Geomorphology 63 (2004) 25 – 37
www.elsevier.com/locate/geomorph
DEM-based morphometry as a tool for reconstructing
primary volcanic landforms: examples from the
Börzsöny Mountains, Hungary
Balázs Székely a,b,*, Dávid Karátson c
b
a
Institut für Geowissenschaften, Universität Tübingen, Sigwartstr. 10, D-72076 Tübingen, Germany
Space Research Group, Department of Geophysics, Eötvös University, H-1117 Budapest, Pázmány P. sétány 1/b, Hungary
c
Department of Physical Geography, Eötvös University, H-1117 Budapest, Pázmány P. sétány 1/c, Hungary
Received 29 April 2003; received in revised form 29 March 2004; accepted 30 March 2004
Available online 28 July 2004
Abstract
A complex application of digital elevation model (DEM) derivatives is presented for a highly degraded volcanic area, the
Miocene Börzsöny Mountains, Hungary. We propose unconventional geometrical and mathematical transformations of the
original DEM data in order to enhance the topographic features of the volcanic relief that stem from the primary landforms. It is
the actual ridges that represent the least degraded surfaces of an original, hypothetical volcanic cone. Therefore, the statistical
DEM properties such as ridge pattern (1), slope angle distribution (2) and higher-order slope derivatives (3) should be strongly
correlated with the paleosurface. Automated creation of a ridge pattern image is based on the local histogram of the DEM, and
helps to outline the original surface remnants. A local slope angle histogram may point out structurally coherent parts of the
original cone: for instance, tectonic displacements or large-scale sector slumping does not affect the slope angle histogram of the
original relief. Evaluating the ridge maps and slope aspect maps of the Börzsöny Mountains allows various cone sectors to be
identified and connected to the original volcano-structural elements. Finally, the polar coordinate-transformed (PCT) image (4)
centered on a hypothesized eruptive vent enhances the original, radial valley pattern. In the case of multiple eruptive centers
and/or post-eruptive tectonic modifications, the radial pattern is changed, which may be evidenced in the PCT image. In fact,
the PCT image analysis for the Börzsöny Mountains suggests a complex post-eruptive tectonic scenario. The presented methods
can be recommended to infer the original configuration of highly degraded volcanic structures with poorly known tectonic and
erosional history.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Digital elevation models; Quantitative geomorphology; Polar coordinate transformation; Volcanoes; Börzsöny Mountains; Hungary
1. Introduction
* Corresponding author. Institut für Geowissenschaften, Universität Tübingen, Sigwartstr. 10, D-72076 Tübingen, Germany.
E-mail address: [email protected] (B. Székely).
0169-555X/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.geomorph.2004.03.008
A digital elevation model (DEM) is a wellknown means of representing any internal or superficial relief of the Earth at any scale where
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B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
elevation differences yield relevant geological information. In particular, in volcanic terrains, application of DEM is very useful in deciphering
geomorphic and structural features, especially those
of large-scale edifices and deposits which cannot
be readily studied or identified in the field (e.g.,
Cappadoccia, Turkey: Froger et al., 1998;
Socompa, Chile: Wadge et al., 1995; Etna, Italy:
Favalli et al., 1999). In active volcanoes, it is
useful to recognize small-scale volcano-structural
elements, whereas in ancient volcanic terrains
where original primary landforms are often masked
by postvolcanic tectonism and erosion, DEMs
(along with satellite images) are important tools
in reconstructing paleovolcanic geomorphology. An
advantage of satellite images is the possibility of
spectral analysis of selected channels (e.g., Wadge
et al., 1995), while DEM evaluation offers a great
number of other applications based on the spatial
context of surface data. In addition to the representation of topography by either two-or threedimensional relief images, which are commonly
used for illustration, these applications include
more sophisticated derivative methods such as
elevation and slope category maps and histograms,
maps displaying selected topographical elements
(e.g., ridges or valleys), relative relief maps, exposure maps, and cross-sections. The obtained maps
and diagrams enable a quantitative analysis to be
made, which can successfully augment field work,
aerial photograph interpretation and satellite imagery analysis.
In this paper, we present an application of DEM
derivatives in order to reconstruct paleovolcanic
conical surfaces in a highly degraded Middle Miocene volcanic field, the Börzsöny Mountains, Hungary. In the study area, despite considerable amount
of volcanological, geophysical, geochemical, petrological and geochronological data (Balla and Korpás, 1980; Korpás and Lang, 1993; Karátson, 1995;
Korpás et al., 1998; Karátson et al., 2000; Karátson
and Németh, 2001), there remain some elements of
the paleovolcanic reconstruction that are uncertain.
After briefly overviewing the study area and presenting the applied DEM-based methods and
images, we give a morphometric analysis of selected
problems, for example, areas in the Börzsöny
Mountains.
2. Scope and goals
Quantitative approaches to reconstruct highly degraded conical volcanic edifices are scarce in volcanic
geomorphology (cf. Thouret, 1999). On the other
hand, new computational techniques and rapidly increasing computer power have made it possible to
develop sophisticated DEM evaluation methods in
many fields of earth sciences (e.g., Lucazeau and
Hurtrez, 1997; Mayer, 2000).
The techniques presented here are aimed to extract
either elevation or spatial distribution data of preserved or slightly degraded parts of the primary
volcanic landform/relief. The term primary volcanic
landform here refers to the apparent shape of a
volcano just after its extinction. Although the geomorphic consequences of destructive processes (e.g.,
sector collapse, caldera formation) during the active
period cannot be separated easily from post-eruptive
erosion, those processes mostly affect the central
region of the volcano, and hence leave the lower,
basal part of the cone relatively intact. Consequently,
from the point of view of reconstruction, the topographic analysis of the middle and lower slopes of
cone periphery can yield reliable results.
In our analysis, we are focusing on the ridge
pattern, because erosion is least intense in the area
of the ridges. This pattern defines a theoretical cone
surface of the primary edifice, which may not have
existed in reality, therefore, our reconstruction targets
this (rather mathematical than geological) cone. On
the other hand, if this theoretical cone is influenced by
post-eruptive tectonic movements (e.g., faulting and
displacement), our analysis can indicate the topographic manifestation of such effects.
3. Volcanology and volcanic geomorphology of the
study area
The Börzsöny Mountains (Fig. 1a), North Hungary, belong to the Miocene to Pleistocene calcalkaline volcanic arc of the Carpathians (e.g., Downes
and Vaselli, 1995). The 16 –14 Ma volcanic activity
created a multiple volcanic field (e.g., Karátson et al.,
2000) consisting of medium-sized stratocones with
small calderas (‘‘Paleo-Börzsöny’’), scattered lava
domes, and a relatively large (ca. 25 km3) central
B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
27
Fig. 1. Location and major features of the Börzsöny Mts. Insert map shows the location of the study area in Hungary. (a) Shaded relief DEM
mosaic of the Börzsöny Mts. and their surroundings showing the study area. P – B line indicates the Piliscsaba – Bernecebaráti line. (b)
Simplified volcanology and volcanic geomorphology of the study area. Data integration is based on the methods of Timár et al. (2002).
lava dome complex (‘‘High Börzsöny’’: referred to as
HB hereafter; see Fig. 1b). Although geographically
we can speak of individual volcanic mountains in
North Hungary (that is, Börzsöny, Visegrád, Cserhát,
Mátra Mountains), they have been separated by only
neotectonic (presumably Pleistocene) movements and
in part related fluvial downcut. None of them can be
considered as a single, large compound volcanic
edifice with caldera structures (Karátson et al., 2001;
Karátson and Németh, 2001).
The earliest volcanic activity in the Börzsöny
Mountains took place in a shallow marine environment (Báldi and Kókay, 1970; Karátson et al.,
2000), which gradually changed to subaerial for
the rest of volcanism (Karátson and Németh,
2001). Volcanic products include, in chronological
order, subaqueously emplaced pumiceous dacitic
volcaniclastics, extensive subaerial debris-flow
deposits (related in part to possible caldera formation, see later), and subaerial lava flows and lava
domes; the latter were associated mostly with blockand-ash flow deposits (Karátson, 1995; Karátson et
al., 2000). Significant tectonic faulting and uplift
(e.g., Czakó and Nagy, 1977; Balla, 1978) as well
as some 500-m erosion in total (Karátson, 1996,
1999) have resulted in a considerable degradation of
the original volcanic landforms. As a result, in
addition to the complexity of volcanic evolution,
erosion makes paleo-geomorphic reconstruction extremely difficult.
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B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
For instance, a double northern caldera rim in the
Paleo-Börzsöny (Kemence valley and Nagy valley,
Fig. 1) has been proposed by Balla and Korpás (1980)
on the basis of arcuate ridge sections. Subsequent
volcanological and volcano-geomorphological investigations have shown that the inner ridge can indeed
be interpreted as an eroded, retreated small caldera
rim (Karátson, 1995). Since deposits of large calderaforming eruptions correlative to the reconstucted caldera rim have not been identified, formation of the
original caldera morphology is not clear. The outer
‘‘caldera’’ rim of Balla and Korpás (1980) has a quasilinear strike (Nagy valley). It was reconstructed earlier
as a fault (Czakó and Nagy, 1977), which, from a
volcanic geomorphological point of view, has been
confirmed because it is a simple continuation of the
inner paleovolcano slopes (Karátson, 1997) and consists of distal volcaniclastic products of the inner
caldera in a ring plain (Karátson and Németh, 2001;
term based on Hackett and Houghton, 1989). The
abundance of block-and-ash and voluminous debrisflow deposits (Karátson and Németh, 2001) makes it
possible that lava dome and sector collapses were
responsible for producing the truncated inner
(Kemence valley) volcanic cone. A careful morphometric analysis, however, has not been carried out for
the highly dissected relief of the ‘‘double-caldera’’
area.
Further problems are connected to the central
andesitic volcanic edifice, HB, which has a prominent
erosional depression. Its actual size, 5 3 km in
diameter, is a result of significant degradation, that
is, erosional retreat of the original caldera/crater rim
and tectonic effects. The volcanic edifice was first
reconstructed as a stratovolcano by Balla (1978) and,
more recently, a multiple lava dome complex by
Karátson et al. (2000) (cf. Fig. 1). Lava flows, dome
collapse vent breccias and proximal block-and-ash
flow deposits are the only volcanic deposits in the
area of the deeply eroded volcano, resembling dome
complexes such as Unzen (Japan) and Merapi (Indonesia). It was clarified that caldera-forming eruptions
did not occur (Karátson et al., 2000). However, this
paleovolcanic reconstruction here has not yet resolved
the following problems:
(1) The depression is not roundish but has a
rectangular, elongated shape. Although this fact
fits to the recognition of post-volcanic (Pleistocene) tectonic movements (Balla, 1978; Karátson,
1995), it does not provide details of the primary
landforms. Moreover, the elevation of the rim is
not uniform: it is considerably higher to the SE
and S, and lower to the NW, and there is an
extremely low section in the west, while the outlet
draining the central depression heads towards
NNW. In accordance with varying altitudes of the
pre-cone deposits cropping out on the HB outer
slopes, the differently elevated rim sections have
been explained by differential uplift (Balla, 1978;
Karátson, 1995) and, to the W, by a deeply
truncating sector collapse (Karátson, 1995).
(2) To the north, the aforementioned Paleo-Börzsöny
(Kemence valley) caldera rim is composed mostly
of lavas and breccias petrographically identical to
those of HB basic andesites. Is the ridge really a
caldera rim belonging to a distinct paleocone, or
merely a fault escarpment enhanced by young HB
lavas? Although detailed paleomagnetic data have
shown an older age for the deeper parts of the
caldera rim, this is contradicted by the similar
lithology and younger (HB-aged) K/Ar data
obtained on the old caldera rim (Karátson et al.,
2000). It was proposed by Karátson et al. (2000)
that the old caldera may have been buried by
subsequent HB products, similar to the Somma–
Vesuvio southern lava flows, then tectonic movements have exhumed the rim again, but a detailed
morphometry to validate this explanation has not
been done.
4. Calculation of DEM derivatives
A commercially available DEM (MH Térképészeti Kht., Hungary) with nominal horizontal resolution of 10 m was used in this study. The theoretical vertical resolution is 1 m; however, possibly
due to the DEM creation and interpolation technique, the vertical accuracy seems to be on the
order of 5 m on the steepest slopes, while the data
are more reliable at moderate slope angles. Despite
this slightly reduced accuracy, our derivative data
are reliable, because the calculated parameters are
context-sensitive, the actual individual elevation values playing a minor role.
B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
A number of derivative data sets have been calculated from the aforementioned 10 m DEM. Apart from
the standard aspect map, three types of computed data
sets are presented in this paper:
(1) On the basis of the relative invariance of the slope
distribution to subsequent tectonism, slope category maps have been produced and various
domains that are characterized by specific local
slope histograms have been delineated.
(2) To study the general outline of the supposed
conical structure, a polar coordinate-transformed
map (hereafter referred to as PCT map) was
calculated centered on a hypothesized eruptive
vent.
(3) The ridge system (assumed to be the least eroded
surface) is evaluated by means of an automatically
generated ridge enhancement technique; the
resulting image has been vectorized, and local
orientation histograms have been calculated based
on the extracted vector data.
The idea behind creating these derivatives is to
analyze three contrasting aspects of the degraded
morphology: (1) the slope categories being influenced
by long wavelength changes may contain inherent
information about the various domains of the primary
surface, (2) the PCT map helps to detect slight
directional inconsistencies in a more or less concentric
setting such as a volcanic cone, (3) directional analysis of the ridges may point out sectors of the primary
landscape formed after extinction (e.g., by tectonic
movements).
4.1. Ridge analysis
There are numerous techniques to extract ridges
from a DEM (Chang et al., 1998). Here we applied a
rather robust but calculation-effective method: the
local elevation histogram has been calculated with
an appropriate moving window and a cut-off limit was
applied to the resulting histograms, leaving the locally
highest points in the data set and filtering out anything
else (see Székely, 2001 for details). This method also
enhances the completely flat areas (in this case, the
histogram is very peaked, therefore no separation is
possible). These areas have been masked out from the
image.
29
The resulting raster image has then been automatedly vectorized, and the ridge lines have been compiled into rose diagrams in the following way: a rose
diagram has been calculated for each 1-km radius
circular window with 500-m overlap. The weighting
of a ridge section is proportional to its length. This
method results in a set of rose diagrams referring to
grid points of a km-sized grid on the original map.
Due to the creation technique, the angular resolution
of these rose diagrams cannot be very high, especially
at reference points around which ridges are infrequent.
Here we have used a 22.5-deg resolution.
4.2. Slope categories
The slope categories have been composed similarly
to the method of Favalli et al. (1999), but instead of
taking a general histogram of the complete area, local
histograms have been calculated. The advantage of
this rather computer-exhaustive step is to separate
local, but large wavelength changes from the general
conical trend. The theoretical conical surface would
prescribe a rather narrow slope histogram, being only
dependent on the distance from the geometrical eruption center. Theoretically, the radial erosion, though
modifying the actual surface and the slope histogram
by introducing steeper valley sides, occurs more or
less invariantly with respect to the central distance.
Of course, in reality, the slope histograms are more
variable. Obviously, categories with progressively
higher slope angles have decreasing areal percentage.
As a consequence, the range of higher slope categories decreases: for instance, the 5– 10j slope category
may have a range of 30– 50%, while the 35 –40j
slope category typically has a range of a few percent.
Histogram stretching has been applied to increase the
dynamics of the slope category maps. The described
computation has the advantage that it is insensitive to
the actual elevation, therefore, tectonic uplift or
subsidence will not change the categorization.
4.3. Polar coordinate-transformed (PCT) map
Another, mathematically well-known but geomorphologically unconventional method is the creation of
the polar coordinate-transformed (PCT) map. Its computation principle is very simple: every elevation
point P with Cartesian coordinates (x,y) is remapped
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B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
to PV with polar coordinates (u, r) , where r is the
distance between P and an assumed symmetry center
point O, while u is the oriented angle between the line
OP and the x axis of the original Cartesian system. For
further details, see Appendix A, which contains an
example based on a DEM of the Mount St. Helens,
USA. PCT maps any concentric and radial feature to a
radius-axis parallel or angle-axis parallel feature,
while any non-concentric and non-radial feature will
become rather scattered. In volcanic geomorphometry,
this behavior is especially advantageous, because in
the case of a basically conical surface, even slight
horizontal displacements will become non-concentric
with respect to the original center, and therefore will
be less enhanced in the PCT image. Mass movements
such as sector collapses or slumps are also detectable,
because typical elevation changes at a given central
distance make them obvious.
5. Evaluation of DEM derivatives
5.1. Ridge orientation domains
According to ridge pattern and ridge orientation
(Fig. 2a – c), five major domains can be distinguished:
Domain 1: The best-defined domain is the High
Börzsöny volcanic cone. Outside of the central
caldera (having a modified centrifugal pattern), the
ridges are definitely outward dipping. However,
they are not unambiguously radial, but concentrated in sectors: the NE, NW and SE sectors, each
characterized by a quasi-parallel ridge pattern. This
feature is interpreted as a consequence of tectonic
influence, i.e., ridges are adjoined to a NE –SW
and NW – SE tectonic lineament pattern, characteristic all over northern Hungary (Gerner et al.,
1995). This pattern is disturbed in only the SW
sector, without any dominant ridge direction. As
mentioned before, that sector could be affected by
landslides (Karátson, 1995; Karátson et al., 2000).
Domain 2: In the northern part, north of Kemence
valley (see Fig. 1), the ridge pattern is markedly
changed. Just north of the NE sector of the High
Börzsöny domain, ridge orientation is roughly N –
S, whereas more northward, NW – SE-oriented
ridges also appear.
Domain 3: In the NW periphery of the Börzsöny, a
less defined, narrow domain is the hillfoot area of
the Paleo-Börzsöny. Low topography as well as
narrow ridge sections make ridge orientation
patterns less well evaluable. However, the most
characteristic direction is NW – SE.
Domain 4: In the SW Börzsöny—a relative narrow
but long sector—the most characteristic direction is
W –E, although NW – SE directions predominate in
the north. Low topography causes some uncertainty here as well. This sector has been interpreted as
an outer cone area of one of the Paleo-Börzsöny
calderas by Karátson (1995) and Karátson et al.
(2000; see Fig. 1b).
Domain 5: South of the High Börzsöny cone, low
topography and short ridge sections would make
orientation patterns less reliable, but a dominant
NW – SE direction is so characteristic that this is
one of the best defined domains. This direction
should be interpreted as result of the abovementioned, North Hungarian neotectonic overprinting (Gerner et al., 1995; Fodor et al., 1999).
The local trellis-type drainage pattern fits with such
a tectonic control.
5.2. Aspect map
Ridge-map domains are also supported by the
aspect map of the central-southern part of the Börzsöny Mts. (Fig. 3a).
The existence of sectors in the High Börzsöny
cone (ridge domain 1) is obvious: there are four
sectors with contrasting aspects (NW, NE, SE and
SW), with uniform aspects in the first three sectors,
and mixed aspects in the SW one. All sectors are
cut toward the periphery by well-defined valleys
(that of Kemence caldera to the N, and Hosszú
valley to the SW).
The southern domains are also apparent. In the SW
Börzsöny (ridge domain 4), north-trending aspects
predominate and are fitting to the arcuate, assumed
caldera rim, whereas to the SE (ridge domain 5),
aspects tend to be south-oriented.
5.3. Slope category maps
In Fig. 3b– c, slope categories 10 – 15j and 30– 35j
are displayed, respectively, on a shaded relief back-
B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
31
Fig. 2. Ridge map and ridge orientation map of the Börzsöny Mts. lain over a shaded relief background. (a) Result of the ridge extraction
procedure following the vectorization phase. (b) Rose diagrams of the local ridge pattern in a 500-m grid calculated for 1-km radius circular
windows. (c and d) Outlines of the derived ridge orientation domains (1 – 5) laid over the ridge map (c) and rose diagrams (d). See text for
discussion.
ground. In each map, a color index shows the percentage of the given slope category.
In Fig. 3b, moderately steep slopes of 10 –15j
dominate (in ca. 25– 28%) the SW part having relative
gentle topography. However, the blue colors occurring
mostly in the HB indicate that the mountainous areas
are also characterized by a moderate-to-high (ca. 15–
20%) percentage of 10– 15j slopes. Within the HB,
the NE part has the lowest percentage, characterized
by much steeper slopes, as shown in Fig. 3c. In
contrast, in the SE Börzsöny (S of the HB cone),
the 10– 15j slope values occur with similar frequency,
but steep slopes are missing (cf. Fig. 3c), the topography being dominated by lower slope categories. To
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B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
Fig. 3. Aspect and slope category maps of the Börzsöny Mts. For orientation, outlines of major volcanic structures are shown (cf. Fig. 1). (a)
Aspect map with a color index of yellowish colors corresponding to E-, whitish to S-, cyan to W-, and darkish to N-exposed (or zero dipping)
slopes. (b – c) Slope category maps colored according to the percentage of 10 – 15j (b) and 30 – 35j (c) slopes.
the north, Kemence valley (boundary between HB and
the northern Paleo-Börzsöny caldera) clearly separates
the steep southern and moderately steep northern
parts.
In Fig. 3c, the steepest parts of the Börzsöny can be
seen (30 – 35j slopes occurring up to 4%). In HB, the
NE part of the caldera rim is the steepest (highest
percentage in pinkish color). Blue areas (at least 3%
for 30– 35j slopes) are found not only within HB but
also to the SW of HB, a coincidence that may imply
similar origins.
5.4. Polar coordinate transformation (PCT) map
As a first step towards the PCT image, its simplified version is presented in Fig. 4b. As shown in Fig.
4a, this image has been produced from elevation data
along 20-km sections by 11.25j and using a hypothetical symmetry center (hereafter referred as to
projection center) in the HB caldera. Each section is
displayed like a wide ribbon colored according to
elevation values. As mentioned before, horizontal
lines (ridges, valleys) in Fig. 4b correspond to con-
B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
33
Fig. 4. Polar coordinate images of the Börzsöny Mts. (a) Colored elevation map showing sections by 11.25j and with a hypothetical symmetry
center. (b) Simplified polar coordinate image constructed as a diagonal representation from a (see text for details). Lines correspond to sections
in (a). (c) Complete PCT image of the study area in a radial representation (with projection center on bottom).
centric circles (e.g., a circular caldera rim) if the
projection center is concordant with those of the
circles. Vertical lines represent radial features aligned
with the projection center, e.g. remnant ridges of the
original cone. From the hypothesized center of the
caldera depression (horizontal line running across the
orange dot) to 1 –2 km outward, the relief is progressively higher. Orange lines go through the highest
elevations (practically, the HB caldera rim). Due to the
non-concentric rim, these lines are not horizontal but
slightly arcuate. This is best seen for the W caldera
rim that is not circular but linear in reality. The NE
and SE rim, although somewhat rectangular, can be
considered as a ‘‘regular’’ caldera rim.
In Fig. 4c, a real PCT map is presented, where all
points of the original DEM were remapped into the
PCT image, enhancing ridges and valleys. It is important to note that the ridge and valley pattern is
realistic only over 1 km or so (from the lower part of
section), because in the central part of the projection,
relatively large areas with few data are displayed.
Beyond ca. 3– 4 km, to the left and right (ca. 20 –180j
and 270– 340j sectors of the image), dominance of
vertical lines (a radial valley and ridge pattern) is well
developed in the outer caldera slopes. In contrast, in
the center (180 –270j), where the W caldera rim is not
horizontal but arcuate, outer drainage pattern is less
developed. To the left and right of this rim, deeply
incised valleys correspond to the west sector collapse
area of the HB and the outlet valley of the HB caldera.
The aforementioned irregularities—i.e., non-parallel caldera rims and contrasting drainage outside—
suggest a displacement within the original cone. In
Fig. 1a, there appears a striking SW– NE trending
lineament (termed as Piliscsaba– Bernecebaráti line)
that seems to be a normal fault affecting other, non-
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B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
volcanic structures to the south. Crossing the HB
cone, this fault may have resulted in a downthrow
of the western part to the NW, in turn causing a NW –
SE elongation of the caldera area.
6. Discussion: implications for volcano-structural
elements
DEM derivative images have been produced to
help answer some volcano-structural questions not
readily resolved by field geological or geomorphological methods. In the Börzsöny Mts., these questions
are the existence of the northern calderas (‘‘PaleoBörzsöny’’), and the nature of the central HB caldera
(i.e., single or multiple vents, influence of tectonic
control).
In the northern part of the study area, the ridge map
supports the existence of a caldera and a distinct paleocone north of Kemence valley. Striking differences in
ridge orientation north and south of the valley argue for
differently positioned paleosurfaces, i.e., the existence
of paleocones with different centers (domains 1 and
2 in Fig. 2). This conclusion does not exclude the
possibility of a young cover of HB deposits (Karátson et al., 2000), but unambiguously distinguishes
between two volcanic cone remnants north and south
of Kemence valley. On the other hand, the area north
of Kemence valley shows no significant differences
in ridge orientation, e.g., around Nagy valley; there
are no sectors with different directions. This feature
(supported by volcanological data, Karátson and
Németh, 2001) argues for a uniform, extended paleocone remnant to the north. A further implication,
coming from the evaluation of ridge orientation and
slope aspect images, is the possible existence of a
truncated paleocone in SW Börzsöny (domain 4 in
Fig. 2). There, both ridge orientation pattern and
slope aspect differences point out a well-defined
morphological unit.
Analysis of processed DEM images of HB reveals
important details about its structure. As the existence
of sectors of ridge orientation and slope aspect (Figs.
2 and 3) indicates, tectonic control may have modified
the original cone surface, if there was a simple cone at
all. This is also supported by PCT image analysis (Fig.
4). Although this image shows paleocone morphology, caldera rim irregularities imply both a tectonic
influence and a multiple center. The first conclusion is
also based on shaded relief image interpretation (Fig.
1a), while the latter aspect fits to the volcanological
reconstruction of a dome complex.
Slope category maps (Fig. 4) show that apart from
the HB cone (with highest elevations), some SW and
S areas also display relatively steeper morphology
(with a high percentage of 10 –15j slope values).
Similar slopes can only be found in the HB cone,
especially its N part. Also, precipitous slopes (30 –
35j), identical to those of the majority of HB,
characterize the peripheral, lower-elevated, SW part
of the HB cone, suggesting similar origins. Karátson
(1995) and Karátson et al. (2000) proposed giant
landslides on the western HB edifice, some individual hills in the SW part being remnants of large slide
blocks. The similar lithology and buildup as well as
similar K/Ar ages and magnetostratigraphy (Karátson
et al., 2000) to the central HB rocks are in accordance with this hypothesis. The slope category map
seems to support the genetic relationship. We do not
state that the original slope angles have been preserved, but it is possible that the basic morphological
similarities of the primary volcano and the slide
blocks have survived.
7. Conclusions
Combining field geomorphical and volcanological
data with the evaluation of volcanic form-specific
DEM derivatives helps verify and develop ideas for
the original shape of deeply eroded and destructed
volcanic edifices. This may be true even if the
reconstructed shape more of a theoretical envelope
and not strictly the paleosurface that existed in reality.
A complex morphometric analysis of a DEM for
the Miocene Börzsöny Mountains in Hungary, an
area of highly degraded volcanic cones, has yielded
relevant results for reconstructing the primary landforms. In our experience, the DEM-derived ridge
axes, slope distribution, slope aspects, etc. are in
close correlation with the paleosurface, therefore,
their present pattern is a direct consequence of the
original surface properties.
Although original shape may be modified by
tectonic overprint and erosion, from statistical point
of view, the properties seem to survive and typically
B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
are not completely destroyed. A main feature and
advantage of the processing methods presented here is
that the conclusions on the original volcanic structure
as well as its further modifications are based on
statistically evaluated data.
35
original data (except for the reference or projection
center) using the following simple equations:
r ¼ ððx x0 Þ2 þ ðy y0 Þ2 Þ0:5
ðA1Þ
)
u* ¼ arctanððx x0 Þ=ðy y0 ÞÞ
if y p y0
Acknowledgements
u* ¼ 0
if y ¼ y0
The authors are deeply indebted to A. Duncan
(Luton) and an anonymous reviewer for their
constructive comments and linguistic improvements
of manuscript. Research work has been carried out
partly during DK’s Bolyai Fellowship and BSz’s
Békésy György fellowship and was supported by a
DAAD-MÖB cooperation between the Universität
Tübingen, Germany, and Eötvös University, Hungary.
Financial support of the German Research Foundation
(DFG), Hungarian National Scientific Funds FKFP
00/175 and OTKA T43644 is also acknowledged. T.
Tóth (Budapest) and G. Timár (Budapest) are thanked
for providing a part of the DEM data and for raw data
conversion.
where r (radial distance) and u* (orientation) are the
new polar coordinates, x and y are the original Cartesian coordinates of the point to be mapped, x0 and y0
are the Cartesian coordinates of the projection center.
Note that according to Eq. (A2), in case of x = x0
and y = y0 (i.e., the point to be mapped is the reference
center), the mapped object, although formally, is also
a point, but appears as a line instead of a single point.
Another consequence of projection is that there is low
data frequency in the vicinity of the center. However,
this fact does not have any importance in practice.
Concerning the dimensions of the resulting coordinates, r is scaled in units of x and y, while u* is
given in radians. If the result is needed in degrees, it
can be calculated simply using
ðA2Þ
Appendix A . Derivation of the PCT map
Polar coordinate-transformed (PCT) map of a
DEM is a one to one map transformation of the
udeg ¼ 180j=p u*
ðA3Þ
This system for u* (or udeg) is eastward-oriented
(u* = 0 refers to E) and increases anticlockwise. It
may be advantageous to have N as zero angle refer-
Fig. 5. Demonstration of the effect of polar coordinate transformation (PCT). In diagram a (map view), some simple geomorphic features are
indicated, in b, their transformed counterparts are displayed. Note that radial features (relative to the projection center) map to vertical lines,
while non-radial objects appear as oblique or arcuate ones.
36
B. Székely, D. Karátson / Geomorphology 63 (2004) 25–37
Fig. 6. Shaded relief map (a) and PCT image (b) of Mt. St. Helens after the 18th May 1980 eruption. The original nominal DEM resolution is 30
m, although it is clear that the data contain some artefacts as well. In our case, these otherwise unimportant artefacts help demonstrate the
advantages of the method. In the PCT image (b), the strip-like artefacts become a series of curved ‘‘shadows’’ (to the W) showing the tendency
of the non-radial features to be diffused. The N sector that was affected by the collapse is evident in b. The newly formed caldera rim appears as
a horizontal line because of its almost perfect circular shape, while the almost radial valleys become vertical lines. Note that in this example, the
caldera is large enough to have a good resolution rim in the transformed image, while the central area, due to the projection, is overrepresented
in the resulting map, and hence is not suitable for analysis.
ence direction and clockwise increasing orientation, in
this case
u* ¼ arctanððy y0 Þ=ðx x0 ÞÞ
if x p x0
u* ¼ 0
if x ¼ x0
)
ðA4Þ
can be used.
Fig. 5 shows the effect of the transformation for
some selected points and features. Points P1(3/2, 3M3/
2), P2( M2/2, M2/2) and P3 (M2, M2) (all coordinates
are in km) will be mapped to points (3 km, 30j), (1 km,
315j) and (2 km, 45j), respectively. In this example,
the north-oriented, clockwise system is used according
to Eq. (A4). Note that in Fig. 5, radial features map to
vertical lines, circles centered on the projection center
become horizontal lines, while other linear features are
transformed to slanted or arcuate objects.
As a simple demonstration of the method, the PCT
image of the DEM of the Mt. St. Helens (after the
1980 eruption) is presented here (Fig. 6). In Fig. 6a,
the original DEM data are shown, in Fig. 6b, the PCT
image is displayed. The almost perfectly circular
caldera rim becomes a horizontal line, while the valley
of the Toutle River being radial up to ca. 2-km radial
distance maps to a vertical line. From this point, the
modified trace of the valley appears as a slant line. In
this example, the north-oriented clockwise system was
used according to Eqs. (A1), (A3) and (A4).
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