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Structural and stratigraphic basin modelling has been used to examine quantitatively the Cretaceous and Tertiary post-rift subsidence history of the northern North Sea Basin following Late Jurassic extension. 2D forward and reverse, syn-rift and post-rift modelling has been used to determine the magnitude and timing of departures from the McKenzie post-rift thermal subsidence trend for regional stratigraphic profiles in the Outer Moray Firth, the South Viking Graben and the North Viking Graben. Observed stratigraphy has been reverse post-rift modelled using flexural backstripping combined with decompaction and reverse thermal subsidence calculations, and forward modelled through the syn-rift and post-rift period using the flexural cantilever model of continental rift basin formation. Long-term global eustasy has been included in the analysis. Only reliable palaeobathymetric markers, such as erosion surfaces and coals, have been used to constrain subsidence history. Both forward and reverse 2D modelling show that a Palaeocene regional uplift followed by a rapid Eocene subsidence must be superimposed on McKenzie post-rift Cretaceous and Tertiary basement subsidence in order to generate the stratigraphy observed. The magnitude of Palaeocene uplift deduced from modelling was of the order of 375 m in the Outer Moray Firth (central North Sea) increasing to 525 m in the North Viking Graben (northern North Sea). Rapid Early Eocene subsidence was of the order of 160–310 m. The most likely mechanism for regional Palaeocene uplift and rapid Eocene subsidence in the northern North Sea was the Palaeocene development of the Iceland plume situated at a distance of 700–900 km from the study area in the Early Tertiary. Forward and reverse modelling predict axial bathymetries in the graben of up to 1300 m for the Early Cretaceous and 900 m for the Upper Cretaceous. The large palaeobathymetries at the end of the Cretaceous provided much of the accommodation space for Tertiary sedimentation.

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The Paleogene stratigraphy in the Outer Moray Firth is part of the North Sea post-rift sedimentary sequence that was deposited in a thermally subsiding basin following Late Jurassic rifting. Previous studies have drawn attention to anomalous uplift and departure from the McKenzie (1978, Earth Planetary Science Letters , 40 , 25–32) post-rift subsidence trend in the early Paleocene followed by an accelerated phase of basin subsidence in the early Eocene before returning to the normal post-rift subsidence. 2D forward and reverse stratigraphic modelling incorporating first-order global sea-level variations have been used to determine the timing and magnitude of departures from McKenzie post-rift thermal subsidence in the early Paleogene for the Outer Moray Firth. Reverse post-rift modelling, consisting of flexural backstripping, decompaction and reverse thermal subsidence, has been used to produce restored post-rift sections from present-day stratigraphy, which have been constrained by palaeobathymetric data. Forward syn-rift and post-rift structural and stratigraphic modelling uses the flexural cantilever model of rift basin formation and has been constrained by syn-rift structural data, present-day stratigraphy and palaeobathymetric markers. Forward and reverse modelling show that observed Cretaceous and Tertiary stratigraphy of the Outer Moray Firth was generated by the combined effects of inherited Late Jurassic syn-rift accommodation space, post-Jurassic rift thermal subsidence, sediment supply, long-term eustasy and an additional transient uplift event in the Paleocene. The much thicker Tertiary compared with Cretaceous can be explained by sediment infilling of starved Cretaceous palaeobathymetry. Reverse and forward post-rift modelling predict regional Paleocene uplift in the Outer Moray Firth of the order of 375–390 m (375 m reverse modelling, 390 m forward modelling), followed by c. 160 m of rapid Eocene subsidence, both superimposed on post-rift thermal subsidence following Late Jurassic rifting. Regional Paleocene uplift in the Outer Moray Firth is attributed to dynamic uplift associated with the development of the Iceland plume.

Forward and reverse 2D flexural modelling of syn-rift and post-rift stratigraphy, has been used to investigate departures from McKenzie post-rift subsidence for the Cretaceous-Tertiary following Late Jurassic rifting in the northern North Sea Basin. The analysis shows uplift in the Palaeocene of 375–525 m relative to calibrated McKenzie subsidence curves, followed by a rapid decrease in uplift in the Early Eocene of 160–310 m. Both Palaeocene uplift and Eocene subsidence increase northwards. The timing, distribution and magnitude of regional Palaeocene uplift is consistent with an origin relating to the development of a mantle plume between 65 and 55 Ma. Transient regional Palaeocene uplift in the northern North Sea Basin was produced by long wavelength dynamic uplift generated by the flow field of a mantle plume. Heating of the asthenosphere or lithosphere beneath the North Sea by hot plume material, or magmatic underplating are not believed to have contributed to Palaeocene uplift in the northern North Sea Basin. Rapid Early Eocene subsidence was generated by a decrease in dynamic uplift caused by a reduction in plume activity. The plume responsible for North Sea Palaeocene uplift may have been the early Iceland plume or a distinct British Tertiary Igneous Province plume related to the same mantle convection event.