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, APRIL 2014, 65, 2, 163—174 doi: 10.2478/geoca-2014-0011
Introduction
The Danube Basin displays peculiar anomalies in the gravity
and magnetic fields that are supposedly associated with deep
seated sources within the pre-Neogene basement (Kubeš et
al. 2001, 2010). According to Kubeš et al. (2010) the inter-
pretations of these sources are insufficient and problematic
and thus remain open for further investigation. Here we
present a new interpretation of both the Kolárovo gravity
anomaly (gravity high) and the Kolárovo magnetic anomaly
(anomaly “N4” in Kubeš et al. 2010) by means of a 3D in-
version of gravity and magnetic data based on depth-wise
separation of sources and the so-called “method of local cor-
rections”. This non-linear inversion method can invert gravity
or magnetic data in terms of interface (contact) surfaces or
anomalous source bodies, as well as a combination of these
two classes of sources. The inversion yields several admissi-
ble solutions – admissible from the viewpoint of potential
field data. This is the strength and advantage of the method:
the interpreter has at hand a multitude – a set – of model
solutions that satisfy the observed surface potential data and
can take a look at them from the viewpoint of constraining
information, if available from other earth science disciplines.
Joint interpretation of gravity and magnetic data in the
Kolárovo anomaly region by separation of sources and the
inversion method of local corrections
ILYA PRUTKIN
1
, PETER VAJDA
2
, MIROSLAV BIELIK
2,3
, VLADIMÍR BEZÁK
2
and
ROBERT TENZER
4
1
Institute of Earth Geosciences, Jena University, Burgweg 11, 07749 Jena, Germany; Ilya.Prutkin@uni-jena.de
2
Geophysical Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 05 Bratislava, Slovak Republic; Peter.Vajda@savba.sk
3
Department of Applied and Environmental Geophysics, Faculty of Natural Sciences, Comenius University, Mlynská dolina,
842 15 Bratislava, Slovak Republic; bielik@fns.uniba.sk
4
Institute of Geodesy and Geophysics, School of Geodesy and Geomatics, Wuhan University, 129 Louyu Road, 430079 Wuhan, China
(Manuscript received June 21, 2013; accepted in revised form December 10, 2013)
Abstract: We present a new interpretation of the Kolárovo gravity and magnetic anomalies in the Danube Basin based
on an inversion methodology that comprises the following numerical procedures: removal of regional trend, depth-wise
separation of signal of sources, approximation of multiple sources by 3D line segments, non-linear inversion based on
local corrections resulting in found sources specified as 3D star-convex homogenous bodies and/or 3D contrasting
structural contact surfaces. This inversion methodology produces several admissible solutions from the viewpoint of
potential field data. These solutions are then studied in terms of their feasibility taking into consideration all available
tectono-geological information. By this inversion methodology we interpret here the Kolárovo gravity and magnetic
anomalies jointly. Our inversion generates several admissible solutions in terms of the shape, size and location of a
basic intrusion into the upper crust, or the shape and depth of the upper/lower crust interface, or an intrusion into the
crystalline crust above a rise of the mafic lower crust. Our intrusive bodies lie at depths between 5 and 12 km. Our lower
crust elevation rises to 12 km with and 8 km without the accompanying intrusion into the upper crust, respectively. Our
solutions are in reasonable agreement with various previous interpretations of the Kolárovo anomaly, but yield a better
and more realistic geometrical resolution for the source bodies. These admissible solutions are next discussed in the
context of geological and tectonic considerations, mainly in relation to the fault systems.
Key words: Western Carpathians, Danube Basin, intrusion, applied geophysics, gravity, magnetic field, Kolárovo
anomaly.
Additional geophysical or other geoscientific data can be
used, such as geological and tectonic, to discriminate be-
tween these admissible solutions, and to favour the likely
and most realistic one.
The Kolárovo gravity anomaly (high) is located in the
south-eastern part of the Danube Basin, in the northern part of
the Pannonian Basin, near the village of Kolárovo, southern
Slovakia (Fig. 1). The anomaly is one of the largest and most
famous gravity highs in the Western Carpathian-Pannonian
area. Therefore it has been of great interest to geophysicists
and geologists since the early 1960s. In terms of complete
Bouguer anomaly the Kolárovo high is fairly isometric and
reaches a magnitude of + 28 mGal (1 mGal = 10 µm/s
2
). After
removing the gravitational effect of the sedimentary basin fill,
the gravity high in terms of a stripped Bouguer anomaly has
an amplitude of + 74 mGal, which, relative to the ambient
field, amounts to some + 26 mGal (Bielik et al. 1986).
According to the existing geological and geophysical re-
sults (Gaža 1966, 1967, 1970; Fusán et al. 1971, 1987; Bielik
1984; Sitárová et al. 1984, 1994; Bielik et al. 1986; Šefara et
al. 1987; Šefara & Szabó 1997), the Kolárovo gravity high
indicates the existence of a higher-density mafic (basic)
anomalous body within the Pre-Tertiary basement of the
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southern part of the Danube Basin. In the Kolárovo anomaly
region and its vicinity the Neogene sediments reach a thick-
ness of 2.3 to 3.7 km (Fusán et al. 1987; Šefara et al. 1987).
The boreholes Kolárovo 2, 3, and 4 around the anomaly de-
tected the basement at the depths of 3050, 2690, and 2640 m,
respectively (Gaža 1966, 1967, 1970). The basement is made
up of granitoid rocks and crystalline shists of the Hercynian
basement now included in the Veporicum Alpine tectonic
unit. In the Kolárovo anomaly region the Mesozoic and the
Paleogene complexes are missing below the Neogene sedi-
ments, which implies uplift and erosion of Mesozoic com-
plexes and of Paleogene sediments. It is suggested that the
apical part of the anomalous body is nearest to the surface in
the area of Kolárovo. The quantitative interpretation of this
gravity high (Bielik 1984; Sitárová et al. 1984, 1994; Bielik et
al. 1986; Šefara et al. 1987) has revealed that the density of the
anomalous body varies from 2900 to 3050 kg/m
3
, compared
to the density of the upper crust of 2700 kg/m
3
, the upper
boundary of the anomalous body being interpreted at about
4.5—5.0 km. The depth of the center of mass of the body was
interpreted at about 9.5—12.5 km. The geophysically indicated
higher density mafic body below the Kolárovo gravity high
has not been verified by drilling yet. Seismics also has not so
far verified what this body is composed of.
Sitárová et al. (1984) interpreted the Kolárovo anomaly us-
ing stripped gravity anomalies, where the gravitational effect
of Tertiary sediments was removed from the Bouguer anomaly.
They interpreted a source body by means of two methods:
multipole analysis and integral characteristics. They deter-
mined the source body as a right-rectangular homogenous
prism of a 280 kg/m
3
density contrast with a top plane at 4.5
to 5 km with a center of mass at 9.5 to 12.5 km. Bielik et al.
(1986) interpreted the Kolárovo high Bouguer anomaly
stripped of the gravitational effect of the sediments by means
of 3D forward modeling using polyhedra. The determined
source body (ibid) of a 300 kg/m
3
density contrast descends
steeply from its apical part at depth 4.5 to 5 km to depths of
10 to 12 km, and then gently down to some 20 km. Sitárová et
al. (1994) interpreted the Kolárovo high using stripped gravity
anomalies by means of the so-called “option method” that uti-
lizes automated minimization of a multiparametric functional
approximating the source body by vertical steps. In this method
source masses can concentrate and grow. Their solution con-
sists of a set of blocks (ibid). The upper boundary of their
source body ascends to depths of 5 to 6 km (still below the
basement of the Tertiary sediment basin fill) while its bottom
boundary is at 13 km. A novice inversion method of Pohánka
(2001), called the “harmonic inversion” yields a new interpre-
tation in terms of the anomalous body generating the Kolárovo
high, the center of mass of which appears to be at 10 km or
even lower. The Truncation Filtering Methodology interpreta-
tion of the Kolárovo high yielded an estimate of the depth of
the center of mass of the body at 8.7 km (Vajda et al. 2002).
The Kolárovo magnetic high (N4 anomaly in Kubeš et al.
2010) coincides with the Kolárovo gravity high (Fig. 1).
Bezák et al. (1997) interpret the magnetic anomaly as caused
by basic crystalline complex rocks or mafic remnants from a
suture of the Meliatic ocean due to emplacement of astheno-
lith associated with extension processes in the Neogene.
Other anomalies in the vicinity of Kolárovo were also inter-
preted in this manner. Valach & Váczyová (1999) interpret
their ground-measured magnetic profile across the anomaly
by means of a damped approximate modeling technique (for
potential field data inversion) in terms of a 2D basaltic intru-
sion of a polygonal shape rising from a basalt stratum. Their
body has its lower boundary at 18 km while its top boundary
rises to depths of 5.3—6.6 km depending on the number of ver-
tices of the modeled polygonal body. Kubeš et al. (2010) in-
terpret the Kolárovo magnetic anomaly (N4 of their map
based on aeromagnetic data) by means of modeling (using the
Oasis Montaj geophysical software) in terms of a basic intru-
sive body with its top interface at depths of 5.5 to 6 km (ibid),
and so still within the bedrocks of the Tertiary sediments.
Data
The gravity data set, given in an equidistant regular grid,
was obtained from Pohánka (2001), who preprocessed the
gravity data of (Kubeš et al. 2001). The origin of the local
planar coordinate system chosen for our gravity study area
lies at the point of latitude 47°57’N, longitude 18°00’E,
and height above sea level of 110 m, the x-coordinate being
easting and y-coordinate northing. The gravity data are rep-
resented by the vertical component of the gravitation accela-
ration vector. Since the given area lies in lowlands and is
relatively flat (variations in height are of only a few meters),
no topographic correction was applied, while the data were
vertically reduced to the reference altitude of 110 m using
the free air gradient. The regular equally spaced grid of data
was produced from the original irregularly placed data points
by an in-house interpolation method described by Pohánka
(2001). The interpolation method smoothes the data accord-
ing to a given parameter, the so-called smoothing distance.
Gravity data were interpolated onto a 200 by 200 meter grid.
A smoothing distance of 400 m was chosen, while the mean
minimum distance between the original data points was
425 m, which resulted in minimum smoothing effect. A mean
value over the regular grid was subtracted from the gridded
gravity, resulting in a local gravity anomaly relative to the sur-
rounding regional field. The gravity data are shown in Fig. 1c.
A magnetic profile data set was made available to us by
Fridrich Valach (Valach & Váczyová 1999). This profile of
total magnetic field measurements, striking at 15° north-
west, crosses borehole K288 (latitude 47°57’01”N and lon-
gitude 18°02’09”E) at its 18
th
km. The profile magnetic
data are shown in Fig. 9. Arial magnetic data for the Kolárovo
area were taken from Kubeš et al. (2001) on a selected rect-
angle specifying our study area (Fig. 1d). The towns of
Kolárovo and Nesvady are displayed in Fig. 1 for geographi-
cal orientation.
Inversion method
The inversion method used in our study is the so-called
“method of local corrections” that has been developed by
Prutkin (1983, 1986). It has been applied in global studies
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Fig. 1. a – Location of the study area (rectangle) within the Carpatho-Pannonian Region; b – Location of the study area (rectangle) within
the Danube Basin of southern Slovakia; c – Observed gravity data (mGal). Horizontal coordinates are local easting (x) and northing (y)
both in [km], specifically chosen for the gravity dataset; d – Observed magnetic data (nT). Horizontal coordinates are local easting (x) and
northing (y) both in [km], specifically chosen for the magnetic dataset.
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when inverting gravity or magnetic data in terms of major in-
terface surfaces in planetary bodies (Prutkin 1989, 2008). In
regional studies it has been applied to invert gravity and
magnetic data in order to determine the Moho boundary in
the Red Sea area (Prutkin & Saleh 2009). The capabilities of
the method for interpreting gravity data in local/regional struc-
tural studies were demonstrated also on the Kolárovo gravity
high (Prutkin et al. 2011). Here we attempt a joint interpreta-
tion of both the magnetic and gravity data in the area of the
Kolárovo anomaly taking into consideration previously pub-
lished interpretations, as well as tectono-geological evidence.
This inversion method for potential data consists of two
main steps. In the first step the data are pre-processed so as
to extract (separate) the signal contained in the data that orig-
inates from sources in a preselected depth interval. This is
achieved by subsequent harmonic upward and downward
continuations of the data in the region. The second step rep-
resents the 3D inversion. This step depends on whether a
contrast contact surface or an anomalous source body is
sought. In the case of solving for sources represented by
anomalous compact bodies, first the 3D position and approx-
imate shape of the sources is estimated using 3D line seg-
ments approximation. Next a non-linear inverse problem is
solved in terms of integral equations, seeking the geometry
of the surfaces of arbitrary compact convex anomalous bodies.
In doing so, the line segments approximation is necessary to
initiate the inversion procedure and to arrive at a solution. In
the case of solving for sources represented by contrasting
contact surfaces, the non-linear inverse problem, given also
in terms of integral equations, is solved without the need for
line segments approximation, seeking the geometry of the
contrast contact surfaces. In both cases – bodies and contact
surfaces – no linearization is applied to solve the inverse
problem. Instead, a method of local corrections is adopted.
All the procedures of the inversion method, to be applied
here, are described mathematically in detail by Prutkin et al.
(2011). Below we describe them only phenomenologically,
to make the manuscript transparent and briefer.
Depth-wise signal separation of sources
The purpose of the depth-wise signal separation is to iso-
late the signal of multiple vertically distributed sources. In the
case of the Kolárovo anomalies, the source (causative) body/
bodies are assumed to be in the crystalline basement beneath
the Neogene sediments. The thickness of the sediments in the
lowland varies between 2.3 and 3.7 km in the Kolárovo area.
We chose to eliminate the signal of sources between the topo-
graphic surface and the depth d = 2 km. Later we also separate
the signal into that of a lower crust elevation and that of an
intrusion above it, by preselecting a depth d of the division
level. The separation is accomplished by making the observed
field harmonic down to the depth d. Our numerical procedure
is based on subsequent triple harmonic continuations: upward
over d, downward over 2d, and upward again over d.
First we continue the observed data upwards from the topo-
graphic surface to the height h = d to attenuate the effect (sig-
nal) of the sources in the near-surface layer. This numerical
procedure causes major errors in the vicinity of the geographi-
cal boundary of the study (survey) area. To reduce these trun-
cation errors and edge effects we need a model of the regional
field to be subtracted from the observed field prior to the up-
ward continuation. The regional field is determined mathe-
matically as a harmonic function (in 2D sense) within the
study area matching the observed data on the boundary of the
study area. The gravity and magnetic regional fields deter-
mined by this method are shown in Fig. 2. When we subtract
the regional field, the residual field will be equal to zero at the
geographical boundary of the area. By harmonically continu-
ing the data with such a trend removed, no truncation errors
are introduced by numerical integration (evaluation of the
Poisson integral of the upward continuation in planar approxi-
Fig. 2. a – Regional gravity trend (mGal); b – Regional magnetic trend (nT).
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mation) over the residual field. Due to properties of harmonic
functions, the regional trend (field) has no extremes (minima
or maxima) within the study area, so we do not create false
anomalies (and respective false causative bodies).
Second, we continue the obtained function downwards to
the depth d below the earth’s surface, which means vertically
over the distance 2d. While the upward continuation repre-
sents a direct problem solved by numerical evaluation of the
surface Poisson integral, the downward continuation repre-
sents an inverse problem formulated by an integral equation
(the Poisson integral). As it is a linear ill-posed inverse prob-
lem, some regularization must be, and is, applied (cf. also
Pašteka et al. 2012).
Third, the field is harmonically continued upward from
depth d back to the surface. This three-step continuation pro-
cedure (Vasin et al. 1996) produces a field that is harmonic
everywhere above depth d. Consequently the resulting field
represents a signal of causative bodies (sources) from below
the depth d. The detailed description of this procedure includ-
ing the mathematical apparatus is given in section 2 of (Prut-
kin et al. 2011). We apply the above described procedure to
the Kolárovo gravity anomaly. Our goal is to remove the sig-
nal of shallow sources down to the depth of 2 km, which cor-
responds to a safe minimum thickness of the Neogene
sediments. In Fig. 3 we present the Kolárovo gravity anomaly
after removal of the signal of shallow sources with the regional
trend restored. The amplitude and pattern are practically un-
changed (compare with Fig. 1a). The obtained field is very
similar to the original one. It is a confirmation that the Kolárovo
gravity high is caused mainly by deeper sources.
The Kolárovo magnetic anomaly after removing the re-
gional field (trend) and after removing the signal of shallow
sources down to the depth of 2.5 km, namely the residual
magnetic field, is shown in Fig. 10.
Line segments approximation of sources
Next the sources are approximated by 3D line segments
that approximately generate the residual field (data) obtained
by removing the regional trend and the signal of shallow
sources. The line segments indicate the location and geome-
try of the causative bodies (sources), as well as their relative
strengths or relative contributions to the residual field. Each
line segment is defined by 7 parameters: 3 for the position of
each end point, and 1 for its density/magnetization. The pa-
rameters are resolved from the residual field data by means
of non-linear minimization (Prutkin et al. 2011).
Fig. 4. a – Residual gravity anomaly (mGal); b – Gravity field of 3 line segments (mGal).
Fig. 3. Observed gravity data after removal of signal of shallow
sources down to the depth of 2 km (mGal).
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Three line segments are sufficient for fairly accurate ap-
proximation of the Kolárovo gravity data. The RMS of dif-
ferences between the residual gravity data and the field of
the line segments is 0.57 mGal. The residual gravity field (a)
and the field of the three line segments (b) are presented in
Fig. 4. All three line segments lie at depths between 6 and
9 km. It should be noted that we were seeking 21 parameters
of the line segments respective to nearly 60,000 observa-
tions. Hence, this procedure is quite stable.
Inversion by the method of local corrections
Next the residual field is inverted. The inversion is carried
out for restricted classes of causative bodies. When we seek
the geometry (shape) of an unknown homogenous body; the
only requirement is that the sought body is assumed to be
star-convex relative to some point of the body. The position
of this point is chosen with the help of the 3D line segment
approximation. The boundary of the body is described by a
radius vector from this point, the radial distance being a
function of two angles of the local spherical coordinate system
centered at this point. The body is assumed to be homogenous
and of a preselected density contrast. The gravitational in-
verse problem can be reduced to a non-linear integral equa-
tion respective to an unknown function – the 3D geometry
of the boundary (Prutkin et al. 2011). For this restricted class
of solutions and for a fixed preselected value of the density
contrast, the solution of the inverse problem is unique. This
inverse problem is solved by the so-called “method of local
corrections”. The integral equation for the boundary is upon
discretization turned into a system of non-linear equations
that are solved in an iterative fashion. Again, the problem is
ill-posed and requires regularization. The method is de-
scribed in detail including the mathematical apparatus in
(Prutkin et al. 2011). The method of local corrections can
also be used for another class of restricted solutions – for a
contact surface of a density contrast (density interface). In
this case the line segments approximation is not required.
The density contrast and the vertical position – depth D of
the horizontal asymptotic plane – are pre-specified. The
mathematical apparatus for this inversion procedure is de-
scribed in detail in (Prutkin & Saleh 2009). The solution of
our non-linear inversion can also consist of a combination of
anomalous bodies and contact surfaces.
Inversion results
In this section we will present several solutions that can be
reached by the inversion method based on the method of lo-
cal corrections. In the case of the Kolárovo gravity anomaly,
we found three line segments representing the sources. The
central line segment has a substantially higher line density
than the other two. In “solution A” we relate the field of the
two lighter segments to the bedrock topography (bottom
boundary of sediments) that we determine – using the
method of local corrections – as a contact surface. We at-
tribute the effect of the main (central) line segment to an
anomalous body representing an assumed mafic intrusion.
For this body we assume a density contrast of 300 kg/m
3
.
The intrusive body found in this way is located entirely be-
low the upper boundary of the crystalline basement (Fig. 5).
The depths to the basement obtained by inversion vary be-
tween 2 and 3 km (Fig. 5). Figure 5a shows a plan view of
the mafic intrusion (including its respective line segment), as
well as the basement topography presented by means of
depth isolines. Figure 5b and 5c show W—E and S—N cross-
sections of “solution A”, respectively. In the vertical sec-
Fig. 5. a – Solution A, plan view. Depth isolines [km] define the
shape of the basement interface; b – Solution A, W—E vertical sec-
tion; c – Solution A, S—N vertical section.
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tions the solid line above the surface corresponds to residual
gravity and the dashed line to the gravity generated by the
obtained sources of “solution A”. Depths to the center of
mass of the intrusion, as well as to the upper and lower
boundary of the body, are in good agreement with the previ-
ous interpretations of Sitárová et al. (1984, 1994) and with
the upper part of the anomalous body of Bielik et al. (1986).
By means of our methodology we can obtain an alternative
solution, denoted as “solution B”, that is also admissible from
the viewpoint of gravity data. We can attribute all gravity sig-
nal to an elevation of a contact surface of a density contrast of
300 kg/m
3
, representing the density interface between felsic
crystalline crust and mafic lower crust. In this case, we do not
need the approximation by 3D line segments. We directly in-
vert the residual gravity data. The method of local corrections
provides depths to the contact surface. They vary from
22.5 km at the outskirts of the study area to 7.5 km respective
to the peak of the gravity high. Solution B is presented in
Fig. 6 in two ways: (a) as a map of the contact surface topo-
graphy (depth isolines), and (b) as a shaded 3D surface. For
visualization of 3D objects we use the Poisson Surface Recon-
struction software (Kazhdan et al. 2006).
Fig. 6. a – Solution B: Upper/lower crust interface (depth isolines
[km]); b – Solution B: Upper/lower crust interface (3D shaded
view).
Fig. 7. a – Mafic intrusion of solution C (3D shaded view);
b – W—E vertical section of solution C.
Another admissible solution, denoted as “solution C” is
shown in Fig. 7. Therein, we attribute the whole residual
gravity signal (Fig. 4a), approximated by the field of the
three line segments (Fig. 4b), to a single causative body rep-
resenting a mafic (basic) intrusion. In this case, we obtain an
intrusive body similar to that of “solution A”, presented in
Fig. 5, but with a more complex geometry. Figure 7b shows
its W—E cross-section running through the center of the grav-
ity high at y = —2.5 km.
Yet another admissible solution, denoted as “solution D”
(Fig. 8), is based on the following considerations. By the tri-
ple harmonic continuation procedure (of sec. 3.1) we have
removed from the observed gravity data the signal of sources
between the surface and the preselected depth of 10 km. The
remaining gravity signal has an amplitude of 10 mGal
(roughly a half of the original amplitude). This is a clear in-
dication that a part of the source of the Kolárovo gravity
high may lie below the level of 10 km. The gravity signal of
the deeper source looks like a low-frequency isometric
anomaly. We relate this signal to an elevation of mafic lower
crust (density contrast of 300 kg/m
3
relative to the felsic
crust). After subtracting this low-frequency signal, we re-
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ceive a remaining field. This remaining field can be approxi-
mated quite accurately (on the level of 0.75 mGal) by two
3D line segments. By the method of local corrections a com-
pact anomalous body respective to these two line segments
is found, which represents an intrusive mafic body. Hence
“solution D” consists of the upthrust of the mafic lower crust
above which is the mafic intrusion. Compared to solution C
the intrusion is smaller and of different shape. Figure 8a
shows solution D in 3D, while Fig. 8b its W—E vertical
cross-section running through the center of the gravity high
at y = —2.5 km.
We can see that in the case of gravity data there are several
admissible solutions, within the class of restricted solutions
defined in terms of density contrast contact surfaces (inter-
faces) and star-convex homogenous causative bodies that
can satisfy the observed gravity field. These solutions may
help to resolve the tectono-structural geological situation.
Once a solution is selected and a density contrast specified,
the geometry of a causative body or a contact surface is de-
termined by the inversion method uniquely. All the presented
gravimetric solutions were obtained by assuming a density
contrast of 300 kg/m
3
, meant to represent the contrast be-
tween upper and lower crustal material. Theoretically a dif-
ferent density contrast could have been selected, leading to
Fig. 8. a – Solution D: Mafic intrusion fed by lower crust upthrust
(3D shaded view); b – W—E vertical section of solution D.
Fig. 9. Inversion results for Kolárovo magnetic profile data.
similar gravimetric solutions of different sizes and shapes,
which would expand the number of admissible solutions.
Let us now turn our attention to inverting the magnetic
data in the same area. The profile of magnetic data was ap-
proximated by means of a set of thin layer magnetic anoma-
lies. This 2D source represents a cylinder the section of
which is, by any perpendicular plane, a line segment. Only
one thin layer is sufficient for reasonable approximation of
magnetic data (see Fig. 9). Since this source is determined
by 5 parameters only (scalar magnetization and 4 coordi-
nates of 2D line segment ends), our inversion for thin layer
parameters is very stable. Results are slightly better than for
the best model, “Model 1”, of Valach & Váczyová (1999).
Residuals between magnetic data and thin layer anomaly
have RMS = 5.97 nT, while the model of Valach & Váczyová
(1999) has RMS = 7.81 nT. In the left part of the profile the
approximation by the thin layer anomaly performs definitely
better. The length of the line segment in Fig. 9 is probably
too big, because we treat the source of the Kolárovo magnetic
anomaly as a two-dimensional source. The depths to the seg-
ment ends are again between 6.5 and 10 km. This indicates
that the intrusive body is magnetic in this interval of depths.
In terms of areal magnetic data at Kolárovo (Fig. 1b), we
first calculate a 2D harmonic function, which represents a
model regional field, namely a trend to be removed (Fig. 2b).
This regional trend is assumed to represent the effect from
sources beyond the area of investigation. After removing this
trend we apply the triple harmonic continuation procedure to
remove the signal of shallow sources down to the depth of
2.5 km. This results in a residual magnetic field (Fig. 10).
Next we transform this residual magnetic field into pseudo-
gravity. For this purpose we exploit a simple layer integral
distributed on a surface parallel to the physical one. This
procedure is described in detail mathematically in (Prutkin et
al. 2012). The computed pseudo-gravity is shown in Fig. 11.
Pseudo-gravity is then approximated by one, two and three
line segments. They are located at depths between 5 and
10 km, just like those in the case of the Kolárovo residual
gravity anomaly. This coincidence gives a strong case for the
notion that both the gravity and the magnetic fields are
caused by the same source, and that the source body is mag-
netic down to at least the depth of 10 km. Finally the method
of local corrections is applied to invert the pseudo-gravity
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Fig. 10. Residual Kolárovo magnetic anomaly (nT).
Fig. 11. Residual Kolárovo pseudogravity anomaly (mGal).
Fig. 12. Magnetic contact surface (depth isolines [km]).
and to obtain a magnetic model of the anomalous causative
bodies in terms of a magnetic contrast contact surface
(Fig. 12). Depths to the contact surface are between 7.7 and
23.5 km, which approximately matches the solution of the
Kolárovo gravity anomaly in terms of a density contrast
(300 kg/m
3
) contact surface (solution B in Fig. 6). Depth iso-
lines of the magnetic contact surface are presented in Fig. 12.
The shape of this contact surface is similar to that obtained by
gravity data inversion, but does not coincide entirely. A possi-
ble explanation is that the up-thrusted lower crustal mafic ma-
terial is magnetically heterogenous, or not entirely magnetic.
The Curie temperature isotherm in this area lies just above the
Moho boundary (Dérerová et al. 2006; Grinč et al. 2013), so
an intrusive body would start losing its magnetization only at
depths approaching the Moho.
Tectono-geological interpretation of inversion
results and discussion
The inversion results of gravity and magnetic data in the
Kolárovo anomaly area must be viewed in the context of the
tectonic evolution of the Pannonian Basin and particularly of
its northern part, the Danube Basin, including the build-up of
their basements. Several tectonic events and processes took
part in forming the Pannonian Basin. According to current
knowledge (e.g. Ratschbacher et al. 1991; Csontos et al. 1992;
Horváth 1993; Kováč et al. 1993; Nemčok et al. 1998), among
the most significant are: (a) escape of crustal fragments from
behind the Alps into the space of the closing flysch basin al-
ready during the Paleogene and Neogene, (b) oblique collision
of these fragments with the European platform, movement on
strike-slip faults, (c) origination of an asthenolith due to fin-
ishing subduction, (d) thinning of crust as a result of partial
melting and assimilation of lower crust, (e) subsequent exten-
sion and subsidence, sedimentation and volcanism finishing
with basaltic intrusions due to differentiation of mantle mate-
rial. The basin basement is very inhomogenous, formed by
several crustal tectonic units (Fusán et al. 1987; Vozár et al.
2010). Tectonic borders between the segments are represented
by fault zones, which mean weak zones, suitable for the ris-
ing of magmatic material or eventually mantle material. One
such zone, the Hurbanovo tectonic zone, between the Ve-
poricum tectonic unit of the Western Carpathians and the
Pelso Unit of the Hungarian Midland also runs in the vicinity
of the Kolárovo anomaly (Fusán et al. 1971).
When interpreting the Kolárovo anomaly there are two
contrasting environments available – the upper crust (aver-
age density of 2700 kg/m
3
) and the basic material (average
density of 3000 kg/m
3
), either in the form of an intrusion or
in the form of elevated (arced up) lower crust. From the geo-
physical viewpoint, according to our inversion results, three
scenarios are available: intrusion body, convex elevated con-
tact surface, a combination of the two. We consider as signif-
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Fig. 13. The Kolárovo anomaly in its tectonic context: 1 – assumed relics of South Penninic oceanic crust; 2 – supposed relics of Meliatic
oceanic crust; 3 – faults (after Tectonic Map of the Slovak Republic, Bezák et al. 2004): La – Láb, MK – Malé Karpaty, Pv – Považie,
Mo – Mojmírovce, Pa –Palárikovo, Le – Levice, Ht – Hont, Hu – Hurbanovo, Ko – Komárno, Ra – Rába; 4 – Kolárovo boreholes:
K – Kolárovo anomaly.
icant our finding that the magnetic source body pretty well
coincides with the heavier source body interpreted from
gravity data, which supports a previous assumption that the
source body is made up of basic material.
We comment on the individual inversion results as fol-
lows: solutions A and C – a single intrusive body of basic
magma (gabbro) is acceptable with respect to its shape, but
its dimensions in the context of Western Carpathians would
be too rare (unique), solution B – an elevation of the upper/
lower crust boundary alone would thin the upper crust in the
studied region, which would also require an uplift of the Moho
boundary (not considered in the inversion), solution D – a
combination of an elevated lower crust surface with an intru-
sive body above it seems to us more likely.
According to the hypothesis/interpretation of Bezák et al.
(1997) the Kolárovo anomaly is caused by mafic remnants of
the Meliaticum oceanic crust inside a suture zone at which an
asthenolith rose at an angle. The rise of the modified lower
crust material or asthenosphere material was facilitated by an
extension process that gave rise to the Danube Basin. How-
ever, our inversion results do not indicate an asthenolith or
mafic remnants in a slanted position under an angle as is indi-
cated by Bezák et al. (1997). To us a more likely explanation
seems to be that the suture only served as path of least resis-
tance for the rising magma, while the intrusion which origi-
nated shows no slanted shape. Another admissible solution
consistent with both the gravity and magnetic data is a combi-
nation of an elevation of the upper/lower crust boundary and
a mafic intrusion into the felsic upper crust above it, the geo-
metry of which is given in Fig. 8. It is also possible to invert
the magnetic and gravity data in terms of an isolated contrast-
ing heavy compact anomalous body, as shown in Figs. 5, 7
and 9. However, from the viewpoint of geology and tectonic
development, it makes more sense to assume a support for this
body, or source of partially melted intruding upper mantle ma-
terial for it, from well below the 10 or 12 km depths.
Associated with interpreting the Kolárovo anomaly is also
the broader tectonic context. It is curious that this anomaly
falls into a line of other magnetic and partially also gravity
anomalies located within a band of NE strike along the Rába
Fault, starting in Austrian territory, passing through Hungary,
reaching the Hurbanovo Fault, and continuing in Slovakia in
a W—E direction connecting to the Diósjenő (or Rapovce)
fault system. These fault systems divide the Alpine—West-
Carpathian tectonic systems from the Pelso Unit to the south,
accompanied by gravity and magnetic anomalies (Bielik et al.
2006; Wybraniec et al. 2006). There is a difference between
them, however. While the SW branch around the Rába Fault
might have remnants of the oceanic South-Peninic crust incor-
porated within it, the Hurbanovo branch of the anomalies with
its continuation to the NE is most likely caused by basic intru-
sions into the crust, which during the extension made use of
the weakened part of the crust on the transported suture, only
this time not of the Southern Peninicum, but instead of the
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Meliaticum. The South-Peninicum suture must have occupied
a forefield of the Tatricum and Veporicum complexes, into
which it also extends, or wedges, while the Meliaticum suture
was located more to the south, on the border with the Pelso
Unit (being composed by Paleozoic rocks as the equivalent of
the Graz Paleozoicum of the Upper Austro Alpine Units and
blocks of the Cadomian basement). The Peninic suture was
transported during the Neogene movements of the Inner West-
Carpathian blocks towards the NE, and therefore its remnants,
if they exist, can be located below the Tatricum. Additional
blocks of Pelso type, pulled up from SW, apparently dragged
with them in the forefield remnants of the oceanic Jurassic su-
ture zone of the Meliaticum. The position of the Kolárovo
anomaly has already been defined similarly (Bezák et al.
1997). Šefara & Szabó (1997) prefer an explanation involving
an intrusion of upper mantle material of a laccolith type, but
they link it with the Rába-Hurbanovo system. For reasons
stated above these two tectonic systems should be distin-
guished as distinct. That is why the interpretation of Balla
(1994) regarding a possible continuation of the south-Penninic
structure into the Hurbanovo fault is unlikely. Moreover, the
anomalous bodies such as those in the Ivrea zone have dif-
ferent density and geometric characteristics. From a tectonic
point of view the occurrence of eclogitic bodies in the upper
crust is possible, however, it leads to the same issue, that
such bodies (e.g. Janák et al. 2004) are of a different shape
and size than the Kolárovo body.
The position of the Kolárovo anomaly in relation to tec-
tonic structures is illustrated in Fig. 13. There the position of
the main tectonic units (Austro-Alpine units, Tatricum, Ve-
poricum, Pelso), of the assumed suture zones of the South-
Penninicum and Meliaticum, as well as of the individual
faults according to the Tectonic Map of the Slovak Republic
in the scale 1 : 500,000 (Bezák et al. 2004) is shown.
Conclusions
The inversion methodology presented here represents a
versatile approach to interpreting potential field data in tec-
tono-geological studies. Its flexibility dwells in separation of
multiple source signals. Its merit is in producing several ad-
missible solutions that can be – from the viewpoint of geo-
logical or tectonic interpretation – studied, compared and
evaluated in terms of their feasibility in the context of the
tectono-geological situation and evolution in the studied
area. This versatility of the applied inversion methodology is
demonstrated here by producing several admissible gravi-
metric inversion solutions for the Kolárovo anomaly:
1) A simple intrusive body below the basin sediments at
the depth interval between 5 and 10 km, while determining
also the shape of the bedrock boundary, obtained by dividing
the gravity signal into a contribution of the intrusion and a
contribution of the sediments/bedrock interface (solution A);
2) A more complex single intrusive body at the depth in-
terval between 5 and 11 km, obtained by assigning all the
gravity signal to the intrusion (solution C);
3) An upper/lower crust contact surface defined by its 3D
shape, obtained by attributing the entire gravity signal to an
elevation of this discontinuity (density contrast) surface
(solution B), reaching the altitude of slightly above 8 km be-
low sea level (b.s.l.);
4) A rise of the upper crust (upwards to the level of 12 km
b.s.l.) feeding an intrusive body above it (at an interval of
depths between 5 and 12 km), representing upthrusting of
basic magma into the upper crust, obtained by distributing
the gravity signal to the intrusion and to the lower crust up-
lift (solution D).
All the listed solutions were obtained by assuming a density
contrast of 300 kg/m
3
, meant to represent the contrast be-
tween upper and lower crustal material.
All the presented gravimetric solutions equally well match
the observed gravity anomaly. They cannot be discriminated
based on observed surface potential field data. The discrimi-
nation among these solutions must be carried out on the ba-
sis of additional geophysical or earth science constraining
information and tectonic and geological considerations. In
the light of the tectonic evolution of the Carpatho-Pannonian
area we consider solution D as the most realistic, though not
unique. The joint interpretation of magnetic and gravity data
in the area of the Kolárovo anomaly has confirmed that the
higher density basic intrusive body is to a great extent also
magnetic.
Acknowledgments: This work was supported by the Slovak
Research and Development Agency under contracts
No. APVV-0194-10, No. APVV-0724-11, and No. APVV-
0212-12, as well as by Vega Grant agency under Projects
No. 2/0067/12, 1/0095/12, and 2/0088/12.
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