The influence of lithology and pre-existing structures on

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					Journal of the Geological Society, London, Vol. 162, 2005, pp. 471–480. Printed in Great Britain.

   The influence of lithology and pre-existing structures on reservoir-scale faulting
                         patterns in transtensional rift zones

                        N. D E PAO L A , R . E . H O L D S WO RT H & K . J. W. M C C A F F R E Y
         Reactivation Research Group, Department of Earth Sciences, University of Durham, Durham DH1 3LE, UK

                      Abstract: In transtensional and transpressional deformation zones, bulk 3D strains are often kinematically
                      partitioned into regions of wrench- and extension- or shortening-dominated faulting. Most strain models
                      assume ideal incompressible materials with a Poisson’s ratio (í) of 0.5. It is well known from experimental
                      and geophysical data, however, that natural rocks have values of í ,0.5 and that significant variations in the
                      values of í occur for different lithologies. We demonstrate that for non-coaxial, 3D transtension and
                      transpression, this should lead to an expansion of the wrench-dominated strain field. The effect is especially
                      marked in lithologies with very low Poisson’s ratios (í <0.15), where wrench-dominated deformation can
                      occur even where the regional direction of divergence or convergence is only modestly oblique (e.g. 528). The
                      Carboniferous basin-bounding 90-Fathom Fault, NE England, was reactivated as a dextral transtensional
                      structure during NE–SW regional stretching in post-Carboniferous times. Preferential dip-slip reactivation of
                      pre-existing east–west structures in the underlying Carboniferous basement led to kinematic partitioning of
                      the transtensional bulk strain. In addition, the geometric, spatial and kinematic patterns of minor faulting in
                      Permian rocks located in the fault hanging wall are markedly influenced by the host lithology. Quartz-rich
                      sandstones (í ¼ 0:12) preserve complex faulting patterns consistent with a wrench-dominated transtension
                      whereas immediately overlying dolostones (í ¼ 0:29) preserve simpler patterns of Andersonian conjugate
                      faults consistent with a more extension-dominated regime. We propose that the markedly different strain
                      response during the same deformation reflects pronounced lithologically controlled variations in the value of
                      Poisson’s ratio in the adjacent rock units. Our findings illustrate that micro- to meso-scale faulting patterns are
                      likely to be substantially influenced by lithology in all regions of oblique divergence or convergence.

                      Keywords: NE England, reactivation, rheology, strain partitioning, transtension.

In the last 30 years, geologists have increasingly realized that the              volume change (e.g. Fossen & Tikoff 1993); investigating the
three classic tectonic regimes predicted by the Andersonian                       effects of strain partitioning (e.g. Tikoff & Teyssier 1994; Jones
model of faulting (extension, shortening, strike-slip; Anderson                   & Tanner 1995); modelling heterogeneous strain (e.g. Robin &
1951) do not fully describe the 3D strain patterns that character-                Cruden 1994); including basal and lateral extrusion (Jones et al.
ize crustal deformation zones where convergence or divergence                     1997; Fossen & Tikoff 1998); investigating the effects of oblique
is significantly oblique. There are two main reasons why oblique                   simple shear (Jones & Holdsworth 1998; Lin et al. 1998) and
displacements are commonplace. (1) Oblique convergence or                         incorporating inclined deformation zone boundaries (Jones et al.
divergence is inevitable during motion of plates on a sphere                      2004). In transtensional settings, there have also been a number
(Dewey 1975; Dewey et al. 1998). Woodcock (1986) has shown,                       of field- and laboratory-based studies of deformation styles (e.g.
for example, that the relative plate motions at well over 50% of                  Withjack & Jamison 1986; Dewey 2002; Ramani & Tikoff
modern plate boundaries are significantly oblique. A similar                       2002), although these are less extensive compared with the
percentage is likely in ancient settings. (2) Most crustal deforma-               equivalent literature for transpression zones (e.g. see Dewey et
tion zones contain pre-existing structures, such as layering,                     al. (1998) and references therein).
foliation, faults, fractures and shear zones, which may undergo                      In this paper we begin by investigating how changes in
reactivation when subjected to renewed stress (Holdsworth et al.                  Poisson’s ratio (í) related to host-rock lithology may influence
1997). Many of these pre-existing structures are likely to lie                    the development of brittle structures during transtensional defor-
significantly oblique to the new regional transport direction. The                 mation. We then document this lithological influence using an
Andersonian tectonic regimes have therefore been extended to                      example where reactivation and strain partitioning are also
include transtension (and transpression), which can be defined as                  important controls of deformation patterns.
strike-slip deformations that deviate from a simple shear as a
result of a component of extension (or shortening) orthogonal to
the deformation zone boundary (Fig. 1a; Dewey et al. 1998).
                                                                                  Strain modelling and rock parameters
   Sanderson & Marchini (1984) provided a basic vertically                        In this paper we use the basic Sanderson and Marchini model for
oriented, constant volume, homogeneous strain model that can be                   transtension (Fig. 1b) where the bulk strain can easily be
used for analysing regions of transpression and transtension.                     factorized into pure shear and simple shear components. In all
Many workers have further investigated and modelled 3D                            transtension (and transpression) zones, the relative displacement
transtensional and transpressional strains, often by changing the                 direction across the deformation zone, infinitesimal strain (or
boundary conditions of the original model. These include: using                   stress) and finite strain axes are all oblique to one another.
a strain matrix for simultaneous simple shear, pure shear and                     However, predictable geometric relationships exist between the

472                                                                N. D E PAO L A E T A L .

       Angle of
      divergence α
                                                   Fault boundary                             c
                                              component                                                                b
       Divergent                                                                             lc
          Pure shear
          component                                                                                                         a
                                             a                                                                            b
Fig. 1. (a) A transtension can be viewed as the combined action of extensional pure and wrench simple shear resulting from an oblique direction of
extension relative to the deformation zone boundaries. (b) Sanderson & Marchini (1984) transtensional model: a unit cube (l0 ¼ 1) is deformed assuming
that the fault boundaries are vertical and parallel, with no stretch along the zone (lb ¼ 1). Horizontal extension across the zone is totally balanced by
vertical shortening. Constant volume is assumed (˜V ¼ 0 þ ec þ ea ¼ 0), the fault zone is basally confined and deformation is homogeneous.
Deformation parameters are: extension ei ¼ (li À l0 )=l0 , where i ¼ a, b, c and l0 ¼ 1, and shear strain ª ¼ tan Ø, where Ø is the angular shear.

orientations of the deformation zone boundaries, the axes of                        (Æ ¼ 08) to the boundary fault, we have pure shear coaxial
infinitesimal strain (stress) and the relative displacement direc-                   extension (Fig. 2b) and non-coaxial wrench simple shear (Fig.
tion across the deformation zone. In many cases, therefore, it is                   2c), respectively. These represent end-member strain states for
useful to apply an analysis using infinitesimal strain, which is                     transtension and both are considered in the present analysis to
equivalent to the more conventional, widely used stress-inversion                   lead to plane strain (2D) deformation (Fig. 2b and c). When the
techniques (e.g. Angelier 1979, 1984; Michael 1984). It should                      divergence vector is at an oblique angle, non-coaxial 3D strain is
be noted, however, that this approach is reasonable only in                         always developed (Fig. 2a). In this case, the infinitesimal strain
regions where bulk finite strain (or more correctly, finite non-                      ellipsoid lies in the constrictional field (1 , k < 1) and the
coaxial strain) is reasonably low, so that the misorientation                       (horizontal) maximum principal extension axis (eH x) always lies
between finite and infinitesimal strain axes is limited.                              in the horizontal plane during progressive deformation. The other
   Transtensional infinitesimal strain will occur when the bulk                      horizontal infinitesimal principal extension axis can be either eH z
displacement is at an oblique angle Æ to the deformation zone                       (minimum principal extension axis) or eH y (intermediate princi-
boundary faults (i.e. 08 , Æ , 908) (Figs 1a and 2a). When the                      pal extension axis), depending on the value of Æ. The switch of
divergence angle Æ is perpendicular (Æ ¼ 908) or parallel                           the minimum principal extension axis from a horizontal to a

           0°                   90°                                       = 90°         Pure                                = 0°
      b                               Transtension             b                                                  b                      Wrench
                                                                                        extension                                        regime
           45°          x       90°                                      x=   90°                                         x=   45°
                                        i = y, z
                                          eHi 0                                                                                          eVy = 0
                                         x                                                    eHy = 0
                                                   eVi 0   =                             x
                                                                                                  eHx 0       +                      x
                                        eHx 0                                                                                                eHz 0
                                                                                              eVz 0                   | |                eHx 0
                    |       |
                                                       a                                             a                                               a

                                a                                               b                                                    c
Fig. 2. (a) 3D constrictional non-coaxial transtensional strain (08 , Æ , 908). It should be noted that eH i ¼ eH z and eH y for wrench- and extension-
dominated transtension, respectively. (b) Plane strain pure shear coaxial extension (Æ ¼ 908). (c) Plane strain simple shear wrench deformation (Æ ¼ 08). â
x is the angle between the maximum horizontal extension axis and the boundary fault; jłj is the infinitesimal angular shear; Æ is the divergence angle
between the displacement and the boundary fault; x, y and z are the maximum, intermediate and minimum infinitesimal extension axes; eH i is the
horizontal infinitesimal principal extension axis with i ¼ x, y or z; eV i is the vertical infinitesimal principal extension axis with i ¼ z or y. It should be
noted that the plane of plane strain is vertical for pure extension (i.e. parallel to Cartesian plane ab) and horizontal for wrench regime (i.e. parallel to
Cartesian plane ac).
                                                 R E S E RVO I R - S C A L E FAU LT I N G PAT T E R N S                                                  473

vertical orientation marks the transition between wrench- and                  Table 1. Poisson’s ratio í and the angle Æcrit calculated for a variety of
extension-dominated transtension, respectively. The threshold                  lithologies using equations (3) and (5) (see text for details)
angle Æ between wrench- and extension-dominated transtension
                                                                               Rock type                                    í             Æcrit (deg.)
has been termed the critical angle of displacement Æcrit (Smith &
Durney 1992). It has a value of 208 if one assumes no volume                   Magmatic rocks with Vp /Vs obtained between 200 and 1000 MPa
change during deformation and following the other assumptions                  Andesite                                    0.29              33
of the Sanderson & Marchini model (McCoss 1986). The                           Basalt                                      0.29              33
isovolumetric assumption implies that an ideal incompressible                  Diabase                                     0.28              34
                                                                               Granite                                     0.24              38
material (i.e. a liquid phase) is involved in the deformation, with            Diorite                                     0.26              35
a Poisson’s ratio í ¼ 0:5. Following Withjack & Jamison (1986),                Gabbro                                      0.29              33
we propose a more general transtensional model in which the                    Sedimentary rocks with Vp /Vs obtained at an average pressure of
constant volume condition of the Sanderson & Marchini model                    200 MPa
(equation (1)) has been relaxed to allow volume change at fault                Limestone                                   0.32              31
initiation (equation (2)) as a result of the Poisson’s effect (Fig.            Dolostone                                   0.29              34
                                                                               Silty limestone                             0.29              34
3). The change in volume is expressed by                                       Shale                                       0.25              37
               ˜V ¼ e a þ e b þ e c ¼ e a þ 0 þ e c ¼ 0              (1)       Sandstone                                   0.23              38
                                                                               Quartz-rich sandstone (90%)                 0.12              52
for constant volume transtension with no lateral extrusion                     Mean lowest static value measured           0.15              48
(eb ¼ 0), where ei ¼ (li À l0 )=l0 are the infinitesimal extension
axes for i ¼ a, b, c (see Fig. 3). If the effect of Poisson’s ratio is
included, equation (1) becomes
                       ˜V ¼ e a þ 0 þ Ce c 6¼ 0                      (2)       of Withjack & Jamison (1986)). w is the infinitesimal displace-
                                                                               ment in a direction at an angle Æ to the fault boundary and eH z
where the parameter C ¼ [í=(1 À í)] 6¼ 1 for í 6¼ 0:5 (see Fig.                and eV y are the horizontal and vertical infinitesimal minimum
3). The incorporation of Poisson’s effect will in general lead to              and intermediate principal extension axes, respectively.
positive volume change (˜V . 0) at fault initiation during                        The likely importance of Poisson’s ratio in determining
transtensional deformation (Jaeger 1964), because most rocks                   deformation patterns is illustrated by the Æcrit values obtained
have values of í , 0.5 (Table 1).                                              during experimental analogue modelling studies investigating
   Thus the calculated angle Æcrit is now additionally controlled              structures formed during oblique divergence. These values are
by the parameter C, which is related to the Poisson’s ratio value              significantly greater than the 208 angle predicted by the McCoss
as follows:                                                                    (1986) model, e.g. 308 (Withjack & Jamison 1986; Ramani &
            0:5(w=l0 )(sin Æcrit À 1) ¼ ÀC(w=l0 ) sin acrit :        (3)       Tikoff 2002) and 458 (Smith & Durney 1992). A mean í value
                                                                               of c. 0.3 represents a typical mean value for most rocks in nature
This represents the situation where eH z ¼ eV y (i.e. the transition           (see Table 1). Introducing this value into equation (3), we obtain
strain-state when Æ ¼ Æcrit , equations (2) and (4) in appendix 1              Æcrit ¼ 338, which is consistent with the values observed in the
                                                                               analogue experiments.
                                                                                  We can extend this analysis to investigate the potential control
                                                                               that variations in lithology (e.g. variations in Poisson’s ratio)
          c                       l0 = 1              V 0
                                                                               might exert upon faults forming in a compositionally heteroge-
                                                                               neous bedded rock sequence. Following Christensen (1996) we
                                                    Positive                   calculated dynamic Poisson’s ratio values (see Table 1) using
                                                    volume                     compressional-wave (Vp ) and shear-wave (Vs ) velocities for a
                                             b      change                     range of typical igneous, metamorphic and sedimentary rocks
                                                                               (Christensen 1996, for igneous and metamorphic rocks; Johnston
                                                                               & Christensen 1992, for sedimentary rocks). This is achieved
                                                                               using the equation
   lc                                                                                                                  1
                                                                                                    í ¼ 0:5 1 À                 :              (4)
                                                                                                                 (Vp =Vs )2 À 1

                                                                               The solutions of equation (3) have been plotted on a í v. Æcrit
               la                          | |                                 graph (Fig. 4a) to show the influence of various lithologies on
                                                                               the strain regime formed during transtensional (and transpres-
                                           a                                   sional) deformations. A further equation (equivalent to equation
                                                                               (3) in appendix 1 of Withjack & Jamison (1986)) relates Æ to â x ,
Fig. 3. Volume change induced by the Poisson’s effect in the case of           the angle between the infinitesimal horizontal maximum exten-
uniaxial tension. The Sanderson & Marchini model assumes a volume              sion strain axis and the b-axis of the Cartesian co-ordinate frame,
constant condition (˜V ¼ 0) with í ¼ 0:5 (ideal incompressible                 which corresponds to the deformation zone boundary (Fig. 2a):
material) and C ¼ (í=(1 À í)) ¼ 1. For all the other cases (i.e. real                                â x ¼ 908 À 0:5 tan À1 (cot Æ):                     (5)
rocks), 0 , í , 0.5 and thus C ¼ (í=(1 À í)) 6¼ 1, allowing positive
volume change (˜V . 0), but not lateral extrusion (eb ¼ 0). The general        The solutions to equations (3) and (5) are plotted on an Æ v. âx
condition of volume change is given by the equation                            diagram (Fig. 4b) for four representative Poisson’s ratio values
˜V ¼ ea þ eb þ Cec (see text).                                                 (equivalent to lithologies) listed in Table 1 and also shown in
474                                                        N. D E PAO L A E T A L .

                                                                                                    Fig. 4. (a) í v. Æcrit graph plotting solutions
                                                                                                    of equation (3). d, data for (1) an ideal
                                                                                                    incompressible material, (2) dolostone, (3)
                                                                                                    quartzite (the lowest static value measured
                                                                                                    for real rocks) and (4) quartz-rich sandstone
                                                                                                    (c. 90%). (b) Æ v. â x diagram plotted with
                                                                                                    the field of wrench-dominated transtension
                                                                                                    highlighted (grey area and dashed lines) for
                                                                                                    points (1)– (4) shown in (a) and listed in
                                                                                                    Table 1. TT, transtension; TP, transpression.

Figure 4a (incompressible material, dolostones, the lowest static         present a possible example of this effect from NE England that
value measured for real rocks and quartz-rich sandstones where            additionally illustrates the importance of pre-existing mechanical
quartz content is c. 90%). In all cases, compared with the ideal          anisotropies in bringing about strain partitioning on different
incompressible material, the reduced value of the Poisson’s ratio         scales.
leads to an expansion of the wrench-dominated field at the point
of fault initiation (Fig. 4a and b). This suggests that in quartz-
rich sandstones, for example, faulting could initiate in a wrench-        Case study: the 90-Fathom Fault, NE England
dominated transtensional regime even where displacements are
only modestly oblique (e.g. Æ values up to 528; Fig. 4b).
                                                                          Regional geological setting
Furthermore, in any basin containing markedly differing litholo-          The early Carboniferous Northumberland Basin, NE England, is
gical units (and therefore Poisson’s ratios) it is possible that          one of the northernmost basins that developed in the foreland of
adjacent rock units experience very different infinitesimal strain         the Variscan orogenic belt (Fig. 5a). The basin has an asymmetric
fields at fault initiation for the same regional value of oblique          shape and can be described as a half-graben. It is bounded to the
divergence (e.g. angle Æ). The geometry and kinematics of minor           south by the Stublick–90-Fathom normal fault system, which
brittle structures, at least during the early stages of deformation,      dips to the north and trends ENE–WSW to east–west (Fig. 5b
might then be controlled very significantly by lithology. We now           and c; Collier 1989; Kimbell et al. 1989; Leeder et al. 1989).

                                                                                                    Fig. 5. (a) Location map of
                                                                                                    Northumberland Basin. (b) Detailed
                                                                                                    structural map of the 90-Fathom Fault at
                                                                                                    Cullercoats showing mesoscale structures
                                                                                                    (i.e. normal and strike-slip faults) in the
                                                                                                    hanging wall. (c) Simplified structural map
                                                                                                    of Northumberland Basin, showing main
                                                                                                    bounding faults and location of Cullercoats
                                                                                                    study area. (Change in trend of the 90-
                                                                                                    Fathom Fault should be noted.) (d)
                                                                                                    Exposure of 90-Fathom Fault shear plane in
                                                                                                    cliff. (e) Dip-slip slickenlines preserved on
                                                                                                    main fault plane exposed on foreshore.
                                                   R E S E RVO I R - S C A L E FAU LT I N G PAT T E R N S                                            475

The fault system appears to be segmented, with the main                          ous times (e.g. Collier 1989; Kimbell et al. 1989; Leeder et al.
movement transferred south and east along-strike from the                        1989).
western Stublick Fault to the easternmost 90-Fathom Fault (Fig.
5c). Thickness changes in the lower Carboniferous strata (Dinan-
                                                                                 Deformation patterns
tian) are recorded across the fault system, with more than 4.2 km
of Dinantian sedimentary rocks in the hanging wall, compared                     At Cullercoats the 90-Fathom Fault is an east–west-striking
with a few hundred metres overlying the Alston block, the                        normal fault, dipping to the north and juxtaposing a hanging-wall
structural high in the footwall (Kimbell et al. 1989). This is                   sequence of Permian sandstones and dolostones against a foot-
taken as evidence of syndepositional fault activity (Kimbell et al.              wall of Carboniferous Coal Measures (Fig. 5b). The fault plane
1989). Other intrabasinal faults are recognized based on geophy-                 is well exposed in the cliffs and foreshore and preserves dip-slip
sical evidence, variations in stratigraphical thickness, concentra-              slickenlines (Fig. 5d and e). According to Collier (1989), Coal
tion of channel bodies and dewatering structures (Leeder et al.                  Measures strata are offset by 260 m, whereas the base of the
1989). Collectively, these structures suggest that the early                     Permian is estimated to exhibit 90 m of dip-slip normal displace-
Carboniferous rifting involved north–south-oriented extension                    ment on the basis of cross-sections constructed from British Coal
that is believed to have ended during the Namurian. This was                     mine plans and borehole data.
followed by a thermal subsidence sag phase during the Westpha-                      Kinematically the overall pattern of deformation associated
lian, with thickening of the basin fill towards the basin centre                  with the 90-Fathom Fault at Cullercoats has previously been
(Kimbell et al. 1989). Both the Stublick and 90-Fathom faults                    interpreted to be consistent with a dextral transtensional defor-
offset Upper Carboniferous (Coal Measures) and overlying                         mation caused by post-Carboniferous reactivation of a pre-
Permian strata, suggesting that renewed extensional or transten-                 existing east–west-trending Dinantian normal fault at depth
sional faulting occurred in Permian to Mesozoic times (hereafter                 (Collier 1989). However, in the aeolian sandstones of the
referred to as ‘post-Carboniferous’), probably associated with the               immediate hanging-wall region, ascribed to the mid-Permian
early stages of rifting in the North Sea basin (Collier 1989). A                 (Collier 1989), the faulting patterns appear much more complex
lack of exposure and high-quality subsurface data means that the                 compared with the immediately overlying dolostones (Fig. 6a
overall geometry of the major faults at depth is uncertain,                      and b). The sandstones contain: (1) significantly higher numbers
especially in those segments reactivated during post-Carbonifer-                 of closely spaced faults (i.e. higher fault densities); (2) geome-

a Sandstones
                                      N                                                              S


                    Poles to faults   Dolostones
                    number of data
  Poles to faults
  Slickenlines with sense of shear

                                      N                                                             S

                                                           1                                                Fig. 6. (a, b) Fault data plotted on an equal
b    Dolostones
                                                                                            2               area lower hemisphere projection for both
                                                                                                            lithologies show that normal (east–west-
                                                                                                            trending) and dextral (ESE–WNW) strike-
                                                                                                            slip faults are present in the sandstone
                                                                                                            units, whereas less abundant, discrete
                                                                                                            normal–oblique faults occur in the
                    Poles to faults
                    number of data
                                      d                                                                     dolostone units. Contouring intervals refer
                         18                            N                               S                    to per cent data per 1% of the net. (c, d)
 Poles to faults                                                                                            Contrasts in the patterns of faulting in the
                                                           Dolostones                                       sandstones þ dolostones where they are
                                                               Sandstones                                   interbedded adjacent to their mapped
                          15%                                                           2
                                                                                                            boundary in the field. (e) Line drawing
                                                                                                            showing how the small faults in the
                                                                                                            sandstones terminate against the lithological
                                                                                                            boundary with the dolostones. Compared
                                                                                                            with the sandstones, the dolostones present
                                                       e                                                    a simpler fault pattern, as only the main
                                                                                                            faults propagate into the dolostones.
476                                                          N. D E PAO L A E T A L .

trically different patterns of conjugate fault sets, e.g. quadrimodal           geological setting of the 90-Fathom Fault, three key issues
(Fig. 6a) v. bimodal (Fig. 6b). Two distinct sets of mutually                   remain concerning the post-Carboniferous deformation. (1) The
cross-cutting, and therefore broadly contemporaneous, cataclastic               relationship between the dip-slip displacements along the major
faults are recognized in the sandstones (Figs 5, 6a and 7): east–               fault plane and the multiple kinematics of the mesoscale pattern
west-trending normal faults; and ESE–WNW dextral strike-slip                    of deformation exhibited in its hanging wall is uncertain. (2) The
faults. The cataclastic, deformation-band style of faulting in the              significance of the contemporaneous, but kinematically very
sandstones is generally consistent with strain hardening beha-                  different fault sets in the sandstones requires explanation. (3)
viour and intense grain-size reduction along localized brittle                  Does lithology account for the very different patterns of faulting
faults (Collier 1989; Knott et al. 1996). At the concordant                     in the Permian sandstones and dolostones? A detailed 3D strain
sedimentary contact with the overlying dolostone units, in a zone               analysis has been carried out in the attempt to address these
where sandstone and dolostone are interbedded, many of the                      issues and give some new insights into the development of
smaller faults observed in the sandstones appear to die out as                  complex fault patterns in transtensional settings. Our findings
they are traced into the dolostones (Fig. 6c–e). In the latter                  illustrate the importance of strain partitioning acting simulta-
lithologies a much more straightforward, low-density pattern of                 neously and on different scales during transtensional deforma-
conjugate ESE–WNW-trending extensional–oblique displace-                        tion.
ment faults occurs (Fig. 6b, d and e). The observed difference in
complexity and density of faulting clearly suggests that lithology
has exerted a significant control on the faulting pattern. Previous              Strain analysis: strain partitioning, reactivation and
workers have attributed these differences to changes in rheology,               lithological control
i.e. brittle faulting in sandstones v. more ductile folding and                 In both sandstones and dolostones, individual fault displacements
faulting in dolostones (Collier 1989).                                          are small, rarely exceeding a few tens of centimetres, suggesting
   Despite a reasonably good understanding of the general                       low finite strain intensities. This observation, together with a lack

                                    Dip-slip normal faults
 N                                                              S E                            W



       Sigma 1          Sigma 2           Sigma 3

      Poles to       Slickenlines with     90 Fathom Fault    Poles to faults
      faults         sense of shear                           number of data
                                    Dextral strike-slip faults
N                                                           S ESE                          WNW

                                                                                                           Fig. 7. (a, b) Typical dip-slip normal faults
                                                                                                           and slickenlines in the sandstones, which
                                                                                                e          trend parallel to the main 90-Fathom Fault
                                                                                                           and form an approximately Andersonian
                                                                                                           conjugate system. (c) Stress inversion
                                                                                                           applied to these faults (equal area lower
                                                                                                           hemisphere projection) yields a vertical ó1
                                                                                                           and a north–south-trending ó3 . (d, e)
                                                                                                           Typical dextral strike-slip faults and
                                                                                                           slickenlines, which have an ESE–WNW
                                                                d                                          trend. (f) Stress inversion applied to these
                                                              Poles to faults
                                                                                                           faults (equal area lower hemisphere
                                                              number of data                      f        projection) yields a NW–SE-oriented ó1
                                                                                                           and a NE–SW-oriented ó3 .
                                                                                    R E S E RVO I R - S C A L E FAU LT I N G PAT T E R N S                                             477

of evidence for significant bulk shear-induced rotations (i.e. no                                                  wall region are the product of a residual wrench-dominated strain
sigmoidal vein arrays observed), means that an approximate                                                        (with a displacement component Æ2 ) left over after the exten-
coincidence between the stress and infinitesimal strain axes may                                                   sional component (Æ1 ) of the bulk regional strain was taken up
reasonably be assumed, i.e. ó1 ¼ ez ; ó2 ¼ ey ; ó3 ¼ ex .                                                         by fault reactivation (Fig. 8a–c). Repeated cycles of reactivation
   Stress inversion has been applied to the fault-slickenline                                                     and strain partitioning led to the observed mutually crosscutting
dataset from all faults in the sandstones (Fig. 7). The software                                                  relationships exhibited by the kinematically different sets of
package used (Daisy 2 of Salvini 2001) automatically separated                                                    structures in the sandstones. The stress inversion applied to the
the faults into two groups, each associated with very different                                                   ESE–WNW dextral strike-slip faults in the sandstones yields an
stress fields: respectively, extensional (vertical ó1 , horizontal                                                 angle â x ¼ 708 between the horizontal infinitesimal principal
north–south-trending ó3 ) (Fig. 7a–c) and dextral strike-slip                                                     extension axis direction (taken here as equivalent to ó3 ) and the
(horizontal NW–SE-trending ó1 and NE–SW-trending ó3 ) (Fig.                                                       main strike-slip fault trend (Figs 7f–8c). When plotted on the Æ
7d–f). These two groups correspond exactly to the two-fold                                                        v. â x diagram calculated for quartz-rich sandstones (Figs 4b and
subdivision of faults recognized in the field on kinematic                                                         8a), with an appropriate value of Poisson’s ratio, this suggests a
grounds; i.e. the stress inversion results and the field observations                                              divergence angle Æ2 of c. 508 between the local extension
suggesting strain partitioning are consistent.                                                                    direction and the ESE–WNW-trending strike-slip faults (Fig.
   The quartz content of sandstones at Cullercoats has been                                                       8a–c). The local extension direction expressed as the angle Æ2 c.
estimated at about 80% (T. Needham, pers. comm.) and lies                                                         508 matches the condition Æ , Æcrit c. 528 required to develop a
close to the quartz content of the sandstone shown in Table 1.                                                    wrench-dominated transtensional strain in the sandstone units
Assuming that the Poisson’s ratio of this sandstone (í ¼ 0:12) is                                                 (Fig. 8a–c). The local wrench component Æ2 ¼ 508 is measured
representative of those at Cullercoats, we use an appropriate                                                     relative to the trend of strike-slip faults (ESE-dextral) because
version of the Æ v. â x diagram in the following strain analysis                                                  they represent the active boundary structures accommodating the
(Fig. 8a).                                                                                                        local wrench component of strain (Fig. 8c).
   The preferential accommodation of north–south extension by                                                        The bulk regional transport direction can be estimated using
east–west-trending dip-slip normal faults could be related to                                                     the calculated partitioned components, Æ1 (extensional) and Æ2
reactivation of the suitably oriented pre-existing structures                                                     (wrench), respectively; it must have trended approximately NE–
associated with the 90-Fathom Fault in the Carboniferous rocks                                                    SW, somewhere between the two partitioned components of the
immediately below the Permian strata (Fig. 8b). This is consis-                                                   deformation (Fig. 8d).
tent with the dip-slip slickenlines preserved on the present-day                                                     Compared with the sandstones, the dolostones preserve a
exposed fault plane (Fig. 5e). This condition is fixed by the                                                      much simpler pattern of deformation (Fig. 6a and b) with main
relation Æ1 ¼ â x ¼ 908, which expresses the partitioned exten-                                                   faults having a similar orientation to the main dextral strike-slip
sional component of displacement, Æ1 (Fig. 8a and b).                                                             faults in the sandstones. Unfortunately, no slickenlines are
   We suggest that the dextral ESE–WNW faults in the hanging-                                                     preserved on these fault planes, but the bimodal conjugate style

                                                                                                                                             Fig. 8. (a) Æ v. âx diagram plotted for
                                                                                                                                             quartz-rich sandstones (í ¼ 0:12). 1
                                                                                                                                             (extension) and 2 (wrench) represent the
                                                                                                                                             partitioned components of the total
                                                                                                                                             displacement; the regional displacement
                                                                                                                                             vector lies somewhere between these two
                                                a                                    b                                 c                     partitioned components (region indicated by
                                                                          Extension dominated strain      Wrench-dominated strain            double-headed arrow). (b–d) Analysis of
                                    Quartz rich sandstone
                                              = 0.12                              component                    component                     faulting and infinitesimal strain viewed in
                                                                                                                                 x           plan. (b) The north–south extension
                                                                                                                   z                         component of strain (Æ1 ¼ 908) has been
     0 10 20 30 40 50 60 70 80 90

                                                                                                                           y                 accommodated by reactivation of the 90-
                                    Wrench      2                                                                                            Fathom Fault and by adjacent east–west-
                                    dominated                                                                                                trending normal faults. The minor normal
                                    TT               Extension                                                                 x =70°
                                                                                                                                             faults probably developed in response to the
                                                                           x =90°          1= 90°
 x                                                   TT
                                                                                                         Reactivated 90-Fathom Fault         partitioned extensional strain along the 90-
                                                                                                                                             Fathom Fault. (c) The residual component
                                      Crit =   52°                    Reactivated 90-Fathom Fault                                            of extension (Æ2 ¼ 508) accommodated by
                                                                                                                                             the dextral strike-slip faults in the
                                                                                                                               2 =50°        sandstones can be reconstructed by plotting
                                0 10 20 30 40 50 60 70 80 90
                                                                                                                                             stress inversion and field data (â x ¼ 708) on
                                                                                                                                             the Æ v. â x diagram. The calculated angle
                                                                                                                                             Æ2 ¼ 508 lies in the wrench-dominated field
                                                                      d        The REGIONAL EXTENSION                                        and is therefore consistent with the
                                                                             lies between the two partitioned                                development of dextral strike-slip faults. (d)
                                                                                       components                                            The regional displacement vector must lie
                                              Partitioned                                                                                    somewhere between the two partitioned
                                             extensional                                            Partitioned wrench
                                                                                                      component of                           end-member directions (Æ1 ¼ 908 and
                                           of displacement
                                                                                           2          displacement                           Æ2 ¼ 508), i.e. NE–SW trending. Its precise
                                                                                                                                             orientation cannot be determined in the
                                                                                                                                             absence of information concerning strain
                                                                     Reactivated 90-Fathom Fault                                             magnitude.
478                                                                            N. D E PAO L A E T A L .

of faulting and the extensional stratigraphic offsets seem to                                        Lithology has exerted a clear influence on the style, density,
suggest an extension with a small component of dextral shear.                                        geometric and kinematic complexity of faulting in adjacent units,
Significantly, this is consistent with what is predicted if we plot                                   as the same displacement component (Æ2 ) resulted in very
the previously calculated value Æ2 for the partitioned wrench                                        different patterns of faulting. Lithologically controlled changes
direction on an Æ v. â x diagram for a material with a Poisson’s                                     are here explained mainly by differences in the value of the
ratio appropriate for a dolostone (Fig. 9a–c). In this case, an                                      Poisson’s ratio, which are seen as being particularly significant as
angle Æ2 c. 508 matches the condition Æ2 . Æcrit c. 348 required                                     they lead to changes in the threshold angle Æcrit between wrench-
to develop an extension-dominated transtension (Fig. 9a). Thus,                                      and extension-dominated transtension. In our interpretation, the
for the same value of Æ2 , the dolostone will experience a                                           90-Fathom Fault represents a system where mechanical decou-
markedly less non-coaxial deformation compared with that                                             pling occurred during oblique regional extension. A perfect
experienced by the adjacent sandstones undergoing wrench-                                            partitioning and mechanically decoupling of the different
dominated transtension (Fig. 9d–f). Inclusion of the Poisson’s                                       fault sets seems unlikely but seems to represent a reasonable
effect mainly results in a change in the simple shear–pure shear                                     approximation.
ratio, i.e. the kinematic vorticity. For a fixed regional displace-
ment direction, this should lead to changes in the orientation and
shape of the infinitesimal strain ellipsoid in different lithologies.
Unfortunately, we cannot quantitatively analyse this further in the                                  Our interpretation of the complex faulting patterns associated
present case study because of the lack of exposed kinematic                                          with the 90-Fathom Fault is relevant to the continuing debate
indicators in the limited outcrops of dolostones.                                                    concerning whether it is stress or the imposed displacement
   Independent validation of the NE–SW direction of bulk                                             (strain) that controls the faulting process (e.g. Tikoff & Wojtal
regional extension derived from our analysis (Fig. 8d) is provided                                   1999). The 90-Fathom Fault illustrates that the only parameter
by the patterns of offshore normal faulting in the immediately                                       not affected by the orientation of structures accommodating local
adjacent Mesozoic rocks of the southern North Sea (Petroleum                                         deformation is the regional imposed displacement, i.e. the NE–
Exploration Society of Great Britain 2000).                                                          SW opening direction during post-Carboniferous times. The
   In summary, we have demonstrated that the mesoscale pattern                                       stress (equivalent to infinitesimal strain) distribution in the
of deformation in the Permian hanging wall of the 90-Fathom                                          hanging wall of the 90-Fathom Fault appears to be highly
Fault can be interpreted as resulting from partitioning of a bulk                                    partitioned (Fig. 7a–d) and depends on local controls such as
transtensional strain, induced by the obliquity between the pre-                                     lithology and reactivation of pre-existing zones of mechanical
existing east–west-striking, basin-bounding fault and the NE–                                        weakness in the subjacent basement. In an ancient structure of
SW regional direction of post-Carboniferous extension. This                                          this kind we have no independent evidence to constrain the
transtension has been partitioned into an extensional strain with a                                  orientation of the regional stress. Traditionally, the observed
displacement component Æ1 , manifested by the dip-slip normal                                        heterogeneities in apparent stress or strain patterns encountered
reactivation of the 90-Fathom Fault and associated structures,                                       here might be interpreted as being due to polyphase deformation.
together with a more highly oblique displacement component Æ2 ,                                      This is at odds with the field observations.
which led to wrench- and extension-dominated transtension in                                            More generally, our findings illustrate that kinematic partition-
immediately adjacent sandstone and dolostone units, respectively.                                    ing is particularly likely to occur during the deformation of

                        a                                         b                                     c
           DOLOSTONE            = 0.285
     90                                      1
                          2                                 Normal/oblique-slip
     70                                                          faults
                              Extension                                                                                        Fig. 9. The lithological control on style and
     40     Wrench          dominated TT                              2 =50°                                                   geometry of faulting is evident when Æ v.
     30     dominated                                                                                                          â x diagrams are plotted for each lithology.
                                                      1 =90°                                                                   (a, b) The calculated angle Æ2 ¼ 508 for the
     10                      = 34°
                        Crit                                                                                                   oblique partitioned component of
                                                 Reactivated 90-Fathom Fault       Poles to faults
          0 10 20 30 40 50 60 70 80 90                                             number of data           Poles to faults    displacement, accommodated in the
                                                                                        18                                     hanging wall of the 90-Fathom Fault, plots
                                                                                                                               in the extension-dominated field for
                        d                                        e                                      f                      dolostone rocks. (c) The deformation in the
            SANDSTONE = 0.12
                                                                                                                               dolostones is accommodated by
            (quartz = 90%)                   1
     90                                                                                                                        extensional–oblique slip normal faults
     80                                                                                                                        (equal area lower hemisphere projection).
                          2                                    Strike-slip                                                     (d, e) The same component of displacement
                                                               faults                                                          (Æ2 ¼ 508) plots in the wrench-dominated
     60                         Extension
     50                       dominated TT                                                                                     field for quartz-rich sandstones. (f) The
     40        Wrench
                                                                      2 =50°                                                   pattern of deformation observed in the
     30        TT                                                                                                              sandstone units is consistent with that
     20                 0.12                            1 =90°                                                                 predicted by the strain modelling (equal
                             = 52°
     10                 Crit
                                                                                     Poles to faults                           area lower hemisphere projection). (Note
                                                  Reactivated 90-Fathom Fault        number of data          Poles to faults
          0 10 20 30 40 50 60 70 80 90                                                    254                Slickenlines      that (b) and (e) are in plan view.)
                                             R E S E RVO I R - S C A L E FAU LT I N G PAT T E R N S                                                       479

heterogeneous anisotropic crust where pre-existing structures are          Fathom Fault, with a residual oblique component accommodated
often significantly oblique to regional tectonic transport direc-           in the hanging wall of the fault. Three-dimensional strain analy-
tions (e.g. Dewey et al. 1998; Jones et al. 2004). It is important         sis suggests that the calculated divergence angle Æ2 ¼ 508 for the
to note that the direction of the infinitesimal principal extension         residual oblique component of extension has led to wrench-
axes (â x ) does not correspond to the bulk extension direction            dominated transtension for quartz-rich (c. 90%) sandstones (í c.
accommodated by the overall fault system; this is a consequence            0.12) where Æcrit is c. 528 (Figs 8 and 9). In immediately adjacent
of strain partitioning and non-coaxial strain component present            dolostone units (í c. 0.29), however, the same analysis suggests
during 3D transtensional strain (Dewey et al. 1998).                       that extension-dominated transtension has occurred, where Æcrit is
   Our findings further illustrate that the use of 2D strain ellipse        c. 348 (Fig. 9). Field data match the assumptions of the strain
models to describe faulting patterns (Wilcox et al. 1973; Harding          modelling and seem to explain well both the kinematically
1974) is inappropriate when dealing with complex deformation               complicated patterns of deformation and the lithological control
patterns arising from 3D strain. Such 2D methods are still used            on style of faulting.
widely in the interpretation of faulting patterns in sedimentary
basins, including the 90-Fathom Fault (e.g. Collier 1989). Given           The authors would like to thank the following for help during fieldwork
the marked differences between faulting patterns that arise during         and many discussions: P. Clegg, J. Imber, R. Wilson and R. Jones. N.D.P.
2D and 3D finite strain, this practice is unwise in any areas               gratefully acknowledges the financial and scientific support provided by
                                                                           M. Barchi and the University of Perugia (Italy). The RRG acknowledges
where there is evidence for obliquely divergent plate motions or
                                                                           the continuing support of NERC, Statoil and BP. Finally, the authors very
rifting oblique to reactivated basement faults.
                                                                           much appreciate the detailed reviews provided by the journal referees S.
   Our findings also have significant implications for structural
                                                                           Giorgis and S. Wojtal, and the editor A. Maltman.
models of fracture interconnectivity and fluid flow in hydrocar-
bon reservoirs. For example, the association of contemporaneous
normal and strike-slip faults produces a potential mixture of              References
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                                                   Received 5 April 2004; revised typescript accepted 27 September 2004.
                                                                    Scientific editing by Alex Maltman

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