3-D palinspastic restoration of normal faults in the Inner Moray Firth: implications for extensional basin development

Earth and Planetary Science Letters, 75 (1985) 191-203

191

Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands

[2]

3-D Palinspastic restoration of normal faults in the Inner Moray Firth: implications for extensional basin development D a v i d Barr British Geological Survey, 19 Grange Terrace, Edinburgh, EH9 2LF (U.K.) Received December 16, 1984; revised version received June 14, 1985 Balanced cross-section techniques, and the construction of a restored section, permit 2-dimensional palinspastic restorations to be made in both compressional and extensional terraines. In 3 dimensions, an equivalent restoration can be made by assuming conservation of bedding-plane area and considering the volume of a stratigraphic interval rather than its cross-sectional area. Extensional basins displaying upper crustal listric normal faulting are particularly amenable to this approach. Computerised 3-D restorations have been made of the Inner Moray Firth basin, offshore Scotland. This basin is not isostatically compensated, and was produced by 7-8% post-Triassic extension, of which 2.5-3% is post-Jurassic, above a detachment surface at 20-25 k m depth, close to the base of the crust. Limited lower crustal thinning (and lithospheric stretching) has affected the eastern part of the basin, but this can account for no more than half of the measured upper crustal extension. Some of this shallow extension is probably coupled by low-angle faults or shear zones into major zones of lithospheric stretching such as the North Sea grabens, where it may help account for discrepancies between estimates of lithospheric thinning and upper crustal extension.

1. Introduction Balanced cross-section techniques have been widely used as an interpretive tool in areas of compressional tectonics (e.g. [1-4]), and have also been applied to areas of thin-skinned extensional tectonics (e.g. [5,6]). By making certain simplifying assumptions, strains and displacements can be determined and a restored cross-section constructed in which material points have been translated to their pre-deformation positions; by combining several cross-sections, a palinspastic map can be generated which shows the pre-deformation distribution of chosen geological markers (e.g. [1, fig. 15]). A more direct approach is to generate structure contour maps for several subsurface horizons from a set of cross-sections and then to balance and restore each horizon. Such structure contour maps are a basic exploration tool in the hydrocarbons industry and are routinely produced from reflection seismic sections. By restoring a map rather than individual cross-sections, local anomalies or errors in interpretation are minimised, and useful information such as finite strain and depth 0012-821X/85/$03.30

© 1985 Elsevier Science Publishers B.V.

to detachment can still be obtained where the extension direction is not known a n d / o r in cases of non-plane 'strain. Computerised techniques for the construction of such "3-dimensional" palinspastic restorations have been developed within the British Geological Survey [7,8]; this paper describes the results of their application to the Inner Moray Firth basin, offshore Scotland.

2. Geological background The Inner Moray Firth basin lies to the west of the Buchan/Witchground graben, a branch of the main North Sea rift system (Fig. 1). Although complex in detail, it is essentially a NNW-dipping half-graben in which Jurassic and Lower Cretaceous sediments reach a thickness in excess of 3000 m in the vicinity of the Great Glen fault [9] and south of the Smith Bank fault (Fig. 2a). Several hundred metres of Permo-Triassic sediments form a relatively uniform blanket across the basin, and extend beyond its northern and southern boundaries. They rest unconformably on De-

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vonian sediments and Caledonian basement. The basin floor was at or near sea level until the end of the Middle Oxfordian [10]. As in the Witchground graben to the east [6,11], active half-grabening with stratigraphic growth and sediment wedging peaked in the Late Oxfordian to Volgian. There are no indications that footwall blocks within the basin were emergent, although they record relative uplift [12,13], and indeed shallow marine sediments (now eroded) extended beyond the Helmsdale fault onto the mainland and fed deeper-water clastics within the basin [I4]. Most of the minor faults were quiescent during the Lower Cretaceous, but major faults within the basin and at its margins remained acti+e; the marginal faults also show significant post-Upper Cretaceous movement. Following McKenzie's [15] model of lithospheric stretching, the structural history of the main North Sea rifts (Jurassic to Lower Cretaceous fault-bounded subsidence, Upper Cretaceous to Tertiary regional subsidence) has been attributed by a number of authors to initial exten-

sion followed by thermal subsidence [16-18]. The Inner Moray Firth basin shows clear evidence of Jurassic to Lower Cretaceous extension but lacks the thermal subsidence stage, and indeed the westernmost part of the basin underwent post-Lower Cretaceous uplift (probably early Tertiary, in view of the easterly-prograding Palaeocene deltas and submarine fans which are present in the Outer Moray Firth--J19]). Donato and Tully [20] backstripped the gravity effect of known Mesozoic sediments in the North Sea and interpreted a residual positive anomaly as representing Moho topography. They confirmed that the crust is thinner beneath the major grabens and that their sedimentary fill is isostatically compensated. In contrast, most of the Inner Moray Firth lacks a residual positive anomaly. McQuillin et al. [21] used the 0 mgal Bouguer contour to delimit this uncompensated basin (Fig. 2b) and suggested that it was produced by extension parallel to the Great Glen fault, and that the crust was decoupled from the mantle. Tertiary uplift in the west of the basin may reflect an attempt to recover

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tion at the crust/mantle boundary, this column would balance a crust of similar composition but 26-27 km thickness. The Central Highlands column consists entirely of metamorphic basement, while the Inner Moray Firth was the site of major Devonian and Permo-Triassic sedimentation. These sediments may have been isostatically compensated by thin crust, and any remaining discrepancies can perhaps be accounted for by the fact that Smith and Bott made no explicit correction for the extreme basement relief implied in Fig. 2a. In any case, the implication of the gravity modelling is that there was little post-Triassic crustal thinning.

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isostatic equilibrium [13]. Simple 1-D modelling of the new dataset discussed below (Fig. 2b) confirms these earlier gravity interpretations. Note how Upper Cretaceous and Tertiary sediments (representing the thermal subsidence phase) are restricted to the area of thinned crust. In fact, the southwest part of the basin has residual negative anomalies, which derive from buried Caledonian granites [22]. Despite the strong evidence against Mesozoic crustal thinning beneath their seismic refraction line (Fig. 2b), Smith and Bott [23] concluded that the Inner Moray Firth is characterised by thin crust (22-23 km as against 29-30 km on the mainland). Part of this thinning is to be expected. The LISPB onshore refraction profile [24] yielded Moho depths of ca. 32 km in the Central Highlands of Scotland, much of which exceeds 1 km above sea level. Assuming isostatic compensa-

3.1. Structural models It is clear from reflection seismic sections that upper crustal extension has taken place in the Inner Moray Firth, yet gravity and subsidence evidence indicate that the lower part of the lithosphere was not significantly extended. Thus a sub-horizontal d6collement surface must lie within or at the base of the crust. Since the dips of fault planes within the basin can be seen to decrease at moderate depths ( < 10 km), and since the presence of major half-grabens with changes in dip across bounding faults suggests that these faults too are curved, a listric fault model was chosen. Listric normal faults have been mapped seismically in the nearby Witchground graben [6] and west of the British mainland, where they often reactivate older thrusts [25,26]. The N E - S W trend. of the Inner Moray Firth faults suggests that these are Caledonian structures reactivated as obliqueslip faults during Mesozoic extension. In at least one case (the Lossiemouth fault, Fig. 2a), a steep Mesozoic fault associated with (strike-slip) flower structures can be traced downwards into a planar feature which dips at 25-30°SE within the basement--presumably a Caledonian thrust. In order to measure extension across a system of listric normal faults, it is necessary to make some assumptions about the nature of haning-wall deformation. The two simplest models are represented in Fig. 3. Either the hanging-wall is permitted to collapse vertically under gravity, so that beds in the outer arc of the rollover are deformed

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Fig. 4. Schematic plan representation of an areally-extended basin, ofinitial area A and final area A + AA. Model B

Fig. 3. Hanging-wallgeometry of listric normal faults. A line of original length l has been extended to /', above a basal detachment at depth d; the extension e = / ' - / . In Model A, the hanging-wallhas deformed by vertical simple shear, and the fault heave h equals the extension e. In Model B, bed-length is conserved, and h =~e. The difference between the fault heave h and the true extension e is defined as the rollovercorrection, r, and e = / ' - l = / ' - El~. in vertical simple shear (Model A), or all hangingwall deformation is assumed to take place on mappable faults, with conservation of bed-length round the rollover (Model B). The geometry of Model A is implicit in the method used by Gibbs [5] to graphically reconstruct a listric normal fault from the shape of the rollover. Other possible geometries are rejected, either because they cannot maintain compatibility with undeformed basin margins, or because they cannot provide unique estimates of extension or depth to detachment. If the sole fault did not move vertically during extension (a reasonable assumption in an uncompensated basin), depth to detachment can be determined from area-balance constraints [5]. In Fig. 3:

A a=A2=e.d

(1)

Note that where the principal fault plane has a staircase ( r a m p / f l a t ) geometry (e.g. [27, fig 5]), area-balance calculations will in general yield the depth to the deepest flat. Analogous equations can be written for the 3-dimensional case. Fig. 4 is a plan view of an areally-extended basin. Representing the volume of sediments within the basin by V, V=

AA.d

(2)

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(100) 1+~--.z

(3)

where p is percent area change (100.2xA/A), and z the mean depth to the basin floor. Where extension has been measured at two horizons, the extension during that stratigraphic interval can be determined, and depth to detachment obtained from the subsidence z ( = sediment thickness) recorded during that interval: d= (1+ 100).(1+

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p2 )

(4)

Here, p~ is the extension recorded during the stratigraphic interval z, and P2 corrects for subsequent extension which will have thinned the sediment pile. Analogous equations can be written to take account of a component of non-extensional subsidence, either subsequent to or during extension [7].

3.2. Techniques of palinspastic restoration Two structure contour maps of the Inner Moray Firth were restored: near base Jurassic and near base Cretaceous. Full details of the geometric and computational techniques employed are available in B.G.S. open-file reports [7,8]. These maps had been prepared by the author and other B.G.S. geologists during 1980-1982 from a ca. 1 km grid of commercial seismic reflection sections, as part of a programme which provides the U.K. Department of Energy with confidential, independent interpretations of commercial well and seismic

195 data. Permission was obtained from the Department to publish a simplified version of the maps, at the level of detail represented by Fig. 2. In order to make the computer model tractable, and to preserve confidentiality over prospective exploration targets, minor faults were aggregated together and their extension added to that of a nearby major fault. Some editing of the data was carried out at this stage: critical lines were reinterpreted and new, better-quality data incorporated where possible. The maps were digitised and depth-converted on a 5 km grid. As well as grid intersections, fold axes, hanging-wall and footwall cutoffs and other boundaries (e.g. subcrops) were recorded. Palinspastic restoration took place in two stages. Firstly (Model B only), each horizon was restored to the horizontal by performing a "rollover correction". An algorithm was developed to "unroll" bedding while preserving its surface area. Footwall cutoffs were kept fixed in the XY-plane, the net effect being to reduce the width of fault zones. The corrected "fault gap" (Fig. 5) represents true extension, and can be closed up to produce a palinspastic restoration. For Model A, this "rollover correction" was omitted. In plan view, all material points in the hanging-wall of a particular fault were considered to move in a common extension direction (Fig. 5). Variations in extension along a single fault result from variations in the magnitude of hanging-wall displacement. This displacement field corresponds to heterogeneous simple shear within the XY-plane, and conserves bedding-plane area. Each fault was assigned its own extension direction, and where the necessary information was available, faults were restored in reverse order, i.e. beginning with the most recently active. Restoration of all the faults produces a deformed grid which can be compared with the original square grid, a set of deformed basin margins which can be compared with the present basin margins, and a set of faults which now appear as lines with zero extension. These data can also be represented by contour maps showing magnitude and direction of displacement. By statistical comparison of the deformed and undeformed data points, a least-squares strain tensor can be derived which represents the overall deformation of the basin or parts thereof. An associated strain ellipse yields information such as percent

i

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Fig. 5. Technique for palinspasticallyrestoring a normal fault. The digitised grid representing a geological horizon is rotated so that the chosen extension direction is N-S, then all points "N" of the fault are moved parallel to the Y-axisby a displacement equal to the "fault gap" at the corresponding X-coordinate.

area change ( = extension), and the orientations of the principal axes of extension.

3.3. Results of palinspastic restorations Displacements and strains. Three different restorations were made of each horizon. For Restoration 1, all faults were assigned an extension direction of 035 °, parallel to the Great Glen fault (cf. [21]), regardless of their orientation. For Restoration 2, each fault was assigned an extension direction at right angles to its mean trend, i.e. they were all assumed to be essentially dip-slip. For Restoration 3, each fault was assigned an extension direction corresponding to the vector mean of its rollover corrections, i.e. at right angles to the axis of the rollover anticline. An additional version was run of Restoration 2 (Restoration 2A) in which no rollover correction was made, i.e. following Model A of Fig. 3. The base Jurassic model boundaries for Restoration 2 are shown in Fig. 2; for Restorations 1 and 3, the area northwest of the Great Glen fault was omitted. Base Cretaceous is shallow in the west and obscured on seismic records by sea-bed multiples, so this model was also terminated at the Great Glen fault. The original and deformed grids produced by Restoration 2

196 (base Jurassic) are plotted in Fig. 6a. Magnitudes and directions of displacements from the deformed grid of Fig. 6a to the original square grid are represented in Fig. 6b (as a moving average which samples points within a 5001 m radius). Maximum displacements are ca. 5 km and most are broadly N - S ; the divergence of the displacement vectors implies some degree of E - W extension in the north of the basin. The N - S trend of the easternmost contours is an edge effect, as is the compress.ion of the extreme rows and columns of the grid. Elsewhere, contours at right angles to the vectors imply dip-slip movement, while contours parallel to the vectors imply strike-slip movement. Restorations 2A and 3 are broadly similar to Restoration 2. Fig. 7a shows data for Restoration 1 (base Jurassic) and implies N N E - S S W extension with up to 7 or 8 km displacement parallel to the Great Glen fault. The contours are more irregular, even after some manual smoothing, because the extension direction is close to the trend of many of the faults. This exaggerates errors in the initial seismic interpretation. The average displacement of the northern boundary parallel to the Great Glen fault can be calculated from the percentage area change of the basin and the outcrop length of the Great Glen fault--this yields ca. 6.4 km displacement since the Triassic (cf. McQuillin et al.'s [21] suggestion of 8 km post-Carboniferous displacement). A similar calculation for the (smaller) base Cretaceous basin yields 2.5 km of postJurassic displacement. Restorations for base Cretaceous are similar to those for base Jurassic, except that overall displacement is less and proportionately more extension is recorded in the east of the basin ((Fig. 7b). Cartoons depicting Restorations 1 and 2, base Jurassic, are presented in Fig. 8. It is likely that neither restoration is strictly correct. Extension perpendicular to fault trends is clearly unrealistic, since it implies major northwesterly displacement of the Northern Highlands .relative to the Central Highlands south of the Great Glen. Extension parallel to the Great Glen fault raises less serious objections, but provides no obvious explanation for the Jurassic depocentre adjacent to the Great Glen and Helmsdale faults. The slight N W - S E shortening associated with Restoration 1 (Fig. 8a) reflects the rollover correction derived from this northwesterly-dipping basin. It will be suggested

below that basin formation involved a component of areal extension. Whole-basin strains associated with the restorations are listed in Table 1. Restorations 2 and 3 give broadly N - S extension, but Restoration 1 implies N N E - S S W extension and approximates to plane strain. Base Jurassic extension is close to the figure of 6.63% proposed on independent grounds by McQuillin et al. [21]. In theory, all three restorations should yield identical values of p (percent area change). In practice, Restorations 1 and 3 give lower values of p than Restoration 2, largely because they permit faults to trend sub-parallel to the extension direction; this creates narrow bands of very large displacement which will only be recorded if they intersect a basin-margin data point. In addition, the Great Glen and Helmsdale faults were not included in Restorations 1 and 3. Depths to detachment cluster around 20 km; those for Restoration 2 should be the most reliable. Estimates which take account of sediment compaction will be made below. Model A (ignoring the rollover correction) gives a 10-20% increase in extension and a corresponding decrease in depth to detachment. Depth to detachment. Because all measurements were made on horizons lying within the sediment column, rather than at top metamorphic basement, depths and sediment thicknesses must be corrected for sediment compaction. A backstripping procedure was employed, analogous to that used by Sclater and Christie [17] to determine the isostatic load of a sediment column with downwards-increasing density. However, instead of performing an isostatic correction, their "shaly sand" compaction curve was used to determine how much basin-floor subsidence was due to compaction of earlier sediments, rather than to extension. The stratigraphic interval of interest was first decompacted to sea level, so removing the effects of subsequent burial, and this new thickness was then reduced by an amount equal to the compaction undergone by older sediments during deposition of the interval of interest. Permo-Triassic sediments were assumed to be present within the basin, but absent from its margins; a typical thickness in a basinal well is ca. 1000 m. Higher values (e.g. 2000 m) exceed likely Permo-Triassic thicknesses but may be ap-

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199 TABLE 1 Least-squares strains associated with palinspastic restorations of the Inner Moray Firth basin Restoration

x

y

O(°)

p

d

024 168 169 168

5.545 6.972 8.260 6.263

25049 24107 20687 22432

032 000 001 166

2.422 2.847 3.005 2.491

28007 24013 22816 27266

018 158 161 168

3.049 4.011 5.102 3.680

22596 24175 19368 19013

Base Jurassic to Present 1 2 2A 3

1.058 1.060 1.071 1.058

0.998 1.010 1.011 1.004

Base Cretaceousto Present

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1.024 1.026 1.028 1.017

1.000 1.002 1.002 1.008

Base Jurassic to Base Cretaceous 1 2 2A 3

Fig. 8. Present-day (solid lines) and restored (broken lines) basin boundaries for (a) Restoration 1, base Jurassic and (b) Restoration 2, base Jurassic. Note the small total strain, and in (a), the concentration of displacement at the northeastern margin of the basin. The axes of the least-squares strain ellipses are also indicated, together with their principal extensions (in

%).

propriate if underlying Devonian sediments were not fully compacted by the start of the Jurassic. A simple basin-volume calculation will underestimate depth to detachment because Lower Cretaceous sediments have been eroded over much of the Inner Moray Firth. Jurassic sediments have only been eroded from a small area near the Helmsdale fault, so the Jurassic interval balance should not be significantly affected. U p p e r Cretaceous and Tertiary sediments are absent from 44% of the basin area (Fig. 9). Top Lower Cretaceous lies at ca. 1 km depth over major horsts at the eastern boundary of the model, and by extrapolation should reach 678 m above sea level at the western boundary. This figure is consistent with onshore topography, which rises to 200 m immediately west of the Helmsdale fault and to 600 m within 5 km. The construction in Fig. 9 yields an average basin-margin depth of 160 m (ignoring

1.034 1.035 1.044 1.041

0.997 1.006 1.007 0.995

x and y are the long and short axes of the strain ellipse associated with basin formation, O the azimuth of the long axis (i.e. the principal extension direction), p the percent area change (extension) of the ellipse and d is a depth to detachment, taking no account of sediment compaction.

the very thin Lower Cretaceous sediments). Depths to detachment calculated on this basis, using equations (3) and (4), are plotted in Fig. 10a. 190 m of (decompacted) Jurassic sediments are present on the basin margins. Depths to detachment calculated by attributing these to non-extensional subsidence are shown in Fig. 10b. Because the three calculations are not independent, the " J K " and " K " curves will always lie on either side of the " J " curve (Fig. 10). Where the

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200 (a)

/

extensional subsidence only

35 1

35

- -30 d (km)

with rollover correction - - withoul rollover correction -~

\

Jurassic subsidence - with rollover correction --

without rollover correction

30 d (kin)

25

iK

'

(b) 190m of non extensional

--. "-" ~-JK

25

~

~

~

~ K K ~

17

1000

2000

Permo Triassic thickness {rn}

1000

~

J

~

JK

20-00-

Permo Triassic thickness {m}

Fig. 10. Decompacted depths to detachment, d, based on base Jurassic restoration (J), base Cretaceous restoration ( K ) and base Jurassic to base Cretaceous interval (JK), given various assumptions about hanging-wall deformation and sediment compaction (see text).

" J K " curve lies at much higher values, this suggests either that extension from base Jurassic to the present day has been underestimated or that extension from base Cretaceous to the present day has been overestimated. This could be because hanging-wall deformation was accommodated by ductile strain or small-scale faulting, since the rollover correction is proportionately larger for the more steeply dipping base Jurassic. The curves obtained without rollover corrections lie within 1 km of one another for reasonable Permo-Triassic thicknesses. If a component of non-extensional Jurassic subsidence is permitted (Fig. 10b), the curves agree more closely. Assuming a crustal thickness of 22-23 km [23], those depths quoted in Fig. 10a and obtained by applying a rollover correction would lie within the upper mantle. The other three methods yield depths to detachment of 20 25 kin, which would lie close to the base of the crust and may correspond to the major d6collement recognised on deep reflection data west of Orkney [25]. Alternatively, they could reflect detachment at the Moho. Variations in extension direction. Geological evidence indicates that overall strain in the Inner Moray Firth basin is not plane: faults in virtually every orientation underwent extension at some stage in their history. The E N E - W S W faults (parallel to the Wick and Banff faults) define

Jurassic half-grabens, but they also display features indicative of Jurassic strike-slip movement (en echelon folds and minor faults, flower structures, scissors faulting, anomalous rotations or changes in sediment thickness). The Great Glen and Helmsdale faults, on the other hand, define the major half-graben with the thickest Jurassic sediments. In contrast, the strike-slip movement of the Great Glen fault identified by McQuillin et al. [21] most obviously affects the Lower Cretaceous, and the thickest Lower Cretaceous sediments are deposited against the N W - S E Little Halibut fault and a N W - S E embayment in the Halibut Horst. This suggests that Jurassic extension had a significant E W component, perhaps related to the minor crustal thinning shown in Fig. 2, but later extension accorded more closely with McQuillin et al.'s [21] model of extension parallel to the Great Glen fault.

The rble of lithospheric stretching. The presence of thinned crust beneath part of the Inner Moray Firth raises the possibility that the basin was produced by inhomogeneous lithospheric stretching, i.e. that a narrow zone of mantle and lower crustal thinning widened upwards (with a corresponding decrease in the stretching factor/3) into the observed broad zone of upper crustal extension. The zone of thinned crust precisely underlies the zone of Upper Cretaceous and Tertiary subsidence, so it is reasonable to suppose that the two are related (Figs. 2, 11). Following McKenzie [15] and Le Pichon and Sibuet [28], initial stretching subsidence S i and subsequent thermal subsidence S t (after ca. 120 Ma) can be approximated by: Si

=

(1 - 1//3) 7.5 km

S t = (1 - 1//3) 8 km

(5) (6)

(assuming pointwise isostasy and sediment fill with average density 2200 kg m-3, ignoring compaction of earlier sediments since basin-margin data was used, and taking typical published values for the other parameters [15,28-30]). The ca. 1000 m of post-Lower Cretaceous sediments at the eastern margin of the model implies a/3 value of ca. 1.14, which is slightly greater than that measured in a cross-section from the Halibut Horst to the Peterhead Ridge. By integrating the depth to top Lower Cretaceous where it lies below sea level, a total thermal subsidence of 2850 km 3 is obtained,

201

Smith and Bott (1975)-],

thermal subsidence (volume = 2850 km 3 )

Permo-Triassic and predate the measured upper crustal extension. Extension within the Inner Moray Firth thus involved both an "internal" component related to local lithospheric stretching, and an "external" component coupled by a lowangle fault or shear zone to stretching outside the basin.

\

Jurassic and Lower Cretaceous proportion due to lithospheric stretching

~ru~ta[ thinning/-(volume 5370 km 3)

....

Fig. l 1. Schematic cross-section through the Inner Moray Firth, showing the relationship between crustal thinning and extensional (Jurassic to Lower Cretaceous) and thermal subsidence. The intersection with Smith and BoWs [23] seismic refraction line is indicated.

which corresponds to an average thickness of 300 m and an average fl value of 1.038. This may be an overestimate, since part of this subsidence is probably a flexural response to loading in the Witchground/Viking graben [20]. Present-day crustal thinning, predicted from gravity data (Fig. 2b), is 5370 km 3, so prior to 2850 km 3 of thermal subsidence, the crust had been thinned by (5370 + 2850) km 3 = 8220 km 3 (Fig. 11). The proportion of the Jurassic and Lower Cretaceous sediment volume which is attributable to lithospheric stretching (crustal thinning) can be obtained by application of equation (5). For a 22.5 km initial crustal thickness [23], this sediment volume will be about half the Moho uprise of 8220 km 3, i.e. 4110 km 3, so the total basement thinning due to lithospheric stretching is (8220 + 4110) km 3 = 12330 km 3. Since the present, stretched basin area is 11025 km 2, conservation of volume requires that /3 = 1.050. If the same calculation is performed for a 30 km thick crust, 2740 km 3 of initial subsidence is predicted, which yields 10960 km 3 of basement thinning, and fl = 1.033. These figures for average lithospheric stretching (3-5%) are significantly less than the measured post-Triassic extension of 7.0-8.3%, and so part of the extension within the Inner Moray Firth must be coupled to lower lithosphere stretching outside the basin--particularly since the lithosphefic stretching calculation was based on the 1-D gravity model, which predicts more crustal thinning than Donato and Tully's [20] 3-D model. In addition, some of the crustal thinning may be

4. Discussion

Unlike the major North Sea grabens, the Inner Moray Firth basin is not isostatically compensated and cannot be explained by the simple McKenzie [15] lithospheric stretching model: rather, it appears to have been produced by listric normal faulting, above a basal d6collement surface which couples shallow extension to whole-lithosphere stretching elsewhere. Palinspastic restorations indicate that the basin was produced by 7-8% postTriassic extension (including 2.5-3% post-Jurassic extension) above a d6collement surface at 20-25 km below sea level, i.e. close to or at the base of the crust. The results are broadly compatible with McQuillin et al.'s [21] m o d e l whereby the Inner Moray Firth basin was produced by dextral movement on the Great Glen fault, implying 6.4 km of post-Triassic movement and 2.5 km of postJurassic movement, but other, geological evidence suggests that extension was areal, i.e. not plane strain. Although the eastern part of the basin was subjected to limited crustal thinning and lithospheric stretching, this can account for no more than half the upper crustal extension, and probably less since the degree of crustal thinning is well constrained by gravity and stratigraphic data and may include a pre-Jurassic component, but upper crustal extension may have been underestimated and was measured at the base Jurassic level. To balance extension, the Inner Moray Firth must be coupled to a basin in which the crust has experienced less extension than the mantle lithosphere. The d6collement may have cut down-section into a diffuse zone of lower lithosphere stretching (cf. [31]). Alternatively, it may remain at the same horizon and terminate at a point where upper and lower lithosphere stretching are in balance (cf. Fig. 12, which represents a possible scenario for Mesozoic stretching in the Moray Firth area). In parts of the North Sea and the Atlantic continental margins, crustal thinning inferred from

202

W

E A

B

A"'

B"

C

C"

D

D"

Fig. 12. Simplified model of heterogeneously-stretched lithosphere with brittle upper plate and ductile lower plate, prior to thermal subsidence and ignoring isostatic effects. Overall extension of ADD'A' balances that of A'D'D"A" and so the d6collement terminates at D'. Segment AB is analogous to the Inner Moray Firth basin in that upper plate ABB'A' has undergone greater extension than lower plate A'B'B"A" and the upper plate has been translated eastwards on the d6collement. In segment BC ( = the Witchground graben?), upper plate BCC'B" has undergone less extension than lower plate B'C'C"B" and so upper plate displacement decreases eastwards. At CC'C", upper plate (ACC'A') and lower plate (A'C'C"A") extensions balance and displacement on the d6collement is zero. In segment CD ( = the Viking graben?), overall upper plate (CDD'C') and lower plate (C'D'D"C") extensions balance and upper plate displacement is either eastwards, westwards or zero, depending on the detailed relationship between upper and lower plate stretching.

subsidence or seismic refraction data implies a larger value of the stretching factor fl than that measured directly on reflection seismic sections. These discrepancies have led some authors to question either the structural interpretation of reflection data or its ability to resolve small-scale but cumulatively large strains (cf. [32] and [33] or [34] and [35]). Confirmation by deep seismic reflection techniques of the depth to detachment in the Inner Moray Firth would provide a useful test of the method. Currently available data implies that the major d6collement is deeper than 10 km, and so the measured strains and calculated depth to detachment are plausible, but slightly larger strains are possible. Two features distinguish the Inner Moray Firth from the major North Sea grabens: the lack of major lithospheric stretching

and the relatively low bulk strain. If it transpires that the reflection seismic method records true extension in the Inner Moray Firth but discrepancies remain elsewhere, three possible explanations exist: (1) the seismic method is accurate at small strains but not at large strains, e.g. because several generations of faults are required [36]; (2) special factors operate in stretched basins, e.g. "basification" of crust; (3) part of their upper crustal extension is coupled by low angle faults to satellite basins which lie some distance from the main graben or continental margin. Where the third explanation applies, post-stretching subsidence will be controlled primarily by the thinning of the mantle lithosphere, but syntectonic subsidence will be controlled primarily by the thinning of the crust, and in extreme cases, where flcrust is much less than flman,e, syntectonic uplift may occur [37]. A further possibility which arises where crustal thinning has been inferred from seismic refraction data only is that the graben or ocean was preferentially located over already-thin crust and so /3 estimates cannot be based on nearby crustal thicknesses. The apparent development of the Inner Moray Firth basin above thin pre-Mesozoic crust tends to favour this last suggestion, as do recent results from the Central Graben [18].

Acknowledgements The ideas developed in this paper have benefitted greatly from discussions with Vic Loudon and Bob McQuillin, whom I thank. I should also like to thank Chris Deegan, Head of the Hydrocarbons (Offshore) Research Programme of BGS for his active encouragement, the other members of the Inner Moray Firth mapping team (Heather Auld, Ian Andrews and Ian Jacksor~), past and present members of the Hydrocarbons Unit for their comments and discussion, and Keith Mennim, who draughted the diagrams. The U K Department of Energy funded the original mapping project, and kindly gave permission for the results to be incorporated in this publication in a generalised form. This work forms part of the Spatial Modelling Research Programme, and is published with the approval of the Director, British Geological Survey (NERC).

203

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