats and info HRG2000 HRG2009 HRG2015 HRG2018

Basic 2000Basic 2009, Basic &

Bjelotomic 2014Bjelotomic 2015 Varga 2018

min [cm] -27.5 -7.8 -11.8 -9.7

max [cm] 24.2 5.8 15.8 12.3

mean [cm] -2.4 -1.2 0.4 0.0

st. dev. [cm] 11.4 3.5 4.7 3.0

comp. method RCR/LSC RCR/LSC KTH RCR/Stokes

no. gravity points 7500 ∼ 29300 ∼ 28000 ∼28000

no. GNSS/lev. 59 59 59 495

10

HRG2018: latest gravimetric quasi-geoid model

(e) HRG2018 quasi-geoid model (f) Estimated accuracy

11

Geomagnetism in Croatia today

13 ° 14 °

15 ° 16 ° 17 ° 18 ° 19 °

43 °

44 °

45 °

46 °

47 °

Figure 9: Basic Croatian Geomagnetic Network (Brkic et al.2013)

Description

� more than 200 years of geomagnetism in Croatia� 1st Geomagnetic Information Renewal Cycle project from 2004. to 2010.� successful cooperation with Tihany geomagnetic observatory on the

project Joint Croatian-Hungarian Geomagnetic Repeat Station Survey

(Brkic et al. 2013)� gravity anomaly maps (Varga 2014)� recent geomagnetic information models (Brkic 2019)� project in progress: 2nd Geomagnetic Information Renewal Cycle (Brkic et

al. 2018)

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Future ideas

� absolute gravity re-observations

� re-adjust all orders of gravimetric networks

� densify terrestrial gravity database

� shipborne gravimetry

� modernize height reference system

13

Thank you!

Matej Varga, PhD

Post-doc researcher and teaching assistant

Faculty of Geodesy, University of Zagreb

Zagreb, Croatia

mvarga@geof.hr13

References i

References

Basic, T. (2000). Detaljni model geoida Republike Hrvatske HRG2000. Izvjesca

Drzavne geodetske uprave o znanstveno-strucnim projektima, 11–22.

Basic, T. (2009). Unique transformation model and new geoid model of the republic

of croatia. In 1. cropos konferencija. (URL)

Basic, T., & Bjelotomic, O. (2014). HRG2009: New High Resolution Geoid Model for

Croatia. In Gravity, Geoid and Height Systems (pp. 187–191). Springer. (DOI:

10.1007/978-3-319-10837-7 24)

Basic, T., Markovinovic, D., & Rezo, M. (2006). Osnovna gravimetrijska mreza

Republike Hrvatske. Geodetski list, 60(2), 73–91. (URL)

Bjelotomic, O. (2015). High Resolution Geoid Modelling of Croatia (PhD thesis).

Faculty of Geodesy, University of Zagreb.

Brkic, M. (2019). Monitoring geomagnetic information in the territory of Croatia.

Geofizika, 36(1). (DOI: 10.15233/gfz.2019.36.3)

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References ii

Brkic, M., Basic, T., & Verbanac, G. (2003). Geomagnetism in Croatia: a Historical

Overview. Geodetski list, 57(3), 183. (URL)

Brkic, M., Pavasovic, M., Varga, M., & Grgic, M. (2018). 2nd Geomagnetic

Information Renewal Cycle in the Republic of Croatia–First Results. Kartografija i

geoinformacije: casopis Hrvatskoga kartografskog drustva, 17(30), 4–15. (DOI:

10.32909/kg.17.30.1)

Brkic, M., Vujic, E., Sugar, D., Jungwirth, E., Markovinovic, D., Rezo, M., . . .

Posloncec-Petric, V. (2013). Basic Geomagnetic Network of the Republic of

Croatia 2004 - 2012, with Geomagnetic Field Maps for 2009.5 epoch (M. Brkic,

Ed.). Zagreb, Croatia: State Geodetic Administration. (In Croatian)

Francula, N. (2007). Kratki zivotopisi preminulih dobitnika priznanja HGD-a te

pocasnih i zasluznih clanova njegovih prethodnika. In Spomen-knjiga povodom 55

godina Hrvatskog geodetskog drustva 1952 - 2007 (pp. 114–138).

Gavazzi, A. (1913). O tezi u Hrvatskoj i Slavoniji. Rad Jug. akad. znan. umjetn. knj.,

148(I-II). (URL)

Hanzek, B., Kren, T., & Vucetic, M. (2012). Geoznanstvenik Artur Gavazzi:

nepoznato (rijetko ili nikad objavljeno) o poznatome. Prirodoslovlje - casopis

odsjeka za prirodoslovlje i matematiku Matice hrvatske, 12(1-2), 3–48. (URL)

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References iii

Markovinovic, D. (2009). Gravimetrijski referentni sustav Republike Hrvatske (PhD

Thesis). Faculty of Geodesy, University of Zagreb. (In Croatian)

Szabo, Z. (2016). The history of the 125 year old Eotvos torsion balance. Acta

Geodaetica et Geophysica, 51(2), 273–293. (DOI: 10.1007/s40328-015-0126-4)

Varga, M. (2014). Geomagnetic Anomalies over the Territory of the Republic of

Croatia. Geodetski list, 68(3), 173–184. (URL)

Varga, M. (2018). The Application of Crustal Models in Regional Modelling of the

Earth’s Gravity Field (PhD thesis). Faculty of Geodesy, University of Zagreb. (DOI:

10.13140/RG.2.2.11800.08963/2)

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