I 
GEOL. CROAT. 49/2 211 - 2 15 7 Fi gs. I Tab. I ZAGREB 1996 I 

Scientific paper 

A Geodetic-Gravimetric Method for Better Modelling of 
Geological Structures in the Test Area of Croatia 

Kres imir COLIC. Tomislav BASIC. Bosko PRIBICEVIC and Damir MEDAK 
PROCEED[NGS 

Key words: Gravity fi e ld mocielling, Verti cal clcllcc­
lions, Gravity anomalies, 3D seismics, Geophysical 
prospection, Bjclovar depression, Croatia. 

Abstract 
A new approach to the modelling oflhc Earth's crust, especially 

ils upper portion, uti lising different kinds of geodeti c (vert ical den ec­
liol1 components, geoid su rface), gravimetric (Bouguer and other 
gravity anomalies) and geo ph ys ica l (3 D seis mi c from bore ho le 
prospecting) data is presented in Ihis paper. Thi s scient ific research 
formed part of a special contract between the Faculty of Geodesy and 
INA-Naf1ap lin, wit h th e aim of establ ishing the grav ity field over a 
test area in northern Croati a. [t shoul d improve th e geo physica l 
prospection for minerals, part icu larly in the fi eld of hydrocarbo n 
exp loration. 

1. INTRODUCTION 

Detailed knowledge of the Earth' s crusta l structure, 
espec ially in the layers closest to its surface, is very 
important in geodesy, but also in geophysics, e,g, for 
hydrocarbon exploration in some local areas . In order to 
increase the quantity and quality of additional informa­
ti on abo ut mass distribution for poss ible oil -explo­
ration , a broad range of scientific research has been 
undertaken by the Faculty of Geodesy over the last four 
years in the area of the Bilogo ra Hill s and Bjelovar 
depress ion. All previously existing geophysical and 
gravimetrical information was combined with carefully 
planned new geodetic and astronomi cal measurements. 
This undertaking req uired special methodology, based 
on the ex istin g TC-eomputer program (FORSBERG, 
1984). whieh has been developed and success full y 
applied l

. 

2. DATA 

There arc a number of existing data sets for the test­
area, som e of whic h were taken from the ex isting 
archi ves : gravim etric measurements, borehole dens ity 

University of Zagreb, Faculty of Geodesy, Kac iceva 26, HR 10000 
Zagreb, Croatia. 

data, and a p::ut of Rs7 and Pt depths. However, a lot of 
necessary file s required const ruction ; includi ng those 
1'01' a digital te rrain model, digital density Illodel of 
upper crust masses, digitising of Pt and Rs7 shapes in 
the larger part, filtering and re-ealculation of Bouguer 
gravi ty anomalies and complete determination of astro­
geodet ic deflections of the vertica l. 

The data files used refer to the following: 

a) a digital terrain model with block resolution of 4x5 
arcsec (app, IIOx120 m) obtained from the digitised 
Based State Map 1:5.000 (see Fig. 1), 

b) a di gital mod el of Terti ary Base (Pt) shape (more 
than 220.000 discrete points). 

e) a digital model of Rs7 shape (more than 210.000 dis­
crete points), 

d) a digital surface density model recalculated from the 
existing 2.5x2.5 arc sec model (Fi g. 2). 

e) a digital density model of Rs7 and PI shapes, empiri­
cally obtained from the existing borehole dens ity data 
in the tes t area (Fig. 2). 

D gravimetrical measurements at more than 30,000 
points, 

g) astro-geodetic deflec tions of vertical at more than 50 
points. 

3. METHODOLOGY 

The gravi metric approach in hydrocarbon prospect­
ing has been known for a long time. However, the den­
s ity contrast be tween normal and oil-filled strata was 
usually based on ly on the gravi ty anomalies - one (verti­
cal) component of the gravitational vector. In the pre­
sent research , the idea of using all three vector compo­
nents (vertical + both, W-E and N-S, components of the 
veltical deflection - sand 11) was applied. It is based on 
its stronger sensibility for small variations in mass-di s­
tribution and also smaller loses of accuracy caused by 
necessary reductions. For Ihis purpose, precise astro-

, COLIC. K .. BASIC. T .. PRIB ICEVIC. B. & MEDAK . D. t 1995), 
App[ying of th e new combined geodetic-gravimet ri c method in 
determining of geologic-geophysical st ructu res ill chosen test area 
in Croat ia.- Unpublished Final Report for Oil Company lNA -Nafta­
plin, Faculty of Geodesy, University of Zagrcb, 38 p. 



212 

Surface heights 

PT depths 

//<:fp 

~~~ /~:,., 

Fig. I Digilal modcts of surface heights, Rs7 and PI depths (in m), 

!lamica l measurements wilh the Telescope Zenith Cam­
era (TZ K2) and partly with the Zeiss Ni2-astrolab appa­
ratu s we re pe rformed on more than 50 points over our 
les t-arca (Fig 3). 

Art e r de te rmining deflections of the vertical al the 
measured po ints and calcu lating Bou guer anoma li es 

Fig. 3 Measured aud ca lcu lated vert ical de fl ecti on po in ts in the lest 
:Irca (in arcscc). 

Geologia CrO:llica 49n 

Surface density 

Fig. 2 Digi tal density model s of Earth 's sur face, Rs7 and PI shapes 
(in kg/Illl). 

us ing GRS 80 (MORITZ, 1980 ) fo r the da ta se ts men­
tioned above , we look advantage of the pre pa red sur­
fa ce de ns ity mode l (COLIC e t aI. , 1992) as we ll as 
empiri cally obtained de nsity mode ls a l Rs7 and PI 
depths (JELIC, 1984 ), in calc ul a ting te rrain influe nces. 
The lls llal method way of mass-mod e llin g ass um es a 

DenSllyanomalies 

h 

'55. 

[ i'SS . " 
" 

Fig.4 MOdelling of topog r<t phic Illnsscs. 



Colic. Basic. Pribicevic & ,v1edak: A Geodetie-Grnvimctric Method for Better MocklliTlg ... 213 

46 

45 

45 

'5 

46 

4590! 

45801 ./._ 
lL C~ , ~,' '1 .~.J 

' 57oj -~. 

40 1650 1660 16 70 1680 1690 1700 1710 

constant density for approximating polyhedra. The aim 
of the requi red method was the usc of variable density 
in all three directions (Fig. 4). 

In this case, the Earth' s crustal masses, i.e. between 
[he Earth 's surface and the Mohorovicic discontinuity, 
arc presented as three layers, characterized by heights II 

(digita l terrain model) and depths dss, and dss2 of the 
Rs7 and PI surfaces, followcd by the corresponding 
dens iti es pss, and pssr The third layer of the Earth 's 
crust, between dss2 and MohoroviciC's discontinuity, 
was assumed to have thc constant density pssJ equal to 
the density of the referencc body, i.c. the reference 
ellipsoid with the reference crust density Po' Therefore, 
[he topographic effect is more complex: bes ides the 
el imi nation of surface topography influences, effects or 
"covered" topographies (which lead [0 some compensa­
tion) arc al so el iminated. In this way a topograph ic 
reduction was defined in addition to other physical 

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~,, ~~ 

~() 

?[", 

.!() 

'" 
" 

, 
, 
, 
, 
, 
, 
o 

o 

1 0 Fig . 5 a) Topographic correction from 
3D density model (i ll 10-5 ms·2) : b) 

deflections of vertical rrOTll 3D 
: 05 

00 
density model (in arcscc) . 

effects which fu lly utilize information on ncar-surface 
(see BRKIC, 1994 for details). 

The input -data was data file s forming coarse and 
fine grids of the following data: relief heigh ls, Rs7 and 
Pt depths with corresponding density values. All coarse 
grids cover the area 45.00°-46.75° (latitude) with 15.0°­
IS .So (longitude) with a 60x90 arcsec raster. The fin e 
grids arc given in a 4x5 arcsec raster covering the area 
45.50°-46.25" (latitude) and 16.25°-17.50° (longitude) . 
The computational area is defined by 45 .625°-46.125° 
(latitude) and 16.375°-17 .375° (longitude). 

A special software package in Fortran77 was devel­
opcd to provide thc numcrical solution for th is method­
ology. It uses even coarscr grids of the above men ­
tioned data , resulting in a larger arca of computation. 
This program facilitates the calculation of the all impor­
tant topographic effects: topo-isostatic, relief correction 
and [he so called residual correction (RTM). 

Filename Mean Sf. dev_ Min Max Description 

rDTMS 160.80 79.56 91.00 863.00 D igita l terrain model 

FDllSRS7 - 161 3.61 1382.81 -6097.00 479.00 Rs7-deplhs model 

FDBSPT - 1981.81 1569.40 -6848.00 722.00 Pt-depths model 

FDDMS 2 121.16 168.64 1970.00 2800.00 Density model - surface Table t The final in-

FDDMSRS7 2250.65 14 1.27 1970.00 2800.00 Density model - surface/Rs7 
put data files (hei-
gilts and depths in 

FDDMRS Iyr 2403 .12 2 14.41 1970.00 2800.00 Density model- Rs7IPt metres. dens iti es 
in kgm·3) . 



\"J 

<'0 

4. RESULTS 

The final input data fil es arc not the most important 
resulL but deserve to be mentioned with their statistics 

Crabl e I). 
We have computed output grids of topographic eor­

reclions (complete Bouguer anomaly) and total deflec­
tions of the vertical (Fig. 5), as well as geoid undula­
tions. The Bouguer anomaly map is the result of the 
interpolation of more than 24,000 filtered gravimetric 
measurements involved with a 3D geological model. 
The mean value is 21.40 x 10-5 ms-2

, standard deviation 
±9.80 x 10-5ms·2, maximal value 60.89 x 10-5ms-2 and 
minimal value -9.81 x 10-5ms -2 . A digital model of 
Bouguer anomalies was also calculated for the constant 
dcnsities of 2120 kgm-:> and 2670 kgm-3• 

'fhe calcu lated geoid surface using a 3D-geological 
model shows that the undulations vary approximately 
40 cm over Ihe entire area. The most important result is 
a digita l model of vertical dellections based on 53 mea­
sured points (see Fig. 6). The maximal difference 
be tween the measured and topographic deflections is 
8.92 arcsec , minimal 0.39 aresec, with standard devia­
tion ±1.8 I arcscc. 

5. CONCLUSIONS 

The main aim of this rcsearch was to acquire new 
information for potential hydrocarbon exploration. 
Arter careful examination it was discovercd that the 
residual map (d ifferences between measured and calcu­
latcd deflections of vertical) shows a very significant 
anomaly of 6 arcsec near Bjelovar. This cannot be 
intcrpreted as a relief disturbance (because the area is 

Geologia Croatica 49/2 

Fig. 6 Differences between measured 
and calculated vertical deflections 
(in aresee). 

flat), and more detail ed measurements and further 

investigations are required. 
It is very inte resting that the same narrow area is 

highlighted on the map of differences between Bouguer 
anomalies with a 3D density model and Bouguer anom­
alies with a constant density model (2120 kgm -3), see 

Fig. 7. The two different approaches tend to have the 
same results over the same local area, thus justifying 
both the invesment and effort involved in this multidis­
ciplinary project. 

Acknowledgment 

We would like to thank Mr SC. Mario BRKIC for his 
contribution in this research, Dr. Rene PORSBERG for 
provid ing his excellent TC-software package and Prof. 
Wolfgang TORGE, IrE. Univcrsity of Hannover for the 
lean of the telescope zenith camera (TZK2). This inter­
esti ng research project was g ranted by the Croatian 
State Oil-Company "INA-Naftaplin ". 

6. REFERENCES 

BRKIC, M. (1994): An improved method of Earth's 
crust masses modelling ror geodet ic and geop hysi­
cal purposes.-Unpublished M.Sc. Thesis, Faculty of 
Science, University of Zagreb, 9S p. 

COLIC. K .. PRIBICEvIC, B .• RATKAJ EC. i'vl. , STO­
PAR, R. , SUMANOvAC, F. & vELIC. J. (J992): 
Init ial digi ta l density model of the surrace Earth's 
core masses in the test area "Slovenia and surround­
ing palt of Croatia" for the regional uses in physical 
geodesy.- Geodetski lis t. 46/3, 263-281, Zagreb. 



(:oli~, Basic, Pribii::evic & Mcd:tk: A Geodelic-Gr:lIIimelric Mcthod for Ileuer Modelling ... 2 1 S 

Fig. 7 Differences or I30uguer anomalies: dgJD-dg212o (in I0 5ms·\ 

r:ORSBERG , R. (1984) : A Study of Te rra in Reduc­
tions, Density Anomali es and Geophysica l In ver­
sion Meth ods in Gravity Field Modelling.- Depart­
ment of Geodetic Sc ience and Surveying, Ohio 
State University, Colu mbus, Report, 355, 129 p. 

JELlC, K. ( 1984) : Odnos gustocc i poroznosti S dubi­
nom Iitostratigrafskih formacija savskc i drav skc 
potoline.- Naha, 35, 637-643, Zagreb. 

4.00 

3.00 

2.00 

MORITZ, H. (1980): Geodetic Refere nce System 
1980.- Bulletin Geodesique, 58/3, 388-398. 



216 Geologia Croatica 49n