4.4.2. Temperature Model

The temperature calculations are done by a finite di fference scheme. The grid resolution is very high around magmatic sills and in areas of irregular structures. Fjeldskaar et al. [7] showed that the numerical temperature results for magmatic sills match the analytical solutions quite well, both spatially and temporally. On this basis, we argue that the uncertainty of the conduction-temperature calculations is of minor importance.

In our model we assume that the sills cool by conduction, but it is possible that the process could be accelerated by convection. Water convecting in the vicinity of sill intrusions could significantly modify the temperature and maturity e ffect of intrusions. Convection of hot fluids from the magma, the host-rock water, and decomposition products of kerogen is dependent on the permeability of porous host rocks or hydrofracturing in less porous host rocks (cf., [60,61,82–84]. How the fluids from magma and host rock a ffect the fluid pressure and flow is determined by the host-rock porosity, permeability, and amount of fluids present [85]. Wang and Manga [83] showed that for rocks with low permeability (<10 mD) symmetrical contact aureoles are produced, implying that conduction is the favorable cooling method for sills and host rocks after emplacement. On the other hand, rocks of high permeability (>50 mD) show maturation asymmetry above the sill, implying occurrence of convection-influenced maturation [83]. Annen [84] studied the maximum temperatures of three rocks of di fferent water saturations: dry, hydrated and total water saturated, and found that in close proximity to an intrusion (~10 m) there were no di fferences in the temperatures, whereas at a distance of 50 m there was a ~50 ◦C maximum temperature di fference. Dry rock has the highest temperature and water saturated rock the lowest. This means that convection of water lowered the temperature by ~50 ◦C. It was concluded that di ffusivity contrasts between magma and host rock and incremental sill emplacement had more e ffect on the aureole thickness than host-rock water content [84]. For the present study this implies that for highly porous and permeable lithologies (e.g., sandstone) the predicted time for cooling might be overestimated. However, for less porous and permeable lithologies (e.g., shale) the estimated cooling rates would be adequate. This was also shown by temperature and maturity modeling on data from offshore Norway [7].

Another aspect of convection, is the possible increased permeability that occurs when sills are emplaced. Sill emplacement may potentially induce stresses high enough on the surrounding host rocks to reactivate or produce new shear fractures or open up tensile fractures (e.g., [86,87]), allowing for increased permeability and possibly increased convection. However, accumulation of stresses and reactivation and/or production of faults and fractures are highly area specific and dependent on, e.g., the lithology, deformation features and existing weakness zones. Although increased convection due to emplacement of sills have been identified on seismic images (e.g., [67]) it is too area specific to be included in a study aiming for some general conclusions.

Radioactive decay within the sedimentary section itself can generate heat, but is not accounted for in this study. Rybach [88] found, however, that the contribution of radioactivity in the sedimentary section was generally no more than a few percent of the overall heat budget, which support that the errors by not accounting for radioactive heat, is insignificant. Others have concluded for the opposite and advocate for including radiogenic heat production in the thermal history modeling (e.g., [89,90]), but also emphasize the large area-variations in radiogenic heat production for the same lithologies [90].

Frictional heating from fault displacement may potentially have implications for the thermal history in a basin. ter Voorde and Bertotti [29] calculated for shear stress of 100 MPa and an extension rate of 2 mm·year<sup>−</sup><sup>1</sup> that the thermal contribution from frictional heat would be 2.5 ◦C. They concluded that this could not influence the thermal situation in the basin to a significant degree. However, with higher extensional rates and larger shear stress the frictional heating may become important.
