A part of the Upper Oligocene sand-rich turbidite systems of the Central Carpathian Basin is represented by the Zuberec Formation. Sand/mud-mixed deposits of this formation are well exposed in the northern part of the basin, allowing us to interpret the turbidite succession as terminal lobe deposits of a submarine fan. This interpretation is based on the discrimination of three facies associations that are comparable to different components of distributive lobe deposits in deep-water fan systems. They correspond to the lobe off-axis, lobe fringe and lobe distal fringe depositional subenvironments, respectively. The inferences about the depositional paleoenvironment based on sedimentological observations are verified by statistical analyses. The bed-thickness frequency distributions and vertical organization of the facies associations show cyclic trends at different hierarchical levels that enable us to reconstruct architectural elements of a turbidite fan. First, small-scale trends correspond with shift in the lobe element centroid between successive elements. Differences in the distribution and frequency of sandstone bed thicknesses as well as differences in the shape of bed-thickness frequency distributions between individual facies associations reflect a gradual fining and thinning in a down-dip direction. Second, meso-scale trends are identified within lobes and they generally correspond to the significant periodicity identified by the time series analysis of the bed thicknesses. The meso-scale trends demonstrate shifts in the position of the lobe centroid within the lobe system. Both types of trends have a character of a compensational stacking pattern and could be linked to autogenic processes. Third, a largescale trend documented by generally thickening-upward stacking pattern of beds, accompanied by a general increase of the sandstones/mudstones ratio and by a gradual change of percentage of individual facies, could be comparable to lobe-system scale. This trend probably indicates a gradual basinward progradation of lobe system controlled by allogenic processes related to tectonic activity of sources and sea-level fluctuations.
The Upper Oligocene sand-rich turbidite systems, representing an important component of Central Carpathian Paleogene Basin (CCPB), were controlled by fast subsidence in concurrence with the sea-level fluctuations [e.g. 1–5].
The interpretation of ancient turbidite systems requires to study architectural elements of the depositional system [e.g. 6–11].A key outcrop-derived characteristic of submarine fan deposits is the presence of systematic vertical patterns in bed thickness and grain size distribution. In general, thickening or coarsening-upward cycles are considered to be a sign of submarine lobe environment and thinning or fining cycles may relate to channel and levees environment [e.g. 12–16]. The bed thickening- and/or coarsening-up packages of lobes were considered to reflect progradation [e.g.11, 13, 17–20]. However, vertical patterns in bed thickness may also correspond to compensational cycles as a result of the smoothing of the depositional topography associated with lobe abandonment and switching [9, 10, 21–25].
This study is focused on turbidite succession which we interpret as terminal lobe deposits of a turbidite system. These deposits crop out in the northern part (Orava–Podhale Basin) of the CCPB and they are referred to as the Zuberec Formation  or Chochołów beds [sensu27, 28].
The Zuberec Formation was defined on the basis of lithology and according to Gross et al. , it differs from others “flyschoid” formations in the CCPB mainly by sandstone/mudstone ratio and by stratigraphic superposition (see chapter Geological setting). However, the later research indicates that many turbidity sequences in Orava and Podhale regions are lithologically identical to the definition of the Zuberec Formation but they are younger and rather correspond to the Biely Potok Formation that is typically characterized by massive sandstone sequences [2, 4, 29, 30]. This suggests that the simplified model of vertical development of the basin fill [c.f. 26] during sequence-stratigraphic development of the CCPB, does not reflect the lateral depositional variability of the deep-water depositional system.
Turbidite sequences of the Zuberec Formation were studied recently at several outcrops in the Orava region, but these outcrops are often poorly exposed, discontinuous and usually include a rather smaller number of beds, and are mostly too small to be compatible with a modern deepwater turbidite system. However, floods in 2014 excavated long parts of a turbidite succession in the bedrock of Dunajec river in Chocholow, near the Polish–Slovak border (Figure 1D). This turbidite section completely exposed more than 1000 beds, and provided a unique opportunity to study vertical variation in bed thickness and sedimentary structures. The study enables to define the sedimentary facies and depositional mechanisms that have shaped them. An occurrence of individual facies, their frequency, vertical relationships, the ratio of sandstone and mudstone, and dominant facies transitions are an important aspect for discrimination of the facies associations and the interpretation of the depositional environment. A vertical organization of the facies associations can be described as thickening- or thinning-upward units that are helpful in reconstruction of architectural elements and classification their distality within turbidite fan. Facies associations can be interpreted within the framework of a lobe system suggested by Prélat et al. .
2 Geological setting
The CCPB lies inside the Western Carpathian Mountain chain (Figure 1A) and belongs to the basinal system of the Peri- and Paratethyan seas. The basin accommodated a forearc position on the destructed Alpine-Carpathian Pannonian microplate margins and in the hinterland of the Outer Western Carpathian accretionary prism [e.g. 3]. The opening and evolution of the CCPB probably related to crustal thinning, either as a result of subcrustal erosion [e.g. 31], or due to the extensional collapse of the overthickened Central Western Carphatians crust and the pull of the retreating subduction of the External Western Carpathians oceanic lithosphere .
The basin covered most of the Central Western Carphatians area (Figures 1A, 1B) and is mainly filled up by flyschlike deposits, which overlap the substrates of the pre-Senonian nappe units and their thickness reach up to a thousand metres. The age of the sedimentary formations ranges from the Bartonian [e.g. 32, 33] to the latest Oligocene [c.f. 3, 34–37] (Figure 2). The sediments of the CCPB are preserved in many structural sub-basins, including the Žilina, Rajec, Turiec, Orava, Liptov, Podhale, Poprad, and Hornád Depressions (Figure 1B). In the study area, the CCPB sediments are bounded by the Central Carpathian units in the south, while the northern boundary is represented by the Pieniny Klippen Belt (Figure 1C).
The CCPB deposits (the so-called Podhale Palaeogene in the Poland or the Podtatra Group sensu Gross [26, 38]) are commonly divided into the following formations  (Figure 1C, Figure 2) (their equivalents in the Podhale basin sensu Gołąb and Watycha [27, 28] are given in brackets). The lowermost, Borové Formation (the so-called Tatra Eocene or Nummulitic Eocene) consists of breccias, conglomerates, polymictic sandstones to siltstones, marlstones, organodetrital and organogenic limestones. These represent basal terrestrial and shallow-marine transgressive deposits [33, 39–44]. This formation is overlain by the Huty Formation (the Zakopane beds) which mainly includes various mud-rich deep marine deposits [e.g. 3, 45, 46] with occurence of sandstone megabed events . The lowermost part of the Huty Formation includes Šambron Beds sensu Chmelik  (Szaflary beds in the Podhale basin) which occure in the northen part of the Podhale-Spiš Magura area and embraced shaly and thin-to medium-rhythmic turbidite deposits with intraformational conglomerates and breccias. The overlying sediments of the Zuberec Formation (Chochołów beds) and Biely Potok Formation (the Ostrysz beds) consist of rhythmical bedded turbidites and massive sandstones, which represent the various facies associations of sand-rich submarine fans [1–4, 49–52]. The sand/mud-mixed turbidite deposits of the Zuberec Formation are generally typical by a balanced ratio of sandstones to mudstones [e.g. 26]. These deposits are dated as the end of early Oligocene to the late Oligocene [e.g. 35, 37].
The youngest Biely Potok Formation is characterized by the marked predominance of sandstones with sporadic occurrences of thin mudstones and conglomerates. Sandstone deposits of Biely Potok Formation show the late Oligocene [e.g. 35] to the Oligocene–early Miocene transitional interval [2, 37].
The research involved sedimentological evaluation of the section. Eight samples were randomly taken from various parts of the section and evaluated by planimetric analysis in order to identify petrographic composition. Palaeocurrent analysis included measurement of erosive current marks and postdepositional tilt of the directions were restored by simple rotation along horizontal axis. Measurement of bed thicknesses was a key for further statistical analysis. Determination of the bed thickness becomes complicated if the bed is thinning out laterally, contains preserved bedforms morphology or has been eroded. In these cases, the average was used. Amalgamated sandstone beds as a result of multiple flows with no obvious bed interface are inferred to represent a single bed. Only thickness of sandstone was measured for turbidite beds because related mudstones can not be distinguished from overlying pelagic deposits. No correction was made for compaction.
The vertical variation of bed thicknesses of sandstones shows thickening-upward or thinning-upward trends of bed thicknesses. These cyclic intervals were allocated as individual units and used as a group of data for subsequent statistical analysis.
Dataset contains 1015 measured thicknesses of sandstone beds in cm scale. We used modified dataset of layers thicker than 1cm (664 beds) for time series analysis (autocorrelation) and original dataset with all thicknesses of sandstones for computation of Hurst coeficient, simple statistical analyses and bed-thickness frequency distribution. We used simple graphical method –boxplot that summary shows variability in thickness of beds in whole profile and facies associations. We also evaluate the sandstones/mudstones ratio within the entire section, individual facies associations as well as allocated units. Similarly, we analyzed the percentage of sandstones and siltstones facies within different units.
We used autocorrelation to determined time series/periodicities. Autocorrelation  was carried out on separate column of every sampled layer from modified dataset. The autocorrelation function is symmetrical around zero. A predominantly zero autocorrelation signifies random data - periodicities turn up as peaks .
The Hurst exponent or coefficient (also „index of depence“ / “index of long-term depence“) is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series [55–57]. Computation of the Hurst K random shuffling of original sequence to generate 300 randomly shuffled sequences and the assessment of the significance of the Hurst K values . This analyses was completed by using R-cran. We ploted recalculated K to D, number of dimension. The clustering in final plot indicate depositional environment .
We used cumulative distribution function, which typically shows varying degrees of variation from the powerlaw (straight-line) distribution. The cumulative thickness distribution is calculated and its shape examined on a log plot. Two-dimensional model simulates effects of proximal (within-channel) vs. distal (non-channelized) environment .
We used the ABC index after Walker  for evaluation of proximality or distality of lobe systems. The sand fraction of turbidites was splited to A, B, C division. This divisions cover gradient from graded division (A) to current rippled division (C). We use a numbers of beds in each group (A, B, C), ABC index or P is an equivalent of proximality and it is calculated as A (and all groups started with division A) to C ratio:
P express percentage of distance from A to C (percentual values of proximality). It means small percentual value correspond with higher distality of environment. ABC index was calculated separately for whole section and individual units. Point of percentage of beds belonging to group A, B or C in triangular diagram reflects flow regime. Plotted values of A, B, C division fall to four defined areas in diagram .
4.1 Sedimentary description
Sedimentary succession of the Zuberec Formation exposed in the studied section represents rythmic-bedded deposits, similarly as at other localities in the Podhale and Orava region [e.g. 4, 27, 33, 61]. The succession is formed by sandstone–mudstone sets of beds (Figure 4) which are by their textural and structural features largely reminiscent deposits of high- to low-density turbidites and hemipelagic mudstones. The 199,5 m long section near Chocholow is disturbed by several faults but only with maximum 1.5 m offset which allowed a complete reconstruction of vertical succession of the beds. The dominant lithological components are mudstones which form 65,8% of the full section. The sandstones and siltstones form 34.2% of the overall lithology of the studied section. Conglomerates are not present. Petrographic analysis shows that all sandstones are lithic greywackes. The beds contain locally large amounts of plant and wood debris as well as coal fragments.
Thickness of sandstones varies from less than 1 cm up to 1.4 m. However, the thickest beds are usually amalgamated of several layers. The average thickness is 6.7 cm (Figure 7B). The succession is dominated markedly by the thin beds up to 10 cm (Figure 7D), that makes up 83.94% of all measured beds. Medium-thick beds (10–30 cm) occupy 11.62% and thick beds (>30 cm) form 4.43% of all measured beds. Most of the sandstones are fine- to very fine-grained. Medium- to coarse-grained sandy fraction is mostly present only at the bases of the layers where it forms thin graded intervals (Figure 3A). The study of granularity shows that the grain size is generally independent from the bed thickness and the fine-grained sandy fraction often forms entire beds which are tens of cm thick.
4.2 Sedimentary facies
The description and classification of the sedimentary succession near Chocholow is mainly based on lithology and primary sedimentary structure. The sandstones are referred to as lithofacies S, the siltstones as lithofacies Si, and mudstones as lithofacies M. The deposits of the Zuberec Formation near Chocholow are classified into 8 individual facies with their possible hydrodynamic interpretation.
S1 facies: Ungraded- to graded coarse- to fine-grained sandstone (Figures 3A, 3C)
Description: Poorly sorted, usually ungraded, sometimes with normal grading, fine- to coarse-grained sandstones sometimes with dispersed granule up to 2 mm. S1 facies ranges in thickness from a few cm to 80 cm. In the upper part of S1 facies there may be signs of crude horizontal laminations.
Interpretation: A rapid accumulation of sand from biparite turbulent flow in which the basal part dominated by a near-bed high-density suspension (S3 flow type after Lowe ; Ta division after Bouma ; or F5 and F8 facies after Mutti [64, 65]).
S2 facies: Stratified, inverselly graded coarse-grained sandstone (Figure 3C)
Description: Poorly- to moderately sorted, crudely horizontally-stratified, granule coarse-grained sandstones which form up to 25cm thick beds.
S3 facies: Parallel-laminated medium – to fine grained sandstone (Figures 3A–3C)
Description: This facies is formed by a medium- to fine-grained sandstone laminae. S3 facies ranges in thickness from a few centimetres up to some decimetres. Occasionally, centimetre thick laminated muddy sandstone intervals (S3m) occure within S3 facies (Figure 3A).
Interpretation: The plane-parallel stratified sandstone could represent the deposit of a near-bed suspension generated by progressive turbulent mixing at the head of a sandy dense flow with relatively low rates of deceleration . Each lamina can be considered to represent a traction carpet that is driven by basal shearing of an overlying turbulent flow. (S3 flow type after Lowe ; Tb division after Bouma ; F7 and F9 facies after Mutti ). The repetitive occurrence of muddy sandstones within clean laminated sandstones of S3 facies would be interpreted as a result of fluctuations in supply of sediment and speed of the flow.
S4 facies: Sandstone with asymmetrical cross-lamination (Figures 3A, 3B, 3F)
Description: This facies is made up of fine- to very fine grained sandstones showing small-cross-lamination corresponding to current ripple bedding. The height of individual ripples is less than 5 cm (usually up to 2 cm) and the length is less than 20 cm. Ripples may be developed in the form of climbing-ripple lamination occasionally. S4 facies ranges in thickness from a few centimetres up to 20 cm.
Interpretation: Lower flow regime; traction movement with fallout processes from waning turbidity currents [e.g. 68, 69]; Tc division after Bouma ; F9 facies after Mutti ). Climbing-ripple lamination is a typical traction plus fallout structure in which the interaction between rate of fallout and bedforms migration allows the formation of climbing sets of ripples [68, 70].
S5 facies: Soft-sediment deformation of medium- to fine grained sandstone (Figures 3D, 3G)
Description: Sandstone deformations vary from gentle to moderately strong upwardly-concave dish structures to convolute lamination. Dish structures mainly affect the lower parts of parallel laminated sandstones (facies S2) in close overlying of massive sandstone intervals. Convolution affects mainly fine-grained sandstone intervals with ripple bedding (facies S3). Soft-sediment deformations of the contacting bedding plane with flame structures may occure rarely (Figure 5A).
Interpretation: Dish structure formation is connected with compaction and dewatering of unconsolidated sediments  and they are related to upward movement of water and fluidized particles that cutting and deforming overlying sediments [72, 73]. The generating mechanism of convolute structures is linked to fluidization processes, which create gravitational instabilities [73–75]. The triggering mechanism of these structures is often related to processes of sediment gravity flows, overloading of sandstone beds [e.g. 71, 76, 77], or they should be induced by seismicity [75, 78].
Si1 facies: Laminated siltstone (Figure 3E)
Description: This facies is composed of coarse-grained to fine-grained laminated siltstone. The laminae of this facies are thinner, and finer than those of facies S2. Si1 facies forms a few centimetres up to decimetre thick beds.
Interpretation: The depositional mechanism of siltstone laminae reflects traction plus fallout processes associated with deposition from suspension during weak turbulent motion in low-density turbidity currents . Si1 facies can be considered equivalent to Bouma Td interval .
Si2 facies: Laminated muddy siltstone (Figure 3E)
Description: Siltstones with an increased clay content, which are characterized by fine, sometimes discontinuous wispy lamination. Si2 facies forms up to decimetres thick beds.
Interpretation: Suspension fall-out during final deposition from a dilute sediment gravity flow . The repetitive alternation of clayey and silty laminae would be interpreted as a result of fluctuations in supply of sediment and speed of the flow.
M facies: Massive dark mudstone (Figure 3E)
Description: This facies is composed of massive mudstones. Although some parts reveal an increased contents of silt (graded mudstones), the mudstones are mostly devoid of structure. M lithofacies shows the sedimentary characteristics of the Bouma turbidite division Te or Stow division T6 and T7 (graded and ungraded turbidite muds respectively).
4.3 Facies association
Three facies associations were distinguished based on the predominant facies, sandstone bed thickness (Figure 4A), and proportion of mudstone facies. These facies associations (FA) are comparable to different components of distributive lobe deposits in deep-water fan system and within the classification in the sense of Prélat et al.  corresponding to the lobe off-axis (FA2), lobe fringe (FA3) and lobe distal fringe/inter-lobe (FA4) (Figure 4B) [cf.10, 25].
For easier comparison we denote the related facies associations identically as So et al. . Within the studied section the facies association corresponding to the lobe axis (FA1) sensu Prélat & Hodgson  can not be identified therefore, the following description begins with FA2.
Facies association 2 (FA2): lobe off-axis (Figure 4A)
The FA2 may consists all defined facies, but sandstone lithofacies is predominant and occupy more than 60% of total measured thickness of the FA2. The medium-thick and thick sandstone beds are main component of this facies association. The average thickness of turbidite sandstone facies within FA2 is 34.5 cm and 50% of all measured bed thicknesses falls within the range 7 to 52.5 cm (Figure 7B).
The lower sides of the beds within FA2 are mostly plain, with common small-size erosional current marks (Figures 5F; 6A–6D). However, the lower bedding planes of some beds are slightly modified by load structures (Figure 5B) and are uneven. In thicker sandstone beds (>10cm), massive bedding is the most common (S1 facies). At the base of massive sandy interval, thin gradation interval is developed locally. S1 or S2 facies within thick beds is commonly overlain by S3 facies or may fining upwards with relatively sharp transition to siltstone and mudstone facies. The ripple bedding (S4 facies) is rather sparse in thick sandstone beds and is poorly developed. They form only thin intervals at the top of the beds, near the transitions to siltstones. Thick beds locally contain claystone intraclasts and coalified plant detritus (Figures 5C, 5D). Softsediment deformations (S5 facies) are relativelly common and may affect all the bed (usually up to 20 cm thick) (Figure 3G) or may occure as the thinner interval, usually in the upper parts of thick beds. Geometry of each bed is tabular or sheet-like. Within FA2, thick sandstone beds may occure in association with thin- to medium- rythmic bedsets (up to 1m thick) which contain thin beds of sandstonemudstone couples with well developed S3, S4, Si1, Si2 and M facies. This facies association occurs in the whole section studied near Chocholow and it is commonly underlain and overlain by FA3 and less commonly FA4 (Figure 9).
The relative abundance of amalgamation within thick sandstone beds, the medium- to fine grain sizes of the most of sandstones, small amount of mudstone turbidite, occurence thin- to medium-bedded sandstone turbidites, tabular geometry of beds, absence of both - large scours and evidences for channels suggest deposition within depositional lobe [e.g. 6, 9, 83]. Absence of some metres to tens metres thick bedseds of massive, frequently amalgamated thick sandstones; intercalation of thin- to medium-bedded turbidites with abundant S3, S4, and Si facies might indicate deposition in lobe off-axis environment [9, 10, 25].
Facies association 3 (FA3): lobe fringe (Figure 4A)
In this facies association, mudstone beds are predominant (60–80%). The main component of FA3 is rhythmic thinbedded sequence with sandstone and mudstone beds that are generally range in thickness from several cm to tens cm. The average thickness of turbidite sandstone facies within FA3 is 5.7 cm and 50% of all measured bed thicknesses falls within the range 1 to 6 cm (Figure 7B). FA3 mainly comprises S3, S4, Si1,2 and M facies. S1 facies usually builds the rare thicker beds (up to 15–20 cm) or lowermost part of the thiner turbidites. However, the S1 facies is less common as in the FA2. The beds have a good lateral continuity. The lower bed interfaces are sharp with common small-size erosional current marks (Figures 6A–6C). The beds are graded and often show complete developed Bouma sequences (Ta-e, sensu Bouma ). Especially thin, very fine-grained, up to 5 cm thick turbidites consist only of S4, Si and M facies.
A regularly thin-bedded, rhytmic, some metres thick sequence with a high proportion of mudstone, thinbedded finely-structured sandstone with good lateral continuity supported interpretation of FA3 as lobe fringe deposits [10, 25].
Facies association 4 (FA4): lobe distal fringe and inter-lobe (Figure 4A)
The main component of FA4 is bed configuration with thinbedded fine to very fine-grained sandstones, siltstones, and medium- to thick-bedded mudstones. In this facies association, mudstone beds (M facies) are in a strong dominance and often take up more than 80% of total thickness of FA4. The average thickness of turbidite sandstone facies within FA4 is 2.6 cm and 50% of all measured bed thicknesses falls within the range 1–3 cm (Figure 7B). The S4, Si1,2 facies are frequent, the S1, S2, S3, S5 facies are very sporadic. FA4 generally ranges in thickness from 1m up to 7m. This facies association occurs in the whole section but a maximum thickness reaches at the lower part of studied succession near Chocholow. The FA4 is most often a part of a gradual transition between the FA 2-3-4, but especially in the lowermost part of the succession this facies association underlain and overlain isolated, some decimetres up to 1 metres thick beds which contain facies typical for FA2 (Figure 4F).
A regularly thin-bedded, fine- to very fine-grained turbidites with good lateral continuity and hight contents of relative thick mudstone facies supported interpretation of FA4 as lobe distal fringe and inter-lobe with the deposition of dilute low concentration turbidity currents or basin plain with slow hemipelagic deposition .
4.4 Sole marks and palaeocurrent analyse
A typical feature of the thin- to medium-bedded, fine-grained turbidity sequences are palaeocurrent indicators such as frondescent marks (Figure 5E), flute marks (Figure 6A), longitudinal furrows, ridges and tool marks (Figures 5F, 6B–6D). Paleocurrent data derived from these indicators provide general flow orientation SW–NE with transport direction to NE. Currents show only a relatively small variance (Figure 6E) and an orientation remains constant throughout the studied section. We have not identified any contradirectional measurements which could occur in confined basins bounded by tectonic slopes or which would indicate feeding of depositional lobes from several sources. On the lower planes of some fine-grained sandstone beds was also identified relatively poor assemblage of ichnofossils inclusive Thalasinoides, Scolicia, Artrophycus. (Figures 6F–6E). These softground traces occur in relatively well-oxygenated environments and belong to ecological cathegories of domichnia and pascichnia .
4.5 Statistical analysis
The large dataset of the bed thicknesses allows us to use autocorrelation for determination of time series/periodicities. We compare determined periodicity with the boundaries of individual units identified on the base of documented meso-scale trends of bed thickness (see chapter Hierarchy, units and trends). Time series analysis (autocorrelation coefficient) shows significant periodicity on 45-th bed (Figure 7A) from modified dataset (bed thickness more than 1 cm). Mean of numbers of beds within unit is 44.3, which generally corresponds well with time series analysis. However, considerable variability in the number of beds within individual units occurs (see chapter Hierarchy, units and trends).
We used the Hurst coefficient to verify the assumed interpretation of depositional palaeoenvironment based on identified facies and facies associations. Hurst K computed from original dataset is 0.77. Deviation D from the mean K for randomly shuffled series, and significance levels for the sandstone thicknesses was computed as 5.71.This section of Zuberec Formation passed the Hurst K test for sandstone thicknesses at a significance level a=0.15. After plotting K to D the locality was placed to cluster of lobe–inter-lobe environment  that corresponds with our prediction on the basis of grain-sizes and identified facies associations, and fit with results of other statistical analysis.
Boxplots show distribution of sandstone bed thicknesses among full section and assigned facies associations (Figure 7B). Differences between 1st and 3rd quantile, median and mean are obvious and correlate with the definition of individual facies associations.
We tested the cumulative distribution of the complete dataset covering all measurements of sandstone thicknesses within the entire succession near Chocholow, as well as datasets of sandstone thicknesses corresponding with defined facies associations (Figure 7C). The shape of cumulative bed-thickness frequency distributions depends on the number of thick beds (and its amalgamation). The strong curve of line in FA2 reflects an occurrence of thick sandstone beds with common amalgamation. Conversely, the shape of line in FA4 corresponds with frequent occurrence of thin, well deffined turbidites in FA4. The shape of line of cumulative distribution within the complete dataset of Chocholow section best corresponds with middle fan environment .
Calculated P values (ABC index) of whole section and all units show a small percentual values of proximality (1.9–20.7%) (Figure 8B), i.e. high values of distality (79.3–98.1%).
Percentual values of A, B, C divisions are clustered after ploting in Field 1 (Figure 8A) which provide opportunity to interrpret whole section and all units from Chocholow section as sediment deposited mostly in lower flow regime. Only one entry (Unit 9) is located on the border between Filed 1 and mixture zone.
4.6 Hierarchy, units and trends
The fundamental building element in a distributive system is the ‘bed’ that consists of one or more facies. Sets of beds with similar facies, bed thicknesses, proportion of mudstones and a certain pattern of vertical arrangement are grouped into facies associations (FA) representing different components of lobe elements (Figure 4A, B; Figure 10). Each flow tends to fill topographical lows, thus turbidity currents incline laterally down to the slightly sloping surface of the lobes [e.g. 21, 83]. Therefore, bed thicknesses preserved in distal depositional lobes form cyclic compensational pattern of bed arangement. Compensational cycles identified within lobe element are smaller-scale, they are formed usually by 3 to 9 turbidite beds, stack up to a few metres thick series and they are represented by thickening-upward and thinning-upward trends of bed thicknesses (Figures 4C–4E, 9, 10).
One or more genetically related lobe elements stack to form a ‘lobe’ (Figure 10). Depositional lobes are bounded by thicker (usually up to several metres thick) units of predominantly thick-bedded mudstones and thin-bedded fine- to very fine-grained sandstone turbidites (FA4) representing inter-lobe and basin plain environments. Vertical alignment of the facies associations within lobe distributary and inter-distributary areas is accompanied by vertical variations in bed thickness. This variation reflects an occurrence of meso-scale intervals with thickeningupward or thinning-upward trends of bed thickness and also intervals where it was not possible to clearly identify any trend (Figure 9). These meso-scale trends (or no trends) are documented within 7–30m thick intervals (Units 1–15), each comprising about 30–115 beds. Well-developed trend was recognized in units comprising medium- to thick beds. The thickest beds (> 70 cm) usually separate individual units.
Throughout the studied section, one more large-scale trend – generally thickening-upward trend of bed thicknesses involving hundreds of beds with a total thickness up to 175m can be identified. This trend is doccumented by gradual increase of medium thick and thick sandstone beds towards the upper part of the section (Figure 10). However, this trend can not be applied to the thickest, often amalgamated beds which are appear more or less regularly over the entire section. The thickening-upward trend of beds is accompanied also by the general increase of the ratio of sandstones/mudstones (Figures 11A, 11B) in the upper part of the section in comparison with the lovermost part, where the ratio is about 1:5. Similarly, the percentage of individual facies in sandstone-siltstone parts of turbidites changes upwards the section (Figure 11C). S1–S3 facies occure more frequently in the upper part, while S4 and Si lithofacies strongly dominate in the lower part of the section.
The cyclicity of the upward-thickening or upwardthinning units of any scale cannot be correlated with the grain-size changes of the sediment, and the relative monotonous and narrow grain-size range reduces the utility of coarsening- or fining-upward trends in architecture interpretation.
The different scale trends in stacking pattern of beds are demonstrated within turbidite succession near Chocholow. Two of them resemble a compensational stacking pattern. First, small-scale lobe element stacking patterns, stack up to a few metres thick series (Figures 9, 10), could demonstrate a small-scale shift in the lobe element centroid between successive elements (Figure 12) and could be linked to autogenic compensation processes and migration of small-scale distributive channels [9, 21].
Second, meso-scale trends in stacking pattern of beds are identified within lobes and correspond with units of which thickness usually up to several metres (Figures 9, 10). Units that include a markedly smaller number of beds compared to significant periodicity in time series analysis (Units 6,7 or Unit 12) could be in fact linked to a larger bedsets. Conversely, the units which contain markedly larger number of the beds (Units 10,13) may include several unrecognized, genetically unrelated bedsets. At the lobe scale, stacking patterns could demonstrate shifts in the position of the lobe centroid within the lobe complex. The position of a lobe, which tends to fill subtle topographic lows, is influenced by a sea floor relief, formed by elevations (the upward-convex form of lobes) and depressions (inter-lobe area), both inherited from the underlying lobes [e.g. 25]. This effect could indicate an autogenic control on lobe stacking and shape. Intrabasinal factors such as depositional topography, fan-channel switching, channel bifurcation and avulsion, lobe shifting and other processes seem to be likely to cause random shifting of architectural elements and sedimentary facies.
The last, a large-scale generally thickening-upward trend in stacking pattern of beds, accompanied with the general increase of the sandstones – mudstones ratio (Figures 11A, 11B) and gradual increase of the percentage of sandstone (S1,2,3 facies) and decrease of siltstone (Si) lithofacies (Figure 11C), is documented within nearly entire studied section. This large-scale stacking pattern could represent a part of an architectural element comparable to lobe system scale (Figure 10) and could indicate gradual basinward progradation (growth stages) of lobe system. The increasing volumes and efficiency could be interpreted as a result of relative sea-level fall and/or increased sediment supply from the hinterland and would therefore indicate allogenic control on lobe system development. The fine-grained sediments with mature siliciclastic composition documented in Chocholow section appear to be accummulated formerly by rivers, which fed the basin from tectonically active sources [cf. 85]. Numerous sandy turbidites are generated during falling sea-level stages which result in progradation and cannibalization of the deltas [e.g. 86]. The large amount of plant debris, coal fragments and wood fragments in sandstone- to siltstone facies of the Chocholow section could also indicate a source in the delta deposits or riverine input of sedimentladen flows seaward of high bedload deltas [e.g. 69, 87, 88]. Riverine input of hyperconcentrated bedload during catastrophic floods that flow seaward due to inertia could generate voluminous flows (hyperpycnites) which deposited sandstone-siltstone beds [e.g. 67, 89–91] and could form hyperpycnal-fed turbidite lobe [e.g. 24].
The beginning of siliciclastic turbidite deposition in the CCPB well corresponds with major glaciation in Antartica at around 30 Ma [92–94] accompanied by a decrease of global sea-level. The subsequent formation of sand-rich submarine fans of the Zuberec and Biely Potok Formations was influenced both by tectonic activity of sources as well as transgressive-regressive cycles during Oligocene (late Rupelian and Chattian) [1, 2, 85, 95]. The forming sandrich depositional system gradually progressed through the rhythmical thin- and medium-bedded turbidite successions of the lower fan (growth stages; Zuberec Fm.) to medium- and thick-bedded sandstone lithosomes, which coalescing lobes grade up to form the mid-fan lobe complex [3, 4] (growth and build stages; Biely Potok Fm.).Deposional lobes of the Orava-Podhale basin does not show a direct connection to channel-leeve complex, resembling the submarine fans of the Hecho basin [e.g. 20, 96]. A similar model as Hecho-type of lobe stacking was suggested by Westwalewicz-Mogilska  or Wieczorek  in the CCPB.
These proposed depositional models placed source area of clastic material and location of channel-leeve complexes which fed the Oligocene submarine fans of the Orava-Podhale basin (Zuberec & Biely Potok Fms) to the south, in the Liptov basin (hypothetical “Sliače channel” sensu Westwalewicz-Mogilska  which does not correspond with the paleocurrent data (generally from W to the E); respectively to the south-west, in the Orava region near Dolný Kubín (hypothetical “Pucov channel” sensu Wieczorek ) which does not correspond with stratigraphic position of the Pucov conglomerates [e.g. 36] as well as with depositional model of these conglomerates .
The Orava-Podhale basin was filled probably mostly from the raised Outer Carpathian accretionary wedge complexes and late Oligocene turbidite systems, which laterally prograded from opposite sides of the basin suggest localization of their sources in the north-west (Rhenodanubian and Magura units) and from the Iňačovce-Kričevo and Szolnok zones in the south-east .
Given the different hierarchical level of identified architectural building elements in Chocholow succession we tried to classify them within a spatial and temporal hierarchy for deep-water deposits proposed by  (Figure 10). The smallest scale building units we compare with fifth order turbidite beds, the lobe elements could represent fourth order turbidite sub-stage, the lobes could correspond to the third order turbidite stage. The large-scale thickening-upward trend of bed thickness could represent a part of lobe system comparable to second order turbidite system sensu Mutti and Normark [6; cf. 10].
Exposure in the Dunajec river near Chocholow allow accurate measurement of single bed thicknesses, and therefore allow an insight into bed thickness patterns at different scales of the hierarchy. A long vertical succession enabled to obtain enough dataset which is used successfully in statistical analyses. These represent an appropriate tool for the verification of assumed depositional environment identified by the determination on the grainsize, lithology, vertical arrangement of beds and facies, the shape of individual beds, sedimentary structures or palaeotransport analysis. However, the lateral scale of the architectural elements is far greater than the studied outcrop and these studies lack information on the lateral development of individual facies associations and architectonical elements, their lateral stability, changes in thicknesses or estimated volumes. Therefore some of our interpretations are only prediction based on a comparison with published model of submarine fan lobes [e.g. 9–11, 25].
The studied section is situated in distal parts of the lobe system which is also demonstrated by the ABC index sensu Walker  and result positions of the division percentage in triangular diagram which correspond with location in field of lower flow regime  (Figure 8). The result is that sets of thick-bedded sandstones corresponding to the lobe axis facies association (FA1 sensu ) can not be identified within the Chocholow succession. The lobe-axis sandstones in the sections of the lobe center form a distinct contrast with thin-bedded and mudstonepredominant facies associations surrounding them [e.g. 9]. On the other hand, more distal (we mean the radial distance from the lobe center) sections of the lobes (Chocholow section) are represented only by less thick sets of thick-bedded sandstones, intercalated by thin- to medium-bedded turbidites, which are related better to the lobe off-axis facies association (FA2). Within the distal parts of the lobes or more distant laterally from distributaries, the thinbedded turbidites and mudstone-predominant facies associations (FA3, FA4) occure generally more frequently in comparison with their proximal and central parts. Obvious diferences in distribution and frequency analysis of sandstone bed thicknesses between defined facies associations (Figures 7B, 7D) probably reflect a gradual fining and thinning in a down-dip direction. The thinning trend of bed thicknesses outwards the lobe axis as well as the changes in depositional mechanisms are documented also by the degree of line curvatures in cumulative distributions of single facies associations (Figure 7C).A power-law shape of line in FA4 can be diagnostic as deposits far from source .
High-frequency variability, relatively small lithological contrasts as well as occurrence of similar facies in the distal part of lobe system could partially misted the interfaces between architectural elements and it makes difficult to interpret the vertical changes in turbidite succession. Therefore, the interpretation of the geometry and migration of depositional lobes following the vertical stacking pattern of beds would be complicated, particularly when the interaction between allogenic and autogenic controls occurs [e.g. 98]. For example, in outcrop scale, we can not clearly recognize if thickening-upward sequences indicate basinward progradation of the lobes or if they are the result of the gradual filling of interlobe topographic lows connected to lateral shift of lobe elements. Conversely, the thinning-upward trends/sequences do not necessarily imply landward retrogradation but they can be the result of the lateral migration when successive lobe elements stack away from a fixed point (Figure 12).
The meso- to large scale boundaries between each lobe system or lobe complex are generally identified by distinct mudstone intervals which show large lateral continuity (ranging kilometers) indicate starvation of clastic sediment to the deeper part of the basin, probably related with relative sea-level rise [9, 11, 99].
Such thick, mudstone predominanted facies associations could be identified in a Unit 1 and Unit 2, where thick mudstones intervals (2–4.5 m thick) with minor abundance of siltstones and scarce thin sandstones (> 80% of mudstones) occur. However, in outcrop scale, we can not recognize the lateral continuity of these intervals over more than tens of metres and therefore can not clearly exclude the possibility that mudstone facies association of the Unit 1 and 2 corresponds to the interlobe environment in the outher fan lobes. In this case, the mudstone facies association should be passed laterally into lobe fringe and lobe axis facies associations. The thick individual sandstone beds, directly surrounded with mudstones of FA 4, which are documented within Unit 1 may represent isolated lobes reaching more distal parts of outer fan during the inicial stage of fan development – type II of outer fan lobes (fan fringe & basin plain, sensu Pickering ). Such a system shows no or only a weak trend in the bed thickness (Figure 9).
Less significant mudstone intervals, mainly characterized of FA4, are also in the higher parts of the studied sections. However, we suppose that these intervals rather represent an inter-lobe environment, away from the main input of sandy lobe elements, and FA4 is laterally in direct connection with the FA2 and FA3. Therefore, the thickness and lateral reach of these facies associations are limited by lateral shifting of lobe elements documented by thickening-upward and thinning-upward trends (Figure 9).
Sedimentary succession of the Zuberec Formation exposed in the bedrock of Dunajec river near Chocholow in the northern part of the CCPB well corresponds to lobe deposits of submarine fan. This interpretation is based on the recognition of the facies associations that indicate different components of the distributive lobe deposits in deep-water fan system corresponding to (1) lobe off-axis, (2) lobe fringe and (3) lobe distal fringe/inter-lobe depositional environments. The depositional environment identified by the determination of grain-size, lithology, vertical arrangement of beds and facies, shape of individual beds, and sedimentary structures or palaeotransport analysis was supported by statistical analyses. The shape of the cumulative bed-thickness frequency distribution best corresponds to the middle fan environment and the value of the Hurst coefficient indicates lobe-interlobe environment. The calculation of the percentage of Bouma divisions in turbidite sandstones and ABC index, together with bed-thickness frequency distributions and vertical organization of the facies associations, that show thickeningupward and thinning-upward cyclic trends, enable us to reconstruct architectural elements of turbidite fan and classify their distality and flow regime. Trends at three different hierarchical levels in vertical stacking pattern of beds are demonstrated within turbidite succession. First, a small-scale trend corresponds to shifts in the lobe element centroid between successive elements. Statistical analysis of bed thickness confirmed the expected differences in distribution and frequency of sandstone bed thickness between individual facies associations, probably reflecting a gradual fining and thinning in a down-dip direction. The thinning trend of bed thickness outwards the lobe axis as well as the changes in depositional mechanisms are documented also by the shape of cumulative bed-thickness frequency distributions of individual facies associations.
Second, meso-scale trends are identified within lobes and they generally correspond to the significant periodicity identified by the time series analysis of the bed thickness. The meso-scale trends could demonstrate shifts in the position of the lobe centroid within the lobe system. Both scale of these trends have a character of a compensational stacking pattern and could be linked to autogenic processes.
Third, a large-scale trend documented by generally thickening-upward stacking pattern of beds, accompanied with the general increase of the sandstones – mudstones ratio and gradual change of percentage of individual facies, could represents a part of an architectural element comparable to lobe system scale. This trend probably indicate gradual basinward progradation (growth stages) of lobe system controlled by allogenic processes related to tectonic activity of sources and sea-level fluctuations.
This work was supported by the scientific grant agency of the Slovak Republic (Vega 2/0017/15) and Slovak Research and Development Agency under the contract No. APVV-14-0118. We thank J. Soták and anonymous reviewer for the detailed review of this paper and constructive comments.
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