**3. Methodology**

In order to model the thermal evolution of the Nordkapp Basin, we considered two processes: (1) the evolving basin geometry, and (2) the evolution of thermal boundary conditions, i.e., basal heat flow and sediment-water interface temperatures. The evolving basin geometry was reconstructed from structural restoration of two sections, one across the central sub-basin (section A) and another across the eastern sub-basin (section B) (Figure 2). Section A has deeply rooted, narrow and closely spaced diapirs (Figure 2A), whereas section B contains a shallower rooted, wider, isolated diapir (Figure 2B). Before the restoration process, the sections were depth-converted using the velocity model from Rojo et al. [18], which uses interval velocities and k factors (change in interval velocities vs depth) from wells 7228/9-1, 7228/7-1, 7125/1-1, 7124/3-1, and 7229/11-1 (Figure 3).

Details of the restoration are described in Rojo et al. [18]. In short, kinematic restorations were performed using the *Move* software (Midland Valley). These restorations account for uplift and erosion in the Late Cenozoic, restore the Cenozoic and pre-diapir units using flexural slip, restore the syn-diapir units using vertical shear, and assume flexural isostasy with a lithospheric elastic thickness of 20 km [41].

Thermal modeling of selected restoration stages (paleo-geometries) was performed using the *PetroMod* software (Schlumberger). Each stage was imported into the software, and polygons representing each seismic unit (Figure 2B,D) were digitized. At each stage, the lower boundary condition of the thermal model is the heat flow at the basement-sediment interface. The evolution of this basal heat flow through time was reconstructed from the present thermal gradient of the basin from nearby wells, the history of rifting and evolution of the stretching (β) factor [42], and inverse modeling using a modified McKenzie model [43]. The upper boundary condition of the thermal model is the sediment-water interface temperature (SWIT). This surface temperature was reconstructed from the paleo-latitude of the basin and water depths over time. The following section describes the input paleo-geometries, thermal boundary conditions, and model parameters in detail.

**Figure 2.** (**A**) Uninterpreted seismic section A across the central sub-basin. The central seismic panel is from a higher-resolution, full azimuth seismic data provided by WesternGeco Multiclient. (**B**) Interpreted section A. The base salt was estimated based on parallel seismic sections that extend to 7000 ms. (**C**) Uninterpreted seismic section B across the eastern sub-basin. (**D**) Interpreted section B. Legend shows the interpreted seismic units (Figure 1C). See Figure 1B for location of these sections. Figures modified from Rojo et al. [18].

**Figure 3.** (**A**) Plot showing calculated interval velocities vs depth from wells 7228/9-1, 7228/7-1A, 7125/1-1, 7124/3-1, 7229/11-1. (**B**) Seismic section B showing the location of the main velocity transitions. (**C**) Seismic section B displaying the interval velocities used to depth convert the seismic profile (modified from Rojo et al. [18]).

### **4. Paleo-Geometries, Boundary Conditions, and Model Parameters**
