Relationship of seismic rupture with foliation and lithology

Within the GSZ, amphibolite-hosted pseudotachylyte-bearing faults are localized close to the lithological boundaries, but are not recorded along the actual boundary interfaces; indeed, they occur at distances up to 80 m laterally away from them. Exploitation of these boundary zones is also seen in pseudotachylyte faults occurring in the other lithologies that host the GSZ (Park 1961). Spacing and orientation of fracturing has been observed to vary between the lithologies of the GSZ, with amphibolites hosting typically foliation-parallel brittle deformation with a high factor of clustering (Beacom et al. 2001). Such a foliation-parallel fracture pattern is replicated in the pseudotachylyte-bearing faults and is compatible with the understanding that strong anisotropy tends to guide shear failure orientation, even if it is somewhat misorientated relative to the principal stress directions (Donath 1961).

The amphibolite host rock presents a contrast in the thermal properties of its constituent minerals – hornblende has a single-crystal melting temperature of 750°C, whilst quartz and An_30–50 plagioclase will melt at c. 1550° (if melting occurs before the high temperature phase change to β-christabolite) and c. 1350°, respectively (Petzold & Hinz 1976; Spray 2010). Under disequilibrium frictional melting, this leads to preferential melting of the amphibole, which is clearly illustrated by the clast in Figure 6c and d. In the wall of the fault, melting of amphibole between preserved quartz and plagioclase has led to increased roughness of the fault surface on the grain scale (e.g. Fig. 6b), contrary to mechanical wear processes that tend to smooth the fault walls with progressive slip (Brodsky et al. 2011), examples of which may also be observed in these pseudotachylytes in the formation of sidewall shortcuts (Figs 3a and 6e). Preferential melting of amphibole is also observed in the walls of some injection veins, indicating that the melt temperature in these off-fault tensile fractures also remained above 750°C (Spray 2010) and hence was still molten at the tip of the vein, requiring quenching to be slower than the fracture propagation (Rowe et al. 2012).

The volumetric ratio of survivor clasts relative to melt-derived matrix within any individual pseudotachylyte fault vein is an indication of the thermodynamic balance between melting and mechanical wear processes (O'Hara 2001). In the GSZ pseudotachylytes, the mean 2D clast to matrix (representing the melt, includes microlites plus the finer-grained crystalline matrix) area ratio is 0.11, at the lower boundary of the 0.1–0.7 range which has been previously reported for pseudotachylytes from a collection of different fault zones (O'Hara 2001), indicating that an increased proportion of melt was generated relative to products created purely by mechanical wear during slip. The breakdown of rock via mechanical wear and melting is influenced by the mineral yield strengths and thermal energy needed for melting, respectively. Although the ratio of these properties is fairly constant for many common minerals, amphiboles, particularly hornblende, have slightly lower melting points relative to their strength (O'Hara 2001; Spray 2010). Therefore, frictional melting of a hornblende-rich rock might be expected to generate an increased volume of melt along the fault relative to the volume of unmelted clasts, in comparison to a quartzo-feldspathic lithology. Additionally, even low coseismic temperature rises, associated with small increments of seismic slip, may still allow for widespread melting of the amphiboles. This relative ease of coseismic melt production may have implications for fault structure, with high melt pressures (i.e. fluid pressure) potentially contributing to opening tensile off-fault cracks (Swanson 1992) alongside dynamic rupture-tip stress fields (Di Toro et al. 2005b; Griffith et al. 2009; Ngo et al. 2012) and exploitation of pre-existing fractures. Interaction of locally high fluid pressure along the fault plane with the opening of dilational sites controlled by fault geometry will drive high fluid pressure gradients and consequential rapid flow of melt towards the dilational zone, potentially causing brecciation (Sibson 1975; Bjørnerud & Magloughlin 2004), all within the duration of coseismic slip. Hence, the interaction of the lithological control on melting and the foliation control on fault geometry has implications for the relative contributions of coseismic fault plane processes to the seismic energy budget and structural development of the fault zone.

Depth and temperature conditions of seismic faulting in the GSZ

The depth of brittle faulting and seismicity in the GSZ is not well constrained but occurred within lower greenschist-facies temperatures (Park et al. 1987; Beacom et al. 2001), giving a likely ambient rock temperature between 250 and 350°. The geothermal gradient has been estimated for the GSZ as 22−4+7∘Ckm−1 during Laxfordian ductile deformation phases (Droop et al. 1999). Whether this was still the case for the later brittle phase is not clear, but as Droop et al. (1999) regard this as a moderate estimate for stable Precambrian crust, and considering the errors and the time-gap, we use an approximation of 25°C km⁻¹ as the geothermal gradient in calculations. This gives a depth range of 9–13 km for the ambient temperature range 250–350°C.

Coseismic fault temperature, displacement, magnitude and slip direction

Pseudotachylyte-bearing faults in the GSZ capture individual episodes of seismic slip, thus capturing elements of the source parameters of the individual earthquakes. The energy budget required to melt a given volume of the host rock allows the coseismic heat rise in particular to be estimated, and is related to the seismic displacement, which scales with the seismic magnitude. Direct measurement of displacement in the field is not routinely possible in the GSZ, because there are few markers within the amphibolite that may be cut and offset across the faults. Calculating the necessary displacement required to produce a certain volume of pseudotachylyte melt is therefore a useful estimate of the magnitude of earthquake displacement recorded on these faults. The volume of coseismic melt is approximated by the average thickness of a pseudotachylyte fault vein (Di Toro et al. 2005a). Thickness measurements are best undertaken across fault veins with constant thickness and limited melt loss into sites such as injection veins and breccia. Although such geometrically simple veins are not common in the GSZ, a typical thickness of the pseudotachylyte along linear faults is around 5 mm (e.g. Fig. 4a). The relationship between the thickness of melt, the displacement and the thermal properties of the rock isd=ρ×wτ[(1−ϕ)H+cp(ΔT)] (1)where d is the displacement, ρ the density, w the width of the vein, τ is the shear stress on the fault, φ is the area of clasts in the vein as a fraction of the total vein, H is latent heat of melting, c_p is the specific heat and ΔT is the difference between the coseismic melt temperature and the ambient temperature before and after the earthquake, T_melt ­– T_ambient (Di Toro et al. 2005a). Values used for these parameters are given in Table 1. Values for the shear stress resolved along the fault are estimated from the lithostatic stress state by equating the lithostatic stress (P_c = ρgh, where g is gravitational acceleration, and h is depth) with the mean stress of a strike-slip stress field. Assuming a Poisson's ratio of 0.25 (Jaeger & Cook 1979) and an angle of 30° between the maximum principal stress and the fault plane, this places the expected range of resolved shear stress at 107–155 MPa for the estimated depth range of 9 to 13 km (Fig. 7a). Constraining ΔT relies on estimating the maximum temperature reached by the coseismic melt (T_melt), which in many pseudotachylytes is reported within the range c. 1000–1500°C (O'Hara 2001; Di Toro & Pennacchioni 2004; Caggianelli et al. 2005; Nestola et al. 2010) from a combination of thermal and thermodynamic modelling, matrix indicator phases and melting temperatures of surviving clasts relative to melted phases. For the GSZ pseudotachylytes we use the latter method, which places upper and lower bounds on the melt temperature. The lower bound for the melt temperature is 750°C, the melting temperature of hornblende. Plagioclase is partially preserved as unmelted survivor clasts, placing a reasonable upper bound for coseismic fault plane temperature at the An_30–50 melting temperature of 1350°C (Spray 2010). Using these parameters in equation (1), the resulting mean values of coseismic displacement equivalent to a pseudotachylyte thickness of 5 mm range from d = 123 ± 40 mm at 9 km depth to d = 76 ± 28 mm at 13 km depth (Fig. 7b), scaling inversely with depth-dependent shear stress.

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Fig. 7.

Estimation of shear stress and coseismic temperature change on GSZ seismic faults: (a) Mohr circle construction for lithostatic stress state and strike-slip fault regime; (b) range of minimum seismic displacement necessary to produce thickness of 5 mm pseudotachylyte along a fault slipping at different depths in the crust. Equivalent moment magnitudes (M_W) are indicated for faults with the maximum and minimum estimated lengths of 100 m and 1 m respectively.

Earthquake magnitude for these events may be loosely constrained based on this displacement range. The seismic moment, M₀, is related to the displacement (d), rupture area (A) and the shear modulus (G) as M₀ = dAG. The typical rupture size on pseudotachylyte faults in the GSZ is somewhat uncertain, because the pseudotachylyte extent may represent only part of a larger fault plane that is not always fully exposed or easily traced (Kirkpatrick et al. 2012), especially if faults are foliation parallel and/or segmented. Rupture area is calculated from fault length based on the assumption of a circular fault with diameter equivalent to the fault length, a simplification of the elliptical geometry solution demonstrated by Eshelby (1957). A reasonable range of GSZ fault lengths (i.e. a maximum rupture length) would be between 1 m and 100 m, in which case the range of moment magnitudes (M_w) converted from the seismic moment would be between 0.1 and 3.1 M_w based on the empirical relationship Mw=((LogM0)/1.5)−6.07 (Kanamori & Brodsky 2004)_. The uncertainties arising from the unknown fault length are clearly large (Fig. 7b), but nonetheless illustrate that many of the pseudotachylytes in the GSZ were generated by a series of relatively small magnitude earthquakes.

The slip direction of the brittle faults in the GSZ is typically thought to have been sinistral (Park et al. 1987; Beacom et al. 2001; Sherlock et al. 2008). The sense of slip on the pseudotachylyte faults presented here is frequently difficult to determine, but where evidence for slip direction exists there are also dextral examples (e.g. Fig. 5a), indicating that seismicity likely occurred with both apparent dextral and sinistral kinematics. This is not incompatible with a dominantly sinistral tectonic regime, because small ruptures that occur as aftershocks or which occur in the damage zone or even further away from the major fault planes are often observed to have varying slip senses in observations of present-day seismicity (Cheng et al. 2018; Cooke & Beyer 2018).

Segmentation and branching

A common feature along GSZ pseudotachylyte-bearing faults is a stepover between parallel but laterally offset segments of the fault (e.g. Figs 4, 5a, 8a and b). These macroscopically stepped faults represent linkage of several fault segments, which, in the examples seen, tend to lie parallel to the amphibolite foliation. There appears to be two mechanisms of linkage between fault segments containing pseudotachylytes in the GSZ. Firstly, there is linkage driven by curvature of the segment tips once they overlap with an adjacent segment (Fig. 8a). The best example of this process is illustrated in Figure 4. This fault has a number of steps along strike, most of which have a completed through-going linkage linked and so evidence of the linkage mechanism is obscured. However, in the stepover detailed in Figure 4b–e, linkage is not quite complete, and ductile shear zones are preserved ahead of the fault tips, representing the process zone that precedes a propagating shear fracture (Misra et al. 2015). Both the overlapping tips display this process zone (Fig. 4d and e), indicating that both fault segments were propagating towards the other, in opposing directions (Fig. 8a). The presence of pseudotachylyte in the fault segments indicates that this propagation occurred during earthquake rupture, i.e. at least parts of these fault segments were newly formed during the earthquake which produced the pseudotachylyte, and the interaction of the segment tips indicates that all the segments must have been actively slipping during the same episode of coseismic rupture. Where linkage of the segments has occurred at other steps along the fault, the pseudotachylyte is continuous across the step, indicating that complete linkage of the segments also occurred during the same earthquake. A further implication is that nucleation of slip occurred at several sites on adjacent foliation planes, each growing into a short slip segment before a through-going slip plane was established. This fault therefore records the various stages of centimetre-scale growth, interaction and linkage of fault segments that can occur within a single earthquake, the duration of which is typically <0.2 s for events <M_W 3 (Kanamori & Brodsky 2004). The growth of the through-going fault in this manner is very similar to the model of fault growth from segments which exploit pre-existing weaknesses (Segall & Pollard 1983), but in the case of the GSZ the initial weakness plane is probably the amphibolite foliation, although the apparent overprint of a cataclastic zone by the pseudotachylyte segment in Figure 4c may indicate that pre-existing faults were partially exploited by the later rupture event recorded in the pseudotachylyte. The vein margins are frequently stepped at smaller scales of c. 1 mm vein-normal separations (Fig. 6a and b), which suggests that segmentation of slip may be applicable at several scales and that, on rupture initiation, slip may have nucleated simultaneously across a diffuse suite of foliation planes spaced only a few grains apart. Coalescence of these would have occurred forming the larger segments typically spaced c. 1 cm apart (e.g. Fig. 4). After segment linkage or branching, the fault wall geometry would be liable to be progressively modified by processes such as the creation of sidewall shortcuts (Figs 3a and 6e), which act to smooth out steps in the vein by by-passing protruding asperities to create a more planar fault margin (Fig. 6e). This rip-out process has been linked specifically to strike-slip faulting along planes of anisotropy (Swanson 1989) but in the GSZ appears to predominantly straighten curved or stepped faults rather than creating lensoid ramps into the fault walls from an initially planar fault, as in the model of Swanson (1989), likely due to the segmentation control on the initial fault geometry.

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Fig. 8.

Models of formation of stepping ruptures and dilational sites through a single episode of seismic slip: (a) linkage of pseudotachylyte-bearing rupture segments in the ‘dilational crack’ style; (b) linkage of rupture segments via secondary faults forming dilatational pull-aparts in extensional stepovers; (c) formation of elongate tabular breccias via paired ruptures and internal faults, here exploiting a shear band structure.

The curvature of overlapping segment tips (Fig. 4c) is an expression of the modification of the local fault tip stress field due to interaction between two closely spaced overlapping cracks (Pollard et al. 1982; Pollard & Aydin 1984; Nicholson & Pollard 1985) which causes the propagation path to curve. This style of linkage is well documented in dilatant crack systems, including veins and dykes (Pollard et al. 1982; Nicholson & Pollard 1985), in contrast to shear planes which more typically form sets of secondary fractures and/or folds in the overstep region (Fig. 8b), rather than propagate the primary crack tips towards each other in this way. The pull-apart in Figure 5a is an example of a typical extensional stepover between shear cracks (e.g. Sibson 1986) and is an example of the second mechanism of fault segment linkage demonstrated in the GSZ pseudotachylytes. In Figure 5a, the fault is right-stepping and has an apparent dextral sense of slip, creating an extensional overstep which is now filled with a pseudotachylyte rhombochasm. These pull-apart stepovers are well documented between strike-slip fault segments and on releasing bends at all fault scales, from millimetre-width (Peacock & Sanderson 1995) to hundreds of kilometres (Mann et al. 1983), and are also well described for pseudotachylyte-bearing faults (e.g. Sibson 1975). Unlike the crack-tip linkage (Fig. 8a), the multiple parallel slip segments do not necessarily need to exist pre-linkage because transfer of the rupture across to potential adjacent slip planes (the foliation, in the GSZ amphibolites) may occur via the formation of secondary faults in the future overstep (Sibson 1986; Harris et al. 1991; Melosh et al. 2014). Because this form of linkage is so common, it is interesting that the first mechanism via propagating crack tips also occurs across these faults, especially when it is more typical of dilatant mode I cracks (Pollard et al. 1982; Pollard & Aydin 1984). Some numerical models show that this curved propagation of crack tips can also occur on mode II shear fractures (Du & Aydin 1993; Ando et al. 2004). Alternatively, dilation of the fault segments could be introduced via local high fluid pressure driven by voluminous coseismic melt generation, leading the propagating rupture to behave as hybrid extensional-shear fractures. High coseismic fluid pressure has several implications for dynamic fault strength, potentially including transient loss of shear strength if the fluid/melt pressure becomes equal to or greater than the normal stress on the fault. However, evidence for high melt pressure is typically only locally seen in pseudotachylytes, for example in the dynamic creation of pseudotachylyte injection veins at the fault tip (Rowe et al. 2012; Sawyer & Resor 2017) and in breccias where extreme rotation of the clasts suggests fluid-supported implosion (Bjørnerud & Magloughlin 2004). Along relatively simple fault geometries, such as that shown in Figure 4, where off-fault melt escape routes are not apparent, the melt has instead been trapped along the fault plane, forming a continuous film and influencing dilatant-crack geometries across the propagating fault segments. Whichever the mechanism of segment linkage, the resultant stepped fault geometry is also observed in kilometre-scale active fault zones and in earthquake surface rupture patterns (Tchalenko & Berberian 1975; Bilham & Williams 1985), indicating that some of the processes of fault linkage observed in the GSZ pseudotachylytes could be potentially up-scaled. However, the influence and interaction of coseismic melt-pressure and closely spaced rupture-tip stress fields are perhaps not so easy to simply scale up across larger spatial distances.

Branching faults are common in the GSZ (Fig. 5d and e) and represent synchronous seismic slip on both branches where the pseudotachylyte is continuous across the branch intersection (Rowe et al. 2018). Such branching is a recognized feature of kilometre-scale fault zones and can also be linked on that scale to single earthquake ruptures (Poliakov et al. 2002; Fliss et al. 2005). Without good evidence for sense of displacement across the GSZ faults it is difficult to interpret the kinematics of these branches, as numerical models suggest that branching in both forward and backward directions relative to the direction of rupture propagation is possible (Fliss et al. 2005). As noted by Rowe et al. (2018), intersecting branches that slip in the same rupture must also experience different slip vectors and magnitudes of slip, so that the geometry has a direct influence on the spatial heterogeneity of rupture source properties. In the observations of Rowe et al. (2018), two thin fault branches coalesce into the wider main fault plane. We observe some additional detail by noting that one fault branch is typically wider than the other (Fig. 5d and e), which may signify that relative differences in seismic slip speed or magnitude, and hence melt production, are common between coalescing branches. In the case of the branch in Figure 5e, the discordant branch has a thicker pseudotachylyte vein and also appears to be longer than the other fault branch which forms an extension to the main fault vein and remains parallel to the foliation. Ruptures exploiting a pre-existing fault branch can sometimes terminate the rupture on the main fault branch if the secondary branch has significant length and is inclined at a shallow angle to the main fault (Bhat et al. 2007), as in Figure 5e. Typically, this termination of rupture on the main fault occurs when the branch is situated in the extensional field of the propagating rupture tip (Bhat et al. 2007). This branch configuration might also encourage the development of tensile veining (Fig. 5e) and dilational brecciation (Fig. 5f) in the intersection of the fault branches, given accommodating slip on the secondary branch. In the cited models of branching faults (Fliss et al. 2005; Bhat et al. 2007) the secondary fault branches must exist as a pre-existing structure before the rupture in question is generated along the fault. Similarly, in cases such as Figure 5e, where the secondary fault branch is discordant to the foliation, we suggest that some pre-existing heterogeneity within the amphibolite fabric may be necessary to divert the rupture down the secondary fault branch and away from the dominant plane of weakness formed by the foliation. In Figure 5f, and also in Figure 5b and c, branching faults within the confines of a paired fault zone are observed, in the sense that slip on the ‘internal’ faults is coeval and continuous with slip on the boundary faults, as indicated by brecciation in the branch intersection (Fig. 5f). However, in these cases the length of the secondary fault branch (the internal fault) is limited by the width of the controlling structure (the shear band), and so branching of the rupture along these small faults is unlikely to inhibit the continuing rupture along the main boundary fault, whatever the configuration of the secondary branch faults with respect to the main fault and stress field (Bhat et al. 2007).

Brecciation sites

Within the GSZ pseudotachylytes, there are several examples of localized dilation associated with coseismic slip and pseudotachylytes. These dilational sites are controlled by the fault geometry. Under the classification scheme of Rowe et al. (2018), these can be described as angular breccias (Fig. 5f), pull-aparts/rhombochasm (Fig. 5a) and tabular breccias (Fig. 5c). The pseudotachylyte faults in the GSZ show progressive stages of breccia development, which illustrate how these features evolve (Fig. 8).

Angular breccias are associated with dilational sites within the intersections of branching faults (Fig. 5f), although they may potentially also form between oblique adjacent fault segments. In both cases, they signify coeval seismic slip on the bounding structures. Pull-aparts filled with pseudotachylyte may contain breccia clasts (Fig. 5a) and, in the case of rhombochasms, are typically formed by dilation at extensional stepovers between fault segments. These rhombohedral pull-aparts form via secondary tensile and shear fractures which form the through-going link between overlapping faults (Fig. 8b), and do not necessarily require fluid (including melt) to fragment the rock in the overlap (Sibson 1986; Melosh et al. 2014) although high fluid pressures may assist this process (Sibson 1975; Bjørnerud & Magloughlin 2004). A similar final geometry is formed via the crack-tip propagation mechanism of segment linkage, where the isolation of a ‘bridge’ between curving, overlapping fault tips and the resultant influx of melt might induce tensile fragmentation of the bridge (Fig. 8a) once it is surrounded by melt and confinement is lost (Nicholson & Pollard 1985). The resulting breccia geometry would be defined by the curvature of the fault segments, likely producing a more rectangular stepover breccia than the rhombohedral pull-aparts (Fig. 8a and b).

The tabular pseudotachylyte breccias in the GSZ portray clearly how these structures progressively form within a single earthquake (Fig. 8c). A pre-existing shear band has been reactivated by concurrent slip on both boundaries, with exploitation of the internal oblique foliation for pseudotachylyte injection and/or potential shearing (Fig. 5b). The geometry of this stage is very similar to the ‘strike-slip duplexes’ observed in the Ikertôq Shear Zone, Greenland (Grocott 1981) and the Norumbega Shear Zone, USA (Swanson 1988), where internal Riedel shear sets are a product of interaction between the paired boundary faults and also may contain pseudotachylyte, as in the GSZ examples. The offset on these internal faults implies that they are not a product of dynamic tensile fracture as in the brecciation model of Melosh et al. (2014). In the GSZ the internal faults are extensional and orientated at a moderately high angle to the boundary faults, suggesting that they could be X-type Riedel shears which tend to indicate layer-parallel extension (Swanson 1988). This condition is considered ideal for the progressive formation of breccias from paired fault zones (Swanson 1988), which requires a combination of increasing internal fault formation combined with increasing volumes of melt in the internal zone until catastrophic fragmentation brecciates domains of the rock (Fig. 8c). In order for the paired fault zones to form, an anisotropic rock is thought to be necessary, with Swanson (1988) suggesting that these may mainly form in mylonites near the base of the seismogenic zone. However, the foliation in the Gairloch amphibolites, primarily defined by parallel orientation of prismatic amphiboles, also provides an appropriate fabric, especially where reinforced by pre-existing structural heterogeneities such as shear bands. Paired fault zones may therefore be a feature, at least at this centimetre to metre scale, of any level in the brittle crust where systematic anisotropy is present.

The presence of foliation also favours the progression to fragmentation and breccia formation due to preferential utilization of the foliation planes for fracturing (Melosh et al. 2014) and in the GSZ this is supported by the injection of pseudotachylyte along the internal foliation planes (e.g. Fig. 5b). It is not clear, however, whether this rupture geometry would be a feature of large tectonic-scale earthquakes. Riedel shears may form part of large ruptures (e.g. M_W 7.8 Kunlun earthquake, Lin & Nishikawa 2011), and strike-slip duplex geometries with paired boundary fault zones are observed at 5–10 km scales (Cembrano et al. 2005). However, the synchronous propagation of rupture along parallel segments (i.e. the paired boundary faults) has so far not been identified in active earthquakes (Rowe et al. 2018). The mechanisms allowing the paired faults to propagate past each other, rather than form linked stepovers similar to Figure 8a, is therefore of interest, although once the paired slip planes are in motion the process of forming the internal dilational pull-apart is probably much the same (Sibson 1975; Cembrano et al. 2005). Such rupture geometries may therefore be closely controlled by the spacing between the two faults (Harris et al. 1991; Ando et al. 2004) along with the favourability of the initial slip planes (Donath 1961). The aspect ratio of these elongate structures is such that even if scaled up to tens of kilometres, the separation between the boundary faults might be unresolvable at the spatial resolution of seismological observations or from geodetic observations of surface deformation.