Abstract
The aim of this study was to examine the relationship between structural elements and the socalled genetic lithofacies in a clastic deepwater depositional system. Processsedimentology has recently been gaining importance in the characterization of these systems. This way the recognized facies attributes can be associated with the depositional processes establishing the genetic lithofacies. In this paper this approach was presented through a case study of a Tertiary deepwater sequence of the Pannonianbasin.
Of course it was necessary to interpret the stratigraphy of the sequences in terms of “general” sedimentology, focusing on the structural elements. For this purpose, welllogs and standard deepwater models were applied.
The cyclicity of sedimentary sequences can be easily revealed by using Markov chains. Though Markov chain analysis has broad application in mainly fluvial depositional environments, its utilization is uncommon in deepwater systems. In this context genetic lithofacies was determined and analysed by embedded Markov chains. The randomness in the presence of a lithofacies within a cycle was estimated by entropy tests (entropy after depositional, before depositional, for the whole system). Subsequently the relationships between lithofacies were revealed and a depositional model (i.e. modal cycle) was produced with 90% confidence level of stationarity. The nonrandomness of the latter was tested by chisquare test.
The consequences coming from the comparison of “general” sequences (composed of architectural elements), the geneticbased sequences (showing the distributions of the genetic lithofacies) and the lithofacies relationships were discussed in details. This way main depositional channel has the best, channelized lobes have good potential hydrocarbon reservoir attributes, with symmetric alternation of persistent finegrained sandstone (Facies D) and muddy finegrained sandstone with traction structures (Facies F)
1 Introduction
Vertical variations of lithofacies have an important role within a sedimentary sequence in recognition of depositional environment. According to Walther's facies correlation law [1], only those facies can be settled on each other which can exist next to each other at a given time. Thus a quasigradual transition from one facies to another represents that the two facies were adjacent laterally once.
In deepwater depositional systems (i.e. submarine fan complex [2]) the distribution of the facies, the coarsening and fining upward successions, the geometries and sand/mud contents of each parts lead to detect the socalled structural elements. Structural elements (i.e. sedimentary subenvironments) have been emphasized for decades in the major regionalscale models, according to the works of Normark [3], Mutti and Ricci Lucchi [4], Mutti [5], Reading and Richards [6], Bouma [7] etc. By revealing these, potential hydrocarbon stratigraphy traps of these systems can be understood more efficiently.
Sediment deposition occurs mainly from gravitydriven processes (such as slumps, slides, cohesive debris flow, sandy debris flow, turbidiy currents) in these systems. Sediment concentration and deposit thickness as fraction of flow thickness decreases from slumps and slides to turbidity currents. Redeposition by bottom currents also has an important role in these systems [8]. By application of the principles of process sedimentology (it is concerned with establishing connectivity between the deposit and the physics of the depositional process), one can attach the identified faciological attributes (grainsize, textural and compositional maturity, sediment structures etc.) to the related depositional process. Thus genetic (corresponding to the depositional process) lithofacies (GLF) can be obtained.
In order to determine regularity and cyclicity in sedimentary sequences, Markovchains are common and useful methods. By using Markovchains with the established genetic lithofacies, modal cycles (i.e. depositional model) can be developed.
Through the case study from a Tertiary (Late Miocene and Lower Pliocene) deepwater sedimentary sequence of the Pannonian Basin, the following methods are applied:

recognizing the GLFs (on core samples), and deducing the significant vertical lithologic transitions in the examined sequences;

analysing cyclicity and significance of successions by chisquare and entropy tests (postdepositional, predepositional, wholesystem entropies), respectively;

interpreting the “general” sedimentary sequences by the help of welllogs and regionalscale models focusing on structural elements;

consequently, revealing connectivity between structural elements with potential hydrocarbon reservor character and modal cycles, cyclic patterns (sets of post versus predepositional entropies [9]).
2 Available data and the General geological setting of the region of the case study
The case study is located in one of the deep subbasins of the Pannonian Basin in the Great Hungarian Plain. Related to the research, the data comes from a single well, which is labelled as WELLA hereinafter. The available and applied data were composed of calibrated spontaneous potential and gammaray logs. They are the most responsive to the real lithological attributes. Approximately 35 metres of core sample (total interval: 35.5 metres) were investigated.
At the beginning of Late Miocene the Central Paratethys had become a hydrologically isolated large lake (Lake Pannon) [10], until it was completely filled (Pliocene). The process of filling up showed progradational feature and was controlled particularly by fluvial and deltaic systems during Late Miocene and Lower Pliocene. The sedimentsupply was derived from northwest and northeast, east [11]. Flora and fauna of Lake Pannon reached great endemic diversities [12].
The following main depositional environments characterized Lake Pannon [13]: (1) fluviolacustrine and deltaic plain (2) delta front and delta slope (3) prodelta (4) deepwater systems (5) basin plain.
The growth of deepwater systems belong to Szolnoki Formation [14]. In the Great Hungarian Plain its thickest sequences (approx. < 1000 m) take place in deepsubbasins (Jászság Basin, Derecske Trough, Makó Trough, Békés Basin) [11].
3 Methods
As previously mentioned, the analytical procedure consists of three steps: (1) interpreting the “general” sedimentary sequence (2) recognizing GLSs (3) quantitative stratigraphical analysis based on GLSs (embedded Markovchains, entropy and chisquare tests).
3.1 Interpretation of general sedimentary sequence
Average grainsize distribution, regularity of alternations of litofacies in each parts and welllogs (calibrated spontaneous potential, gammaray) are applied to reveal structure elements. The wellknown log motifs refer to the structural elements in deepwater systems after [15]:

bell: finingupward succession, channellevee complex, unchannelized lobe, abandonment of any channel or lobe;

funnel: coarseningupward succession, development of distal lobe;

cylindrical: wedgebodies, proximal main depositional channel, channelized lobe, lobe without channellevee complex;

irregular: zone of slides and slumps, zone of sand sheets (inactive or distal part);

symmetric: development then abandonment of channelized/unchannelized lobe.
3.2 Characterization of genetic lithofacies
The main gravitydriven processes dominating in deepwater systems are: (1) slides and slumps (2) cohesive debris flows and sandy debris flows (3) turbidity currents. Reworking bottom currents also operate.

(1) ”Aslide is a coherent mass of sediment that moves along a planar glide plane and shows no internal deformation” ([8, p. 49]). ”A slump is a coherent mass of sediment that moves on a concaveup glide plane and undergoes rotational movements causing internal deformation” ([8, p. 52]). General features of deposits of slide and slump: (1) gravel to mud lithofacies (2) basal zone of shearing (3) tension faults (4) clastic and sand injections (5) secondary internal glide planes (slides) (6) alternations of contorted and uncontorted layers, chaotic bedding (slumps);

(2) ”Debris flow is a sediment flow with plastic rheology and laminar state from which deposition occurs through freezing en masse” ([8, p. 59]). Sandy debris flow is a transformation between cohesive debris flow and turbidity current, with a lower laminar and an upper turbulent part. The term “highdensity turbidity current” is also used for this type of process (e.g. Lowe [16]). It is misleading, because the bigger volume of the deposited sediment is derived from the lower part of flow, which is clearly not in turbulent state [8]. In this work, deposits of cohesive debris flow and of sandy debris flow is handled altogether. General features of deposits of cohesive or sandy debris flow: (1) gravel to mud lithofacies (2) floating mudstone clasts near top of the beds (3) projected, brecciated mudstone clasts (4) inverse, normal, inverse to normal, and no grading;

(3) “Turbidity current is a sediment flow with Newtonian rheology and turbulent state in which sediment is supported by turbulence and from which deposition occurs through suspension settling” ([8, p. 77; 17]). General features of deposits of turbidity current: (1) finegrained sand to mud lithofacies (2) normal grading without any other structures (3) erosional (flute marks) basal contact (4) thin layers, mainly few centimetres;

(4) Bottom currents (induced by tidal, thermohaline or wind forces [18]) are responsible particularly for traction structures in deepwater systems [8]. Their deposits can be characterized by: (1) finegrained sand and mud lithofacies (2) thinbedded, laminated sand with mud, and its rhythmic occurence (3) lowangle cross laminae, ripplecross laminae (4) flaser, lenticular bedding.
3.3 Embedded Markovchains, entropy analysis and chisquare test
The idea of cyclicity in sedimentary systems implies that one state (i.e. lithology) determine the succeeding state. In the case of the method of embedded Markovchain, only of lithologic changes (abrupt change in character) are recorded, regardless of the thickness of each lithology member (or bed). Counting the transitions in the sequence, one step embedded tally count matrix (fij) is structured (where i, j corresponds to row and column number). By means of it, upward (pij) (i.e. transition probability matrix) the and downward (qij) probability matrices are calculated [19]. For establishing the expected transition freGLFs quency (eij) and therefrom the independent trials probability (rij) matrices, iterative procedure of Powers and Easterling [19] is applied. Normalized difference matrix (Dij) is obtained by subtracting the value of each cell in the independent trials probability matrix (rij) from the corresponding cell in the transition probability matrix (pij) (Figure 1). The cells where positive values are present (at given limiting 8 value), show those transitions which have Markovian property (i.e. cyclicity). Hattori (1976) introduced the entropy analysis in Markovchains and general cyclic patterns in sedimentary successions [9]. Post E(post), preE(pre) and whole depositional system E(sys) entropy values are calculated from upward and downward probability matrices, respectively, by application of modified Shannonentropy (entropy value gives the rate of uncertainty of the occurrence of a facies). Generally, entropy is likely to increase with the number of states. Thus, entropy values must be normalized (by dividing both of E(post) and E(pre) by E(max), where E(max) is the maximum possible entropy in the system). The nonrandomness of the obtained modal cycles are tested by chisquare test [19]. The calculations and the whole procedure followed Hattori's concept.
Figure 1
4 Qualitative and quantitative results
Figure 2 shows the general sedimentological explanation used in WELLA. Structural elements are revealed. Potential hydrocarbon reservoirs could occur in “channelized lobe 12”, and “main depositional channel”. The recognized genetic lithofacies are: (1) Facies A  deposit of slump – chaotic bedding, mud to finesandstone (ss) (2) Facies BD – deposits of sandy debris flows – graded bedding, floating clasts; B – finess/aleurolite, C – very fine/finess, D – persistent (thickness > 1 m) finess) (3) Facies E  deposit of turbidity current – normal grading, finess and aleurolite (4) Facies F – deposit of reworking bottom current – laminated bedding, ripplecross lamination, cross lamination, flaser and lenticular bedding – mudstone/finess (5) Facies G – hemipelagic settling – marlstone. Based on transitions 9 of the GLFs, another sequence is structured (Figure 2). Approximately relative frequencies of GLFs in each zone of structural elements are deduced.
Figure 2
In aspect of quantitative stratigraphical analysis, all matrices mentioned above and entropy values are calculated. Transition tally count, difference matrices, entropy values and chisquare test can be seen in Table 1. Facies relationship diagram (FRD) based on positive difference values is also constructed (Figure 3).
Transition tally count matrix (p_{ij})  Difference matrix with positive^{*} values (D_{ij})  
A  B  C  D  E  F  G  A  B  C  D  E  F  G  
A  0  1  1  1  0  0  0  0.226  0.226  
B  0  0  1  1  3  10  2  0.155  0.168  
C  1  2  0  0  2  1  1  
D  1  0  0  0  1  5  0  0.370  
E  0  1  3  0  0  4  0  0.258  0.150  
F  0  12  1  5  2  0  1  0.188  
G  2  1  0  0  1  0  0.153  
Norm. E(pre)  Norm. E(post)  Nonrandomness test: chisquare test  
A  0.613  0.613  Degree of freedom = (N  1)^{2}  N  
B  0.603  0.672  where N = observed states  
C  0.823  0.865  DOF = 29, χ^{2} = 39.87  
D  0.444  0.444  Limiting confidence level values at 29 DOF  
E  0.737  0.544  90%  95%  
F  0.726  0.656  39.09  42.56  
G  0.58  0.744  Markovprocess: stationary  
E(sys) = 9.133 E(max) = 2.585 
Figure 3
Facies A can be succeeded by Facies D or Facies B with the same probability. So, there are two possible ways in FRD (heteropic facies), but in one well (i.e. sequence) they cannot appear simultaneously, nevertheless geologically both are equally good. Therefore the line with higher probability value (multiplying the difference values in each way) – lineA – is chosen for developing a modal cycle. The higher justification of LineA is valid only in WELLA. Post and predepositional diagram shows most closely symmetrical figure (Hattori's typeB diagram, Figure 3). The modal cycle has a pattern of GADFCF with 90% confidence level.
Modal cycle suggests that if persistent deposit of sandy debris flow (Facies D, potential HCreservoir) appears once, it is followed by deposit of bottom current (Facies F), which has lower permeability because of its traction structures and finer grainfraction. It means possible capping attributes. Unrestricted alternation of Facies F and C can denote additional reservoircapping relationship with thinner sandstone reservoir (Facies C). Furthermore, Facies C has the highest value of normalized post depositional entropy which implies that its successor varies widely, hence marlstone can overlie on it as the best caprock.
The geological interpretation of the cyclical sequence is: (1) initial state is Facies G, which denotes the hemipelagic settling on basin plain (2) Facies A may denote slumps and slides, related to undercutting of channels. It is followed by (3) channelfills (Facies D). Facies D seizes relatively the thickest part of the whole sequence. It means that this part of the complex is dominated by channelsystems (as main supplier channel or distributary channel). (4) Facies F denotes functioning of bottom currents. It is related to the inactive zones, so the channels migrate. (5) Facies C may show the overflows over the margin of the channels. The symmetrical attribute refers to that the whole system migrates laterally.
5 Discussions
WELLA reveals a part of a typical sandrich submarine fan complex with quasiinactive parts (zone of thin sand sheets and overbank), channelized lobes (persistent sandstones in them may denote distributary channels) and main depositional channel. Potential hydrocarbon reservoirs may take place in channelized lobes (1–2) and main depositional channel.
Channelized lobe1 is composed of mainly Facies D, and then, of lower proportion of Facies B and F. In case of Line1, occurrence of Facies B is random. Subsequently, this part of sequence has cyclic alternation of reservoir sandstone (D) and finergrained rock with traction structures with ability of trapping (F).
Channelized lobe2 is composed of mainly facies D and Facies F. The situation is the same as in channelized lobe1.
Main depositional channel is composed of Facies D, E and in smaller part, Facies F, A. Occurrence of Facies E is random, according to lineA. Facies A usually behave as a reservoir [8]. Presence of Facies D and F denote the same former state. Maybe this is the best hydrocarbon reservoir zone because Facies D reaches its thickest developments here.
6 Conclusions
On the strength of qualitative and quantitative analyses of WELLA, main depositional channel has petrophysically the best, and channelized lobes (1 and 2) have good potential hydrocarbon reservoir attributes, with symmetric alternation of facies D and F (a probably reservoircaprock relationship). Occurrence of facies C is random, but its successor varies widely (it can be marlstone, facies G, as well) due to its high normalized postdepositional entropy.
Generally, linking the structural elements and modal cycles based on genetic lithofacies is a good contrivance to reveal the nature of stratigraphy traps in deepwater systems. By means of it, it is possible to analyse the internal structure of each structural elements. In addition, inferences can be concluded about which depositional processes dominate in the different structural elements.
Acknowledgements
I am grateful to János Geiger and Janina Horváth, University of Szeged, for their helpful assistance and corrections. The quantitative results were calculated by a computer software (written in FORTRAN 77) programmed by János Geiger. I am also thankful to MOL Nyrt. for the welllogs and core samples.
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