Kovacic.indd


�
AB STRA CT
Multiple discriminant analysis (MDA) of Upper Miocene and Pliocene sands of the SW portion of the Pannonian 
Basin System was performed in order to determine the optimum criteria for separating the previously defi ned infor-
mal lithostratigraphic units – Ozalj, Andraševec, Hum Zabočki, Cernik and Pluska. The heavy mineral association is 
employed as independent variables, or descriptors, in the process of discrimination and results of analysis established 
a clear and strong bond between characteristic heavy mineral assemblages in the Upper Miocene and Pliocene sands 
and their affi nity to particular lithostratigraphic units. In this respect, the Pluska unit is especially highlighted, fol-
lowed by the Ozalj and Hum Zabočki units. Close heavy mineral/lithostratigraphic unit relationships were very use-
ful in unravelling the basic sedimentological meaning hidden beneath specifi c discriminant functions in the mathe-
matical model. The most prominent is DF1 accounting for almost 3/4 of the total variance of the investigated 
sedimentary system. In accordance with its 'key' mineral it is labeled kyanite function which indicates the (metamor-
phic) provenance of the siliciclastic mineral detritus. The second most important, DF2, is labeled garnet-zircon func-
tion and, being bipolar, it points at both provenance of siliciclastic material (older sedimentary rocks) and hydraulic 
conditions during the transport and sedimentation of the detritus. Finally, DF3 is of minor importance indicating the 
stability of the heavy mineral association in sandy sediments. Three lithostratigraphic units, namely Ozalj, Pluska 
and Hum Zabočki are clearly separated by the functions labeled after their distinctive ('key') heavy minerals.

Keywords: Discriminant function analysis, heavy mineral association, lithostratigraphic units, Upper Miocene, 
Pannonian Basin System

Discriminant function analysis of Upper 
Miocene and Pliocene sands from the 
southwestern part of the Pannonian

Basin System, Croatia

�
Marijan Kovačić1, Zoran Peh2 and Anita Grizelj2

1 University of Zagreb, Faculty of Science, Horvatovac 95, HR-10000 Zagreb, Croatia;
(mkovacic@geol.pmf.hr)

2 Croatian Geological Survey, Sachsova 2, HR-10000 Zagreb, Croatia; 
(zpeh@hgi-cgs.hr; agrizelj@hgi-cgs.hr)

doi: 10.4154/gc.2009.12

Geologia CroaticaGeologia Croatica

1. INTRODUCTION

The Pannonian Basin System (PBS) is a system of back-arc 
basins the evolution of which started in the Early Miocene 
epoch as a response to continental collision and subduction 
of the European Platform below the Apulian Platform (ROY-
DEN, 1988; HORVÁTH, 1995; KOVÁČ et al., 1998). Sur-
rounded by the Alps, Carpathians and Dinarides (Fig. 1), it 

included a number of different sized, deep, depressions and 
basins separated by a comparatively shallow complex of 
basement rocks (HORVÁTH & ROYDEN, 1981; ROY-
DEN, 1988). The fi rst phase of basin development was chara-
cterized by tectonic thinning of the crust and isostatic sub-
sidence (syn-rift), while the second phase was marked by the 

Geologia Croatica 62/3 189–200 4 Figs. 4 Tabs. Zagreb 2009



Geologia Croatica 62/3Geologia Croatica
190

fi ned groups following the principle of least distance (greatest 
similarity). This being so, the main scope of this work is de-
fi ned as follows: a) to determine the strength of the relation-
ship between the composition of the HMA of the studied sands 
and their lithostratigraphic affi liation after the method of mul-
tiple (multi-group) discriminant analysis (MDA) has been ap-
plied; b) to decide which minerals contribute most to discrimi-
nation between the lithostratigraphic units, and; c) to answer 
to what extent discrimination between individual groups fa-
cilitates interpretation of geological events.

2. LITHOSTRATIGRAPHIC UNITS, FACIES, 
AND SEDIMENTARY ENVIRONMENTS

The investigated area is situated in the central and eastern 
parts of the Republic of Croatia. It consists of three different 
and geographically separated regions over about 200 km dis-
tance – Hrvatsko Zagorje with the Medvednica Mt., Žum-
berak Mt., and Slavonian Mts. (Fig. 2).

During the systematic fi eldwork that included surface 
geological mapping, subject to the requirements of the Basic 
Geological Map of Croatia 1:50000, the Upper Miocene and 
Pliocene sediments were divided into six informal lithostrati-
graphic units, namely the Croatica (Cro), Medvedski Breg 
(MeB), Ozalj (Oza), Andraševec (And), Hum Zabočki (HZb), 
Pluska (Plu), and Cernik (Cer) units. In the Slavonian Mts., 
the MeB unit was, however, referred to as the Pavlovci unit 
while simultaneously the designation Nova Gradiška unit is 
applied to the HZb unit by some researchers (KOVAČIĆ et 
al., 2005). Their stratigraphic position and inter-correlation 
is displayed in Fig. 3. and their description is accepted from 
the works of VRSALJKO (2003), KOVAČIĆ (2004) and 
KOVAČIĆ & GRIZELJ (2006). In contrast to the widely ac-
cepted lithostratigraphic nomenclature in this part of the 
PBS, which is defi ned basically according to the results of 
subsurface geological investigations (ŠIMON, 1973, 1980; 

cessation of rifting and subsidence caused by cooling of the 
lithosphere (post-rift) (HORVÁTH & ROYDEN, 1981; 
ROYDEN et al., 1983; ROYDEN, 1988). In the south west-
ern part of the PBS the syn-rift phase lasted from the Ottnan-
gian to the Middle Badennian, while the post-rift phase ex-
tended from the Middle Badennian to the end of the Pontian 
(PAVELIĆ, 2001). Palaeogeographically, the PBS extended 
over the major part of Central Paratethys – a sedimentary 
basin having passed through a succession of stages of isola-
tion and reconnection to the open oceans (Indopacifi c and 
Mediterranean) during its evolution. The fi nal isolation at 
the end of the Middle Miocene resulted in development of 
Lake Pannon that existed as a separate sedimentary basin 
during the Late Miocene (RÖGL & STEININGER, 1983; 
RÖGL, 1998; 1999; MAGYAR et al., 1999).

From the Upper Miocene to the Lower Pliocene, great 
quantities of clastic detritus were transported to the south-
western part of the PBS from both the surrounding mountain 
ranges and the uplifted areas within the basin itself (ŠĆAV-
NIĆAR, 1979; ŠIMUNIĆ & ŠIMUNIĆ, 1987; KOVAČIĆ 
et al., 2004; KOVAČIĆ & GRIZELJ, 2006; GRIZELJ et al., 
2007), triggering the submersion that marked the onset of 
compressional tectonics in basin development (JAMIČIĆ, 
1995; TOMLJENOVIĆ & CSONTOS, 2001; MARTON et 
al., 2002), and the subsequent gradual and diachronous in-
fi lling of Lake Pannon (MAGYAR et al., 1999; KOVAČIĆ 
et al., 2004).

In earlier research work, the Upper Miocene and Plio cene 
sedimentary rocks of the southwestern part of the PBS were 
typically divided according to their endemic fossil assem-
blages (e.g. ŠIKIĆ et al., 1979; BASCH, 1983). However, ac-
cording to the recent geological investigations related to the 
Basic Geological Map of the Republic of Croatia 1:50000, a 
number of informal lithostratigraphic units were distinguished 
among the investigated sedimentary rocks, based principally 
on the fi eld observations of their lithological characteristics. 
A considerable body of data was thus created including the 
modal composition of sands, which represent the most impor-
tant lithological member of the newly established units. Such 
a large amount of numerical data is quite a propitious material 
for a statistical procedure which employs various multivariate 
methods and techniques. One of the most often exploited tools 
in geosciences is discriminant function analysis which is used 
to compare a number of groups for which there already exists 
a sound (geological) basis for separation. For instance, here, 
lithostratigraphic units can serve as á priori established geo-
logical groups to which the collected geological objects (sam-
ples) can be assigned using some independent geological cri-
terion such as geological mapping (ROCK, 1988). A key 
problem in the study can be summarized in a simple question: 
can such predefi ned groups be distinguished effectively utiliz-
ing the selected suite of known attributes in each sample such 
as, for example, the heavy mineral association (HMA), or sub-
tle differences in the mineral composition that can disturb the 
homogeneity of groups acknowledged on ‘coarser’ geological 
criteria derived from geological mapping, and cause them to 
overlap signifi cantly? It may also be important to allocate each 
new ‘unknown’ object (sample) to one of the previously de-

Figure 1: The Pannonian Basin System and its surroundings (after ROYDEN, 
1988). The area delineated is in the South-western part of the Pannonian 
Basin System, shown in Fig. 2.



Kovačić et al.: Discriminant function analysis of Upper Miocene and Pliocene sands from the southwestern part of the Pannonian Basin System, Croatia Geologia Croatica
191

VELIĆ, 1980), these units are informal in character. How-
ever, some recent investigations could easily assign them a 
rank of formation (KOVAČIĆ, 2004).

The Cro unit (Lower Pannonian) occurs in the region 
of Hrvatsko Zagorje and the Slavonian Mts. The sharp 
boundary with the underlying Sarmatian beds is conforma-
ble, while the lateral-vertical transition to the younger MeB 
and Oza units is gradual (Fig. 3). It is composed of thin-bed-
ded clayey limestones and marls with occasional intercala-
tions of calcareous sands deposited in a shallow water lacus-
trine environment of low salinity.

The Oza unit (Lower–Middle Pannonian) is widespread 
on the Žumberak and Medvednica Mountains, unconform-
ably overlying the Middle Miocene and older deposits, or 
occurring as the lateral equivalent of the Cro unit and the 
lower part of the MeB unit. It consists of medium-grained 
clastic sedimentary material deposited in coastal lacustrine, 
fl uvial, or distributary channel environments. The variability 
of locally derived clastic detritus clearly indicates the diverse 
composition of the parent rocks in the area.

The MeB unit (Lower Pannonian–Upper Pontian) is 
present over the entire investigated area. It conformably 
overlies the Cro and Oza units or Sarmatian deposits con-
sisting mostly of marls deposited in the deep-water brackish 
environment (Fig. 3). Sands and gravels are interbedded 
within the lowermost parts of the unit, along the contact with 
the Oza unit, the composition and origin of which correspond 
closely to the underlying Oza clastics.

Figure 2: The South-western part of Pannonian Basin System with location 
of the study-area (Hrvatsko Zagorje, Mt. Medvednica, Mt. Žumberak and 
Slavonian Mts.).

Figure 3: Schematic geological sections 
of the Upper Miocene deposits with in-
formal lithostratigraphic units of Hrvat-
sko Zagorje, Mt. Medvednica, Mt. Žum be-
rak and the Slavonian Mts. Strati graphic 
position of the litostratigraphic units is 
based on changes of endemic fauna, so 
it is highly speculative.



Geologia Croatica 62/3Geologia Croatica
192

The And unit (Lower Pannonian–Upper Pontian) cov-
ers the entire study area. This unit conformably overlies the 
MeB unit and is also conformably overlain by the HZb unit. 
It is composed of alternating layers of sands, silts and marls 
deposited in the prodelta-deltaic slope lake environment. Sili-
ciclastic detritus is mineralogically and structurally relatively 
mature. Its composition is homogeneous over the entire area 
and derives its origin mostly from metamorphic and older 
sedimentary rocks outcropping in the source area relatively 
far to the north.

The HZb unit (Upper Pontian) is widespread in the 
whole studied area, overlying conformably the older, And 
unit, and passing conformably upward into the overlying Cer 
and Plu units (Fig. 3). It is characterized by alternation of 
sand and silt beds deposited in the delta front in the shallow 
brackish lacustrine environment. According to both compo-
sition and origin of its detritus it is not signifi cantly different 
from the And unit.

The Plu unit (Upper Pontian–Pliocene) crops out in Hr-
vatsko Zagorje and in the Žumberak Mts. overlying conform-
ably the HZb unit, while its upper boundary remains undeter-
mined. It consists of clays, silts and sands with lenses of gravel 
and coal deposited in a river or distributary channels, alluvial 
plains, coastal lagoons and swamps. The clastic detritus is 
comparatively mature in a mineralogical and structural sense, 
and is similar in composition to the detritus of the And and 
HZb units. The latter two differ in their HMA, indicating some 
variations in the composition of the parent rocks.

The Cer unit (Lower Pliocene) is detected only in the 
Slavonian Mts. region, overlying the HZb unit (Fig. 3). It 
consists of clays, silts and sands with lenses of gravel depos-
ited in a sedimentary environment similar to that of the Plu 
unit. The composition and origin of detritus is close to the 
And and HZb units.

3. METHODS

3.1. Sampling, sample preparation and analysis

A total of 101 samples were collected during the fi eld inves-
tigations that included geological mapping and construction 
of the geological columns of unbound sand-silt sedimentary 
material. Sampling was designed to cover the entire study 
area, comprising all relevant time periods and investigated 
informal lithostratigraphic units.

Samples were sieved to the 0.09–0.16 mm size fraction, 
followed by subsequent dissolution of calcite. The heavy min-
eral association (HMA) was separated using bromoform 
(δ(CHBr3) = 2.84 gcm–3). Qualitative and quantitative compo-
sition of the HMA was established after the determination of 
300–400 grains applying the ribbon counting method (MENGE 
& MAURER, 1992). Results are presented in Table 1 (accepted 
and modifi ed from KOVAČIĆ & GRIZELJ, 2006).

3.2. Data processing

Multiple (multi-group) discriminant analysis (MDA) is a 
powerful multivariate technique which is recently widely 
applied to many problems in geology, particularly in cases 

when a large amount of data is collected from different litho-
logical or lithostratigraphical units, in an attempt to defi ne 
their boundaries. Its principal purpose is to establish the major 
sources of difference between the a priori defi ned groups al-
lowing the minimum misclassifi cation error rates for their 
members. Generally, this is achieved in such a way that the 
variance between the original groups is maximized in rela-
tion to the variance within each particular group (DILLON 
& GOLDSTEIN, 1984). In the process, a hypothesis is tested 
that all observed groups have the same multivariate mean, 
against the alternative that at least one mean is different 
(ROCK, 1988). If the alternative hypothesis is not rejected 
(which does not mean that the separation of all groups is 
necessarily optimal), then discriminant scores can be com-
puted from the original data set allocating each object (single 
sample) along one or more mutually independent (perpendi-
cular) vectors – linear discriminant functions (e.g., KRUM-
BEIN & GREYBILL, 1965; DOORNKAMP & KING, 1971; 
DAVIS, 1986). In this way the multivariate problem is sim-
ply and parsimoniously cut down to the least dimensional 
solution depending on the number of groups (K–1), or vari-
ables (p) if the latter is greater (K<p).

Investigation is focused on separation between litho-
stratigraphic units using the data on the HMA from the sam-
pled siliciclastic material of the Upper Miocene and Lower 
Pliocene sands in the SW part of the PBS. Five groups de-
scribed above as Oza, And, HZb, Plu and Cer (lithostrati-
graphic units Cro and MeB are not defi ned as specifi c groups) 
including more than a hundred samples in total were subject 
to investigation. Descriptor variables are represented by 10 
minerals of HMA including chlorite (Chl), dolomite (Dol), 
tourmaline (Tur), zircon (Zrn), rutile (Rt), amphibole (Amph), 
garnet (Grt), kyanite (Ky), staurolite (St) and minerals from 
the group of epidote-zoisite-clinozoisite (EpZoCzo). Regard-
less of the positive skewed frequency distributions of the 
analyzed variables, a bias usually ascribed to complex non-
linear responses within the natural system (siliciclastic ma-
terial of the sands) represented by HMA, the data were not 
subject to transformation. Common transformation proce-
dures were omitted following the idea that data processed 
by various multivariate methods should be left in their orig-
inal form since transformed variables can develop their own 
patterns of behavior (SIZE, 1987; MANN, 1987; AGRAWAL, 
1995). A single variable exhibiting distribution close to nor-
mal was EpZoCzo.

4. RESULTS AND DISCUSSION

Discriminant analysis of the investigated lithostratigraphic 
units represents a multiple-group discrimination involving 
fi ve groups (K=5). In this case discriminant model is built of 
four discriminant functions (K–1) completely explaining the 
differences between the respective groups. Before that, the 
overall signifi cance of their discrimination is tested by appro-
priate multivariate tests (Table 2a) disclosing the vanishingly 
low associated probability (p<0.000), a rationale requir ed 
to safely proceed with computing discriminant functions 
(DFs). With respect to the statistical signifi cance of the vari-
ation between the observed groups (p-level, Table 2b) and 



Kovačić et al.: Discriminant function analysis of Upper Miocene and Pliocene sands from the southwestern part of the Pannonian Basin System, Croatia Geologia Croatica
193

Table 1: Composition of the HMA of Upper Miocene and Pliocene sands from the southwestern part of the Pannonian Basin System. Chl – chlorite, Dol 
– dolomite, Op – opaque mineral, Bi – biotite, THM – Translucent heavy minerals, Tur – tourmaline, Zrn – zircon, Rt – rutile, Amph – amphibole, Grt – gar-
net, Ky – kyanite, St – staurolite, EpZoCzo – epidote-zoisite-clinozoisite, oth – other minerals, + – less than 1%.

Sample Unit
Heavy minerals (%) Translucent heavy minerals (%)

Chl Dol Op Bi THM Tur Zrn Rt Amph Grt Ky St EpZoCzo Oth

Bol 1/2

Oza

+ 34 66 2 + 1 + 4 87 5
5/4 40 60 2 2 + 5 88 2
Dbr-I 2/1 23 77 + + + 4 91 3
4/1 29 71 1 + 1 2 92 3
12/1 16 84 + 1 95 3
Bor 1/1 23 77 + + 3 2 1 87 6
Oza-I 3/2 2 92 6 11 48 38 + 2 +
6/1 1 93 6 14 53 27 2 2 + 1
Sla 3/4 70 27 3 25 6 4 40 2 9 9 5
Top-II 3/1 2 92 + 6 18 27 35 1 12 3 4
6/4 17 56 10 7 13 43 28 1 10 3 2
Kra-I 13/1

And

1 91 6 2 46 5 13 8 2 6 15 5
Mal-I 5/2 1 70 11 18 10 3 7 24 2 15 31 8
7/1 17 41 11 31 8 1 4 1 28 3 14 34 7
KrT-II 16/1 1 61 8 30 4 + 7 + 49 3 11 20 5
8/1 5 34 13 48 6 4 25 5 21 34 5
11/1 5 11 18 66 5 3 41 2 19 26 4
16/1 3 12 85 4 3 4 42 4 12 27 4
Pač-I 1/1 7 11 13 69 3 5 65 1 7 13 6
20/1 2 5 11 82 2 5 72 3 5 11 2
39/1 18 11 14 57 8 + 3 53 2 16 14 3
Pož-I 1/2 1 5 8 86 6 1 5 5 62 1 7 11 2
6/1 21 10 13 56 4 + 3 4 36 1 13 34 4
Mat-I 1/1 4 10 2 84 6 4 + 57 3 3 14 12
Bob-I 10/1 41 27 9 23 6 2 28 7 12 37 8
25/1 35 31 7 27 5 2 2 28 5 18 35 5
Pož-I 23/1 15 24 14 47 3 + 2 4 32 3 17 35 3
And-I 2/1 + 14 + 85 1 + 2 63 1 2 26 4
29/1 19 32 1 48 5 1 1 54 + 7 21 10
Mat-I 8/1 + 10 89 4 3 74 1 4 8 6
14/1 1 11 88 5 2 71 2 4 10 6
Mir-I 2/1 13 21 1 65 8 9 + 37 6 6 26 7
6/1 + 8 92 2 3 + 57 4 3 28 2
6/3 16 84 2 4 57 2 2 31 2
7/4 8 17 + 75 7 2 26 5 8 38 14
12/1 2 13 85 3 3 39 3 7 39 6
Maj-I 1/2 29 31 7 33 4 + 1 2 36 2 12 40 2
3/1 15 16 12 57 6 1 3 33 3 17 34 3
Tol –II 8/1 21 39 4 36 5 5 16 20 4 16 27 7
Bek-I 2/3 3 9 1 87 2 1 4 31 1 3 46 12
MMa-I 5/1 8 92 5 2 3 7 2 12 57 12
11/1 1 6 93 2 2 3 26 1 10 44 12
Bek-II 3/1 21 8 15 56 2 5 1 17 + 3 59
11/1 39 12 49 5 1 13 12 1 5 51 12
Sel-I 1/1 7 10 83 3 + 1 20 28 2 7 28 10
Sem-I 12/1 3 18 + 78 5 2 4 22 4 10 39 14
22/1 1 12 1 86 4 1 3 15 2 9 51 15
BDl-I 5/1 2 15 83 2 3 9 41 2 6 32 5
6/3 1 11 88 2 2 7 40 2 4 32 11
Mil-I 1/3 17 5 15 63 6 4 3 19 2 20 40 6
3/1 6 11 13 70 3 4 1 20 1 27 40 4
PoP 1/1 2 2 7 89 1 1 4 3 35 7 19 25 5
5/4 7 10 6 77 3 1 1 23 3 33 33 3
Nac-III 6/1 21 79 3 + 4 2 3 21 57 9



Geologia Croatica 62/3Geologia Croatica
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Sample Unit
Heavy minerals (%) Translucent heavy minerals (%)

Chl Dol Op Bi THM Tur Zrn Rt Amph Grt Ky St EpZoCzo Oth

Tol-II 14/1

HZb

24 37 6 33 3 2 8 28 3 19 29 5

Sel-I 30/1 47 18 35 4 1 4 9 18 3 58 3

38/1 2 11 + 87 2 2 7 27 3 6 43 10

VV 1 + 14 85 4 1 6 2 19 3 13 41 11

Plu-I 1/1 33 32 6 + 28 2 4 21 23 6 12 20 12

8/1 27 39 3 31 6 + 1 26 18 6 17 15 10

11/1 7 4 10 79 4 + 3 14 28 3 15 23 9

19/1 14 86 4 + 2 22 + 6 14 42 9

Plu-III 1/1 2 + 11 86 3 4 6 38 6 7 28 8

Mal-I 12/2 9 11 18 62 2 2 6 40 4 12 26 8

PG-2 2 8 14 76 2 + 1 7 48 4 5 28 4

D-1 + 7 93 3 2 11 46 4 10 19 5

D-2 8 92 3 2 2 6 19 64 4

Nac-III 6/3 9 91 33 14 23 24 2 4

Plu-II 1/1 21 79 9 2 5 4 5 27 40 8

4/1 14 86 5 1 2 3 5 29 52 3

Plu-III 2/1 + 16 86 5 4 5 1 7 15 56 7

3/1 22 78 6 8 + 7 22 52 4

4/1 34 66 7 + 8 + + 13 28 39 3

PB 1 32 68 8 + 17 11 18 43 2

Mal-I 14/2 29 71 9 + 7 5 24 47 7

Plu-II 6/2

Plu

25 75 11 + 11 + 10 21 43 3

6/1 + 17 82 7 8 + 2 11 38 29 4

Vbo-I 17/1 12 7 81 23 1 3 1 10 26 33 3

Sel-I 45/1 24 76 2 1 6 3 32 5 5 38 8

Dzg-I 3/1 47 53 33 14 23 24 2 4

10/1 48 52 25 1 18 26 23 3 4

20/2 + 46 54 18 + 12 + 25 27 10 7

21/2 + 63 36 20 2 18 21 30 4 5

Plu-II 7/2 39 61 13 2 14 1 17 33 17 3

VTv-I 1/1 53 47 12 3 26 22 32 2 3

6/1 51 49 15 23 24 35 + 2

9/1 55 45 29 2 13 + 29 24 2

17/1 48 52 18 1 15 26 37 + 2

Mal K/1 49 51 33 2 12 22 27 2 2

K/2 51 49 29 1 15 21 29 3 2

Nac-III 12/2

Cer

11 89 25 1 18 26 23 3 4

Nac-IV 1/1 17 83 18 + 12 + 25 27 10 7

5/1 29 71 20 2 18 21 30 4 5

7/1 20 80 13 2 14 1 17 33 17 3

Vrb 7/1 2 29 69 12 3 26 22 32 2 3

13/1 2 32 21 45 15 23 24 35 + 2

17/1 6 26 68 29 2 13 + 29 24 2

22/1 9 21 70 18 1 15 26 37 + 2

27/1 1 13 14 72 33 2 12 22 27 2 2

39/1 1 25 74 29 1 15 21 29 3 2

Table 1: continued.



Kovačić et al.: Discriminant function analysis of Upper Miocene and Pliocene sands from the southwestern part of the Pannonian Basin System, Croatia Geologia Croatica
195

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Geologia Croatica 62/3Geologia Croatica
196

accom panying eigenvalues, only the fi rst three DFs which ex-
plain almost all the variability of the system (98.9%) were se-
lected to defi ne dimensionality of the discriminant space.

4.1. Building a model

To construct a functional model around the computed DFs is 
vital to MDA since it opens the door to the hidden relationship 
between groups not detected by direct observations and mea-
surements. In this way the natural processes can be inferred 
underlying the mathematical structure of analyzed data. Indi-
vidual assessment of each descriptor (HMA) is needed for this 
purpose, and discriminant loadings (structure coeffi cients), 
which represent simple correlations of variables with respec-
tive DFs, are used here to assist the overall discrimination be-
tween the groups. Inspection in a model is particularly helpful 
via the variable diagrams which provide the easiest and most 
informative insight into the structure of discriminant space, 
both indicating which descriptors should be kept in the geo-
logical interpretation of discriminant functions and which de-
scriptors most clearly separate the a priori defi ned groups. In 
this respect, a number of variables with minor contributions 
to discrimination are excluded from the interpretation of the 
model. Among these are Dol, Chl and EpZoCzo which crowd 
together around the main centroid owing to their small dis-
criminant loadings (Fig. 4A, D). Furthermore, the relationship 
between variables and related groups can be likewise dis-
played geometrically, viewing DFs as mutually perpendicular 
vectors (axes) in the reduced discriminant space. However, 
the variable and group diagrams cannot be contrasted directly 
since different scales are employed in each case. The scatter-
plot of variable loadings (Fig. 4A, D) is drawn with the axes 
shown as normalized vectors, while scatterplots of group 
means (Fig. 4B, E) and discriminant scores (Fig. 4C, F) are 
constructed using discriminant score vectors. As a result, in-
terdependence between variables and related groups can be 
elucidated regarding their shared position along the respective 
discriminant axis. In both diagrams, contribution to the over-
all discrimination of points placed close to the axes intersec-
tion is negligible. Typically, a reciprocal relationship between 
the group means (centroids) and variables along the respec-

tive discriminant axis will determine the geological nature of 
the computed mathematical model. Nevertheless, however re-
vealing these diagrams may be about the real geological pro-
cesses generating the character of mutual group relationships, 
the best way to evaluate how much the groups really differ is 
to take a closer look into the distance matrix, (matrix of squ-
ared Mahalanobis distances; Table 3). Based on these values, 
the Plu unit falls farthest away from all other units, namely 
the Oza (69.38), And (43.46), HZb (31.33) and Cer (27.82). 
However, there is some overlap between the Cer, HZb and 
And units. The closest together are Cer and HZb (2.96), then 
Cer and And (4.13), and fi nally And and HZb (5.98). Judging 
from the calculated Mahalanobis distances, the Oza unit is not 
very different from the Cer (15.91), And (16.61) and HZb 
(17.45) units, lying somewhere in the middle of the fi rst two 
cases. The rationale for similarities or disparities between the 
investigated groups (lithostratigraphic units) can be found in 
specifi c geologic processes which control the spatial distribu-
tion of the descriptor variables (HMA) during evolution of the 
tectonic and sedimentological history of the study area.

4.2. Labeling the discriminant functions

Labeling discriminant functions is a starting point in inter-
preting the mathematically computed (structural) model in 
terms of processes. In this manner, the structural model is 
transformed into a process with each DF contributing to a 
single independent (geologic) process in the overall separa-
tion of the groups. Variables participate in this structure-pro-
cess conversion as the building blocks assuming the role of 
process descriptors.

In the computed mathematical model, the fi rst discrimi-
nant function DF1 makes the greatest contribution to dis-
crimination between the groups, accounting for more than 
73% of the total variability. It is essentially monopolar, be-
ing marked by the high positive loadings of dominant trans-
lucent heavy minerals, kyanite (Ky) and, to a lesser degree, 
staurolite (St), while the major part of the HMA suite is con-
centrated around the main centroid (Fig. 4A, D). If compared 
to the scatterplot of group means, it illustrates the separation 
of the Plu unit from the other four groups (particularly Oza) 
based on enrichment/depletion of kyanite in their modal 
composition. While the Plu unit is characteristic for its higher 
content of kyanite, other lithostratigraphic units in the SW 
part of PBS are rather indifferent to it (with the exception of 
the Oza unit showing a slightly decreased content of Ky). In 
accordance with the relative prominence of this mineral, DF1 

Table 2: Tests of signifi cance. a) Multivariate test of the overall signifi cance 
of discrimination. b) Tests of residual roots (discriminant functions).

a) Number of variables in the model 10

Wilks’ λ 0.038

Approximate F ratio 11.387

Degrees of freedom 40; 331

p-level p<0.000

b) DF Eigen-
value

Eigen 
(%)

Canon. 
R Wilks’ λ Chi-Sqr. df p-level

1 5.533 73.06 0.920 0.038 303.1 40 0.000

2 1.390 18.35 0.763 0.247 129.5 27 0.000

3 0.568 7.50 0.602 0.589 48.9 16 0.000

4* 0.082 1.08 0.275 0.924 7.3 7 0.402

Note: DF marked* is statistically insignifi cant

Table 3: Squared Mahalanobis distances.

Oza And HZb Plu Cer

Oza 0.00 16.62 17.45 69.38 15.91

And 16.62 0.00 5.98 43.46 4.13

HZb 17.45 5.98 0.00 31.33 2.96

Plu 69.38 43.46 31.33 0.00 27.82

Cer 15.91 4.13 2.96 27.82 0.00



Kovačić et al.: Discriminant function analysis of Upper Miocene and Pliocene sands from the southwestern part of the Pannonian Basin System, Croatia Geologia Croatica
197

can be readily identifi ed as the kyanite function. Geologi-
cally, the signifi cant abundance of Ky and St in the detritus 
of the Plu unit sands serves as a good indicator of the weath-
ering of rocks of medium grade regional metamorphism in 
the source area. Due to the marked dominance of DF1 in the 
discriminant model it unmistakably highlights the central 
geologic process in the development of the Upper Miocene 
and Pliocene sands in the SW part of the PBS – a process 
controlling the distribution of Ky as the ‘key’ mineral from 
the incipient stage of parent rock weathering through trans-
port to sedimentation and possible re-deposition of sedimen-
tary material in the later stages of the development of the 
sedimentary basin or its particular portions.

The second discriminant function DF2 accounts for only 
18% of the total variance between the groups. In contrast to 
DF1 it is characteristically bipolar and can be interpreted as 
refl ecting the inverse relationship between garnet on the one 
side and zircon with (to a less extent) rutile on the other, af-
ter which it can be properly labeled the garnet-zircon func-
tion. From visual inspection of the related variable and group 
scatterplots (Fig. 4A, B), it is evident that after acknowledg-
ing this variable pattern, DF2 further separates the Oza unit 
from the remaining groups. This partition is based principally 
on the reduced content of garnet and seconded by the higher 
content of zircon and rutile in the Oza unit sand composi-
tion. The content of garnet is slightly higher with part of the 
samples in the And unit (Fig. 4C) while the remaining three 
groups (Cer, HZb and Plu units) remain indifferent in this 
relationship sticking to the middle position with the least 
mean values. This situation highlights their average HMA 
composition with respect to the DF2 labeling minerals. In a 
geological (sedimentological) sense, DF2 must be observed 
through the bond of the two minerals, Zrn and Rt, which are 
amongst the ultra stable detrital minerals in the sedimentary 
systems, against Grt which is considered to be the indicator 
of high energy conditions during transport (ROTHWELL, 
1989). Being a garnet-zircon function, DF2 in a functional 
sense (in a sedimentary system) can either refl ect variations 
in the parent rock mineral composition via its mineral con-
tent in the detrital material. In other words, Zrn and Rt can 
be found in the composition of older sedimentary rocks (most 
probably derived from more acid igneous rocks), or signal 
the prevailing hydraulic conditions closely associated with 
sedimentary environment. This amounts to saying that heavy 
minerals (having great density) are concentrated under high 
energy conditions (Grt) while others, such as Zrn and Rt pre-
fer environments of low stream power. It could be noted in 
passing that a similar pattern of sedimentary process regime 
was already deduced in a quite different environment where 
the Quaternary sediments were divided into several genetic 
groups (PEH et al., 1998). Although results can be inconclu-
sive in this respect due to the still limited volume of similar 
investigations needed for reliable cross-comparison, it is in-
teresting to observe that source rocks seem to play the dom-
inant role in distribution of HMA in the basin systems, at 
least at a regional scale, while the hydraulic conditions con-
trolling their physical and chemical stability during transport 
and deposition are secondary.

The third discriminant function DF3 (explaining barely 
7.5% of the system variance) is also bipolar but dominantly 
loaded with only one variable – amphibole (Amph) – by 
which the HZb unit is weakly separated from the others (Fig. 
4D, E). Amphibole is negatively associated with the set of 
variables weakly loaded on the positive pole of DF3 among 
which some minerals, very resistant to weathering, such as 
Rt, Zrn and Tur, are highlighted. Since amphibole is a highly 
unstable mineral component this discriminant function can 
be interpreted as the amphibole function representing, in sed-
imentological sense, a function of the chemical stability of 
HMA in the investigated arenaceous (sandy) deposits. Obvi-
ously, the HZb unit must have been deposited under condi-
tions of prolonged stability or amphibole would not other-
wise be signifi cantly present to serve as the key mineral in 
its discrimination. Similarly, with respect to environmental 
quiescence and stability, it could be said that all other groups 
are more or less well separated from HZb towards the Zrn(Rt) 
quarter of the diagram, indicating the more turbulent condi-
tions of their deposition.

4.3. Classifi cation results

Classifi cation effi ciency is often proved to be of greater use 
geologically in the process of discrimination than various 
statistical tests (ROCK, 1988). It is particularly evident in 
cases when MDA is applied to a large volume of data scat-
tered across various spatial boundaries such as geological 
(lithostratigraphical) units, depth intervals, or profi le lines, 
being composed of the same suite of observed or measured 
attributes (e.g. physical or chemical properties) (e.g. SAFTIĆ 
et al., 2001; PEH et al., 2008; KOVAČIĆ, 2004; GRIZELJ, 
2008). It is also evident in applying statistical analysis in or-
der to test fro group differences based on lithostratigraphical 
units properties (e.g. MALVIĆ et al., 2005). In this context, 
classifi cation rates in original or a priori defi ned lithostrati-
graphic units can be readily inspected by contrasting the 
mathematically ‘predicted’ (computed) and original (‘natu-
ral’) group membership of individual samples (Table 4).

From Table 4 it is apparent that the discriminant model 
is organized with relatively high effi ciency which exceeds 
80%. However, for certain groups, namely Cer and HZb, 
overlap is considerable which is evident from the low Ma-
halanobis distances (Table 3), and can be visually scanned 
from respective sample diagrams (Fig. 4C, D). For instance, 

Table 4: Classifi cation matrix.

Observed
group
memberships

Predicted group memberships

Oza And HZb Plu Cer %
correct

Oza 10 1 0 0 0 90.91

And 1 40 3 0 1 88.89

HZb 0 5 14 0 3 63.64

Plu 0 0 2 12 0 85.71

Cer 0 4 0 0 5 55.56

total 11 50 19 12 9 80.20



Geologia Croatica 62/3Geologia Croatica
198

only fi ve samples out of nine of the Cer unit are assigned to 
that particular group while the rest are more similar to the 
And unit, which has a classifi cation rate barely in excess of 
55%. In the case of the HZb unit, the success rate is some-
what greater and amounts to over 63%. Here, eight samples 
out of 22 are closer to other groups, including the And (5) 
and Cer (3) units. This information indicates the signifi cant 
inhomogeneity of the Cer unit where more than 44% of al-
locations are unequivocally misclassifi ed (And unit), while 
at the same time, an equal number of samples are a posteri-
ori allocated to the former at the expense of other litostrati-
graphic units: HZb (3) and And (1).

The Oza, Plu and And lithostratigraphic units are distin-
guished by relatively high classifi cation effi ciency. Among 
these, Oza unit is recognized for its homogeneity (Table 4). 
Its modal composition is so unique that one can hardly fi nd 
similar sand grade sedimentary material accounting for the 
fact that only a single sample of this unit is incorrectly clas-
sifi ed changing its group affi liation for And, and vice versa. 
One of the samples originally ascribed to And was later clas-
sifi ed as a member of the Oza unit (Table 4). Such an almost 
optimal separation can be explained by a different source for 
the clastic material in its detrital composition relative to other 
units. Namely, the clastic detritus of the Oza unit is of local 
provenance (after KOVAČIĆ & GRIZELJ, 2006), and is de-
rived from the weathering of older sedimentary rocks while 
the material forming the other units must have been trans-
ported from more distant areas, originating form the weath-
ering of a diverse suite of metamorphic, sedimentary and 
igneous rocks. A cross-exchange of two single group assign-
ments between the Oza and And units can be interpreted in 
the knowledge that both samples were collected in the Žum-
be rak Mt. where clastic detritus from both sources combines.

A high classifi cation rate is also characteristic for the Plu 
unit (Table 4). This is expected in as much as, (after KOVA-
ČIĆ & GRIZELJ, 2006), a signifi cant proportion of its de-
tritus is derived from the alumina-rich metamorphic rocks 
as opposed to other units. Misclassifi cation of two Plu sam-
ples into the HZb unit can be easily explained by the fact 
that the former conformably overlies the latter while their 
boundary is not clearly defi ned.

Also, according to KOVAČIĆ & GRIZELJ (2006), the 
same petrologic province responsible for supplying sediment 
for the And, HZb and Cer units, produces great similarity of 
their clastic material which is the main reason why a consid-
erable number of samples show reciprocally incorrect af-
fi liations. However, almost 90% of the And samples are a 
priori correctly classifi ed, strongly confi rming its homoge-
neous composition (Table 4). In this connection, with the 
And unit being the ‘heaviest’, some samples were assimi-
lated from the other two units, a typical effect where one 
group, being larger than the other, draws the members of a 
smaller group closer to its own centroid. As a result, the post 
hoc assignments of smaller groups inevitably undergo low 
classifi cation rates (slightly over 50%) but a larger group 
better conveys the mean modal composition.

5. CONCLUSION

Multiple discriminant analysis applied to the Lower Mio-
cene and Pliocene sands from the SW part of the Pannonian 
Basin System showed that specifi c mineral associations 
characteristically relate to particular lithostratigraphic units 
outcropping in the area. These relationships allow some de-
fi nite conclusions to be drawn about specifi c stages of the 
sedimentary cycle, and conditions prevailing during weathe-
ring, transport and deposition of the studied sedimentary ma-
terial. Important results of MDA can be summarized as fol-
lows:
(1)  Three discriminant functions account for almost all va-

riance between the groups (99%) and can be easily in-
terpreted in geological terms as: a) DF1 – kyanite (Ky) 
func tion indicating source rock mineralogy (alumi na-
rich, metamorphic rocks); b) DF2 – garnet-zircon/rutile 
(Grt-Zrn/Rt) function explaining the relationship bet-
we en source rock mineralogy (older clastic sediments and 
felsic igneous rocks – Zrn/Rt) and hydraulic conditions 
controlling transport and deposition of detritus (Grt) and; 
c) DF3 – amphibolite function accounting for the pro-
cesses of chemical and physical stability in the sedimen-
tary cycle.

(2)  The Kyanite function is by far the most important part of 
the discriminant model accounting for almost 3/4 of all 
the processes in the investigated area, placing great im-
portance on the area of alumina-rich metamorphic rocks 
as the main provenance of the clastic material.

(3)  Oza, Plu and And units are set apart by the highest clas-
sifi cation effi ciency. The most discrete (most different) 
among these is the Plu unit (by DF1). However, the Ozalj 
unit is recognized for its homogeneity (the greatest clas-
sifi cation rate). The Andraševec unit is the most massive, 
prone to scavenging the members of smaller groups. At 
the other end of the scale, the Cer and HZb units repre-
sent the mean composition of HMA with respect of all 
the investigated groups.

Finally, it must be stated that interpretation of changing 
affi liations assessed by discriminant analysis can greatly im-
prove geological mapping results because otherwise very 
similar sand units, previously differentiated into predefi ned 
lithostratigraphic and chronostratigraphic compartments dur-
ing fi eld work, can now be reconsidered. Inhomogeneity of 
the HMA within particular units can be used as an indicator 
tool for visualizing the dynamics of a sedimentary system 
and of its development, particularly concerning the processes 
of palaeotransport, sedimentation and subsequent re-deposi-
tion. Some widespread lithostratigraphic such as the Andra-
ševec (Hrvatsko Zagorje, Žumberak Mt. and Slavonian Mts.) 
may indicate specifi c variations in lithology, texture, facies, 
sedimentary environments, sedimentary control on deposi-
tional sequences, and even age. In order to specify which 
geologic process had the dominant role in the sedimentary 
cycle resulting in the fi nal differentiation of lithostratigraphic 
units, it is very important in discriminant analysis to associ-



Kovačić et al.: Discriminant function analysis of Upper Miocene and Pliocene sands from the southwestern part of the Pannonian Basin System, Croatia Geologia Croatica
199

ate individual groups with respective variable descriptors 
(HMA). Thus, one can single out the process which is in-
volved, and with what priority, in the sedimentary regime. 
As previously mentioned, the most valid implication emer-
ging from the discriminant model is the complete dominance 
of DF1 since it explains the greatest proportion of the total 
variability. For this reason it unequivocally (in the process 
sense) highlights the most important issues in the genesis of 
the Upper Miocene sand deposits in the WS portion of PBS; 
the provenance of the detritus indicating the alumina-rich 
metamorphic source rocks, typical for the Plu unit.

ACKNOWLEDGMENTS
This study was funded by the Ministry of Science, Education and 
Sports, Republic of Croatia, projects ‘Evolutionary Changes of the Di-
narides from Subduction to Modern Adriatic Beaches’ (119-1191155-
1159), The Map of Mineral Resources of the Republic of Croatia (181-
1811096-1104) and Basic Geological Map of the Republic of Croatia, 
1:50000 (181-1811096-1093).

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Manuscript received March 18, 2009
Revised manuscript accepted June 30, 2009

Available online October 02, 2009
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