The Gjallar Ridge is an area of complex geology situated in the west of the Vøring

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1 6 Fjeldskaar, W., H. Johansen, T. A. Dodd, and M. Thompson, 2003, Temperature and maturity effects of magmatic underplating in the Gjallar Ridge, Norwegian Sea, in S. Düppenbecker and R. Marzi, eds., Multidimensional basin modeling, AAPG/Datapages Discovery Series No. 7, p Temperature and Maturity Effects of Magmatic Underplating in the Gjallar Ridge, Norwegian Sea W. Fjeldskaar RF-Rogaland Research, Stavanger, Norway H. Johansen 1 Geologica AS, Stavanger, Norway T. A. Dodd 2 BP Norge UA, Forus, Norway M. Thompson 3 BP Norge UA, Forus, Norway ABSTRACT The Gjallar Ridge is an area of complex geology situated in the west of the Vøring Basin. Regional structural work in the area suggests multiple phases of rifting during basin development. Seismic refraction data indicate the existence of a low-velocity layer, which can be interpreted as magmatic underplating. The aim of this study was to evaluate the effects of a possible magmatic underplating over the Gjallar Ridge. More precisely, we have estimated the temperature effects and the isostatic effects associated with the emplacement of a lower-density 5-km-thick magmatic body at a depth of km. To model the basin evolution, a series of stretching events was assumed: the opening of the basin during the Permian-Triassic, an event in the Middle Jurassic to Early Cretaceous, an event during the Middle to Late Cretaceous, and an event in the Paleocene. Models were run with and without underplating by a magmatic body emplaced during the early Tertiary. The effect of underplating has dramatic consequences on the interpretation of the early Tertiary stretching event. In the model with no underplating, low stretching ( = ) is required to match subsidence. If underplating is considered, increased stretching is required, with factors up to 1.5. The magmatic underplating has two main effects. One is a short-lived (less then 5 m.y.) increase in heat flow by 100 mw/m 2 related to dissipation of heat. The other is 1 Present address: Verico, Stavanger, Norway. 2 Present address: BP Exploration plc, Houston, Texas, U.S.A. 3 Present address: BP Exploration Operating Company Ltd., Middlesex, UK. 71

2 72 / Fjeldskaar et al. a longer-term effect associated with increased early Tertiary stretching. The combined effects result in an increased temperature of 408C for the Upper Jurassic source rock interval over the Gjallar Ridge. Maturity effects of the magmatic underplating are significant, particularly because the heat pulse gives a kick in the generation 5 10 m.y. earlier, which could be important for oil and gas available to traps formed in Late Cretaceous Paleocene. Models were calibrated to the observed present-day crustal thicknesses derived from seismic refraction profiles. The model with underplating calibrates best to these data. INTRODUCTION The Vøring Basin is a large sedimentary basin province with grabens, subbasins, and structural highs. The basin is terminated to the west by the Vøring Escarpment (see Figure 1), the eastern boundary of the Vøring Marginal High. The formation of this high, during early Tertiary breakup, was associated with massive extrusive and intrusive magmatic activity (Skogseid, 1994). Sills and dykes are mostly observed as intrusives in Mesozoic sediments over a wide area ( km) landward of the continentocean boundary. A lower crustal velocity body has been mapped at the base of the crust beneath the outer margin, a body that is regarded as a magmatic underplating, a part of the total amount of melt generated across the rift during breakup (Skogseid, 1994). This chapter reports a quantification of the effect of magmatic underplating on the paleotemperature regime in the Gjallar Ridge, mid-norway. Magmatic underplating is important because of the potential of affecting the thermal regime of the sedimentary basin. The most obvious effect is increased heat flow associated with the injection of molten rock. The underplating will, however, also affect the basin subsidence and thereby the reconstructed paleoheat flow of the basin by causing regional uplift by decreasing the density of basement materials. The purpose of this study is to analyze and model basin dynamics and factors controlling basin formation and paleotemperature regime. The study has focused on the deep structure of the Vøring Basin and the implications for the temperature regime and maturation history, in case the observed low-velocity layer on seismic refraction data really is a magmatic underplating. BASIN DEVELOPMENT Figure 1. Map showing location of modeled cross section (solid line = offshore mid-norway). The black areas show early Tertiary igneous rocks and dark-shaded areas show sill and flow complexes (from Skogseid et al., 1992a). The seismic section that was modeled is based on deep seismic refraction data interpreted by Skogseid et al. (1992b). The section runs from the middle of the Vigrid Syncline to the eastern edge of the Vøring Escarpment. The geologic section used for the BMT 2 (Tectonic Modelling of Basins, from RF-Rogaland Research; see Lander et al., 1994) modeling also includes

3 Temperature and Maturity Effects of Magmatic Underplating / 73 the crustal structure over the Gjallar Ridge (Figure 2). Figure 2 shows the following: A postulated underplated magmatic body at depth of km, extending from the Vøring Escarpment to the axis of the Vigrid Syncline, is present. Seismic refraction data show low velocities and densities in this anomalous zone. The magmatic body is postulated to have been emplaced during the Paleocene, based on the age of the basalts drilled on the Vøring Marginal High (Skogseid et al., 1992a). Marked topography on the top of this lowvelocity layer is present. Extensive Late Cretaceous to early Tertiary faulting over the Gjallar Ridge is present. The cross section was reconstructed through geologic time by decompaction of sediments (backstripping) and restoration of faults. The structural restoration was conducted using simple vertical shear for the normal fault segments. Additional information on BMT s technique for automatic restoration of faults is given in Lander et al. (1994). Important input data defining the reconstructed geologic section included (1) porosity-depth trends for each lithology for use in sediment decompaction, (2) definition of paleowater depths, and (3) definition of the magnitude and distribution of any erosional event. Lithology properties are presented in Table 1. Porosity-depth Porosity-depth functions (Sclater and Christie, 1980) affect modeling results in three ways. (1) They affect reconstructed thicknesses, which in turn affect the reconstructed geometry of the cross section. (2) They affect reconstructed temperatures by changing thermal conductivity values and burial depths. (3) They affect isostatic subsidence simulations because they are linked to the modeled sedimentary load through time. The porosity-depth parameters used in this study are shown in Table 1. Erosion The crests of several tilted fault blocks caused by Late Cretaceous to Paleocene extensional faulting have been eroded during the Paleocene. The erosion surfaces are relatively planar, suggesting exposure above sea level and the subsequent development of wave-cut platforms. This erosional event is assumed to be limited to the crests of the fault blocks and not to be regional in extent. The maximum erosion is, accordingly, assumed to be only some several hundreds of meters (see Figure 3). Paleowater depths Paleowater depths affect model results in three ways: (1) they affect the geometric reconstruction of the cross section, (2) they affect the modeled isostasy resulting from the load of water, and (3) they affect the observed tectonic subsidence associated with rifting events. Figure 2. Cross section of present-day geology showing faults, depositional surfaces, underplated body, and assumed crustal thickness (partly based on Skogseid et al., 1992a). Mdst = mudstone.

4 74 / Fjeldskaar et al. Table 1. Lithologic parameters used in the modeling. Units Late Tertiary Oligocene Eocene Paleocene Late Cretaceous Early Cretaceous Jurassic Permian-Triassic Basement Asthenosphere Age Porosity-depth trends Conductivity (kv) Heat capacity surface porosity exp. constant kg/m3 Porosity 0.13 Porosity 0.5 J/kg K Paleowater depth profiles for the reconstructed time steps are based on backstripping studies and on the sequence-stratigraphic interpretation of depositional patterns in the cross section. Representative curves of the paleowater depths through time for the cross section are shown in Figure 4. The plot shows several notable features. Density The water depth during the Paleocene is close to zero over the Gjallar Ridge. Deep marine condi- tions are modeled to the east of Gjallar Ridge (in the Vigrid Syncline). The paleowater depths are increasing from the Eocene to the present day. The paleowater depths in pre-tertiary times are uncertain. Based on data on the porosity-depth relations, paleowater depth, and erosion, the basin development was reconstructed. An example of one reconstructed time slice (Paleocene) is given in Figure 3. The resulting movement of the top of the basement is termed total observed subsidence. In the following subsidence analysis, the total observed subsidence will be the basis for defining the isostatic and tectonic subsidence, and thus for estimating the magnitude of stretching over the profile. SUBSIDENCE ANALYSIS Figure 3. Reconstructed snapshot showing the distribution of eroded intervals associated with erosional events in Paleocene time. Subsidence analysis provides the basis for understanding the controls on the depositional, erosional, and structural evolution of the area as well as for quantifying heat-flow variations through time. BMT provides forward models of both isostatic and tectonic subsidence that can be used to generate overall subsidence models for the modeled cross section. These

5 Temperature and Maturity Effects of Magmatic Underplating / 75 forward subsidence simulations are constrained to match the subsidence history generated from the geohistory reconstruction discussed above. Isostatic Subsidence The isostatic subsidence was calculated using the Airy approximation where the subsidence is related only to buoyancy effects. Thus, lithospheric elastic properties are not taken into account in the calculations. Lithospheric properties could have important consequences in the modeling because the elastic lithospheric thickness affects the 2-D isostatic response of the lithosphere to loading and unloading (Fjeldskaar et al., 1993). Therefore, there is a theoretical possibility that the stretching factors are underestimated. However, because of relatively uniform sedimentation rates across the profile, the effect is assumed to be small in this study. The density of the rock intervals must be defined to calculate the total load of sediments used as input for the isostatic model. The values used for the units (given in Table 1) are partly based on standard values (Sclater and Christie, 1980). The values for the thermal conductivity (for 13% and 50% porosity, respectively) are based on in-house measurements from the area. Tectonic Subsidence Tectonic subsidence is modeled with standard McKenzie (1978) extension, where crustal extension is equal to subcrustal extension and based on Airy isostasy. The magnitude of the stretching was determined empirically by matching the combined subsidence resulting from the isostatic and tectonic modeling with the observed subsidence derived from the geohistory reconstruction (Figure 5). The section shows extensive Late Cretaceous to Paleocene extensional faulting. This is the precursor to the eventual separation of Norway from North America/ Greenland and ocean floor spreading during the earliest Eocene. The thermal subsidence associated with these extensional events results in the subsidence pattern observed, with the development of a deep water-starved basin throughout the Tertiary. Stretching Factors To obtain a good correspondence between the observed subsidence and that calculated in the isostatic and tectonic modeling, we defined four rifting episodes based on a regional geologic interpretation (Bjørnseth et al., 1997): Figure 4. Assumed paleowater depth change over the profile in (a) Tertiary and (b) pre-tertiary time. a uniform Permian-Triassic stretching event responsible for the opening of the basin. This is highly speculative due to poor seismic imaging at depth. a Middle Jurassic to Early Cretaceous stretching event. This is also speculative due to poor

6 76 / Fjeldskaar et al. Figure 5. Example of observed and theoretical (isostatic and tectonic) subsidence over the Gjallar Ridge. seismic and stratigraphic resolution in the pre- Cretaceous section. One rifting episode is used for the Middle to Late Jurassic and latest Jurassic to earliest Cretaceous rifting episodes. a stretching event in the Middle to Late Cretaceous. This can be inferred from seismic and stratigraphic evidence in the Vøring Basin. It models rifting during the early Cenomanian to late Campanian. a Paleocene rifting episode. This affected the entire North Atlantic margin. These episodes were modeled as single events at 290, 140, 95, and 65 Ma. The stretching factors tuned to give a fit were = for the Permian-Triassic stretching event and = for the Middle Jurassic to Early Cretaceous stretching event, with stretching factors for the Middle to Late Cretaceous event varying from 1.0 in the west up to 1.5 in the easternmost part of the section, and Paleocene stretching factors of 1.1 with an increase up to 1.4 toward the east (Figure 6). In the calculations so far, we have neglected the possible magmatic underplating in the area. With the basis above, we will study in the following the effects of magmatic underplating on the temperature regime and hydrocarbon maturation. MAGMATIC UNDERPLATING Skogseid et al. (1992a) have been able to construct a model of the magmatic features in the Vøring Basin based on velocity-depth curves from seismic refraction andgravitydata.alargemagmatic body is interpreted to be underplating the continent-ocean transition region (Figure 2). The underplated body is assumed to have been emplaced at 65 Ma (which is the Paleocene horizon) at 13008C. Emplacement of a less dense underplated body will result in uplift, as previously mentioned. Present-day water depth in the VøringBasinisontheorderof 1400 m over the section with 1 2 km of postuplift sediments deposited from Eocene to the present day. It thus seems to be the extension in early Tertiary time that increased the water depth. Extensional faulting of this age over the Gjallar ridge and the presence of ocean floor spreading from the earliest Eocene in the area to the west support this. The underplating is treated in BMT as an instantaneous intrusion of hot material. The additional heat flow associated with underplating is related to two factors: the implied Paleocene rifting needed to overcome the uplift effects of the intrusive magmatic body, and the additional heat caused by the hot mass intruded into the earth s crust (see next section). Thermal Model Overview The temperature calculation is divided into two steps. (1) The paleoheat flow below the sedimentary cover is calculated based on stretching events and magmatic underplating. (2) The paleotemperature regime of the sediments is calculated using the calculated paleoheat flow as the lower-boundary condition. The upper-boundary condition is the sediment-water temperature. In both steps, a 2-D transient finitedifference model is used (see Appendix A). Step 1 uses a rather low-resolution grid whereas step 2 uses a high-resolution grid. The Underplating Model In modeling, it is assumed that the entire magmatic body (Figure 2) is intruded at 65 Ma. The geometries of the magmatic bodies are defined in the present-day geometry of the modeled cross section. The input parameters for the magmatic body are given in Table 2. The thermal development in the subsurface down to the asthenosphere is calculated using a 2-D transient

7 Temperature and Maturity Effects of Magmatic Underplating / 77 Figure 6. Magnitude of crustal and subcrustal stretching used to achieve correspondence between the subsidence history implied by the geohistory reconstruction and the forward models of isostatic and tectonic subsidence. finite-difference model (see Appendix A). The width of the modeling domain is defined by the length of the cross section, and the depth is defined by the lithospheric thickness (depth to 13008C isotherm) and the paleothickness of the sedimentary cover. The modeling domain is divided into three major units, the sediments, the crust, and the subcrust (see Figure 7). The lateral grid resolution (number of columns) is 18 for all three regions. The vertical grid resolution (number of rows) differs among the regions. The sediments (approximately 16 km thick) have a vertical grid resolution of 40 rows, the crust (initially 37 km thick) has a vertical grid resolution of 80 rows, and the subcrust (23 km thick) has a vertical grid resolution of 40 rows. This grid resolution is sufficient for taking the geometry and temperature of the magmatic body into account and for calculating the paleoheat flow. The upper- and lower-boundary conditions are specified as surface temperature and asthenospheric temperature, respectively. No flow conditions are defined on the lateral (left and right) boundaries. The vertical heat flow is calculated along a horizontal line 100 m below the bottom of the basin at each time step (see Figure 7). In this case, the heat flow is calculated at a depth approximately 16 km below sea level for present day. The vertical paleoheat flow is found by using the calculated geothermal gradient and the thermal conductivity in the finite-difference grid at the heatflow calculation depth shown in Figure 7. Both crustal-subcrustal extension and intrusion of magmatic bodies cause a change of the thermal regime of the crust and subcrust instantaneously. A stretching event will increase the temperature gradient compared with the prestretching temperature gradient. This will result in an increased heat flow into the base of the sedimentary cover. After a stretching event, the temperature and heat flow will gradually decrease toward thermal equilibrium. Because of the insulation effect of sediments, the equilibrium heat flow below the sediments will be lower after sedimentation than before sedimentation. The intrusion of a magmatic body into the earth s crust will also instantaneously change the thermal regime of the crust and subcrust. Once emplaced into the modeling domain, the magmatic body will start to cool off. The mass above and below the magmatic body will experience a heat pulse that results in a short-lived increase of temperature. The heat pulse will, after some time (depending on the depth of the underplating), rise upward to the depth where the paleoheat flow is calculated (see Figure 7), and a short-lived increase in heat flow will be observed. A magmatic intrusion consists of several minerals with different melting-solidification temperatures. Therefore, the solidification of a magmatic melt will take place over a temperature interval, depending on the mineralogical constituents. The model assumes that the latent heat is liberated equally over this meltingsolidification interval. The calculation of the latent heat is implemented as an increased specific heat over the 0 melting-solidification interval given by c p = c p + L/ (T max T min )wherelislatent heat (J/kg), T min is start melting temperature (8C), T max is end melting temperature (8C), and c p is the specific heat. Table 2. Intrusion parameters. Density, u (kg/m 3 ) 2650 Thermal conductivity, k (W/mK) 3.1 Heat capacity, c p ( J/kg K) Latent heat, L ( J/kg) 420,000 Start melting temperature, T min (8C) 800 End melting temperature, T max (8C) 1100 Reference temperature, T ref (8C) 600 Initial temperature, T o (8C) 1300 Expansion coefficient, (10 5 8C 1 ) 3.3

8 78 / Fjeldskaar et al. Figure 7. Sketch of tectonic model finitedifference grid with modeling regions and boundary conditions. The uplift effect of the underplating is also modeled. The uplift (U ) caused by a magmatic body with thickness Z, assuming Airy compensation, is U = Z(1 u / m ), where u is the density of the underplating body and m is the density of the mantle. Both densities are functions of temperature ( = 0 /(1 *(T T ref )), where is the actual density; 0 is the density at T ref, the reference temperature; is the thermal expansion coefficient; and T is the actual temperature). With a density of the underplating body of 2700 kg/m 3 and a density of 3300 kg/m 3 for the mantle, the uplift of top basement will be 20% of the thickness of the underplating. A magmatic underplating with thickness of 5 km thus gives a 1-km uplift of the surface. This uplift will, however, be modified during the cooling of the magma due to thermal contraction. As mentioned earlier, the uplift response will require increased thinning to get a match between observed and theoretical subsidence. The underplated body will, therefore, not only increase heat flow due to its own heat, but also, indirectly, give increased heat flow due to the additional stretching needed to match the geohistory subsidence. Effect on Paleocene Stretching The model with magmatic underplating gives the same stretching factors as the model without underplating, except for the Paleocene event. The Paleocene stretching, however, is significantly affected by the underplating if the theoretical subsidence is to be matched with the observed subsidence. The stretching factors are much higher (average of 1.5) and show a significant increase toward the west (Figure 8). Effect on Paleoheat Flow The present surface heat flow of the area is assumed to be approximately 62 mw/m 2, based on figures from Sundvor and Eldholm (1992). Theoretically, the equilibrium heat flow decreases from a calculated starting value of ca. 80 mw/m 2 in Permian-Triassic to the present-day value of approximately 62 mw/m 2. The general decrease in the equilibrium heat flow (except for periods of extensions) is caused by sedimentation, because of the relatively low thermal conductivities of the sediments compared with the thermal conductivity of the basement. The modeled tectonic crustal thinning gives high heat flow related to the Middle Jurassic to Early Cretaceous rifting both on the Gjallar Ridge and in the Vigrid Syncline. The heat pulse decayed rapidly through the Figure 8. Magnitude of crustal and subcrustal stretching used to achieve correspondence between the subsidence history implied by the geohistory reconstruction and the forward models of isostatic and tectonic subsidence, based on an underplating option.

9 Temperature and Maturity Effects of Magmatic Underplating / 79 Cretaceous. However, this increased heat flow had little or no effect on source rock maturation because of the shallow depth of burial of any Late Jurassic source rocks. Another pulse of high heat flow was associated with middle to Late Cretaceous stretching events. These events, coupled with the rapid sedimentation in the Vigrid Syncline, resulted in rapid temperature increase and maturation of any Late Jurassic source rocks in the deep part of syncline, thus expelling all their oil and gas during these events. The modeled heat flow shows the importance of underplating over the Gjallar Ridge. Figure 9 gives the heat flow for the two main modeling options, with and without underplating, for three locations over the profile. A quantification of the direct heat effect is shown by the heat-flow difference for a cold versus hot intrusion. The cold intrusion model assumes an underplating temperature similar to the surrounding sediments. The hot underplating model assumes an initial underplating temperature of 13008C. The effect is significant, temporarily increasing theheatflowbyca.100mw/m 2. The effect is highest were the magma is thickest and short-lived; it has almost died out after 5 m.y. In the model assuming no underplating, only small amounts of stretching are required for explaining the Figure 9. Theoretical paleoheat flow at a depth of 16 km below surface at different locations over the profile: (a) 22.5, (b) 60, and (c) 97.5 km. The three cases are no underplating (dotted line), cold underplating (stippled line), and underplating and latent heat (solid line). The difference between the stippled line and the solid line gives the direct heating effect of the underplated magmatic body.

10 80 / Fjeldskaar et al. subsidence over the Gjallar Ridge (Figures 9a, b), and therewasconsequentlylittleincreaseinheatflowin the Paleocene. In the underplated model, Paleocene heat flows show a pronounced spike associated with the emplacement of the underplated body, superimposed on a longer-lived thermal event associated with the rifting. No effect is noted in the axis of the Vigrid Syncline (Figure 9c) where the underplating body is modeled as pinched out. The Tertiary heat-flow peak will be significantly different in the two cases, partly because of the more pronounced Tertiary stretching for the underplating option. This model gives a heat-flow peak of more than 200 mw/m 2, a really significant increase from the no underplating option, which peaks at approximately 70 mw/m 2. The effect of the latent heat is mw/m 2 (Figure 10). The two effects of the magmatic underplating in Paleocene time are the direct heating effect, which contributes to a heat-flow effect of up to 100 mw/m 2, and increased crustal thinning, which contributes to a heat-flow effect of up to mw/m 2. Temperature Effects Once the paleoheat flow is calculated, the temperature history of the sediments could be calculated using a high-resolution 2-D transient finite-difference model. In our modeling, a grid resolution of approximately Figure 10. Theoretical paleoheat flow at a depth of 16 km below surface at different locations over the profile: (a) 22.5, (b) 60, and (c) 97.5 km. The two cases are both for underplating option, one with latent heat (dotted line) and the other without latent heat (solid line).

11 Temperature and Maturity Effects of Magmatic Underplating / grid cells (with the highest resolution in geometrically complex areas) is used. The surface temperature (upper-boundary condition) is kept constant at 78C. The thermal properties of the sediments are shown in Table 1. Figure 11 shows the maximum total temperature effect of the underplated body at three time steps, 64.5, 62.5, and 56 Ma. The temperature is calculated for the entire profile, but only the sediment temperature is displayed. Five hundred thousand years after the underplating took place, the temperature at the deepest point of the sediments is raised by ca. 508C (Figure 11a). Maximum temperature difference occurs 3.5 m.y. after the intrusion, the temperature difference at the deepest point is now close to 1008C, and the temperature anomaly reaches closer to the surface (Figure 11b). This is the time close to maximum effect of the hot magma. The increased thinning, however, gives a longer-lasting temperature anomaly, and at 56 Ma (Figure 11c), it is still a pronounced temperature anomaly in the basin, close to 808C at top basement. The temperature effects are also shown for four depths in the pseudowell (for location, see Figure 2). Figure 11. Temperature differences at (a) 64.5, (b) 62.5, and (c) 56 Ma over the profile, between models with and without underplating. The plots show the combined effect of the hot magmatic body and the increased Paleocene thinning.

12 82 / Fjeldskaar et al. The presence of significant faulting over the Gjallar Ridge and the nearby Tertiary oceanic crust implies that Paleocene stretching has been significant. The high stretching factors implied in the underplated models provides a better fit to these observations. Figure 12. Total temperature difference for different depths in a pseudowell (see Figure 2 for location) based on paleoheat flow for options with (solid lines) and without (dotted lines) underplating. The maximum temperature difference at 4-km depth below ocean bottom is ca. 408C (Figure 12). CONCLUSIONS This study has shown that underplating has two important effects: (1) additional heat due to intrusion of a hot body and (2) uplift due to emplacement by a light body, which requires additional stretching to explain the observed basin subsidence. The following conclusions can be drawn from these results: Transformation Ratio The effect on hydrocarbon maturation is demonstrated by the oil and gas ratio, which is the ratio of the organic matter that is transformed to oil and gas, respectively (kerogen parameters are given in Table 3). Both the oil and gas ratio show large differences between the two modeling options, with or without an underplating (Figure 13). The effect is increasing with depth. At 4-km depth in the pseudowell, there is a difference from a ratio of 0.2 to 0.4 in the oil generation at about 50 Ma (Figure 13a). It is a similar difference in the gas ratio; a larger amount of the oil is cracked to gas in the model with underplating (Figure 13b). At some depth, there is also a pronounced difference in the timing; the magmatic underplating gives a kick in the generation 5 10 m.y. earlier than the option without underplating (Figure 13), which could be important for the oil and gas available for trapping formed in Late Cretaceous Paleocene. It could have marked effect on estimations of oil and gas accumulations. Crustal Thinning The estimated present crustal thickness by the cumulative thinning (assuming an original thickness of 37 km) differs between the modeling options (Figure 14). The model without underplating gives a poor fit. There was a significant heat-flow effect associated with the Paleocene stretching, which increased heat flow by mw/m 2. The additional effect of the heat associated with the underplated body itself was short-lived but pronounced, which increased heat flow up to 100 mw/m 2. The combined effect results in an increased temperature of 408C for the Upper Jurassic source rock interval over the Gjallar Ridge. Maturity effects of the magmatic underplating are significant, both for oil and gas generation. The heat pulse caused by the underplating gives a kick in the Table 3. Kinetic parameters. Kerogen to oil and gas: Mean E a (kcal/mol) 54 45* Arrhenius factor * Directly to gas fraction: 0.1 Oil to gas Mean E a (kcal/mol) 55 67* Arrhenius factor * Only for Late Cretaceous *

13 Temperature and Maturity Effects of Magmatic Underplating / 83 Figure 13. Calculated oil (a) and gas (b) ratio for different depths in a pseudowell (see Figure 2 for location) based on paleoheat flow for options with (solid lines) and without (dotted lines) underplating. Figure 14. Observed and predicted present crustal thickness (assuming an initial thickness of 37 km) for the modeling options.

14 84 / Fjeldskaar et al. hydrocarbon generation 5 10 m.y. earlier than without underplating, which could be important for oil and gas available to traps formed in Late Cretaceous Paleocene. We have done sensitivity studies on flexure, paleobathymetry, thickness, and depth to intrusion. The story presented here gives one single solution. However, it shows the most likely difference between the options: underplating and no underplating. ACKNOWLEDGMENTS We thank BP Norge UA for support and permission to present and publish this work. We also thank Tom Pedersen, Rolando Di Primio, and two anonymous referees for constructive comments on an earlier version of this chapter. APPENDIX A TEMPERATURE CALCULATIONS The following equation @z @t ðctþ ða 1Þ where T is the temperature, K h is the horizontal conductivity, K v is the vertical conductivity, and c is the heat capacity. Finite differences and a blockcentered grid are used. In the block with indices (ij), is evaluated by the following formula (Thomas, 1982): K hiþ K h 2ðT iþ1;j T i;j Þ x i þ x i ij ¼ x i K hi 1;j 2 2ðT i;j T i 1;j Þ x i 1 1 þ x i : ða 2Þ K hiþ is the value of K 1;j h at the boundary between the 2 blocks (i,j) and (i +1,j). It is computed as the harmonic mean of K hi,j and K hi+1,j. is treated analogously. This gives M N equations to find the T i,j unknowns, where i = 1,2,..., M and j = 1,2,..., N. Here, M and N are the number of blocks in x and z directions, respectively. We use both Dirichlet and Neumann boundary conditions for the temperature model. For Dirichlet boundary conditions, the temperature (T ) at the boundary is given, whereas for Neumann the heat flux K and is given. A Neumann boundary condition with a heat flux of zero is used for the basin edges. An iterative method is used to solve the linear system. Conjugate gradients are used as an acceleration method (Hageman and Young, 1981; Young and Jea, 1981). The conjugate gradient method is preconditioned by nested factorization (Appleyard and Cheshire, 1983). Nested factorization was originally developed to solve the linear systems that arise in oil reservoir simulation. According to our experience, it performs better on heat conduction problems than on reservoir simulation problems. REFERENCES CITED Appleyard, J. R., and I. M. Cheshire, 1983, Nested factorization: Proceedings of the Seventh Symposium on Reservoir Simulation, Society of Petroleum Engineers of AIME, SPE Paper 12264, p Bjørnseth, H. M., S. Grant, E. K. Hansen, J. R. Hossack, D. G. Roberts, and M. Thompson, 1997, Structural evolution of the Vøring Basin, Norway, during the Late Cretaceous and Paleogene: Journal of the Geological Society of London, v. 154, pt. 3, p Fjeldskaar, W., E. Prestholm, C. Guargena, and N. Gravdal, 1993, Isostatic and tectonic development of the Egersund Basin, in A. G. Doré, J. Augustson, C. Hermanrud, D. J. Stewart, and Ø. Sylta, eds., Basin modelling: Advances and applications: Amsterdam, Elsevier, p Hageman, L. A., and D. M. Young, 1981, Applied iterative methods: New York, Academic Press, 386 p. Lander, R. H., M. Langfeldt, L. Bonnell, and W. Fjeldskaar, 1994, BMT user s guide, version 3.2: Stavanger, RF- Rogaland Research proprietary publication. McKenzie, D., 1978, Some remarks on the development of sedimentary basins: Earth and Planetary Science Letters, v. 40, p Sclater, J. G., and P. A. F. Christie, 1980, Continental stretching: An explanation of the post-mid-cretaceous subsidence of the Central North Sea Basin: Journal of Geophysical Research, v. 85, p Skogseid, J., 1994, Dimensions of the Late Cretaceous Paleocene northeast Atlantic rift derived from Cenozoic subsidence: Tectonophysics, v. 240, no. 1 4, p Skogseid, J., T. Pedersen, O. Eldholm, and V. B. Larsen, 1992a, Tectonism and magmatism during NE Atlantic continental breakup: The Vøring Margin, in B. C. Storey, T. Alabaster, and R. J. Pankhurst, eds., Magmatism and the causes of continental break-up: Geological Society (London) Special Publication 68, p Skogseid, J., T. Pedersen, and V. B. Larsen, 1992b, Vøring Basin: Subsidence and tectonic evolution, in R. M. Larsen, H. Brekke, B. T. Larsen, and E. Talleraaas, eds.,

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