**1. Introduction**

It is commonly accepted that major changes in Earth's climate started in Gelasian (~2.6 million years ago), and initiated the growth of ice sheets in the Northern Hemisphere (e.g., [1]). Over the last 2.6 million years, there have probably been more than 30 glaciations with cycles of ice sheets advancing and retreating on time scales of 40,000 to 100,000 years. A glaciation cycle of 40,000 years dominated in the early period, while the 100,000 year cycle has dominated in the past million years or so [2]. The most extensive glaciations are traditionally referenced in the last million years (Late Quaternary; cf. [3]) and the covers on North America and Europe have been estimated to be around 2–4 km thick near the centers of maximum ice accumulation (cf. e.g., [4]), and tapered towards the ice sheet margins. Repeated episodes of growth and withdrawal of huge ice sheets, glacial erosion, and associated sediment deposition lead to geologically dramatic changes in surface loading. The lithosphere responds to these changes by subsiding under loading, and by uplifting when loading is removed. The driving mechanism for this is isostasy.

Di fferential vertical movement of the lithosphere related to glacial isostasy lead to repeated tilting of sedimentary formations and potential petroleum reservoirs therein, which may have greatly a ffected hydrocarbon migration pathways in the former glaciated areas [5]. In addition, the upward and downward bending of the lithosphere due to glaciation leads to flexural stresses [6] likely to a ffect faults and their permeability, which could add to the changes in hydrocarbon migration pathways.

In parts of the Barents Sea, there are clear indications of hydrocarbon spillage (e.g., [7]). Some of the hydrocarbon spillage is linked to isostatic movements due to cycles of Pliocene-Pleistocene ice sheet loading/unloading and glacial sediment redistribution [8–12]. It is suggested that the recent discovery of the giant Johan Sverdrup oil field in the Norwegian North Sea was oil charged during Quaternary, and that the area more than likely underwent tilting and possible leakage several times over the last one million years [13]. Other research, related to the North Sea, showed that influence of ice sheet loading does not result in a significant tilting [14], which may be the result of smaller gradients of the ice thickness. Anyway, detailed control on the glacial isostasy is important and so far an insu fficiently utilized factor for identification of the remaining hydrocarbon resources in sedimentary basins formerly covered by ice sheets.

Faulting related to the last glaciation is reported from northern Scandinavia, where several fault with up to 30 m high fault scarps [15]. Examples include the 80 km long Stuoragurra fault in northern Norway [16] and the 150 km long Pärvie fault in northern Sweden [17]. There is also evidence of such faults in Denmark [18], Germany, Poland, and the United Kingdom ([19–23]). Thus, such faults are found in the center of former ice sheets, as well as at their margins and beyond [24,25].

For the o ffshore areas, the situation is more complicated. However, the number of seismic events recorded in the Barents Sea in the last 20 years is significant ([26,27]). For the Barents Sea, the impact of the glacial isostasy on triggering earthquakes has not ye<sup>t</sup> been investigated. A better understanding of the origin of the seismicity will help to recognize which faults and related areas exhibit a risk of leakage of hydrocarbons from traps.

Stress changes induced by glaciations are related to two main e ffects: 1) direct load introduced by the weight of the ice on the surface and 2) flexural load caused by the subsidence and uplift of the lithosphere due to glacial isostasy [10,28]. Horizontal stress due to stress migration, which is depending on loading time and mantle viscosity, is an additional e ffect that is modeled by Ste ffen et al. [29]. Grollimund and Zoback [30] investigated, by a 2D approach, lithospheric flexure as an alternative mechanism to explain the local stress perturbations observed in the northern North Sea. They found that flexural stresses due to glaciations/deglaciation could explain the observed lateral stress variations.

Johnston [31] used the Mohr–Coulomb theory for the study of faulting and explained the lack of seismic activity in areas of large continental ice sheets. Turpeinen [32] use finite-element models of rheologically layered lithosphere with a thrust fault to investigate its slip evolution during the glacial/ postglacial period. Their modelling results sugges<sup>t</sup> that the rate of thrusting decreases during ice sheet loading and strongly increases during deglaciation. Ste ffen et al. [33] introduced a new approach that is based on a Glacial Isostatic Adjustment (GIA) model. They combined the GIA model with a fault surface to investigate the fault slip and fault activation time during a glacial cycle. Their model allows estimation of the fault throw for former glaciated areas. One of their conclusions is that faults start to move close to the end of deglaciation.

Our approach is flexural isostasy modelling, and we are dealing with two e ffects of the glaciations which we believe future basin modelling has to consider:

