Alteration of σ3 field during the evolution of a polycyclic basement complex

The polycyclic nature of the Migmatized gneiss basement complex of South-western Nigeria is depicted by several tectonic imprints oriented in different manner; such setting is characterized by temporal adjustment of the minimum stress field. Attitude (strike and dip), length, width, average perpendicular distance and aspect ratios were taken for foliations, joints, veins, intrusions and boudinages. These parameters were analyzed on histograms, rose diagrams and stereo nets; outcrop maps were used to elucidate the heterogeneity of the stress field. Joints are the youngest tectonic structures in the study area; they include extensional and shear types, systematic, non-systematic and orthogonal sets with dihedral angle of <90°. The boudinages occur in gneissic rocks; the veins and intrusions are metasome in the host rock and are made of quartz, feldspar and pegmatite minerals. The dominant orientation of structures are NNE-SSW for foliations, E-W, NE-SW, and NNW-SSE for joints, N-S, NNW-SSE and NNESSW for veins, and N-S for intrusions with dip direction of North-west and South-east for foliations and west for intrusions. Initial orientation of σ3 was east-west during the emplacement of the veins and pegmatite intrusions and then ENE-WSW for the quartz-rich intrusions. Joints oriented NE-SW commonly intersected the other structures suggesting they are juvenile and created by NW-SE oriented σ3. Subsequently, shearing of the rocks and rotation of the least stress field produced the boudinages, conjugate joints, and tension gashes. Evidence for horizontally situated σ1 is shown by few slightly folded foliations seen in specific locations. In the study area, the joints were the product of multidirectional minimum stress which was dominantly oriented NW-SE prior to the Pan African orogeny.


INTRODUCTION
Tectonic stress applied to a rock is one or a combination of extension, compression or shearing (Ramsay, 1967). Extensional structures grow perpendicular to a minimum principal stress σ3 (Griggs and Handin, 1960;Kehle, 1964); σ1 is oriented perpendicular to compressional structures, and for strike-slip faults and other tectonic *Corresponding author. E-mail: kamaloomosanya@yahoo.com. Tel: +2348034454405. structures produced by shearing, the intermediate stress is vertical (Anderson, 1936). Extensional structures include normal faults, joints, veins (including unsheared tension gashes), and intrusions, both pegmatite and quartz-feldspar rich. On the other hand, compressional structures are limited to ductile rock types producing folds and thrust faults in their brittle equivalents. Evidence for shearing most often includes the presence of LS tectonites characterized by S-C fabrics or Riedel shears along shear zones (Twiss and Moore, 2007).
Joints as palaeostress markers that provide the record J. Geol. Min. Res.
of stress orientation at the time of propagation are often extensional in nature (Dyer, 1983;Pollard and Segall, 1980); shearing commonly generate conjugate joints sets characterized by dihedral angles (Muehlberger, 1961). This is symbolized by the rotation and subsequent change in direction of σ3. Consequently, joints are ubiquitous and the most dangerous palaeostress markers (Pollard et al., 1982). Intrusions and veins are developed in the same manner as joints except that they are subsequently filled with precipitated minerals such as quartz, feldspar and pegmatite minerals. In addition, boudinages are created by the disruption of layers, bodies or foliation planes within a rock mass in response to bulk extension along the enveloping surfaces (Lloyd and Ferguson, 1981;Swanson, 1992Swanson, , 1999. Similarly, aslip boudinages are formed by bulk shear sense; progressive deformation of arrays of veins by shear stresses can lead to sigmoid tension gashes (Ramsay and Graham, 1970;Pollard et al., 1982;Coelho et al., 2006;Lisle, 2012). The Nigerian basement is characterized by different histories of metamorphism, orogenies and structural modifications (Odeyemi, 1981;Rahaman et al., 1983;Caby, 1989) which is reflected in its complex petrological and structural composition. The polycyclic nature of the basement rock means earlier episodes of metamorphism, magmatism; orogenies and tectonism would have been overprinted, reworked and modified by younger events (De Swardt, 1947;Oyawoye, 1972;Woakes et al., 1987;Ajibade et al., 1987;Omosanya et al., 2010Omosanya et al., , 2011Omosanya et al., , 2012. To reconstruct the palaeostress in such a setting is very problematic, as earlier events are often annihilated by recent tectonics activities, for example, older joints sets could be rotated during subsequent shearing. In addition, relict of the older events is sometimes preserved and do co-exist with the juvenile tectonic activities. Structural analysis of rocks is often done using orientation diagrams such as rosette and stereographic projections. These tools have invaluable application in geology and could unravel history of deformation in several geological setting. In this research, we aim to (a) identify tectonic structures in rocks of the study area (b) evaluate their spatial distribution using simple orientation diagrams (c) and decipher changes in the direction of the principal stresses with time. In this work, we simplify the study of palaeostresses direction associated with deformation observed in the rock using outcrop sketch maps. We start by discussing the geological settings, methods used for the research, results and conclusion on the importance of the study.

Local geologic setting
Regionally, the study area is situated on the Southwestern portion of the Nigerian basement, an extension of the Dahomeyide shield of the West African Craton (WAC). The eastern border of the craton is occupied by series of ancient gneisses, schists and quartzites (Burke et al., 1976). In addition, the metamorphic rocks of the shield are cut by a variety of mainly acid igneous rocks.
The basement complex in South-western, Nigeria is composed of MGC that is characterized by grey foliated Biotite Acid/Biotite Hornblende quartz feldspathic gneiss of tonalitic to granodioritic composition (Rahaman, 1988); Mafic to ultramafic component which outcrops as discontinuous boudinaged lenses or concordant sheet of amphibolites with minor amount of biotite-rich ultramafite; and Felsic component, a varied group comprised of pegmatite, aplite quartz-oligoclase veins, fine-grained granite gneiss, and porphyritic granite.
The MGC of South-western Nigeria is affected by 3 major geotectonic events (a) initiation of crust forming process during the Early Proterozoic (2000 Ma) typified by the Ibadan (South-western Nigeria) grey gneisses considered by Woakes et al. (1987) as to have been derived directly from the mantle; (b) emplacement of granites in Early Proterozoic (2000 Ma) and (c) the Pan African events (450 to 750 Ma) (Oyinloye, 2011). The schist belts represent N-S trending synformal troughs infolded into the MGCs which are best developed in the western part of the country. The schist belts are largely sediment-dominated in contrast to other schist belts of South Africa and Australia. The most important lithologies are pellites, semi-pellites and quartzite. This rock suite provides information on the structural pattern of the basement rocks.
The older granites correspond to the last rock types of the basement; these rocks are the most obvious manifestation of the Pan African orogeny and constitute about 40 to 50% of the basement complex outcrop. They vary in composition from tonalite through granodiorites to granite and syenite granodiorite composition is the most common (Oyinloye, 2011).

METHODOLOGY
In order to accomplish the rationale of this research, 17 rock exposures/outcrops were studied. Mapping of the structures was done by inventory; areas of complex structural architecture were gridded at outcrop locations. Attitudes (strike and dip) of foliation planes, joints, veins and intrusions were estimated using techniques of Barnes and Lisle (2008) and Omosanya et al. (2011). Other parameters measured on the field include the average perpendicular distance between joints sets, veins and intrusions. The average perpendicular distance is the mean of three separations taking diagonally between the structures (Omosanya et al., 2010). The important structural inquiries include a) whether the joints/veins/intrusions are systematic or non-systematic; b) the number of joints/veins/intrusions sets present, c) their cross-cutting relationship; d) the surface appearance of the joints/veins/intrusions; e) spacing and density; f) relationship of the joints/veins/intrusions to other geological structures and g) whether joints/veins/intrusions are isolated or connected to regional network. In addition, boudinages, foliations and intrusions were studied in order to describe the evolution of the entire outcrop and relate the interaction of the main extensional structures. For the purpose of description, the aspect ratio of the boudinages and veins were estimated as length/width.
Consequently, the data collected were plotted on histograms, rose diagrams and stereographic projections. The interaction of the structures at outcrop scale was studied using the outcrop sketch maps. Foliation were described as space and continuous if the shape or arrangement of rock components is greater or less than 0. 001 m; for ease of description, joints were assigned letter J, intrusions, I and veins as V.
The principal stresses responsible for deformation in rocks are mutually perpendicular, σ1 is the maximum compressive stress, σ2 is intermediate, while σ3 is the maximim tensile stress and the least compressive (Anderson, 1936). The use of joint interaction and their cross cutting relationship with other structures have been previously applied for timing the evolution of joints (Omosanya et al., 2011(Omosanya et al., , 2012. In this work, we use rose diagrams to elucidate the direction of minimium principal stress associated with the extension of the joints, consequently, the joint interaction with the other tectonic structures were studied on the sketch maps and used to define the change or variation in the position of this stress field through the history of each of the outcrops.

Description of rock types
Rock types in the study area include biotite-gneiss, banded-gneiss, (Migmatized in some parts and intruded by pegmatite) and granite ( Figure 1). The Migmatized gneisses have similar composition with the gneisses, the minerals are dark colored and are dominantly composed of Mafic minerals such as biotite and hornblende. The banded gneisses are characterized by bands resulting from the segregation of Mafic and Felsic minerals during recrystallization ( Figure 3a). The Mafic bands consist of biotite and hornblende; the Felsic bands are rich in quartz, muscovite, and orthoclase feldspars. In addition, the gneisses are presumably derived from granitic protolith.
Consequently, the granite gneisses consist of quartz, alkali feldspar, muscovite, and hornblende. The minerals are medium grained and coarse textured. These rocks are slightly foliated, with two kind of foliation planes, an obvious alignment of light colored minerals separated Omosanya et al. 25 ~1.4 cm and a faint segregation of minerals characterized by very-thin foliation planes. The pegmatite contains large-coarse textured minerals with individual mineral grains ranging from ~2.2 to 5 cm ( Figure 3e). They are composed primarily of plagioclase, muscovite, tourmaline, quartz and occasionally dark-colored minerals such as biotite. The pegmatites in the study area occurred as dykes, or irregular pockets in the other rock types.

Geometry and orientation of structures
The strike and dip of 79 individual foliations planes were measured in the study area; they are continuous, fine and dominantly oriented in the N-S, NNE-SSW and NNW-SSE direction with principal dip of east and west ( Figure  2a and b). The foliation planes were measured in the migmatite, banded gneiss and the granite gneiss. The principal dip directions suggest the presence of a regional fold in the area. This fold is thought to have an average interlimb angle of ~60° ( Figure 2a).
Joints found in the study area include both extensional fractures and shear joints. Three hundred and twenty-five (325) joints were mapped in the area; these structures are oriented in the E-W, N-S, NE-SW, NNW-SSE and ENE-WSW directions (Figure 4). The joint set includes systematic joints with average perpendicular distance of ~4 cm (J 38 and J 39 , LOC4) up to 67 cm (J 11 , J 15 , LOC 15). The joints sets are parallel to sub-parallel in map view. The non-systematic joints have inconsistent average perpendicular spacing.
In general, the surfaces of the joints appear irregular, haphazard, and curved. The surfaces of the joints lacked common features associated ( Figure 5) with shearing such as grooves, lines and plumose structures. Intersection geometry of the joints includes T-joints and conjugate joints (Figure 6a to c); some of the conjugate joints have dihedral angle of <90° (Figures 7b, d, and f). Tip geometries include gradual dyeing out, branch outs and y tips. Average length of joints is ~23 cm (LOC 5) to ~71.30 cm (LOC 1) (Table 1 and Figure 7). The longest joints are the master joints in most of the visited outcrops. In addition, joints cross cuts all the other structures in the study area; examples are shown in Figure 3.
The other kind of extensional structures includes the 37 veins oriented in the N-S, NNW-SSE and NNE-SSW directions. Average length of the vein in the area is ~156 cm (LOC 6) and ~303.14 cm (LOC 3) (Table 1 and Figure  7), while the average width is <2.29 cm. The vein type includes quartz, quartzo-feldspathic and in few migmatite, granitic veins; 25% of the veins are composed of quartz. Similarly, the intrusions are composed of quartz (I 8 , I 9 , I 10 ; LOC 17), quartz-feldspars (I 2 , LOC 4; I 3 , I 4 , I 5 , LOC 9 and I 11 , LOC 17), and pegmatite minerals (I 6 and I 7 , LOC 12 and I 1 LOC 1), they trend N-S direction with dip dominantly West (Figure 2). Average length and width of intrusion are ~211 and ~14 cm, respectively.
Boudinages are found in the gneissic rocks; they are foliation boudinages oriented in the E-W direction. Average length of the boudinages was ~834 cm, with width and aspect ratios of ~41.35 and ~0.026 cm, respectively. Boudinage in the study area are antithetic (A-slip) with respect to bulk shear sense ( Figure 8); they were found at Locations 2, 4, 12, and 17. Other structures include sigmoidal tension gashes and minor folding that are both evidence of shearing and compression of the rocks (Figures 3b, d and f).

The direction of minimum principal stress
Foliation associated with regional metamorphsim and compression are usually oriented perpendicular to the maximum principal stress, σ1 (Blatt and Roberts, 1996;Vernon, 2004). The dominant orientation of foliation planes in the study area is normal to E-W and ENE-WSW oriented σ1, which implies that σ2 was perpendicular to these orientation during the formation of the foliation planes.
The joints produced by tensile stress fields are oriented essentially E-W, N-S, and NE-SW, which coincide with the direction of σ2 during their formation. However, σ3 was oriented N-S, E-W and NW-SE, respectively; these joints therefore formed through mode I propagation. For the conjugate joint sets, they are thought to be formed in compressive stress fields, with σ3 oriented ENE-WSW and NNW-SSE. In addition, the direction of σ1 is NNE-SSW and NNW-SSE cutting the plane of the acute angle between the conjugate joints. In addition, the curved surface of the joints imply spatial and temporal difference in the direction of σ3 during the growth of the joints (Blatts and Roberts, 1996).

Relative timing of structures
Using 9 representative sketch maps (Figure 10), we reconstructed the tectonic evolution of the study area. At Location 1a, the dominant orientation for the joints is NW-SE, only J 4 and J 15 are oriented E-W and NE-SW, respectively. In contrast, the joint in Figure 9b are oriented in NE-SW, N-S and E-W directions. The NE-SW joints cross cut quartz vein (V 4 ), and are presumably younger than the veins. Similarly, J 15 was terminated on J 14 (Figure 10a), while J 7 and J 5 are pruned on J 6 ( Figure  10b). Initial extension of the NW-SE veins was associated with σ3 NE-SW, which is older than the NE-SW oriented joints produced by NW-SE σ3. In addition, the NE-SW joint are supposedly older than N-S and NW-SE oriented joint. However, the E-W joints predated the NE-SW joints but was unconnected with the NW-SE veins. Thus, it is difficult to establish a timing relationship between these particular joints and the veins. In terms of relative chronology, the oldest extensional joints at Location 1 are the E-W oriented joints, then NE-SW, N-S and NW-SE which were product of σ3 presumably oriented N-S, NW-SE, E-W and NE-SW, respectively.
The sigmoidal tension gashes were produced by NW-SE oriented σ3. The intersection of J 15 and J 13 at Location 1 produced a conjugate intersection geometry with ~60° dihedral angle. South of the outcrop in grid 2 (Figure 10c), the same geometry was also observed though with an acute angle of ~74°. Conjugate intersection was in addition observed between J 2 and J 6 at location 2, these joints were master joints oriented N02°E and N22°W, respectively (Figure 7). The dihedral angle between these joints is ~68°. In addition, the extension was produced by σ3 oriented E-W and N-S directions.
Consequently, at Location 2, the E-W and NE-SW joints were truncated on the NW-SE joints J 4 . The E-W joints taper into the intrusion 1 and 2 and terminated at J 4 ( Figure 10c). This complex orientation of the joint relative to the intrusions may suggest extension of the joints predated the emergence of the intrusion. This assertion invalidates all geologic reasoning, as it is often the case to find intrusion being older than joints in any setting. However, the presence of the conjugate joints sets at Location 2 (Figure 6a) signifies that the intrusion had been sheared in the plane of the conjugate joints. The relative timing of the joints in this setup is cumbersome except in place where the joints are unconnected with intrusions. Furthermore, the oldest joints are NW-SE oriented, then NE-SW and E-W joints. These events were preceded by N-S directed σ3 related to the emplacement of the intrusions.
The intrusions and some veins are oriented N-S, these structures formed presumably by mode I propagation like the extensional joints sets. The direction of σ3 for these structures is E-W. For other veins types oriented NNW-SSE and NNE-SSW, they were produced by ENE-WSW minimum principal stresses. The boudinages oriented E-W are aligned in the direction of σ3 but perpendicular to σ1.
The dominant orientation of joints is E-W at Location 4 (Figure 10d and e). The veins (V 1 ) and pegmatites intrusions (Pg 1 and Pg 2 ) are in the N-S direction. These older structures are cross cuts by the joints. Relative chronology of extension is E-W σ3 for V 1 , Pg 1 and Pg 2 , and predominantly N-S σ3 for the joints. The NW-SE joints truncated against the J 5 . Nonetheless, the sketch covers a section of the location dominated by E-W oriented joints. Consequently, joints in Figure 10f are diagonal to the veins and the intrusion. The latter were produced by presumably NE-SW σ3 and the joints by NE-SW oriented σ3. Conversely, the joints in Figure 10g are parallel to the Quartzo feldspathic intrusion, which signifies that they were produced by N-S oriented σ3. Timing, ideally may preclude the intrusion being older than the joints but this is an oversimplification of the actual evolutionary history of the structures. In terms of geometry and orientation, these structures can be Figure 6. Conjugate joint sets at Locations 1 and 3. These joints are characterized by acute angle of <90° between them. The joints surfaces are rugged and haphazard suggesting spatial and temporal variation in the direction of the minimum principal stress, σ3. NB: Joints numbers are specific to different locations and not used continuously, for example J1 represent the first joint in each of the locations. thought of as contemporaneous extensional fractures related to a similar stress field.
Subsequently, the joints are oriented NE-SW and NW-SE (Figure 10h) at location 1 2 ; J 1 and J 2 are terminated on the intrusions, while J 27 and J 29 were pruned on the NNW-SSE J 14 . Thus, J 14 is older than the other joint sets. The σ3 direction was supposedly N-S for veins, ENE-WSW, NW-SE and NE-SW for the joints.
The intrusion and veins were formed by initial extension of the host rock in a tensile stress field. The opening created during these extensions were infilled by mineral precipitates. The extensional regimes associated with these structures thus indicate the pristine orientation of the σ3 only in places where the intrusions were cross cuts by joints. Similarly, the sigmoidal tension gashes at some of the locations revealed that initial extensions of the veins were succeeded by shearing along the orientation of the veins (Figures 10a and 3e). Some of the gashes were later intersected by joints and veins, which show that the deformation involved several phases of extension and invariably diversity of the σ3 direction through time. In the special cases of boudinages, the joints parallel to the axis of the Boudin were presumably contemporaneous with the extension of the Boudin (Figure 8b). Obliquely oriented joints sets are younger than the boudinages (Figure 8d). Boudinages are formed by the disruption of layers, bodies or foliation planes within a rock mass in response to bulk extension along the enveloping surface (Goscombe et al., 2004).

Joints as complicated palaeostress indicators
Joints in the study area occur as either tensile joints or conjugate shear joints. The shear joints are restricted to specific locations. Unlike, other conjugate sets, the surfaces of the shear joints in the study area are not striated or slicken sided. This may be related to the nature and mechanical competency of the associated host rock. In addition, the conjugate joints thus form in a compressive stress field; the joints develop with the orientation of symmetric fracture planes (the conjugate direction) making the lower angle with the principal stress direction, σ1. The extensional joints are the dominant joints sets, as a rule of thumb; they extend by stretching normal to the tensile stress direction which is usually the minor principal stress, σ3. In the study area, the tension joints are rough and weathered. The shear joints are Mean is the average length of joints in the different locations. The standard deviation provides information on the spread of the length. Range is the difference between the minimum and maximum length estimated in each of the locations.  found in areas where the foliations are prominent. It suffices to think of the conjugate shear joints were formed by compression or rotation of the initial tension joints which is synonymous with anti plane shear (Mode III) (Dyer, 1983). In contrast, the tensile joints formed by opening (Mode I) propagation (Engelder and Geiser, 1980). The absence of plumose marks or hackles on the joint surfaces does not exclude the joints as extensional fractures; it demonstrates how lithology controls the behaviour of the joints surfaces; plumose structures are prominent in sedimentary rock units and hard to map in crystalline rocks. Plumose structure is present on joints in a variety of rock types, but it is most clearly displayed in rocks of uniform fine-grained texture (Twiss and Moores, 2007), and for this reason it was difficult to establish the timing of the conjugate.
The intersection geometry of the joints is an important tool for unraveling the deformational history of structural forms. Evidence from the field mapping revealed that the intersection of the joints are not simple t-joints and cross joints (Figure 9a and b); some of the joints intersect others by a gradual change in their direction of propagation creating bowl-shaped intersection with other joints (Figures 9c and d). This geometry is similar to drag sense common to normal fault, which often indicates their mode of propagation. For joints, the geometry may be related to (1) contemporaneous propagation of the intersecting joints; (2) possible reactivation and rotation of an older joint during a newer stress regimes; (3) deflection of the younger joint in response to boundary conditions of the older one; which is associated with perturbation of the stress of the younger joint by the older one (Dyer, 1983). All these factors point to reconfiguretion of initial extension phases by recent activities.
Furthermore, the architecture of the joints in Figure 9c and d revealed two dominant orientations for the joints, N-S and E-W. The intersection of joint E and D with B ( Figure 9d) implies that E and D were single joints displaced by propagation of the thoroughgoing joint B which in turn was truncated on joint A. This structural style implies that the N-S sets were formed at different times though oriented in the same direction. In addition, the drag at the intersection of G with F could not really provide information on their timing.
Consequently, conjugate geometry implies shear sense of propagation and formation of the joints in a compressive stress field. In contrast to conjugate normal fault that is ideally formed at the same time; conjugate joints traditionally evolve through propagation of a joint at a dihedral angle of <90° with a pre-existing joint. In such a setting, resolving the history of the unassociated tensile joints is complicated by lack of intersection with the conjugate joints as evidenced in Location 2. The older tensile joints are often rotated and re-oriented in response to the newer compressive stress field.

Correlation with regional structural trend
The E-W collision of the WAC and westward moving plate created N-S to NE-SW trending structures parallel to the edge of the WAC (Black et al., 1979;Champenois et al., 1987;Oluyide, 1988;Egesi and Ukaegbu, 2010). The regional effect of these movements is reflected as highly deformed series of multidirectional orientations found in folds, lineaments and faults in the entire Nigerian basement complex and Northern Cameroun (Mc-Curry, 1976;Rahaman, 1976;Onyeagocha, 1984;Toteu et al., 1990).
The N-S and NE-SW structures are presumably associated with the Pan African orogeny, while pre-Pan African structures are oriented differently to these directions in the basement (Onyeagocha and Ekwueme, 1982;Toteu et al., 1990). The Pan African orogeny reconfigured earlier structures in the basement rock of Nigeria (Mc-Curry, 1976;Rahaman, 1976). The N-S trend persistent with some of the intrusions and foliations implies that they are also Pan African orogenic structures. Thus, veins and the intrusions oriented NW-SE are likely pre-Pan African structures. The joints are essentially Pan African structures except for the E-W joints that are oblique with the Pan African trend. Furthermore, these joints type may be associated with earlier deformational phases. The Pan African orogenies as a multiphase events imply that these structures are interconnected in time and space.

Conclusion
The diverse orientation of the structures recorded on the stereo nets and rose diagram shows that the tectonic structures of the study area were the product of heterogeneous stress field. The stress fields were dominant and responsible for the deformation observed in the outcrop at present time; some of them have been overprinted by succeeding orogenies.
In the study area, the N-S and NE-SW oriented joint and intrusions are linked to the Pan African orogeny and were produced by E-W and NW-SE oriented σ3. Earlier extension structures such as E-W joints and NW-SE veins were products of σ3 oriented in the N-S and NE-SW directions antithetic to the main Pan African trend. In addition, the N-S foliation, NNW-SSE veins and conjugate joints sets have trend consistent with Pan African (Egesi and Ukaegbu, 2010;Goki et al., 2011). The multiple orientations of σ3 through the history of the rocks give credence to the polycyclic nature of the basement rock in the study area.