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# Open Geosciences

### formerly Central European Journal of Geosciences

Editor-in-Chief: Jankowski, Piotr

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Volume 9, Issue 1

# Interpretation of sedimentological processes of coarse-grained deposits applying a novel combined cluster and discriminant analysis

Éva Farics
• Corresponding author
• Eötvös Loránd University, Department of Physical and Applied Geology, H-1117, Budapest, Pázmány Péter stny. 1/C, Hungary
• MTA-ELTE Geological, Geophysical and Space Science Research Group, H-1117, Budapest, Pázmány Péter stny. 1/C, Hungary
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• Other articles by this author:
/ Dávid Farics
• Engineering Information Technology, Budapest University of Technology and Economics, Budapest, Hungary
• Other articles by this author:
/ József Kovács
• Eötvös Loránd University, Department of Physical and Applied Geology, H-1117, Budapest, Pázmány Péter stny. 1/C, Hungary
• Other articles by this author:
/ János Haas
• MTA-ELTE Geological, Geophysical and Space Science Research Group, H-1117, Budapest, Pázmány Péter stny. 1/C, Hungary
• Other articles by this author:
Published Online: 2017-10-28 | DOI: https://doi.org/10.1515/geo-2017-0040

## Abstract

The main aim of this paper is to determine the depositional environments of an Upper-Eocene coarse-grained clastic succession in the Buda Hills, Hungary. First of all, we measured some commonly used parameters of samples (size, amount, roundness and sphericity) in a much more objective overall and faster way than with traditional measurement approaches, using the newly developed Rock Analyst application. For the multivariate data obtained, we applied Combined Cluster and Discriminant Analysis (CCDA) in order to determine homogeneous groups of the sampling locations based on the quantitative composition of the conglomerate as well as the shape parameters (roundness and sphericity). The result is the spatial pattern of these groups, which assists with the interpretation of the depositional processes. According to our concept, those sampling sites which belong to the same homogeneous groups were likely formed under similar geological circumstances and by similar geological processes.

In the Buda Hills, we were able to distinguish various sedimentological environments within the area based on the results: fan, intermittent stream or marine.

## 1 Introduction

A coarse-grained clastic bed-set occurs at the base of the Upper Eocene marine succession in the Buda Hills, Transdanubian Range, Hungary (Fig. 1a). The oligomictic and rarely monomictic conglomerate beds contain dominantly dolomite pebbles, but pebbles of volcanic rocks are also common locally. Other rock types are also present sporadically. Due to the rather poor exposure conditions, the sedimentological structures of the basal beds are rarely visible. Therefore, the composition of the clastic material and the size and shape of the clasts may serve as a basis for the determination of both the source area of the clasts and the interpretation of the transport and depositional processes they were subject to. Coarse-grained clastic successions may be deposited in various sedimentological environments forming alluvial, glacial, fluvial, and erosional sedimentary sequences. For the characterisation of these rocks, plenty of petrography and textural parameters (composition of the grains, grain size, roundness and sphericity) are available, and these can then be analysed with statistical methods. The main aim of this paper is the interpretation of the depositional conditions of the Eocene basal conglomerates of the Buda Hills, and the determination of the source of the volcanic clasts–by applying a special grouping method for various clast parameters, measured using our newly developed IT application.

Figure 1

Geological setting of the study area: a., simplified Pre-Cenozoic map of the Transdanubian Range showing the location of the study area (and places mentioned in the article) (after Haas and Budai 2014 [41]), 1 – Pre-Cenozoic rocks on the surface, 2 – Paleozoic-Middle Triassic formations, 3 – Upper Triassic formations, 4 – Jurassic-Cretaceous formations; b., geology map of the Buda Hills showing location of the study outcrops (base map of Budai and Gyalog 2010 [42]), 1 – Budaörs Dolomite, 2 – Hauptdolomite, 3 – Dachstein Limestone, 4 – Csővár Limestone – Mátyáshegy Formation, 5 – Eocene formations, 6 – Oligocene formations, 7 – Miocene formations, 8 – Quaternary formations, 9 – Tectonic elements, 10 – Border of town.

In many cases the suggested parameters for the description of roundness and sphericity (e.g. Szádeczky-Kardoss’ (1933) CPV (C=concave, P=planar, V=convex) [1]) are poorly defined and their measurement in coarse grained siliciclastic rocks is rather subjective. To improve the precision of the measurements, we redeveloped an earlier version of the Rock Analyst application (Győrfy 2015 [2]), leading to major improvements (see Section 3.3). This application is now available at http://faricseva.web.elte.hu/.

For the data obtained using the Rock Analyst application, we applied a multivariate statistical grouping method, Combined Cluster and Discriminant Analysis (CCDA) (Kovács J. et al. 2014 [3]) for the interpretation of the sedimentological processes of the coarse-grained clastic successions. CCDA combines linear discriminant analysis and cluster analysis and its aim is to find not only similar, but even homogeneous groups of sampling locations based on the multivariate samples. The result is a spatial pattern which shows the relationship of the sampling sites (homogeneity or difference and in particular the rate of the latter). This method has been used successfully for hydrological and hydrogeological interpretation [3, 4, 5] and biological analysis [6]. In this paper, CCDA is used in a sedimentological problem. According to our opinion, the sampling sites which form a homogeneous group on the basis of different criteria indicate deposition under similar geological circumstances and by the same geological processes. A sedimentological model based on this concept might be more accurate and objective than former ones owing to the consistency of our approach. More details about CCDA, along the meaning of homogeneity can be found in Section 3.4.

Several studies have discussed the formation of the maximally five meter thick volcanic clast-bearing Upper Eocene coarse-grained clastic succession of the Buda Hills. Early researchers thought that the Eocene volcanic material had been accumulated on the karstified surface of Triassic carbonates (mostly dolomites) prior to transgression, and this was preserved in the fractures and depressions of the basement [7]. Later, some of the researches thought that the clasts were formed and transported via erosion [8], while others proposed a terrestrial depositional environment [9, 10]. Farics et al. (2015) [11] proposed a simple transport model: redeposition of the volcanic clasts from south to north (i.e. from Budaörs to Róka Hill) during the latest Cretaceous to Priabonian period, prior to the onset of the marine sedimentation. However, this interpretation was based on field observations only, which suggested a northward decreasing trend in the size of the andesite clasts. In the present study, along with the clast size, further parameters (e.g. percentage of the components, shape of the clasts) are also considered. Consequently, the previous simple model is significantly refined and modified.

## 2 Geological setting of the study area

The uppermost Anisian to lowermost Carnian Budaörs Dolomite is the oldest formation cropping out in the Buda Hills (Fig. 1b). An andesite dike of Carnian age (based on zircon U-Pb dating) was encountered in the dolomite in well Budaörs-1 [12]. The higher part of the Triassic succession is made up of cherty dolomite and limestone of a basin facies as well as coeval platform dolomites and limestones [13, 15, 16] (Fig. 1b). Bauxitic clay locally occurs on the karstified surface of the Triassic carbonates [9]. The Triassic carbonates are overlain by an Upper Eocene succession starting usually with conglomerate beds. Magyari (1994) [17] distinguished two types of the basal conglomerates: Type 1 which contains exclusively Triassic dolomite and chert clasts and Type 2 which contains remarkable amounts of volcanic clasts along with dolomite and chert pebbles. The andesite clasts yielded Carnian U-Pb ages (I. Dunkl, personal communication).

## 3 Materials and methods

About 20-25 hand-sized conglomerate samples were collected from the volcanic clast-bearing Upper Eocene basal conglomerate successions (Fig. 1b): Apáthy Rock - Stone Gate (AR), Fenyőgyöngye quarry (FQ), Hunyad Peak (HP), János Hill - Virág Valley (JH), Kő Hill of Budaörs (KH), Látó Hill (LH), Róka Hill quarry (RH), Tündér Rock (TR) and Út Hill (UH).

The following parameters of the conglomerates were determined in every outcrop using the Rock Analyst application (see Section 3.3):

1. the size of each clast;

2. the quantitative composition of the clast types in the conglomerates;

3. the roundness and the sphericity of each clast.

The parameters of 500 randomly selected clasts of every sampling sites were measured. The investigation of the thin sections of the whole conglomerate was necessary, as the preparation of small (2-8 mm) clasts individually mostly from the silica-cement is hardly possible. Moreover, microscopic investigation of thin sections was needed for the exact determination of rock types. Based on the results of Farics et al. (2015) [11], the following clast types were distinguished: dolomite, andesite, various acidic volcanic rocks (including dacite-rhyolite tuff, ignimbrite and rhyolite) and chert (Fig. 2).

Figure 2

Macroscopic photos of the volcanic clast-bearing Upper Eocene basal conglomerate in the Buda Hills: a. and b., Kő Hill (KH); c., Apáthy Rock - Stone Gate (AR); d., Fenyőgyöngye quarry (FQ); e., Róka Hill quarry (RH); f., János Hill-Virág Valley (JH).

## 3.1 Roundness definitions

Various methods have been proposed for the measurement of the roundness of clasts. Most of these methods (Wentworth 1921 [18], Cailleux 1952 [19]) only take into account the less rounded sides of the clasts. In contrast, the methods of Wadell (1932) [20] and Szádeczky-Kardoss (1933) [1] take into consideration the whole surface of the clasts for the calculation. We used both of the latter methods for the measurement of roundness.

Wadell (1932) [20] defined a Wr roundness index as follows: $Wr=∑i=1Nri/NR$(1)

where ri is the radius of curvature of the i-th clast corners, R is the radius of the largest inscribed circle, and N is the number of clast corners measured. Only those clast corners are taken into account where r < R (Fig. 3).

Figure 3

The clasts are separated on the cut surface of the macroscopic sample by curves, and Wadell’s roundness values are calculated by the Rock Analyst application. Yellow lines – andesite clasts, red lines – acidic volcanic clasts, green lines – dolomite clasts, purple circle – the largest inscribed circle, blue circle – curvature of the clast corner.

This definition describes a certain thin section of a clast. In practice, one takes a random plane in a conglomerate, leading to a thin section in which then all of the clasts are measured. For the better interpretability of the Wr roundness index, values were grouped by Powers (1953) [21] into very angular, angular, subangular, subrounded, rounded and well rounded (see later Fig. 5).

Figure 4

The quantitative composition of the conglomerates: a., the area percentage of each clast type compared to all clasts in every outcrop; the area percentage of each clast type compared to all clasts within the various size fractions at b., KH and c., JH.

Figure 5

The result of Wadell’s (1932) roundness measure with the classification of Powers (1953): va – very angular, a – angular, sa – subangular, sr – subrounded, r – rounded, wr - well rounded; a., dolomite clasts, b., andesite clasts. Andesite clasts are the most angular in AR, KH and UH and the most rounded in JH and LH. Dolomite clasts are more rounded than andesite clasts.

The CPV method of Szádeczky-Kardoss (1933) [1] is an alternative way of measuring the roundness of clasts based on the concave, convex and planar segments of their surfaces. In contrast to Wadell’s definition, which characterizes roundness with a single value, the CPV method uses three values for the same purpose, namely the ratio of the three curvature elements (C=concave, P=planar, V=convex) of the perimeter. The results of CPV analyses can be displayed on a triangle diagram (see later Fig. 6 for an example). While Szádeczky-Kardoss (1933) [1] defined in which thin sections one has to measure these CPV values exactly, in practice—as with Wadell’s method—we take a random plane in a conglomerate, leading to a thin section in which then all of the clasts are measured.

Figure 6

The roundness of dolomite and andesite clasts based on Szádeczky-Kardoss’ (1933) CPV-based definition in triangle diagrams. The coloured areas are based on multiple measurements of different clasts with 5% outliers left out to make a clear picture.

## 3.2 Sphericity definitions

Wadell (1932) [20] defined sphericity as the ratio of the clast surface area to the surface area of a sphere having the same volume. Unfortunately, the measurement of this index is very difficult. An alternative is the operational sphericity Ψ, which is given by the following formula: $Ψ=Vc(clast)Vscs(smallestcircumscrbingsphere)3$(2)

where Vc is the clast volume and Vscs is the volume of the smallest circumscribing sphere. Sphericity values range from 0 (non-spheroidal) to 1 (perfect sphere).

In practice, if only a two-dimensional thin section is available, the following two options of projection sphericity arise. Wadell’s (1932) [20] projection sphericity Ψ’ (hereinafter sphericity) is defined via $Ψ′=d/D$(3)

where d is the diameter of a circle with an equal area to that of the clast and D is the diameter of the smallest circle circumscribing the clast.

Riley’s (1941) [22] projection sphericity R (hereinafter sphericity) is defined as follows: $R=∂/D$(4)

where is the diameter of the largest inscribed circle and D is the diameter of the smallest circumscribing circle.

## 3.3 The Rock Analyst application

The Rock Analyst application had already been used by Győrfy(2015) [2] and was further developed for this project. The program is available in the Appendix. It is of dual benefit: on the one hand, the program facilitates the measurement of the parameters, while on the other hand, it reduces the error of the measurements and makes the process more objective.

For using this application, we first have to import the scanned image of a cut surface of a siliciclastic rock and/or a thin section. Then we assign the clast types and mark the boundaries of the analysed clasts (Fig. 3). The largest diameter (mm), perimeter (mm), area (mm2), quantitative composition, Wadell’s roundness, CPV values, Wadell’s sphericity and Riley’s sphericity are automatically calculated based on the scanning resolution (DPI – dot per inch, the number of the pixels per 2.54 cm) and displayed in a table. Summarized results for various size boundaries are also available. Specifically, a summary of roundness and sphericity values (average, standard deviation, minimum, maximum, median and quartiles) per clast type and also in each size fraction is displayed. The application is also capable of presenting the results of CPV measurements on triangle diagrams per clast types and/or clast size fractions.

## 3.4 CCDA method

Combined cluster and discriminant analysis (CCDA, Kovács J. et al., 2014 [3]) applies two widely known and applied methods, HCA (hierarchical cluster analysis [23]) and LDA (linear discriminant analysis [24, 25]) in order to find homogeneous groups of sampling sites. CCDA can be applied in settings where one has multiple observations from different origins and wants to determine whether these origins are significantly different from each other or can actually be treated as homogeneous based on the measured parameters. Hence, for each observation (which can be a sample or measurement) we must have a label describing the origin of the observation (which is usually the name of the sampling site where the measurement was taken or where the sample was collected from). Regarding the components, HCA divides data into a hierarchy of clusters, where at the lowest level each item belongs to its own cluster and at the highest level all items belong to the same cluster. The resulting tree-like structure, called dendrogram, can be cut at different heights, resulting in different grouping possibilities of the data. LDA defines linear functions that separate labelled observations of different classes in an optimal fashion subject to specific statistical metrics [26]. These two methods are combined in CCDA as follows: first of all, a basic grouping of the sampling sites has to be found. This can be achieved by taking the means of the observations at each sampling location and then applying HCA with Ward’s method [27] and squared Euclidean distances. While this is the standard way of implementation in the “ccda” R package in Kovács S. et al. (2014) [28], one could also take a different, e.g. expert-based grouping of the sampling sites. The idea then is to take the original point clouds of the measurements in the parameter space and try to separate them using LDA. For a given grouping, one can take the discriminant functions as a decision rule to classify the original observations. Comparing the predicted class labels with the true class label eventually leads to a percentage value describing the ratio of correctly classified observations (the so called “ratio” value) by the linear plane [3]. The latter is a measure for the separability of the groups within that specific grouping, which tells something about the similarity of groups. Similarity is useful in many cases, e.g. [29, 30]. Nonetheless, if the goal is to find not only similarly behaving sampling sites, but even homogeneous groups of sampling sites, one has to find even the most minute differences. This is the ultimate goal of CCDA. The idea is to compare the goodness of a certain grouping with the goodness of a random grouping. The random grouping is obtained by randomly permuting the class labels of the individual observations. One does many of these random groupings and each time evaluates the percentage of correctly classified cases by LDA. The 95% quantile of these percentage values is called q95. If ratio > q95, then significant differences between the groups occur—as the ratio of correctly classified cases by LDA is better than in 95% of the random groupings. Hence, one can take the decision rule based on whether the difference value, d = ratio – q95, is positive or negative. If d ≥ 0, we have significant differences, while in the case of d < 0, groups can be treated as homogeneous. Each grouping possibility obtained by HCA is investigated this way, and the grouping with the highest difference value is considered as optimal. The sub-groups of this grouping then always have to be investigated iteratively until all difference values are negative and thus the grouping under consideration can be treated as homogeneous. Hence, homogeneity in our paper is referred to as a case, where groups cannot be distinguished from each other using linear functions/hyperplanes in a space any better than at random. As a typical case, even if the point clouds very much overlap, once their centres lie sufficiently apart from each other, they become distinguishable by the CCDA procedure, leading to a positive difference value, such that we would not consider them as being homogeneous. In these cases, the groups could at most be regarded as similar, the degree of similarity being described by the difference value; the closer this is to zero, the more similar the groups. The details about CCDA can be found in Kovács J. et al. (2014) [3] and the corresponding “ccda” R package in Kovács S. et al. (2014) [28].

## 4 Results

In our case, the CCDA method was applied to compare each conglomerate of the Upper Eocene succession on the basis of the following: the quantitative composition and the shape parameters (roundness and sphericity) of the andesite and dolomite clasts. As a result, homogeneous groups of sampling sites were determined. In order to make the results of the CCDA analysis more comprehensible, we start this section with some descriptive statistics about size, composition and shape.

## 4.1 Descriptive statistics

Table 1 presents the maximum sizes of andesite, dolomite and chert clasts in all outcrops. The andesite clasts are the biggest at sites KH and UH (maximum 20 cm) while the smallest clasts were found at sites LH and JH (maximum 3 cm). The maximal size of the dolomite clasts is 15 cm at sampling sites JH, KH, LH and UH. The chert clasts are the biggest at site UH (maximum 20 cm). The conglomerates are usually poorly sorted, while at FQ and TR poorly to moderately sorted. The most abundant size fraction is the one between 2-8 mm in each of the outcrops.

Table 1

The maximum size of the clast types in the outcrops.

Dolomite clasts are the most abundant clastic component in all outcrops (ca. 45-94%, Fig. 4a). Volcanic clasts are the most common in RH, KH, UH and AR (ca. 34-39%), and they are rare in JH and LH (ca. 4-6%, Fig. 4a). Compared to the other outcrops, the amount of the chert clasts is extremely high at RH (ca. 18%, Fig. 4a). There are some outcrops (e.g. KH, AR, UH) where volcanic clasts are abundant in the bigger size fractions (Fig. 4b), while at some other outcrops (e.g. JH, LH) volcanic clasts are also absent almost completely in the bigger than 8 mm size fraction (Fig. 4c).

Based on the Wadell and the CPV roundness definitions, andesite clasts are the most angular (except at JH and LH) and dolomite clasts are the most rounded in the samples (Fig. 5 and 6). Various acidic volcanic rock and chert clasts are likely to be more rounded than the andesite clasts, but less rounded than the dolomite clasts (Table 2); however, this statement is taken as somewhat less certain due to the small number of samples from these classes. Dolomite clasts are the most rounded in FQ and TR, but they are everywhere subrounded by Power’s classification (Fig. 5 and 6). Andesite clasts are poorly rounded in KH, UH and AR, more rounded in TR, FQ, HP and RH and most rounded in JH and LH (Fig. 5 and 6). The two roundness definitions (Wadell and CPV) give very similar results to each other, in particular if the fraction of convex segments of the perimeter (i.e. V/perimeter) is compared with Wadell’s roundness score. There are only a few differences in their judgement of roundness (Table 2).

Table 2

The average (A) and the standard deviation (S) of roundness measures (using Wadell’s (1932) definition and Szádeczky-Kardoss’ (1933) V/perimeter score) of the clast types in all outcrops; A. volcanic = acidic volcanic.

Based on the sphericity definitions of Wadell and Riley, dolomite clasts are the most spheroidal in FQ and TR, and the least spheroidal in LH (Table 3), but overall, differences are rather small. Andesite clasts are more spheroidal in FQ, JH, LH, RH and TR, and less spheroidal in AR, HP, KH and UH (Table 3), but the differences are again small. The sphericity of the andesite clasts is not much lower than that of the dolomite clasts. The judgment of both sphericity measures is very similar, which does not come as a surprise, since their correlation at the individual sampling sites ranges from 0.94 to 0.97. The sphericity of the various acidic volcanic and the chert clasts is similar to the andesite and dolomite clasts (Table 3).

Table 3

The average (A) and the standard deviation (S) of projection sphericity measures (using Wadell’s (1932) and Riley’s (1941) definitions) of the clast types in all outcrops; A. volcanic = acidic volcanic.

## 4.2 Results of the CCDA analyses

While a first impression about the similarity of some sampling sites based on measured parameters—in particular based on the plots (Fig. 5 and 6)—can be obtained, this is by no means objective and cannot be carried out if the number of sampling sites is large. Moreover, similarity does not necessarily mean homogeneity, the latter being the case when different sampling sites can no longer be distinguished.

## 4.2.1 The quantitative composition of the clast types

We grouped the outcrops according to their quantitative composition using the CCDA method. First, we had to derive multivariate observations about composition that are suitable for this kind of analysis. For each of the nine examined sites, we randomly partitioned the 500 clasts into 25 non-overlapping blocks, each with 20 clasts. Each of these blocks led to a single multivariate observation by calculating the quantitative composition of the dolomite and the andesite clasts in the given 20 observations. We did not take into consideration the chert and sandstone clasts, because their proportion often took „0%”. In this way, we obtained twenty-five observations for each sampling site.

In accordance with the methodology of CCDA, we first produced a basic grouping determined by the averages of these observations. On the basis of the dendrogram obtained (Fig. 7a), the classification of sampling sites into 1,2,…, or even 9 groups was possible. We denote these groupings by GR1, …, GR9 (GR=group). The nine resulting difference values (d1, …, d9) described how much the respective grouping is better compared to a random grouping. Grouping GR5 was selected as the optimal one as this one had the highest difference value (d5 =11.11%) (Fig. 7b and c). According to these results, we could objectively distinguish five sub-groups (SG=sub-group) with CCDA in its first iteration (Fig. 7). Sub-groups contain the following sampling locations: SG1 = {JH, LH}, SG2 = {HP}, SG3 = {TR, FQ}, SG4 = {RH} and SG5 = {KH, AR, UH}. The question was then, whether these sub-groups are homogeneous. Hence, sub-groups SG1, …, SG5 still had to be examined separately. As SG2 = {HP} and SG4 = {RH} cannot be further subdivided, they form separate groups alone. For SG1, CCDA suggested that no more division is needed, because of a negative difference value (d = −8.33%) for the case of division into two groups. A negative difference value indicates that the considered grouping is not significantly better than a random one. Hence, the group {JH, LH} can be considered as homogeneous. Then SG3 and SG5 were analysed iteratively in the same way. The results indicated that the group {TR, FQ} is homogeneous and that the group {KH, AR, UH} is also homogeneous, as in both cases we had negative difference values when these were divided into further groups. As an overall result, five homogeneous groups were obtained (Fig. 8a).

Figure 7

Results for the quantitative composition of the gravels: a., dendrogram representing the basic grouping; b., the summarized results of CCDA for groupings GR1, …, GR9 ; c., difference values for the grouping of GR5. We were able to distinguish objectively five sub-groups based on the quantitative composition of the clasts with CCDA in the first round. These sub-groups had to be further investigated for homogeneity.

Figure 8

Homogeneous groups obtained by CCDA: a., for the quantitative composition of the clasts; b., for the shape parameters of andesite clasts and c., for the shape parameters of dolomite clasts. The same colours mark sampling sites belonging to the same homogeneous groups.

## 4.2.2 The shape of the andesite and dolomite clasts

We grouped the outcrops according to the shape (roundness and sphericity) of the andesite and dolomite clasts with the CCDA method. For this analysis we used three parameters: Riley’s sphericity values, the C/perimeter and the V/perimeter values. A third value (P/perimeter) from the CPV values was left out, as from two values (C/perimeter and V/perimeter) this already follows. The reason why the CPV values instead of Wadell’s roundness measure were preferred for the analysis is its higher level of complexity and thus, its ability to capture differences: while Wadell’s measure is a single value, CPV-based roundness provides multiple values for the characterization of roundness. Regarding sphericity, Riley’s measure was selected as it is the more recent one. CCDA can handle even more parameters so that other measures could be included in the analysis (e.g. Wadell’s sphericity and roundness measures), but as discussed before, correlations between the same type of measures are high-which could distort the analysis. Hence, a single type of roundness measure (C/perimeter and V/perimeter) and one type of sphericity measure (the one by Riley) were finally selected for the CCDA analysis. In the following, we will refer to these selected parameters as the shape parameters. As sphericity and roundness can be measured for every individual clast, each clast led to a single multivariate observation that was used in the analysis. In the case of andesite, about 130 clasts were taken from each sampling site (at JH, LH, TR and FQ additional andesite gravels were collected and measured to have approximately equal number of samples from each site), while in the case of dolomite, about 200 clasts were taken from each sampling site.

First we investigated the andesite clasts. At first we produced a basic grouping of the outcrops, resulting in a dendrogram (Fig. 9a). With a difference value of 21.18%, GR3, a grouping consisting of SG1 = {AR, KH, UH}, SG2={FQ, HP} and SG3={JH, LH, RH, TR} was selected as the optimal one (Fig. 9b). As the sub-groups might not be homogeneous, SG1, …, SG3 still had to be examined separately. As the result of the exploration, group SG1={AR, KH, UH} turned out to be homogeneous because of negative difference values when splitted further (d=-0.22% and d=-5.34%). For SG2, CCDA suggested a further subdivision into two groups {FQ} and {HP} with a positive difference value (d=0,45%). Hence, {FQ} and {HP} each form a group individually. Regarding SG3, CCDA suggested its further subdivision into two groups {JH, LH} and {RH, TR} with a positive difference value (d=12,02%). {JH, LH} and {RH, TR}then had to be further investigated. The first group turns out to be homogeneous, because it has a negative difference value (d=-5.91%) if divided into two. For {RH, TR}, CCDA suggested a further subdivision into two groups, {RH} and {TR} with a positive difference value (d=4.08%). Hence, {RH} and {TR} each form a group individually. As an overall result, six homogeneous groups were obtained (Fig. 8b) for the shape parameters of the andesite clasts.

Figure 9

Results for the shape parameters of the andesite clasts: a., dendrogram representing the basic grouping; b., the summarized results of CCDA for groupings GR1, …, GR9. We could distinguish objectively three sub-groups regarding the shape parameters of the andesite gravels with CCDA in the first round which were then further investigated so that in the end six homogeneous groups were found.

We investigated the dolomite clasts as well. First, we produced a basic grouping of the outcrops (Fig. 10a). GR4 was selected as the optimal one with a difference value of 4.83%. We were able to distinguish objectively four sub-groups with CCDA in the first iteration (Fig. 10b): SG1 = {AR, KH, UH}, SG2 = {FQ, TR}, SG3 = {HP, JH, LH} and SG4={RH}. While SG1, …, SG3 still had to be examined separately, surprisingly all of these sub-groups remained as homogeneous groups, no further split was necessary. Hence, as an overall result, four homogeneous groups were obtained (Fig. 8c).

Figure 10

Results for the shape parameters of the dolomite clasts: a., dendrogram representing the basic grouping; b., the summarized results of CCDA for groupings GR1, …, GR9. We could distinguish objectively four sub-groups regarding the shape parameters of the dolomite gravels with CCDA in the first round which then also remained homogeneous during the further investigations.

Should someone be only interested in the roundness of the clasts, the analyses could be carried out in CCDA without the sphericity measure, i.e. only with the C/perimeter and V/perimeter scores. For the current study, the homogeneous groups obtained would be exactly the same as described above in the analysis together with the sphericity measure.

## 5 Interpretation and discussion

The area of the Buda Hills became a terrestrial environment probably during the terminal Cretaceous. Then intense karstic erosion took place under hot and humid climatic conditions from the end of the Cretaceous to the Priabonian, which resulted in an indented surface morphology with significant relief differences (i.e. karst terrain). It was followed by deposition of terrestrial deposits into the depressions of the paleotopography.

Since volcanic clast-bearing Upper Eocene conglomerate bed-sets are usually poorly exposed, sedimentary structures (normal gradation) could be observed only at one locality (Kő Hill, Budaörs). This structure may occur both in deposits of alluvial fans and braided rivers. However, subsequent processes significantly modified the original sedimentary structures (subsequent tectonic deformations, neptunian dyke, etc.). Consequently, the sedimentary structures do not provide a suitable base for the interpretation of the paleoenvironments and sedimentary processes.

That is why we attempted to use the measured clast parameters and the spatial pattern of the distribution of the clast properties for an interpretation of the sediment transport and deposition. Although the measured parameters of the clasts show some differences among the studied outcrops, the CCDA method pointed out several homogeneous groups of sampling sites. The spatial pattern of homogeneous groups assists in the interpretation of the geological processes that played a crucial role in the formation of the conglomerates. It can be assumed that the measured parameters of rocks classed to the same homogeneous group were formed under similar geological circumstances and by the same geological processes. It is worth mentioning that based on three different parameters (quantity and shape of the andesite and dolomite clasts) the CCDA method classed several successions-although they are located 6-10 km apart from each other-to homogeneous groups (Fig. 8).

Group 1 (KH, UH, AR; Fig. 8) can be interpreted as small fanglomerate deposits. The following textural and petrographical characteristics constrain this interpretation: the conglomerate is poorly sorted; there is a small silt- to sand-size ground mass; it contains high amounts (35-39 area%) and relatively large volcanic–predominantly andesite—clasts; the andesite clasts are relatively poorly rounded with some large angular rock fragments; and high amounts (55-60 area%) and relatively large dolomite clasts of moderate roundness. The weaker roundness and sphericity values of the andesite clasts compared to those of the dolomite clasts is not surprising in the same environment, because the hardness of dolomite is less than the hardness of strongly silicified andesite [31]. These fanglomerates were deposited in the proximal zone of small fans formed along the toe of slopes [32].

JH and LH form a unique homogeneous group (Group 2) based on the quantitative composition and the shape of the andesite and the dolomite clasts (Fig. 8). HP forms a single homogeneous group (Group 3) on the basis of the quantitative composition and the shape of the andesite clasts, but forms a homogeneous group with JH and LH based on the shape of the dolomite clasts (Fig. 8). Based on the amount and shape of the andesite clasts, these two groups are interpreted as deposits of intermittent streams transporting and redepositing clasts along the valleys, with clasts originating from andesite clast-bearing fans. The following sedimentological characteristics refer to this transport mechanism: the conglomerate is poorly sorted, but the scarce andesite clasts are small and much more rounded than in Group 1. The andesite clasts have similar petrographic characteristics (they are strongly silicified) in every sampling site. Consequently, changes in the amount, size and shape of the andesite clasts depend predominantly on their transport distance. Stream transport reduced the size and abundance of andesite clasts, and increased their roundness and sphericity. Based on the roundness of andesite clasts, Group 3 was deposited in the proximal zone and Group 2 was deposited in the distal zone of a supposed intermittent stream. The deposition in the distal zone is indicated by the most rounded andesite clasts at sites JH and LH. At HP, these clasts are more rounded than in Group 1, but less rounded than in Group 2. The transport distance may have been somewhat shorter here than that at JH and LH. In Groups 2 and 3, the relatively abundant, large, and less rounded, less spheroidal dolomite clasts which occur together with andesite debris suggest that they were derived also from nearby small toe-of-slope fans. They are slightly less rounded than in Group 1, indicating that their transport distance was probably slightly shorter than that of Group 1.

Based on the characteristics described above and the geological setting, we can assume that these volcanic clasts derived from volcanic sources of rather limited surface exposure. In contrast, the outcrops of dolomites (and locally cherty dolomites) were widely extended, providing large amounts of dolomite and chert clasts all along the valleys. In light of the relevant publications on the sedimentation of modern alluvial fans [33, 34, 35, 36] we summarize the major characteristics of the potentially analogous fans as follows. In the case of a steep slope, the size of the debris is reduced by orders of magnitude within a maximum 5-10 km distance, meanwhile the roundness of the debris increases. Andesite clasts are maximally 20 cm in size, and they are less rounded at KH, UH and AR; therefore we suppose essentially local sources of these clasts. It means that in this area, andesite debris may have been accumulated on fans formed at the foot of slopes where the source rocks were exposed in the Early Eocene. In the area of the Buda Hills, Middle-Late Triassic andesite rocks have been exposed only in the well Budaörs-1 [11, 12, 37, 38, 39]. Based on similar petrographic features (porphyric pilotaxitic texture with labradorite/basic oligoclase plagioclase, hypersthene and a few augite, biotite phenocrysts) as well as age data (Carnian), the andesite intersected in this well may have been the source rock most of the andesite clasts [8, 11]. Although we do not know of any andesite rock (neither on surface, nor in a borehole) close to the AR, the results of our studies suggest the presence of a local andesite source, most probably an outcrop of a dike.

There are two occurrences (TR and FQ) forming a homogeneous group (Group 4) based on the percentages of the components and the shape of the dolomite clasts, but they do not form a homogeneous group based on the shape of the andesite clasts (Fig. 8). According to our interpretation, the peculiar characteristics of these conglomerates may reflect marine sediment redistribution of previously deposited terrestrial sediments after inundation of the area when the former continental slopes became abrasional rocky coasts. A part of the previously accumulated terrestrial sediments would have been redeposited under marine conditions and mixed with sediments. This is evidenced by the presence of rounded to well-rounded and smaller dolomite pebbles with traces of boring organisms at FQ and TR. However, their deposition could hardly have happened in the active zone of the abrasion since the andesite clasts show poorer roundness than that of the dolomite clasts. Moreover, these conglomerates are poorly to moderately sorted and clasts are embedded in a silt- to sand-size matrix. According to our interpretation, dolomite clasts were transported from higher level abrasion terraces by gravitational mass movement to the site of deposition at the foot of the submarine slopes.

RH we can hardly fit into our model. Namely, the conglomerate from RH differs from the other conglomerates of the Buda Hills based on grouping with CCDA. The calculation creates a separate homogeneous group (Group 5) based on the quantitative composition, and the shape of the andesite and dolomite clasts (Fig. 8). Most probably, the volcanic rock debris was derived from the Middle Triassic succession occurring on the northern side of a major regional fault zone, the Nagykovácsi Line [40]. In this belt, the Middle Triassic volcanic rocks were probably exposed on the surface prior to the Eocene transgression.

## 6 Conclusions

Due to the scarcity of observable sedimentary structures, statistical methods (i.e. descriptive statistics of the textural parameters using our newly developed Rock Analyst application, and the spatial pattern of these parameters obtained through CCDA) provided the most suitable tool available for the interpretation of the provenance, transport processes and depositional conditions of an Eocene coarse grained clastic succession in the area of the Buda Hills. In this way, various depositional environments (terrestrial toe-of-slope fans, intermittent streams and abrasional rocky coast) could be distinguished.

According to our hypothesis, during the terminal Cretaceous to Priabonian period the study area was a karstic terrestrial environment with significant relief differences. Mostly Triassic formations were eroded at this time. Outcrops of dolomites (and locally cherty dolomites)—i.e. the sources of dolomite clasts—were widely extended, but the volcanic clasts (mostly andesite) were derived from volcanic sources of rather limited surface exposure (as dikes intruded into dolomite). During the long continental period prior to the Late Eocene transgression, small fans were formed at the foot of slopes which supplied intermittent streams. Those fans, which were located close to the andesite source rocks, along with dolomite (and chert) clasts, contained significant amount of andesite clasts. These clasts may have been transported and redeposited by intermittent streams along the valleys. After the marine inundation of the area in the Late Eocene, a part of the previously accumulated terrestrial sediments reworked under marine conditions and mixed with sediments.

## Acknowledgement

This study was funded by the National Research, Development and Innovation Office (Hungarian National Science Fund (OTKA)) under grant number K 113013 (to L. Fodor). We thank the three anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. We thank Solt Kovács for his suggestions regarding the statistical analysis. This work was supported by the European Union, co-financed by the European Social Fund: EFOP-3.6.1.-16-2016-00004.

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## Abbreviation definition

AR

Apáthy Rock – Stone Gate

CCDA

combined cluster and discriminant analysis

CPV

Szádeczky-Kardoss’ CPV method (C=concave, P=planar, V=convex)

FQ

Fenyőgyöngye quarry

HCA

hierarchical cluster analysis

HP

GR

Group

JH

János Hill – Virág Valley

KH

Kő Hill of Budaörs

LDA

linear discriminant analysis

LH

Látó Hill

q95

95% quantile of the percentages for the random groupings

RH

Róka Hill quarry

SG

Sub-group

TR

Tündér Rock

UH

Út Hill

## Appendix A

The Rock Analyst application and the user manual are available at the following website: http://faricseva.web.elte.hu/

Accepted: 2017-06-12

Published Online: 2017-10-28

Citation Information: Open Geosciences, Volume 9, Issue 1, Pages 525–538, ISSN (Online) 2391-5447,

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