The influence of paleo-bathymetry on total organic carbon distribution tested in the Cretaceous Hammerfest Basin, Barents Sea

Accepted Manuscript The influence of paleo-bathymetry on total organic carbon distribution tested in the Cretaceous Hammerfest Basin, Barents Sea Benjamin Emmel, Anindito Baskoro, Gerben de Jager, Arnt Grøver, Ole-Andre Roli PII:

S0264-8172(18)30367-2

DOI:

10.1016/j.marpetgeo.2018.09.003

Reference:

JMPG 3483

To appear in:

Marine and Petroleum Geology

Received Date: 29 January 2018 Revised Date:

29 August 2018

Accepted Date: 3 September 2018

Please cite this article as: Emmel, B., Baskoro, A., de Jager, G., Grøver, A., Roli, O.-A., The influence of paleo-bathymetry on total organic carbon distribution tested in the Cretaceous Hammerfest Basin, Barents Sea, Marine and Petroleum Geology (2018), doi: 10.1016/j.marpetgeo.2018.09.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT The influence of paleo-bathymetry on total organic carbon distribution tested in the Cretaceous Hammerfest Basin, Barents Sea • • •

Stochastic paleo-bathymetry reconstructions TOC distribution models for end-member paleo-bathymetries Nonlinear uncertainty propagation from bathymetry to TOC models

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Benjamin Emmel1, Anindito Baskoro2,3, Gerben de Jager1, Arnt Grøver1, Ole-Andre Roli1

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1) SINTEF Petroleum; Basin Modelling, S. P. Andersens veg 15 B, Trondheim 7031, Norway 2) Department of Geoscience and Petroleum, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway 3) Research and Development Centre for Oil and Gas Technology 'LEMIGAS', Ciledug Raya street 109, South Jakarta, Indonesia 12230

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Keywords: Paleo-bathymetry, Barents Sea, Hammerfest Basin, Cretaceous, Total Organic Carbon, Basin Modelling

Abstract

In basin modelling and petroleum system analysis geometries during deposition of sediments (paleowater depth) and distribution of organic matter are initial parameters used for further interpretation or

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modelling. This paper presents an approach, combining backstripping with a probabilistic forward sedimentary model to calibrate paleo-water depth (PWD). The stochastic PWD results serve as an input for organic facies models and the study demonstrates how PWD will influence models for total

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organic carbon distribution in a sedimentary basin. For the Late Cretaceous Hammerfest Basin, mainly shelfal to upper bathyal bathymetries (average PWD values vary between 118 and 318 m) result in

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average total organic carbon (TOC) varying between 0.47 and 5.24 wt% across the basin. For the different models basin averaged TOC values are similar but vertical and lateral distribution pattern change significantly, especially towards the shallow end-member PWD. The results indicate that PWD uncertainties propagate non-linearly into source rock distributions.

1. Introduction Redistribution of mass on the earth's surface is mainly guided by local directions of slopes, set up by the existing topography and bathymetry (e.g., Allen, 2009). Together with understanding the coupling

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ACCEPTED MANUSCRIPT of climate and tectonic activity, a precise imaging or characterisation of (paleo-) morphologies will improve the possibility to simulate and predict mass movements and accumulation along these landscapes, e.g., the influence of mountain chains and sea-floor bathymetry on sediment distribution (e.g., Curray and Moore, 1971; Lobo et al., 2006), submarine fans (Normark, 1978), landslides (Korup

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et al., 2007), ocean currents (Ledwell et al, 1999) or distribution of marine organic matter (e.g., Tselepides et al., 2000). A detailed imaging of the present-day topography or bathymetry is mainly limited by the resolution of geodetic observation systems. If one tries to reconstruct ancient landscapes more unknowns related to the basin-fill (e.g., lithology away from well control), or erosional history

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will add on to these observational uncertainties. In petroleum systems modelling this process is referred to as the prediction of paleo-bathymetries or the reconstruction of paleo-water depth (PWD).

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In an extensional tectonic setting, during the stretching of continental crust, basins will develop and subsequently be filled up with sediments. By knowing sediment thicknesses through time, it is possible to backstrip sedimentary units and reconstruct earth surface geometries during the time of deposition (Allen and Allen, 2013). Many parameters are based on simplified assumptions such as

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lithologies, compaction trends, decompaction behaviour and isostasy, among others. The number of unknowns suggests that any deterministic PWD reconstruction based on backstripping has a high degree of uncertainty. In most cases a verification of backstripped absolute values is not possible

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because suitable geological tools with a comparable vertical resolution are missing. For example, micro-fossil assemblages or sediment structures can be used to estimate PWD empirically (e.g.,

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Seilacher, 1967; Setoyama et al., 2011) or classify depositional environments (Dalland et al., 1988) but usually they represent a broad range of water depth and absolute values are rarely given. However, predicting source rock distributions within a basin using more sophisticated petroleum system models requires precise quantitative paleo-bathymetries (e.g., Littke et al., 1997, Mann and Zweigel, 2008). Several techniques have been published to numerically describe source rock deposition (Schwarzkopf, 1993; Tyson, 2001, 2005; Katz, 2005). These works describe the main processes that control variation within deposition, mainly focussing on the three most important processes: production, preservation and dilution of organic matter. The process descriptions from these papers have uniquely been combined in a consistent three-dimensional context (Mann and Zweigel, 2008), which is able to apply

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ACCEPTED MANUSCRIPT the relationships described above in a high resolution, process-based numerical model. In this model PWD is an important input which effects all results. The capability of this modelling approach has been demonstrated in several case studies (Knies and Mann 2002; Tømmerås and Mann, 2008; Mann et al, 2009; Mann and Zweigel, 2008; Pathirana et al, 2014, 2015; Gambacorta et al., 2016).

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This study, relates on the impact of PWD on the total organic carbon (TOC) distribution in the Cretaceous Hammerfest Basin, western Barents Sea (Figs. 1, 2). Here, the Cretaceous is well-defined by seismic reflectors and exploration wells giving the opportunity to reconstruct quantitative,

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calibrated paleo-bathymetries using the approach described in Emmel et al. (2015). Furthermore, by using detailed geochemical well data and an organic facies model the study demonstrates the

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significance of PWD model for the source rock part of a petroleum system model. The results will constrain locations and quantity of TOC, a major component controlling source rock quality, the

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starting point for every petroleum system analysis.

Figure 1: Location of the working area with main structural elements in the SW Barents Sea (left), inset shows the location of the Barents Sea within the Arctic region (modified from Clark et al., 2013; based on Jakobsson et al., 2008 and Faleide et al., 2008). Detailed map (right) with well locations and structural elements. The red box outlines the working area. The used coordinate reference system is ED50-UTM34. Abbreviations: COB: continent–ocean boundary, FP: Finnmark

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ACCEPTED MANUSCRIPT Platform, HB: Hammerfest Basin, LH: Loppa High, OB: Ottar Basin, SV: Sørvestsnaget Basin, TB: Tromsø Basin.

2. Geological overview

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The study area is situated in the Barents Sea on the northern Norwegian continental shelf (Fig. 1). It incorporates the western part of the Hammerfest Basin, the most prolific hydrocarbon region in the Barents Sea, and the eastern Ringvassøy-Loppa Fault Complex. The E-W striking Hammerfest Basin extends over ca. 150 km with a width of ca. 70 km (Fig. 1). In the following, we provide a summary of

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the main phases during basin development.

During the Carboniferous intracontinental rifting with sand-prone sedimentation started in the

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Hammerfest Basin. Thereafter, during the Permo-Carboniferous a carbonate platform was established (summarized in Ramberg et al., 2008). The basin was gradually filled with Triassic marine to continental siliciclastic sediments starting with the deposition of three progradational units the Havert, Klapmyss, and Kobbe/Steinkobbe Fms. A Late Triassic regional subsidence led to the deposition of

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the Snadd, and Fruholmen Fms (Fig. 2). The overlying mainly siliciclastic sedimentary rocks of the Tubåen, Nordmela and Stø Fms indicate the development of a delta system during the Early and midJurassic (summarized in Rodrigues Duran et al., 2013). The main architecture of the basin relates to a

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rift episode during Late Jurassic to Early Cretaceous times (Gabrielsen, 1984; Gabrielsen et al., 1990; Indrevær et al., 2017) associated with mainly east-west extension along the western margin and an

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oblique north-south extension in the eastern part of the basin (Berglund et al., 1986; Faleide et al., 2008; Hermanrud et al., 2014). The major structural characteristic of the basin, a central faulted domestructure following the strike of the basin, relates to this episode. During the Early Cretaceous, the marine shales of the Knurr and Kolje Fms were deposited, followed by a renewed transgression and deposition of the Kolmule Fm. (Fig. 2). The Cretaceous is terminated with a marine transgression with the deposition of the Kveite Fm. (Nøttvedt et al., 1993). In the Paleocene the North Atlantic-Arctic rifting started, with the final break-up at the Paleocene-Eocene transition (Faleide et al., 2008). The shear movement resulted in local transtension and transpression and led to the reactivation of some older faults in the Hammerfest Basin (Hermanrud et al., 2014). During this time the Torsk Fm.

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ACCEPTED MANUSCRIPT probably covered a wide part of the basin. Following, the mid-Oligocene passive margin development in the western Barents Shelf, with associated tectonic uplift, caused deep erosion in the eastern part of the basin (Berglund et al., 1986; Rodrigues Duran et al., 2013). The formation of interest is the early Barremian to early Aptian Kolje Fm. (Fig. 2), which was

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deposited in a distal marine shelf environment with good water circulation (Mørk et al., 1999). The Kolje Fm. is very homogenous, thickens westwards but thins towards the central part of the Hammerfest Basin (Dalland et al., 1988). In the type well 7119/12-1 shale and claystone, with minor interbeds of limestone, dolostone and in the upper part interbeds of siltstone and sandstone make up

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the 437 m thick Kolje Fm. Pyrite frequently occurs in several wells including the type well

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(completion reports of specific wells from the Kolje Fm. at npd.no).

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ACCEPTED MANUSCRIPT Figure 2: Litho-stratigraphy of the Hammerfest Basin (from npd.no/Global/Engelsk/2Topics/Geology/Lithostratigraphy/BH-OD1409003.pdf; based on Dalland et al., 1988) and input data used for the PWD reconstruction.

3. Method

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3.1 Stochastic paleo-water depth calculation Paleo-bathymetry is the PWD at the time of deposition, which determines the position of the sea-floor relative to a datum (Immenhauser, 2009). To reconstruct 3D paleo-bathymetries for the Kolje Fm.

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(including the Knurr Fm.) we used a backstripping approach (Allen and Allen, 2013) and a calibration based on sand-fraction distribution (Emmel et al., 2015). In brief, the PWD reconstruction can be

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described in three steps. At first, the initial PWDs for the boundary layers of a sedimentary unit are calculated, correcting for effects of isostasy and compaction (no correction for tectonic subsidence). Secondly, the space between the two layers is filled with a fuzzy logic sedimentary model (Nordlund, 1998) calculating the sand-fraction distribution. The sedimentary model is based on three geometrical properties for each location in the basin: distance to shore, PWD and slope (Nordlund, 1998; de Jager

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et al., 2016). Finally, all PWD reconstructions are classified by evaluating the fitting between measured and modelled sand-fraction data. The basic premise is to mimic the previously ignored tectonic effects by applying elevation and scale changes (multiplying the grid with varied factors) to

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the backstripped initial PWD estimates. Subsequently, the sand-fraction distribution in each of these incremented basin shapes is calculated using the same stratigraphic model (Fig. 3).

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The final PWD models are the mean PWD values for top and base of the Kolje Fm. derived from the 5% of best-fitting simulations. This percentage has no statistical meaning. It is based on typical distributions of the error values in our models. There are a limited number of models that fit the data good (i.e., with low error values) but many models with an acceptable fitting (medium error values). Often these acceptable models will dominate the statistics. It was observed that the 5% hurdle gives reasonable values, i.e., resulting in models with a best-fit solution close to the mean PWD framed by acceptable water depth reconstructions. The standard deviations of this 5% of acceptable PWD reconstructions describes the PWD uncertainties. A more detailed description of the method is given

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in the appendix A1.

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Figure 3: Sketch illustrating the PWD calibration method. An initial paleo-bathymetry model of a unit is reconstructed applying back-stripping to its top and base. Between two PWD surfaces a sedimentary model is built to fit measured well sand-fractions. The modelled PWD is then incrementally changed and a sand faction is calculated based on depth, slope and distance to shore. A mismatch between the measured (well log based) and modelled sand fraction can be calculated and used as a calibration criterion.

3.2 Organic facies model

SINTEF's software OF-Mod (Mann and Zweigel, 2009) was used to model the TOC distribution for the different PWD realizations. OF-Mod is a process-based sedimentological tool used to model the deposition of sediments rich in organic matter, potential source rocks for hydrocarbon generation. The modelling procedure mainly includes two steps (Fig. 4). At first, the distribution of the inorganic fraction is modelled via a sand-fraction distribution. Here we use the same sedimentary model as in the PWD reconstruction. Secondly, the organic matter distribution is modelled. The amount of

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ACCEPTED MANUSCRIPT accumulated organic matter depends on marine preservation (bacterial degradation and scavengingreworking by benthic fauna), water depth (transit time of organic matter in the water-column), sediment grain size, and sedimentation rate (Allen and Allen, 2013). The organic facies model is based on interplay of three organic matter source types (Felix, 2014; de Jager et al., 2015):

and degraded during settling to the sea-bottom;

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(i) Marine organic carbon (Cmar) is produced by primary productivity (PP) in the upper water-column

processes; (iii) Residual organic carbon (Cres) is detrital organic matter;

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(ii) Terrigenous organic carbon (Cterr) comes from the continent through erosion and sedimentation

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The distribution of Cmar is modelled based on spatially and temporally changing paleo primary productivity (PP), as well as degradation of organic matter in the water column and in the sediments based on redox conditions and sediment rate. It includes the calculation of carbon flux (Betzer et al., 1984) based on PP (Mann and Zweigel, 2009), burial efficiency based on sedimentation rate (Betts and Holland, 1991), and carbon accumulation rate (Mann and Zweigel, 2009). To obtain a fit between

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modelled and measured data (Tab. 1) the input values for PPcoast, PPocean, Cterr and Cres are changed through time (Tab. 2). The best-fit solution was obtained by iterative try and error testing different combinations of variables. Primary productivity values similar to the present-day values in the Barents

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Sea which vary between 54 gCm-2 a-1 and 134 gCm-2 a-1 (Reigstad et al., 2011) are used as input. Furthermore, the PP input values are also in the range of other marine settings (Schwarzkopf, 1992

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and references therein), e.g., similar to coastal zones (ca. 100 gCm-2 a-1), closed basin like the Mediterranean Sea (40-60 gCm-2 a-1) and open ocean (50-60 gCm-2 a-1). The Cterr and Cres distributions are modelled in relation to grain size sorting in different hydrodynamic regimes (de Jager et al., 2015). Accordingly, Cres concentrations will be highest with low sand-fraction, whereas Cterr concentration will be highest with high sand-fraction. Oxic preservation conditions are used. Once the distribution of the inorganic sediment and the three organic matter types has been modelled, TOC and HI values are calculated (Fig. 4). TOC is simply the percentage of organic matter in the sediment, whereas HI is calculated as the weighted average of the three organic matter types based on

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ACCEPTED MANUSCRIPT their relative concentrations and their respective HI values. The original organic matter values used here are Cmar=500; Cterr=100 and Cres=10 mg HC/gTOC. We chose a low HI-end-member and used original HI values without back-calculation due to little thermal alteration, as most wells give low vitrinite reflectance data varying in general between 0.35 and 0.57 %Ro (Tab. 1) with two outliers of

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0.82 and 0.97 %Ro (from npd.no/factpages/; geochemical information for wells 7121/4-1 and 7121/52). Back calculation to HI values during deposition was not necessary, for such low %Ro values (immature source rocks) the transformation ratio for type II organic matter is less than 0.02 (Cornford et al., 1998). To validate the forward models, we compared measured TOC and HI values with

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modelled data (Fig. 4). More details about the organic facies model are given in the appendix A2.

7120/6-1

V

V

7120/6-2S

V

-

7120/7-1

V

V

7120/7-2

V

V

7120/7-3

V

V

7120/8-1

V

7120/8-2

V

7120/8-3

V

7120/8-4

V

7120/9-1

V

7120/9-2

V

V

0.50-0.71

7121/4-1

V

-

0.97

7121/4-2

V

V

-

7121/5-1

V

V

0.48-0.56

7121/5-2

V

V

0.36-0.82

7121/5-3

V

-

-

7121/7-1

V

V

-

V

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Geochemical data

7120/5-1

GR log V

VR (%Ro) 0.54 -

0.48-0.52 -

V

0.48-0.55

-

-

-

-

V

0.55-0.57

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0.35-0.50

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wellbore name

Table 1: Well-data availability and vitrinite reflectance (VR) data (from npd.no/factpages/; collected from well specific geochemical information) in the study area. GR: gamma ray log. Geochemical data consist of total organic carbon (TOC) and hydrogen index (HI). V: data is available.

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Figure 4: Input data and modelling of the organic facies. In light grey the user input, and in dark grey the final model results. Abbreviations: OM: organic matter (Cmar, Cterr, Cres); HI: hydrogen Index, TOC: total organic content. We focus on the TOC distribution and HI values are solely used for the calibration of the organic model and not discussed further. For the PWD and organic facies reconstructions the same inorganic sedimentary model was used.

3.3 Model work-flow

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The aim of the modelling exercise is to test the influence of PWD reconstructions on organic facies distribution models. The carbon flux (e.g., Tyson, 2001) is the major parameter controlling the Cmar fraction that reaches the sediment surface which itself relates to PP and water depth (Fig. 5). This simple relationship is complicated in a 3D model by other processes such as dilution and preservation. Therefore, we will compare the results of three organic facies distribution models based on different PWD input (Fig. 6). At first, a stochastic, calibrated PWD for the top and base of the Kolje Fm is calculated. For both horizons, a mean PWD ± standard deviation is calculated obtained from the 5% best-fitting realizations (Fig. 7). The PWD together with the organic forward model is used to

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ACCEPTED MANUSCRIPT calculate the TOC distribution in the basin (Fig. 6). Finally, the maximum and minimum PWD reconstructions serve as input in the same organic facies model (Fig. 6). To assess the sensitivity of PWD all other factors in the model are fixed for the different modelled realisations. This approach enables to see the effect of PWD on all other model results including the mismatch between measured

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and modelled TOC values (Fig. 6).

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Figure 5: Simplified model of carbon flux and its relationship to primary productivity and water depth in the upper 500 m of a water column under oxic preservation conditions. Carbon flux is calculated using relationship from Betzer et al. (1984). Highest carbon flux occurs with high primary productivity and shallow water, whereas the lowest values occur for low primary productivity and deep-water depth. White dashed lines indicate ranges applicable to this study.

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Figure 6: Work flow diagram showing the applied techniques to get the different models. We used only the mean PWD reconstruction to fit model and well data for the organic facies model. For the organic facies models B and C we used the same input data used for the validation of Model A. The results are different TOC distribution maps (grey) for mean, maximum and minimum PWD reconstructions keeping all other input parameters fixed.

Primary productivity [gC/(m2a)] Age (Ma)

Coast

Ocean

Basic input [wt%]

Cterr

Cres

70

50

1.5

1.5

114

70

50

1.5

1.7

90

70

1.5

100

80

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115 144

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113

2.5

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Table 2: Time variable input for the organic model. Primary productivity varies linearly between the assigned ages. The border between PP related to ocean and coast is set to 35 km away from the closest shore line. Cterr: terrigenous organic carbon, Cres: residual organic carbon.

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3.4 Model input and model dimension The main model input are twelve formation tops obtained from interpretation of seismic lines, three reconstructed horizons (Fig. 2) and data from 18 wells including gamma-ray log, ages, and geochemical data (Tab. 1). Surface maps of formation tops were provided by Statoil ASA, well and geochemical data are from the Norwegian Petroleum Directorate factpages (collected from different well specific reports at npd.no). Top Lower Permian and top Lower Carboniferous are reconstructed by using the mean sediment thicknesses reported on the Norwegian Petroleum Directorate factpages and shifting the top Permian surface map accordingly. The top basement was reconstructed by digitizing a regional map for the Barents Sea (Marello et al., 2013). Another input is the paleo

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ACCEPTED MANUSCRIPT coastline for the Cretaceous. Here, it is assumed that the coastline at present-day position and an emerged Loppa High (e.g., Indrevær et al., 2017), created a narrow Cretaceous Hammerfest Basin. The PWD model was built on a grid of 672x526 cells with lateral resolution of 100 m and vertical discretisation of 10 layers. The organic model consists of 348.800 cells in the gridding of 67x52 cells

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with lateral resolution of 1000 m and vertical discretization of 100 layers.

Figure 7: Calibration results of the PWD reconstruction. a) During a first calibration run a large increment of possible PWD and scale changes were used to test the sensitivity of the model. This relationship shows the misfit for different incrementally changed PWD along one profile. Scaling is here not included. b) Error matrix of the first run including depth and scale changes. c) Second calibration run using a narrow increment of possible PWD changes. Inset shows the results for the top of the Kolje Fm. along a cross-section in the northern part of the Hammerfest Basin. Note that changing the slope also influences the depth changes. d) Error matrix of the second run giving relative similar results for the best-fit and mean PWD. The maximum misfit value is 2.

4. Results

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ACCEPTED MANUSCRIPT Here we show first the results of the PWD reconstruction and then the TOC distribution for the different organic facies models. The mean, maximum (mean + SD) and minimum (mean - SD) PWD reconstructions for the top and the base of the Kolje Fm. served as an input in the organic facies modelling.

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4.1 Paleo-bathymetries Two calibration runs based on the sand-fractions of 18 wells are used to calibrate the mean PWD. In the first simulation run the sensitivity of the model was tested by simulating100 water depth changes incremented by 50 m. Thereby, 50 scale changes by multiplying the grid with factors varying from 0.1

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to 2 are allowed (Fig. 7a, b). The best-fit reconstruction indicates a water depth 50 m deeper than the initial reconstruction and scaled by a factor of 0.1 (Fig. 7a, b). During the second run 50 water depth

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changes (increment by 10 m) and 10 scale changes (factor from 0.5-1.5) are tested. The best-fit PWD reconstruction was achieved by adding 70 m and scaling the initial reconstruction by a factor of 0.5. Compared to the initial reconstruction the weighted mean PWD (best 5%) is 45 m deeper and scaled by a factor of 0.59 (Fig. 7c, d). This reconstruction with its uncertainty (Fig. 8a, b) is further used in

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the study and described below.

The top of the Kolje Fm. has a mean PWD of 219 ± 46 m with a smooth bathymetry. In the SE part the water depth ranges between ca. 150 to 200 m and the bathymetry is gently increasing to ca. 250-300 m

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in the NW part. The maximum water depth of ca. 405 m occurs in the westernmost area in the Ringvassøy-Loppa fault complex (Figs. 1, 8a). The model uncertainties for the top of the Kolje Fm.

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vary between 28 m and 270 m with the deepest PWD associated with the highest uncertainty (Fig. 8a). The base of the Kolje Fm. revealed a mean PWD of 150 ± 84 m with maximum water depth of ca. 490 m in the NW part of the working area. The minimum water depth of ca. 10-40 m follows the strike of the basin in the central part. The uncertainties range from ca. 28 m to 68 m with highest uncertainty associated to deepest PWD estimates (Fig. 8b). In general, during the deposition of the Kolje Fm. the average PWD reconstructions suggest shelfal to upper bathyal bathymetries with deepest PWD within the Ringvassøy-Loppa fault complex (Figs. 1,

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ACCEPTED MANUSCRIPT 8). In the models the paleo-bathymetry reconstructions strongly relate to the distribution of grain sizes

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which was used for the calibration.

Figure 8: The large maps show the mean PWD of the best fitting 5% after calibration for the top (a) and the base of the Kolje Fm. (b). The histograms display the depth distribution of the mean PWD and the small maps give the uncertainties related to the mean defining the maximum and minimum PWD used as input in the organic facies model. The sand-fractions from 18 wells are used for the calibration.

4.2 Total organic carbon The average TOC values for Model A (mean PWD) vary between 1.86 and 2.68 wt% with a mean value of 2.16 wt% (Fig. 9f, Tab. 3). The TOC is fairly homogenous distributed in the basin. Model C

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ACCEPTED MANUSCRIPT (max PWD) occurs in a similar distribution pattern but TOC values are higher ranging between 2.08 and 2.81 wt% with a mean of 2.39 wt% (Fig. 9i, Tab. 3). A more complicated, patchy distribution pattern gives Model B (min PWD). The average TOC values vary between 0.47 and 5.24 wt% with a mean value of 2.01 wt% (Fig. 9c). For some well locations and depths TOC is not modelled (Fig. 10

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not defined e.g., in wells 7120/9-1 and 7121/7-1) because the reconstructed minimum PWD at the base of the Kolje Fm. is close to zero or on land (Tab. 3). This causes a patchy distribution pattern in the center of the Hammerfest Basin (Fig. 8b) where areas with high average TOC values (up to 5.2 wt%)

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are directly located beside areas with low average TOC values (0.48 wt%).

By comparing the average TOC values of models A, B and C (Tab. 3) the influence of PWD

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reconstruction on the different TOC models varies from 7 to 19 %.

Figure 9: Average sand-fraction, primary productivity and TOC distribution maps and differential TOC maps for a, b c) Model B (min PWD); d, e, f Model A (mean PWD) and g, h, i) for Model C (max PWD).

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ACCEPTED MANUSCRIPT Model A Mean 219 405 135 149 490 7 2.16 2.68 1.86

Model B Model C Mean - SD Mean + SD 120 318 288 676 5 186 118 180 423 558 -26 40 2.01 2.39 5.24 2.81 0.47 2.08

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PWD reconstruction Average PWD top (m) Maximum PWD top (m) Minimum PWD top (m) Average PWD base (m) Maximum PWD base (m) Minimum PWD base (m) Average TOC (wt%) Average Max TOC (wt%) Average Min TOC (wt%)

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Table 3: Summary of the main results. Negative PWD values are given for models above sea-level. The TOC values are averaged for the whole working area and all sub-layers. The average values are the result of 100 modelled values. Maximum TOC values from a single sub-layer can exceed the average values given in this table. SD: standard deviation.

5. Discussion

5.1 Limits and implications of the modelling approach

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The introduced stochastic PWD reconstruction approach is restricted to a siliciclastic dominated depositional environment in a sedimentary basin formed during extensional tectonics. Several simplifications in the modelling procedure affect the results of the initial deterministic PWD model: (i)

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Airy isostasy operates throughout the simulation; (ii) decompaction accounts only for mechanical compaction; (iii) the accuracy of the model and calibration depends largely on data availability. In the presented approach Airy isostasy is used, whereby compensation is calculated locally,

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(i)

e.g., vertically at every grid point. Compared to a flexural isostasy model, Airy isostasy overestimates the degree of isostatic rebound and neglects any flexural compensation. As a consequence the locations of maximum subsidence might differ and a flexural bulge is neglected. However, in order to generate a meaningful flexural model a good knowledge about the effective elastic thickness (Te) of the lithosphere, and flexural compensation along major faults is necessary. For the Barents Sea Te estimates range between <5 km and 50 km depending on location, time and geological setting (e.g., Rasmussen and Fjeldskaar, 1996; Breivik et al., 1999; Dörr et al., 2013; Gac et al., 2016) and present day Te in the Hammerfest Basin is estimated to be between ca. 40-20 km

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ACCEPTED MANUSCRIPT (Gac et al., 2016). If constant Te through time is assumed this would cause an overestimate of isostatic response and thus too shallow PWDs. However, in general flexural strength during extension is typically low (e.g., Fowler and McKenzie, 1989; Watts and Steward, 1998) and in a complex marine basin Airy isostasy may give reasonable results (Allen and Allen, 2013).

affected by mass loading and unloading have to be taken into account. (ii)

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Furthermore, for a consistent 3D flexural isostatic model of the Hammerfest Basin all adjacent areas

Physico-chemical reactions can reduce the amount of pore space by producing cement

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between the grains. This process can reduce compactibility to zero. In a siliciclastic dominated setting, the most important process is quartz cementation during burial (Walderhaug et al., 2001).

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Quartz cementation is mainly a temperature related reaction that occurs normally above 70-80 °C (Walderhaug et al., 2001). The stratigraphic units under consideration are at present day depths of ca. 300 to 6300 m. Assuming a geothermal gradient of ca. 31-38 °C/km (Smelror et al., 2009), rocks are at temperatures between 10 oC and 240 oC, and most of the stratigraphy was in the temperature range prone

to

quartz

cementation.

If

quartz

cementation

occurred,

this

can

bias

our

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compaction/decompaction calculation. In the extreme case, quartz cementation fills all the pore space and the compactibility of a startigraphy would be zero. Our decompaction model would give too thick decompacted units and therefore to deep PWD estimates. The misfit depends on timing and

(iii)

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degree of quartz cementation.

The presented workflow neglects any effects of erosion, although published values range from

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0.5-1.5 km for the Cenozoic in the Hammerfest Basin (e.g., Green and Duddy, 2010; Ktenas et al., 2017; Zieba et al., 2015). Incorporating erosion would affect the results by changing the isostasy estimates by assuming different porosity trends. However, because erosion estimates are relatively constant over the entire study area, the effects on the initial PWD surface including erosion are predictable. The entire PWD surface will be slightly shallower and steeper, but the general topographic trend will not change, e.g., local highs and lows will remain. within the later PWD reconstruction workflow the initial PWD estimates will be shifted and scaled (Fig. 7) and estimates including or neglecting erosion, fall within the tested ranges.

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ACCEPTED MANUSCRIPT The authors emphasize that all results represent hypothetical modelled PWD and TOC distributions based on the given assumptions for critical parameters entering the simulations. The cumulative effect of all unknowns is difficult to asses and will vary case by case. Uncertainties relate in part to timing (e.g., erosion, quartz cementation), magnitude or degree (all discussed assumptions) and both. By

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applying the calibration step with testing different increments in water depth and scales it is assumed to reconstruct a representative PWD which captures all water depth related uncertainties and processes (including eustatic sea-level variations).

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For the TOC distribution modelling we used an process based foreward model to obtain the best fit solution for the whole working area. The modelling results depend on the quantity and quality of the

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input data and are highly uncertain. Thus, many varying models might fit available data or any conceptual model. The results presented here might not match every single measurement from well data but rather represent three possible 3D realizations.

5.2.2 Paleo-bathymetry

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5.2 Model verification, comparison with published data

The Norwegian petroleum directorate classifies the early Barremian to early Aptian depositional

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system of the Kolje Fm. as distal open marine (Dalland et al., 1998) but quantitative estimates are not available. That applies for most studies elaborating the Cretaceous paleo environment in the

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Hammerfest Basin area. For example, deep shelf conditions are reconstructed for the Valanginian stage (Dypvik et al., 2010). For the Turonian to Maastrichtian a marine, predominantly bathyal environment is assumed based on sediment distribution (Mørk et al., 1999) and an outer shelf – upper bathyal environment indicated by foraminiferal assemblages (Setoyama et al., 2011). These general trends are comparable to the reconstructed quantitative results indicating a PWD deepening trend from the east towards the west of the Hammerfest Basin. However, a direct comparison is not possible because explicit water depths are not provided. Only in figure 12 of Setoyama et al. (2011) a

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ACCEPTED MANUSCRIPT conceptual model places the Late Cretaceous environment at a water depth between ca. 150(?)-500 m

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comparable to the presented results with average water depths of 120 m to 318 m (Tab. 3).

Figure 10: Well logs showing a comparison of measured TOC data with modelled TOC values for the different PWD reconstructions. In general, the PWD becomes deeper towards the top of the Kolje Fm. For most wells the three different PWD reconstructions end in the same facies and thus TOC values are very similar. Only for wells 7120/9-1 and 7121/7-1 the minimum PWD/TOC model gives zero values relating to a PWD reconstruction above sea-level. Root mean-square (RMSE) error's are given for the deviation between the modelled and measured TOC values (grey dots). Abbreviations: Hek: Hekkingen Fm., Kolm: Kolmule Fm.

5.2.3 Total organic carbon Globally, Cretaceous source rocks are important contributors to hydrocarbon charge but apparently not the Kolje Fm. in this part of the Barents Sea. These globally important deposits are typically

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ACCEPTED MANUSCRIPT associated with anoxia, and therefore marine organic material. The presented models indicate also large amounts of terrigenous organic matter, highlighting the atypical organic depositional model in this area. The models result in average TOC values varying between ca. 0.47 and 5.2 wt% (Tab. 3) with highest modelled values of up to 8 wt% (Figs. 9 and 10). For Model A and C all TOC values are

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in the range of an average shale source rocks with TOC of ca. 2.2 wt% (Chinn, 1991) and measured data TOC (mostly 1-3 wt%) from Kolje Fm. wells in the western Barents Sea (summarized from factpages at npd.no). In the same range are values from the nearest well with published TOC between 1.1 and 3.8 wt% in the Norkapp Basin (Bugge et al., 2002). Also, claystones of the Kolje Fm. from the

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Troms III area (SW of the Hammerfest Basin) contain 0.9 to 5.5 wt% TOC (Smelror et al., 2001).

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Higher TOC values of 3 to 12 wt% are reported from the Norwegian petroleum directorate for the Kolje Fm. type well (7122/2-1) which located on the northern periphery of the Hammerfest Basin outside our working area (gis.npd.no/factmaps/html_21). Our Model B shows the highest average TOC values (5.24 wt%) at a location where PWD is close to sea-level. Individual TOC values for sublayer in our models (comparable to a single TOC measurement at a certain depth) can reach 8 wt%

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(Fig. 10). However, in general the models indicate that high TOC values observed in the type well are

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not typical for the Hammerfest Basin.

5.3 PWD relationship with organic matter distribution

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The effect of water depth and specifically sea level has been recognised as an import factor attributing rich source rocks to sea level high stand (e.g., Tissot, 1979). Several conceptual models describe the relationship between sea level and organic matter distribution, e.g., Langrock et al. (2003) suggest that Early Cretaceous sea-level variation determine organic matter distribution in the near-shore parts of the Barents Sea. Also, 3D modelling studies emphasize the importance of basin geometries on the distribution of organic-rich sediments demonstrated for the Early Jurassic marine organic matter in the Lusitanian Basin, Portugal (Bruneau et al., 2018). However, these studies are mainly descriptive. Here, it is demonstrated more rigorously how the paleo-bathymetry can influence the TOC distribution in a

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ACCEPTED MANUSCRIPT basin and the complexity of the interaction between PWD and TOC through a variety of secondary processes is shown. Such a complex model is based on assumptions, e.g., the organic model assumes oxic preservation conditions. The authors emphasize that in the OF-Mod software PWD has no significant effect on the TOC distribution if anoxic preservation conditions prevailed during deposition

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of the sediments. The Kolje Fm. well record gives no clear indications for preservation conditions. The formation was deposited under open marine conditions partly with good water circulation (factpages/stratigraphy/lithostratigraphy/formations/Kolje Fm at npd.no). But also, restricted environments with anoxic perseveration conditions are indicated by pyrite occurrence. Furthermore,

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the reconstructed PWD for the top Kolje Fm. falls into the range of present day oxygen minimum zones mapped typically between 200 and 700 m (e.g., Levin, 2003). However, the relatively low

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maximum TOC values in the study area (Fig. 10) compared to localities in northern Europe with proven anoxic condition where organic carbon levels locally reach values up to 20 wt % (summarized in Jenkyns, 2010) might support our assumption of oxic preservation conditions with decreasing carbon flux with increasing depth of deposition (Fig. 5). The more sophisticated 3D models show that

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carbon flux in the water column is not the only critical parameter indicating a complex relationship between PWD and TOC distribution in the Hammerfest Basin (Fig. 11). Using the modelling data the PWD can be separated into three different zones (Fig. 11) based on the

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dominating processes:

PWD zone 1 relates to shallow water depth and it is defined by large spread in all modelled parameters

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(Fig. 11, Model B). Highly variable TOC and HI values are related to the drastic changes in the depositional environment. Parts of the model will emerge above sea level which effects the modelled grain size and primary productivity values (Fig. 9 a, b). These coarse, proximal deposits will be dominated by Cterr and thus have low TOC and intermediate HI values. To the contrary, more distal but still shallow deposits will be dominated by Cmar and can have high TOC and HI values (Fig. 11, Model B). The visual similarity between the plots of sand fraction and TOC in this area emphasises the role of grain size in controlling the source rock properties in this zone (Fig. 11).

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ACCEPTED MANUSCRIPT PWD zone 2 is at intermediate water depth and defined by a decrease in modelled grain size (Fig. 11, Model B). This zone has continually increasing TOC values, which is caused by increased preservation conditions due to smaller sediment grain sizes. The HI values are caused by the interaction between Cmar and Cres. The initial increase in HI is due to PWD coming below the wave

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base, and thereby increasing preservation of Cmar in the energetically quiet environment. With increasing PWD after a certain depth a balance is achieved between two opposite processes, the increasing preservation due to grain size is compensated by the decreased carbon-flux. This causes stable HI values for the lower part of this zone.

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PWD zone 3 is defined by a slowing of the reduction of grain size and decreasing HI at deep water depth. In this zone also, a shift in the TOC trend is observed (Fig. 11, Models A and C). These deep-

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water deposits are dominated by low Cmar due to lower PP and high degradation when sinking. The relative amount of Cres in the organic matter increases, causing a decrease of the HI values (Fig. 11 Models A and C). All models show no relationship between PWD and PP indicated by the low values

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for the Pearson correlation coefficient (Fig. 11).

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Figure 11: Cross plots showing the relationships between average PWD vs. average sand-fraction,

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primary productivity, HI and TOC for the three models. PCC: Pearson correlation coefficient.

Overpredicting the PWD (Model C compared with Model A) did not change the general TOC distribution pattern (Figs 8a, c, e) but results in the highest average TOC values (Tab. 3). A more obvious influence has an underpredicted PWD (Model B compared with Model A) (Fig. 12). Parts of the basin give PWD values close or above sea-level (Tab. 3) resulting in very high or no organic input (Figs. 9c and 10 wells 7120/9-1 and 7121/7-1), e.g. lenses of extreme low and high TOC values are located close to each other (Fig. 9c). Thus, in general underestimated shallow PWD reconstructions

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ACCEPTED MANUSCRIPT might cause significantly wrong TOC distribution models. This is especially true if the unit of interest is partly eroded. Erosion reduces the original sediment thickness and backstripping would give a too shallow PWD. The Hekkingen Fm. (Fig. 3) in the Hammerfest Basin is such an example where a deterministic backstripped PWD reconstruction might cause severely wrong organic facies distribution

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models. The results also indicate that PWD uncertainties propagate into the TOC distribution models. This is best illustrated in the wells of the Kolje Fm. (Fig. 10). Most wells (except 7120/9-1 and 7122/-1) show

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the highest spread in TOC values in the upper part (top Kolje Fm.) associated with the highest PWD uncertainties (Fig. 10). This spread decreases downhole to a minimum in the lower part (base Kole

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Fm.) correlating with the lowest PWD uncertainties (Fig. 10). Furthermore, the basin wide TOC distribution suggests that the highest spread in modelled values occurs in areas with highest PWD uncertainties (Fig. 12). However, error progradation is not trivial, as it does not follow a linear trend and depends on model assumptions as indicated by data from wells 7120/9-1 and 7122/-1. Also, lateral distribution values might not follow the general trend, e.g., in the southern part of the working area

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where PWD uncertainties are low but TOC spread high (Fig. 12).

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ACCEPTED MANUSCRIPT Figure 12: Maps showing the difference in average TOC between a) Model A and Model B; b) Model A and C; c) Model B and C. The black and grey dashed lines frame the areas with the highest uncertainties in the PWD reconstructions for the top and base of the Kolje Fm.

6. Conclusions

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This study demonstrates the importance of a probabilistic PWD reconstruction for modelling the TOC distribution in the Late Cretaceous Hammerfest Basin. The new PWD reconstruction approach allows to quantify upper bathyal to shelfal paleo-bathymetries in the basin. Using different PWD estimates as

- modelled TOC values vary between 0.47 and 5.24 wt%

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input into an organic facies model shows:

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- PWD can cause significant vertical and lateral variations in TOC distribution - PWD uncertainties propagate non-linear into organic facies models

In general, the study illustrates specific sensitivity for shallow PWD, e.g., mall perturbations in the shallow PWD model lead to substantial changes in source rock properties. We predict that especially

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in these areas interpretation and mapping of source rock potential can be problematic. The presented examples indicate, that although a large uncertainty in PWD is related to an increased uncertainty in the TOC models it is not possible to relate the two uncertainties a priori. The results of the study

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illustrate that a comprehensive numerical modelling work-flow is necessary to allow source rock

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quality forecasting in a sedimentary basin.

Acknowledgements

We thank Statoil ASA for providing the interpreted seismic horizons and fruitful discussions with U. Mann, J. Zweigel and J.I. Haugeland during the project "A new tool to reconstruct and calibrate paleowater depth (PWD)". Comments by anonymous reviewers and the editor B. Katz helped to improve the quality of this paper

Appendix: A1) Paleo-bathymetry calculations

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ACCEPTED MANUSCRIPT The initial estimate of the PWD assumes that no tectonic movement occurs, and all vertical movement is caused by (de-)compaction and isostasy. At first, we fill the sedimentary unit bounded by a top and bottom layer with homogeneous lithologies (hA). Then we calculate the isostatic response (hM) relative to the depth of the top layer. The isostatic response of the formations below the layer of interest is calculated using Airy isostasy. This assumes that the weight of any material added or removed from the top of the sediment column (wA) will be replaced by mantle material (wM). The weight of the removed layer A and the replaced mantle volume are calculated using densities for sediments, mantle material and water (ρA, ρM, ρW): w A = ρ A h A (1 − φ ) dx 2 + h Aφ A ρ w dx 2

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(A1)

wM = ρ M hM dx 2

for a regular grid cell with lateral dimension dx. We used densities of 3300 kg/m3 for the mantle, 2650 kg/m3 for sandstone, 2000 kg/m3 for shale and 1030 kg/m3 for sea water.

ρ A (1 − φA )hA + hAφA ρW ρM

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hM =

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With wA consisting of two terms, the weight of the sediments and the weight of the pore water in porosity (φA). Assuming wA is replaced by wM: (A2)

For the calculation of compaction and decompaction thicknesses we consider a sedimentary unit at a present depth of y 1 (top) and y 2 (bottom). This unit should move to shallower depths y1′ and y2′ . For calculating the new depths, we keep the mass constant, and consider volumetric changes. The total volume of the sediment layer (VT) is the volume due to the pore-filling water (VW) and the volume of the sediment grains (VS):

The pore volume is:

VW = ∫φ d y

φ

is the porosity.

(A3)

(A4)

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where

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VT = VW + VS

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Applying decompaction the sediment matrix volume remains the same, only the pore-volume is expanding. This leaves us with the conservation equation:

VS = VS′

(A5)

Considering a unit in a depth profile we get from equation A5: y 2′

y2

y1′

y1

( y2′ − y1′ ) − ∫ φ d y = ( y2 − y1 ) − ∫ φ d y

(A6)

By solving equation A6 for y2' we get the new decompacted thickness. We have included an Athy type porosity model similar to Sclater and Christie (1980) using initial surface porosities of 0.49 for sandstone and 0.63 for shale:

φ = φ 0 ⋅ e − c ⋅y

(A7)

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ACCEPTED MANUSCRIPT where φ0 is the porosity at the surface and c is the inverse rate of porosity change with depth. A compaction exponent of 0.00027 for sandstone and 0.00051 for shale was applied. The water volume is given using equation A4: y2

∫φ ⋅e 0

y1

− c⋅ y

dy=

φ0 c

⋅ ( e−c⋅ y1 − e−c⋅ y2 )

(A8)

(

φ A = y1′ + y2 − y1 + 0 ⋅ e − c⋅ y2 − e − c⋅ y1 + e − c ⋅ y1′ c

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Collecting the constant terms of equation A6:

)

(A9)

we get

φ y2′ = A − 0 ⋅ e − c ⋅ y2′ c

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(A10)

This equation is solved using numerical methods (e.g., Newthon-Raphson).

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The first step in finding the surface elevation of the backstripping approach (Allen and Allen, 2013) is to find the thickness of the decompacted layer (D) due to removal the layer(s) above (A) using equations described above. The metamorphic basement is assumed to be unaffected by compression. Assuming Airy isostasy, mantle material is added to the column at the base (hM) equal to the weight of A (equations A1, A2) and the water depth of the previous backstripping step (W) the PWD after removal of A can be found by the following equation:

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PW D = W + A − D − hM

(A11)

The PWDs of two layers defining the upper and lower part of a stratigraphy are then used to build a probabilistic sedimentary model between these PWDs. This model is based on fuzzy logic using following exemplary definitions (Fig. A1): depths = [0 0 10 60; 10 60 80 240; 80 240 280 1200 ; 280 1200 10000 10000]

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depthNames = { 'veryShallow' ; 'shallow' ; 'deep' ; 'veryDeep' }

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distances = [0 0 0.3 2.2; 0.3 2.2 2.8 14; 2.8 14 18 70; 18 70 10000 10000] distanceNames = { 'veryNear' ; 'near' ; 'far' ; 'veryFar' }

slopes = [ 0 0 0.5 1 ; 0.5 1 90 90] slopeNames = { 'flat' ; 'steep' }

facies = [ 1 1 0; 2 0 0; 3 0 1; 4 0 1 ;3 0 2] faciesNames = { 'beach' ; 'innerShelf' ; 'continentalShelf' ; 'abyssalPlane' ; 'continentalSlope' } faciesSF = [0.7 0.3 0.2 0.1 0.05 ]

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Thereby depth values separated by a semicolon are associated with the depth names. Accordingly, the distances (to shore) slopes (in degree) and facies. Facies are designated by which parameter class they fall in, e.g., beach is [1 1 0], so veryNear, veryShallow and steep or flat (0 flags a no criteria). For every facies then a sand-fraction is associated, e.g., beach 0.7. SF: sand-fraction. The initial fuzzy logic system is calibrated manually by iterative visual inspections and adjustment of model/well-data fitting.

Figure A1: Summarized fuzzy logic assumptions to calculate the sand-fraction distribution in the Hammerfest Basin. For example, a beach facies is described by using fuzzy logic values from water depth (Fuzzy logic 2) and distance to shore (Fuzzy logic 3) characterised by very shallow (values 0, 10, 60) and very near (values 0, 0.3, 2.2). This beach facies is then associated with a certain sandfraction (SF Early Cretaceous).

n

∑ RMSE

w

nw

2

(A 12) (A 13)

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Em =

−Vsf′ )

sf

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RMSEw =

∑(V

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From this sedimentary model a sand-fraction (V'sf) for every location in the basin can be calculated and used for a calibration against measured sand-fractions from well data (Vsf). The misfit between the well data and model can be calculated for every well location (eq. A12) or cumulative (eq. A13). The misfit is used as a quality criteria for the modelled paleo-bathymetries.

A2) Organic model calculations The software OF-Mod considers three organic-matter source types, marine (Cmar), terrestrial (Cterr), and residual organic matter (Cres), in which every source type has different deposition setting and preservation condition. In general, autochthonous produced Cmar may experience degradation during settling in the water-column and the uppermost sediment layer. The measured Cmar fraction that reaches the sediment surface is carbon flux (CF) which corresponds to the primary productivity (PP) and water-depth (WD) (Betzer et al., 1984).

0.409 ⋅ PP1.41 CF = WD0.628

(A14)

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ACCEPTED MANUSCRIPT OF-Mod calculates the PP distribution as a function of distance to shore and geological evidences (e.g., the input of PP can be modified through time).

log10 BE =

1.39log10 SR + 0.34 log10 ( SR + 7.9)

Carbon accumulation rate (CAR) in oxic conditions is calculated using:

(A 15)

(A 16)

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CAR = CF ⋅ BE

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Another factor that influences the Cmar preservation is an increase of oxygen-exposure time and burial efficiency (Mann and Zweigel, 2009). Burial efficiency (BE) and sedimentation rate (SR) will determine the fraction of Cmar that is preserved within the sediment (Betts and Holland, 1991):

WCorg +Winorg

=

Cmar + Cterr + Cres Cmar + Cterr + Cres + DBD ⋅ SR

HImarxmar + HIterrxterr + HIresxres TOC

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HI =

WCorg

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TOC =

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The distribution of Cterr is highly associated with sand-fraction in which higher sand fraction relates to more Cterr, as described by Huc (1988) for the Black Sea. However, it is not necessary that pure sand will always have high Cterr due to winnowing of the lower density of organic particles in highly hydrodynamic regimes (Mann and Zweigel, 2009). Cres follows a different trend from Cterr as Cres will be highest with low SF (de Jager et al., 2015). Cres is mainly sourced from the degradation of organic matter in the sink. The main output of organic facies modelling is the TOC and HI distribution. TOC is calculated by the fraction of the total organic matter (WCorg in total weight from both WCorg and inorganic matter weight (WCinorg). WCorg consists of Cmar, Cterr, and Cres (gC/m2/a), while WCinorg is computed based on SR and the sediment dry bulk density (DBD). (A17)

(A18)

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The distribution of TOC and HI are computed in the OF-Mod and validation of the results is done by comparing the model with the back-calculated TOC and HI values from the well data.

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