*4.2. Thermal Boundary Conditions*

Thermal boundary conditions determine the primary energetic inputs to reproduce the temperature history of the basin and, consequently, for the maturation of source rocks. As mentioned above, the sediment-water interface temperature (SWIT) represents the upper boundary condition whereas the basal heat flow represents the lower boundary condition. These parameters were constrained to ensure that the modeled thermal field best-fits temperature data in the basin.

For the SWIT, we used the automatic SWIT tool in PetroMod, which extracts a standard temperature at sea level over geological time based on the basin's present-day geographic location and paleo-latitude (Figure 5A). A transformation that corrects the surface temperature against the paleo-water depth was applied and the SWIT estimated. The latitudinal position assigned to the Nordkapp basin was 72◦N, and paleo-water depths (Figure 4B) were taken from [18].

**Figure 5.** Modeled (**A**) sediment-water interface temperature (SWIT), (**B**) water depth, (**C**) lithospheric thickness, and (**D**) basal heat flow through time in the Nordkapp Basin. Yellow rectangles show the three rifting periods. Dots in D are the selected restoration stages in Figure 4.

The basal heat flow was calculated by reconstructing the lithospheric thickness from the Late Carboniferous to the present (Figure 5C). In order to do this, we adopted mean values for the stretching factor (β) of each rift phase (Figure 5, yellow rectangles): Late Carboniferous (320–305 Ma, β = 1.6), Late Permian (270–250 Ma, β = 1.25), and Late Jurassic–Early Cretaceous (165–145 Ma, β = 1.15), as proposed by [42]. The Post-Caledonian lithosphere and crustal thicknesses were defined at the rift initiation. An initial lithospheric thickness of 120 km and an initial crustal thickness of 35 km (17.5 km upper crust, 17.5 km lower crust) were adopted from Clark et al. (2014). The present-day crustal thickness is 18 km (16 km upper crust, 2 km lower crust) as documented by [41,42,44]. The temperature at the lithosphere-asthenosphere boundary was set to 1300 ◦C and the mantle heat flow to 30 mW/m2. Figure 5C,D depict the modeled lithospheric thickness and basal heat flow through time, respectively.

A good fit between measured and calculated temperature values of five exploration wells (7228/7-1B, 7228/7-1S, 7228/2-1S, 7228/7-1A, 7228/2-1S) and three shallow wells in the Nordkapp Basin (7227/11-U-02, 7227/07-U-01, 7230/08-U-01) was achieved using estimated basal heat flow values of ~45 mW/m<sup>2</sup> (Figure 6A). Extrapolating the thermal model calculated in the western sub-basin to the entire Nordkapp Basin is unrealistic due to possible variations in the initial thickness of the Post-Caledonian crust and lithosphere [42], and the magnitude of rifting across the basin. Nevertheless, we chose to do so it in order keep the model as simple as possible and to avoid biasing the model with poorly-constrained inputs. In addition, the effects of episodic glacial loading-unloading and erosion during the Late Cenozoic documented by several authors [45–49] are not considered in the model.

Unlike temperature, vitrinite reflectance data display higher maturities than the calculated trend (Figure 6B). Vitrinite measurements from wells 7228/7-1A and 7228/7-1S in the central part of the basin plot closer to the calculated trend than corresponding values from well 7228/2-1S in the northern rim of the basin (Figure 6B, see Figure 1B for well locations). This most likely reflects different amounts of erosion at different locations in the basin. Well 7228/2-1 S shows a characteristic pattern of increasing thermal maturity with stratigraphic age from Cenozoic to Middle Triassic (Figure 6B). However, at ~3600 m depth, a sudden increase in vitrinite values is observed near the top of the Lower Triassic Havert Formation. Here, the well values define a steeper vitrinite trend, implying higher temperature gradient. Igneous activity could explain this higher thermal gradient, but there is no evidence of such activity. The modeled paleo-heat flow (Figure 5D) depicts higher flow rates (~54 mW/m2) during and immediately after the Late Permian rifting, which seem to be a plausible explanation to the higher thermal gradient. Thus, the modeled heat flow (Figure 5D) is a reasonable scenario for the Nordkapp Basin, and together with the SWIT (Figure 5A), it defines the boundary conditions for the thermal model. Transient heat-flow conditions were assumed at all times.

**Figure 6.** (**A**) Bottom hole temperature measurements of wells 7228/7-1B (black), 7227/11-U-02 (orange), 7227/07-U-01 (light blue), 7230/08-U-01 (light green), 7228/7-1S (red), 7228/2-1S (purple), 7228/7-1A (dark blue), and 7228/2-1S (dark green). Line shows the modeled, present temperature versus depth trend. (**B**) Vitrinite reflectance data from wells 7228/7-1S (red), 7228/7-1A (blue), and 7228/2-1S (green). Line shows the modeled vitrinite reflectance. Figure 1B shows the location of the wells.
