3.1.3. Fault Angle

The previous results show that the largest thermal differences between steady state and transient temperatures are found in the hanging wall part of the basin. For all the tested fault angles the results are broadly similar, but the temperature effect will change with the fault angle. As the fault angle is changed, so is the affected area of the hanging wall. With a steeper fault angle a smaller part of the basin experiences the largest thermal instabilities (Figure 9a). The opposite is the case for lower fault angles, a larger part of the basin will then experience higher thermal instabilities before the basin regain steady state (Figure 9b). Five different fault angles have been tested (Figure 9a,b). All scenarios show temperature differences up to 45 ◦C between transient and steady state models. Around 10 Myr after fault slip all scenarios regain steady state temperatures.

**Figure 9.** Temperature difference between steady state and transient model 10 kyr after fault slip for the steepest (**a**) and the least steep (**b**) studied listric fault.

### 3.1.4. Thermal Conductivity and Specific Heat Capacity

The thermal conductivity (W·m<sup>−</sup>1·K−1) of a lithology relates to the rock's ability to transfer heat. Rocks with low thermal conductivity result in warm basins, while high thermal conductivity rocks give colder basins. A lithology's specific heat capacity (J·kg−1·K−1) is the physical property crucial for the time frame needed to transfer heat through the stratum and thus for the time needed for basins to regain steady state after sediment deposition or erosion. So far the section has been modeled as all shale with properties as listed in Table 2. Commonly, basins consist of altering layers of different lithology types, often shale and sandstone. Therefore, the following four scenarios have been compared: all shale, all sandstone, all shale with one sandstone layer, and all sandstone with one shale layer.

Thermal conductivities and specific heat capacities of shale and sandstone show a large variation (e.g., values in Table 2). The default values are given in Table 2 and to illustrate the span of values within the same lithology segment, we refer to Cerm ˇ ác and Rybach [38]. Their minimum and maximum specific heat capacities and the average and maximum thermal conductivities of sandstone and shale are used in this study (Table 2). In order to determine the thermal conductivity values based on the rock's porosity, the mixing law arithmetic mean model [66] has been used:

$$k = \Phi \cdot k\_f + (1 - \Phi)k\_{s\_f} \tag{1}$$

where the thermal conductivity (*k*) is obtained on the basis of the rock porosity (Φ*)* by combining the thermal conductivity of rock matrix (*ks*) with that of the pore fluid (*kf*).

Generally, sandstones have higher thermal conductivities than shales, resulting in colder basins where they are abundant. The results from the homogeneous basins, either all shale or sandstone, coincide with this, showing high temperatures in the basin when the thermal conductivity is low, and lower temperatures when the thermal conductivities are high. A comparison between two basins with the same fixed specific heat capacity, but with one basin modeled with average shale conductivity, to another basin modeled with default shale conductivity, shows up to 140 ◦C difference between the two models shortly after fault slip (Figure 10a). With fixed specific heat and changing conductivity the results show that the basin needs longer time to regain steady state in basins with low thermal conductivity values due to the higher temperatures obtained in these basins (Figure 10b). This applies for both scenarios with all shale and all sandstone of varying thermal conductivity. Steady state is regained from 3–22 Myr after fault slip and the quickest scenario to regain steady state is the sandstone basin with maximum thermal conductivity.

**Figure 10.** (**a**) Thermal difference between transient temperatures of basin (10 kyr after fault slip) modeled with average conductivity to basin modeled with default conductivity. (**b**) Point plot results from location of point given in Figure 8b, showing the steady state and transient temperatures for the three tested conductivities for shale and sandstone. Conductivity values given in Table 2.

In the case where the thermal conductivity is fixed and the specific heat capacities are changed in the different modeling scenarios (Table 2, lower part), the steady state temperatures for all the scenarios are, as expected, the same (Figure 11). However, with increasing specific heat, the time needed for the basin to obtain steady state increases (Figure 11). This is especially visible in the point plot for sandstone basin in Figure 11, because of large difference in the published heat capacity values of sandstone, but the effect is also visible for the shale basin. For all tested scenarios steady state is obtained between 8–18 Myr after fault slip.

**Figure 11.** Resulting temperatures for the three tested specific heat capacities for shale and sandstone. Location of studied point indicated in Figure 8b. Heat capacity values given in Table 2.

To accommodate the fact that basins commonly consists of different lithologies, the polygon with syn- and post-rift deposits have been changed in the following simulation (Figure 12a). The thermal conductivity is fixed with values as for the default shale or sandstone (Table 2). However, the specific heat capacity is changed using default, minimum, and maximum values for the sandstone and shale (Table 2). With the presence of a sandstone layer in an otherwise shale basin, the results show that the temperatures in the basin increases. For the opposite case, a layer of shale in an otherwise sandstone basin, the temperatures in the basin decreases (Figure 12b).

**Figure 12.** (**a**) Shale and sandstone basins with sandstone layer and shale layer respectively. The red point indicates location for point plot in (**b**). (**b**) Results show the temperatures for the three tested heat capacities for shale basin with one sandstone layer and sandstone basin with one shale layer. For comparison, temperatures for homogeneous basin are also plotted. For heat capacity values see Table 2.

The variation of specific heat capacity in a homogeneous basin resulted in quite a time gap (8–18 Myr) for the sandstone basin to regain steady state (Figure 11). However, the shale basin required less time to arrive at steady state for the tested specific heat capacities (8–10 Myr). For homogeneous basins, shale or sandstone, steady state was regained around 10 Myr after fault slip (Figure 12b). The presence of another lithology influences the basin temperatures and thus the time needed for the basins to regain steady state. For a shale basin with a sandstone layer, steady state was obtained around 13 Myr after fault slip for all the specific heat capacities. Sandstone basin with a shale layer regains steady state around 6 Myr after fault slip regardless of the specific heat capacities (Figure 12b). These results are related to the porosities at the depth at which the di fferent lithology layers are modeled and the contrasting thermal conductivity for shale and sandstone.
