Introduction

Material properties aside, the formation and reactivation of brittle faults and fractures is largely governed by the triaxial stress state within the rock mass and by the pore-fluid pressure, P f, within the rock mass (Hubbert and Rubey 1959; Jaeger and Cook 1979). Recognizing the boundary condition of zero shear stress along the Earth's free surface (taken as horizontal), Anderson (1905) postulated the existence of three basic stress regimes in the crust depending which of the principal compressive stresses (σ 1 > σ 2 > σ 3) coincides with the vertical stress, σ v. Normal faulting prevails where the crust is under extension with σ v = σ 1; strike-slip faulting occurs where σ v = σ 2; and thrust faulting develops where the crust is shortening under horizontal compression with σ v = σ 3. Information from borehole measurements (Townend and Zoback 2001), earthquake focal mechanisms (Célérier 2008), and palaeostress inversions (Lisle et al. 2006) demonstrates that ‘Andersonian’ stress states (one principal stress vertical and the other two horizontal) prevail over large areas of continental and oceanic crust (Zoback 1992). These ‘Andersonian’ stress orientations provide useful reference states for general consideration, though significant departures undoubtedly occur. For example, although a subduction interface shear zone (SISZ) is, in essence, a large-scale thrust fault accommodating underthrusting of oceanic lithosphere, significant departures from vertical and horizontal stress trajectories are expected from: (1) the kinematic control exerted by a weak plate boundary shear zone; (2) force balance analyses associated with a tapering accretionary wedge (e.g. Dahlen 1990); and (3) time variations in the stress field as a consequence of stress cycling associated with intermittent megathrust rupturing along the SISZ (Hasegawa et al. 2012).

Hubbert and Rubey (1959) were the first to apply the simple principle of effective stress to rocks whereby pore-fluid pressure reduces all normal stresses to ‘effective’ values, σ n′ = (σ n − P f), suggesting also that fluid overpressures were a means of reducing basal friction allowing emplacement of thrust sheets along low-angle overthrusts. They also defined a pore-fluid factor, λ v = P f/σ v, usefully relating the level of pore-fluid pressure with respect to the vertical stress. Where fluid pressure, P f, in pore and/or fracture space is freely interconnected up to a water table at the earth’s surface, the pore-fluid pressure is hydrostatic (λ v ~ 0.4). Pore-fluids are overpressured wherever pore-fluid pressures exceed hydrostatic values (i.e. λ v > 0.4). Fluid at a depth, z, is overpressured towards lithostatic values (λ v → 1.0) when P f approaches the lithostatic load (σ v = ρgz, where ρ is average rock density and g the gravitational acceleration). Supralithostatic overpressures (λ v > 1.0) occur where P f > σ v.

Formation and opening of extension fractures perpendicular to least compressive stress, σ 3, in intact rock occurs by hydraulic fracturing when

$$P_{\text{f}} = \sigma_{3} + T_{\text{o}}$$
(1)

where T o is rock tensile strength, provided (σ 1 − σ 3) < 4 T o inhibiting shear failure of the rock (Secor 1965; Etheridge 1983). For competent sedimentary rocks and crystalline rocks with T o ~ 10 MPa and ~20 MPa, respectively (Lockner 1995), differential stresses are restricted to <40 and <80 MPa. A local absence of existing fractures suitably oriented for shear reactivation is also a prerequisite. The tensile overpressure state (P f > σ 3) thus defines portions of the rock mass with the potential for hydraulic fracturing leading to the formation of extension vein arrays.

In compressional settings where σ v = σ 3, the tensile overpressure state (P f > σ 3) equates to the maximum sustainable overpressure and is close to lithostatic (Sibson 2003). It is conducive to the development and fluid activation of dilatant fault–fracture meshes developed in tabular rock volumes around low-angle thrusts and may be responsible for the range of time-dependent slow-slip activity observed around such structures.

Controls on brittle failure of rock

Criteria for all modes of brittle failure in rock include the levels of differential stress and pore-fluid pressure [through the principle of effective stress, σ n′ = (σ n − P f)]. The two drivers to failure, therefore, are (σ 1 − σ 3) and P f, which may act separately or together. In ‘classical’ rock mechanics (e.g. Secor 1965; Jaeger and Cook 1979; Sibson 2000), the composite Griffith–Coulomb failure curve for intact rock in τ/σ n′ space can be normalized to nominal rock tensile strength, T o (half the cohesive strength). The ratio of differential stress to rock tensile strength (σ 1 − σ 3)/T o then determines the potential mode of brittle failure (Fig. 1). For ‘generic’ internal friction, μ i = 0.75 in the compressional field, extension fractures form only when (σ 1 − σ 3)/T o < 4, hybrid extensional-shear fractures require 4 < (σ 1 − σ 3)/T o < 5.66, and compressional shear fractures (faults) form when (σ 1 − σ 3)/T o > 5.66 (Secor 1965). Additionally, as noted above, the presence of existing fractures appropriately oriented for reshear within the stress field suppresses the formation of any new extensional or hybrid extensional-shear fractures. Fluid circulation through a fractured rock mass may, however, restore cohesive and tensile strength by hydrothermal cementation (e.g. silicification), effectively restoring ‘intact’ character.

Fig. 1
figure 1

Potential modes of brittle failure within intact isotropic rock under horizontal compression (σ v = σ 3), in relation to axes of principal compressive stress (σ 1 > σ 2 > σ 3)

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Hydraulic extension fracturing can thus only be induced: (a) within intact rock in the absence of cohesionless faults suitably oriented for shear reactivation; (b) in settings where existing fractures are severely misoriented for reshear (containing the σ 2 axis and lying at >c. 60° to σ 1); and (c) where existing fractures have regained cohesive strength through hydrothermal cementation, etc. Rock tensile strength is thus critical in determining whether rock fails in tension or in shear under increased fluid pressure. Under the same differential stress, fluid-induced failure in heterogeneous material of mixed competence (differing tensile strength) may therefore give rise to mixed-mode brittle failure with volumetric fault–fracture meshes comprising interlinked shear and extensional fractures distributed throughout the rock mass (Sibson 1996, 2000).

Tensile overpressure compartments

Extension veins [often with ‘crack-seal’ infillings of quartz, calcite, etc., reflecting incremental precipitation (Ramsay 1980)] thus diagnose the tensile overpressure state (σ 3′ = (σ 3 − P f) < 0, or P f > σ 3) once having been achieved within the rock mass. In extensional (σ v = σ 1) and strike-slip (σ v = σ 2) stress regimes where σ 3 is horizontal, vertical extension veins may form under hydrostatic levels of fluid pressures in the near-surface (z < 1–2 km), but suprahydrostatic fluid pressures are required for their formation at depths more than a kilometre or so (Secor 1965). In compressional regimes (σ v = σ 3), however, supralithostatic overpressures are required at all depths for the formation of subhorizontal extension veins unless significant stress heterogeneity exists such that σ v < σ 3. Systematic arrays of hydrothermal extension veins are widely developed in both sub-greenschist and greenschist metamorphic assemblages (e.g. Fig. 2) and can be used to define former tensile overpressure compartments where P f > σ 3.

Fig. 2
figure 2

Systematic arrays of hydrothermal extension veins: a quartz vein array infilling subvertical extension fractures in Carboniferous sandstone (strike-slip regime), Millook, North Devon; b array of subhorizontal gold-bearing quartz veins, Damang Mine, Ghana (Tunks et al. 2004; photograph courtesy Andrew Tunks)

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Compressional stress regimes (σ v = σ 3) are particularly effective at containing fluid overpressure because: (1) activated faults and fracture tend to be flat-lying, inhibiting vertical flow and (2) under the same differential stress, faults and fractures in compressional regimes are generally capable of sustaining higher overpressures before activation to provide drainage paths than in other tectonic regimes (Sibson 2003). As with compartmentalized overpressures developed in sedimentary basins (Hunt 1990), development of overpressure generally requires a low-permeability sealing horizon perhaps associated with silicification or some other form of hydrothermal cementation. If the sealing horizon has a tensile strength, T s, overpressure will increase across it to a maximum value, P f = σ 3 + T s, at its base, where hydrofractures form, below which, provided pore/fracture space is interconnected, the pressure gradient reverts to hydrostatic (Sibson and Scott 1998). The supralithostatic overpressure condition, P f > σ v, will be maintained below the base of the seal over a vertical interval:

$$\Delta z = T_{\text{s}} /(\rho {-}\rho_{\text{f}} )g$$
(2)

(where ρ is rock density, ρ f is fluid density, and g is gravitational acceleration) to a depth where the pore-fluid pressure drops below lithostatic.

Vertical and lateral extent of tensile overpressure compartments

Variations in rock tensile strength allow horizontal hydrofracturing throughout the vertical interval of supralithostatic overpressure (Fig. 3). Sealing horizons may also migrate vertically with time. Tensile rock strength ranges from 1 to 10 MPa for sedimentary rocks of low to moderate competence, to 20 MPa or so for high-competence crystalline rocks (Lockner 1995). For T s = 10–20 MPa, Δz = 600–1200 m. These values compare with the vertical extent of horizontal vein arrays observed in Panasqueira Mine, Portugal (Foxford et al. 2000) and Sigma Mine, Val d’Or (Robert and Brown 1986). If the seal to a tensile overpressure compartment extends across a low-angle thrust-sense shear zone with dip, δ (perhaps retaining low cohesive strength through hydrothermal cementation—Fig. 3), the tensile overpressure compartment may extend laterally for a distance, L = cotδΔz. For Δz = 1 km and δ = 10°, 5°, and 1°, L = 5.7, 11.4, and 57 km, respectively. Tensile overpressure compartments may thus extend laterally for considerable distances around low-dipping thrust faults that have regained some cohesion. In reality the permeability structure is likely to be more complex than that pictured in Fig. 3. Upward flow of overpressured fluids along a thrust (cf. Saffer and Tobin 2011) is likely to transport solutes derived from deformation involving pressure solution within fine-grained fault rocks as well as solutes from prograde metamorphism of the footwall—all may contribute to cementation (especially silicification) of the hanging wall.

Fig. 3
figure 3

Vertical and lateral extent of hydrofracture arrays below a sealing horizon in a compressional stress regime. Potential hanging-wall seal discussed in text indicated by dashed shading

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Fault–fracture meshes in compressional regimes

Dispersed fault–fracture meshes may develop in compressional regimes in a number of configurations (Fig. 4). Possibilities to be considered include: (1) refraction of thrust faults across competence layering (e.g. bedding) creating localized sites of dilatation [factors affecting the degree of fault refraction across competence boundaries are discussed by Ferrill and Morris (2003)]—the overall dip envelope then depends on the ratio of extension fractures to thrust-sense shear fractures; (2) dilational thrust stepovers/jogs arising from stress heterogeneity associated with en echelon thrust segmentation; (3) distributed fault–fracture meshes developing within a mixed competence mélange shear zone (Sibson 1996; Fagereng and Sibson 2010). To a greater or a lesser extent, fault–fracture meshes occupy a substantial rock volume rather than being restricted to discrete planar slip zones. An important issue (not further considered) is whether dilatation accompanying opening of extension fractures and their infilling with precipitates is compensated in the long run by volume loss in the surrounding rock mass from dissolution and solution transfer.

Fig. 4
figure 4

Development of fault–fracture meshes in a compressional thrust regime: a low-angle thrust refracting across more competent (high tensile strength) layers which fail by extension fracturing; b extension fracturing localized in a dilatational stepover (jog) between en echelon thrust faults; c extension fracturing concentrated in an aggregate of high-competence pods in a mélange formation

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Frictional reshear of low-angle thrusts

In a simple compressional regime with σ v = σ 3, a low-dipping planar discontinuity (e.g. an existing fracture or fault, a bedding plane, or foliation) may lie at a very low angle to σ 1. The stress condition for frictional reactivation of an existing cohesionless plane with a friction coefficient, μ s, containing the σ 2 axis is:

$$\sigma_{1}^{{\prime }} /\sigma_{3}^{{\prime }} = (\sigma_{1} - P_{\text{f}} ) /(\sigma_{3} - P_{\text{f}} ) = (1 + \mu_{\text{s}} \cot \theta_{\text{r}} ) /(1 - \mu_{\text{s}} \tan \theta_{\text{r}} )$$
(3)

where θ r is the angle of reactivation with respect to σ 1 (Sibson 1985). For the situation where σ v = σ 3, this expression may be rewritten as:

$$(\sigma_{1} - \sigma_{3} ) /(\sigma_{3} {-}P_{\text{f}} ) = (\sigma_{1} - \sigma_{3} ) /(\sigma_{\text{v}} {-}P_{\text{f}} ) = \mu_{\text{s}} [(\tan \theta_{\text{r}} + \cot \theta_{\text{r}} ) /(1 - \mu_{\text{s}} \tan \theta_{\text{r}} )]$$
(4)

defining the reactivation condition plotted in Fig. 5 for μ s = 0.6 [the lower end of Byerlee’s (1978) range for hard-rock friction]. The ratio (σ 1 − σ 3)/(σ v − P f) \(\to \infty\) as θ r → 59° or 0°, requiring P f → σ v. In the case of a thrust fault that retains (or has acquired) some cohesive strength, c, the fluid pressure requirement for reactivation of faults approaching frictional lock-up becomes supralithostatic (P f = σ v + c/μ s) (Sibson 2009). The essential point is that the overpressure condition needed to induce thrust reshear along thrusts at very low angles to σ 1 (P f → σ v) is near-lithostatic or even supralithostatic and very close to the hydraulic fracturing criterion. Under such circumstances, slight heterogeneities in the stress field or in rock material properties may allow hydraulic extension veins to form subparallel to thrust-reactivated planes.

Fig. 5
figure 5

Reactivation factor (σ 1 − σ 3)/(σ 3 − P f) plotted against the reactivation angle, θ r (in accordance with Eq. 4), for shallow-dipping thrust faults with σ v = σ 3

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Tensile overpressure compartments along low-angle intracontinental thrusts

Here we consider geological and geophysical evidence supporting the existence of tensile overpressure compartments associated with both active and ancient low-angle thrust faults developed within continental settings.

San Gabriel Mountains bright reflective zone

The LARSE seismic line (Ryberg and Fuis 1998; Fuis et al. 2001) runs NNE-NE from Seal Beach across the Los Angeles Basin, then crosses the upthrust crystalline massif of the San Gabriel Mountains and the bounding San Andreas fault to the Mojave Desert. The San Gabriel Mountains are made up of Proterozoic age gneisses with a metamorphosed cover sequence intruded by Mesozoic granitoid plutons, all thrust over the Pelona Schist along the Vincent thrust fault. The experiment revealed the existence of a bright reflective zone below the San Gabriel Mountains with two particularly intense bright-spots, deepening from 18 km in the SW to 23 km in the NE (average dip c. 10°), more or less coincident with the base of the seismogenic zone. Recognition of a marked negative velocity step at the top of the c. 500-m-thick low-velocity zone has led to its interpretation as a lithostatically overpressured thrust-sense ductile shear zone serving as a mid-crustal décollement. Arrays of gaping flat-lying macroscopic cracks infilled with lithostatically pressured fluid and lying subparallel to shear zone foliation are inferred to account for the markedly high reflectivity of the shear zone (Ryberg and Fuis 1998).

Cooper Basin induced microearthquake swarm

The Cooper Basin in north-eastern South Australia contains a cover sequence of Late Carboniferous—Triassic sediments, some 3.6 km thick, overlying a mid-Carboniferous granitic basement. The contemporary stress regime is one of regional compression with σ 3 vertical and regional σ 1 oriented 082° ± 5° (Holl and Barton 2015). The basement assemblage below the insulating blanket of cover sediments is a significant source of radiogenic heat, and the region has been assessed as an enhanced geothermal system (EGS) with a temperature of c. 250 °C encountered at the base of a borehole some 4.25 km deep (Baisch et al. 2006). A series of injection experiments down different wells produced a tabular, flat-lying microearthquake swarm <100–150 m thick extending initially over an area of 2 km × 1.5 km, but expanding significantly with further injection experiments (Baisch et al. 2009, 2015; Cox 2016), and dipping very gently WSW (Fig. 6). Of the 525 focal mechanisms obtained from the induced microearthquake swarm, the great majority yield thrust solutions with one very low-angle nodal plane dipping c. 10° W parallel to the sheet dip of the swarm, but a few have more moderately dipping nodal planes (Baisch et al. 2015). Fluid pressure during injection at the bottom of the wells approached lithostatic or slightly supralithostatic (Holl and Barton 2015). The activated structure hosting the swarm is generally interpreted as a simple planar thrust fault, but the volumetric character of the swarm, together with its very low-angle attitude, suggests it may represent a distributed fault–fracture mesh (Sibson 1996) comprising interlinked minor thrusts and extension fractures developed by hydrofracturing (Fig. 6). Note that this swarm was induced by comparatively rapid overpressuring, and the length of time for which overpressuring may be maintained in comparison with natural settings, given the possibility of subcritical crack growth, etc., is questionable. Nonetheless, at the very least the swarm activity provides an example of thrusting activity on low-angle planes almost perpendicular to σ 3 induced by close-to-lithostatic fluid overpressures.

Fig. 6
figure 6

Schematic of Cooper Basin geothermal field with gently inclined tabular belt of induced microearthquakes (not to scale) and inferred fault–fracture mesh developed within a compressional stress field with σ v = σ 3

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Sabie—Pilgrim’s Rest Au-quartz mineralization

The Sabie—Pilgrim’s Rest goldfield of the Eastern Transvaal in South Africa is hosted within the lower Transvaal carbonate-siliciclastic sequence exposed along the westerly dipping rim of the Palaeoproterozoic Transvaal Basin (Harley and Charlesworth 1992, 1996). Au-quartz mineralization is largely hosted along bedding plane thrusts and is likely coeval with early stages of the emplacement of the Bushveld igneous complex (c. 2060 Ma) (Boer et al. 1995). In the Elandshoogte Mine, thin (0.2–0.5 m, locally <2 m) zones of laminated, incrementally deposited Au-quartz mineralization resulting from multiple episodes of brecciation and hydrothermal cementation are concentrated along bedding plane thrusts dipping c. 5°W. The mineralized bedding plane shears are sometimes imbricated in thrust duplexes and are also flanked by bands of silicification in which flat-lying extension veins occur subparallel to the bedding plane thrusts (Fig. 7). Subordinate steep (sometimes subvertical) leader veins also occur locally throughout the goldfield. Plausibly, they formed from time to time as a consequence of transitory switching to an extensional stress field following total shear stress release along the low-angle thrusts.

Fig. 7
figure 7

a Setting of bedding plane thrusts hosting Au-quartz mineralization in the Sabie—Pilgrim’s Rest goldfield, Eastern Transvaal, South Africa; b flat-lying hydraulic extension veins in silicified hanging wall to thrust; c mineralized thrust fault showing repeated fracturing with brecciation and cementation

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The evidence for incremental precipitation coupled with the low transport solubility of gold (c. 10 ppb?) suggests that intermittent high flux episodes of hydrothermal flow passed through the system. Mineralization appears to have developed under a stratigraphic cover of c. 8.2 km (corresponding to an overburden pressure of 220–250 MPa) at a temperature of c. 320 °C, typical of a mesothermal assemblage (Boer et al. 1995). The significance of the vein assemblage occupying bedding plane thrusts with subparallel (within a few degrees) extension veins is the demonstration that thrusting occurred at very close to lithostatic fluid overpressures (Harley and Charlesworth 1996).

Glarus Overthrust, Switzerland

The Glarus Overthrust of Oligocene–Miocene age is well exposed at elevations approaching 3000 m in the Swiss Alps as a generally flat-lying but arched thrust contact (Fig. 8) between overlying Mesozoic carbonates and the Permian Veruccano formation emplaced over Tertiary Flysch (Herwegh et al. 2008). The present flat-lying attitude of the Glarus Thrust differs from its likely low-angle (c. 15°S) orientation when active (Pfiffner 1986). Over 35 km of northward translation has occurred across an ~1-m-thick shear zone of shear zone of highly deformed carbonate—the Lochseiten tectonite—with crystal plastic deformation occurring over temperatures ranging from 230° to 360 °C with increasing palaeodepth.

Fig. 8
figure 8

Cartoon of Glarus overthrust, Switzerland, illustrating ~35 km NW translation of hanging wall (after Badertscher and Burkhard 2000)

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The Lochseiten calc-mylonite was interpreted by Schmid (1975) as resulting from superplastic deformation. However, more recently Badertscher and Burkhard (2000) documented field, petrographic, and isotopic evidence for multiple episodes of cataclasis and hydrofracturing leading to vein formation (indicative of the tensile overpressure state), overprinted by ductile crystal plastic smearing of cataclasites and veins. Most of the calcite in the Lochseitenkalk tectonite thus likely originated as vein calcite. The isotopic evidence suggests that large fluid volumes were channelled along the mylonitic shear zones with periodic build-up of fluid overpressure to near-lithostatic values inducing cataclastic deformation, hydrofracturing and vein formation, followed by renewed crystal plastic deformation once discharge and drops in fluid pressure had occurred.

Similar textures and deformation histories have been invoked for calc-mylonites associated with the Gavarnie Thrust in the Pyrenees (McCaig et al. 1995) and the McConnell Thrust in Alberta (Kennedy and Logan 1997).

Tensile overpressure compartments along subduction interfaces

Megathrust ruptures hosted within subduction interface shear zones (SISZ) (Fig. 9) are also low-angle structures, dipping <5° in the vicinity of the trench inner wall to c. 15° around the maximum down-dip limit of the ruptures at depths of 40 ± 5 km (governed by isotherms in the 350–450 °C range), perhaps 150–200 km inboard from the trench axis (Hyndman 2007; Lay et al. 2012). Details of the internal structure of SISZ and the physical conditions prevailing therein are inevitably speculative, but are constrained by geophysical observations and the structural characteristics of analogous exhumed thrust zones. Mélange formations so typical of exhumed SISZ (Fagereng 2011; Kimura et al. 2012) are of particular interest because of the likelihood of extreme stress and competence (i.e. tensile strength) heterogeneity within such formations (Fagereng and Sibson 2010).

Fig. 9
figure 9

a Schematic of megathrust rupture lying within a subduction interface shear zone (SISZ) based on the 2011 Tohoku-Oki Mw9.0 earthquake, northern Japan; b possible structural features influencing fast- and slow-slip rupturing within a SISZ (schematic and not to scale)

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A strong case can be made that the megathrusts [responsible for >90% global release of seismic moment (Pacheco and Sykes 1992)] are weakened by fluid overpressuring to near-lithostatic values (λ v → 1.0). The hosting subduction interface shear zones (SISZ) likely contain a mélange assemblage of entrained fluid-rich ocean floor sediments (muds, siliceous oozes, etc.), plus trench wall sediments (turbidite sands and muds) along with similar material from the accretionary prism, together with slivers of oceanic crust and occasional seamount volcanics (Von Huene and Scholl 1991; Kimura et al. 2012). Overpressures within the material entrained in SISZ probably arise through a combination of compaction under increasing mean stress together with metamorphic dehydration of the descending oceanic crust under rising temperature (Saffer and Tobin 2011). Force balance analyses taking account of surface and Moho topography limit depth-averaged shear stress along subduction interfaces to <40 MPa (Wang and Suyehiro 1999; Lamb 2006; Seno 2009), as does the lack of evidence for significant shear heating along the interface (Peacock 2004), and the inference of total shear stress release during large megathrust ruptures (Hasegawa et al. 2012). This equates to an ‘effective friction coefficient’ μσ′ ≈ μσ(1 − λ v) of 0.03 averaged over the full depth (c. 40 km) of the seismogenic megathrust (Sibson 2014). Even for the lowest measured friction coefficients (μσ ~ 0.1 for saponite-rich gouge) overpressures with λ v > 0.7 are required to match this effective friction coefficient.

These inferences are supported by geophysical imaging which reveals thin (several km scale) tabular shear zones, locally highly reflective and with anomalously low V P, high V P/V S and low Q (e.g. Kodaira et al. 2002; Abers 2005; Eberhardt-Phillips and Reyners 1999; Song et al. 2009) thought to represent fluid-rich low-permeability SISZ. In a profile across the Costa Rica subduction margin, Bangs et al. (2015) found a high-reflectivity interface extending to depths of c. 6 km, implying an overpressured fluid-rich interface drained by arrays of fluid-rich faults cutting through the hanging wall. MT electrical imaging provides additional constraints on fluid content. For instance, the seismogenic portion of the Cascadia subduction interface below Vancouver Island coincides with an inclined tabular zone of high electrical conductivity (Kurtz et al. 1990; Soyer and Unsworth 2006). In southwest Japan, likewise, a highly reflective low-velocity layer dips c. 7°NW below Shikoku Island, down-dip from a subducting seamount on the inner wall of the Nankai Trough, defining the subduction interface that ruptured in the 1946 Mw8.1 Nankaido megathrust earthquake. This structure also appears to represent a zone of high electrical conductivity which Kodaira et al. (2002) interpret as an overpressured fluid-rich layer. Contained fluids are inferred to be predominantly aqueous (including free water within pore/fracture space and bound water within hydrous minerals) with lesser CO2 and hydrocarbons.

Stress heterogeneity within a subduction interface shear zone (SISZ)

Subduction mélange formations are typically characterized by relatively competent phacoids of sandstone, cherts, and metavolcanics set in a mud-rich matrix (Kimura et al. 2012). In deeper portions of the seismogenic zone (T > 150 °C) where ductile deformation mechanisms (e.g. solution transfer) come into play, progressive simple shear leads to the development of an oblique foliation along X–Y planar trajectories of the finite strain ellipsoid in the fine-grained mud matrix (Fig. 10), the degree of obliquity to the shear zone walls decreasing with increasing shear strain (Ramsay and Graham 1973). As noted by Bridgewater et al. (1973), the finite X stretching direction then ends up lying subparallel to the regional shortening direction. Where present, such foliation anisotropy may become a preferential failure plane for propagating earthquake ruptures.

Fig. 10
figure 10

Schematic of subduction interface shear zone (SISZ) with oblique foliation following X–Y planar trajectory of finite strain ellipsoid and boudin trains of stretched competent layers. While boudins elongate parallel to the maximum finite extension, X, the internal stress state within boudins (shown in inset) arising from fibre stresses differs markedly from the far-field stress field driving thrust-sense shear across the SISZ

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Within mélange formations in the Shimanto Belt of SW Japan, Kimura et al. (2012) noted the predominance of quartz ± calcite extension veins developed in sandstone phacoids, roughly orthogonal to their long axes. The stress state inside a phacoid is dominated by fibre stresses imposed by viscous drag along the boundaries of competent layers (Lloyd et al. 1982; Needham 1987) giving rise to ‘pinch and swell’ features (sometimes involving low-angle Riedel shears), boudinage, and extension fractures/veins developed orthogonal to the long axes of phacoids. Comparable systems of predominantly quartz extension veins disrupt competent phacoids in the Chrystalls Beach mélange of SE Otago, NZ, a mixed continuous–discontinuous shear zone developed in an accretionary setting of Triassic age (Fagereng 2011). However, as well as extension veins developed in the phacoids, innumerable, incrementally developed quartz (and, locally, calcite) slickenfibre veins with consistent shear sense are developed on shear surfaces lying subparallel to the flat-lying matrix foliation. Again, the extension veins are predominantly orthogonal to phacoid long axes and near-perpendicular to the flat-lying foliation developed in the surrounding mud-rich matrix. Microstructural analyses demonstrate that the flat-lying slickenfibre shears and near-orthogonal extension veins in relatively competent sandstone phacoids were coeval, together forming a fault–fracture mesh accommodating brittle shearing along the foliation (Fagereng et al. 2010). It appears that because of the large rotational strains developed within a SISZ, stress states induced within extending phacoids are locally dominant and distinct from the far-field stress field driving thrust-shearing across the SISZ (Fig. 10).

Low-permeability seals within SISZ

For near-lithostatic overpressures to be developed and maintained within a SISZ, bulk permeability must average <10−20 m2, or an order of magnitude lower if the overpressures are contained by a thin (<1 km) caprock seal (Peacock et al. 2011). Among contributing factors to the development of such low permeabilities, the first is the likely presence of a high proportion of fine-grained silicic mudrock and the second, the active hydrothermal environment (150 < T < 350 °C) within at least the lower half of the seismogenic SISZ. Under such conditions solution transfer will tend to reduce porosity and infills fractures with hydrothermal precipitates over short distance and time scales, contributing to silicification seals and adding cohesive strength (Rutter 1976; Kawabata et al. 2007; Rowe et al. 2009; Fisher and Brantley 2014). In addition, high strain shearing during progressive metamorphism will impose a foliation defined by aligned phyllosilicates oblique, but subparallel to the SISZ margins giving rise to permeability anisotropy with foliation-perpendicular permeability significantly lower than that parallel to foliation, thereby impeding vertical fluid transport. Formation of fault–fracture permeability during ongoing deformation competes with permeability reduction as a consequence of hydrothermal precipitation.

SISZ host seismogenic megathrusts which typically rupture at intervals of 100–1000 years, or so. Permeability within a SISZ thus varies with time, changing from extremely low values pre-failure to high localized values postfailure when high fracture permeability is expected within rupture zones with fractures predominantly aligned subparallel to foliation in the SISZ. Postfailure ‘seismogenic permeability’ may be in the range, 10−16–10−13 m2 (Talwani et al. 2007), but will likewise be anisotropic with higher values subparallel to the foliation and the margins of the SISZ. These high postfailure permeabilities are, however, likely to be transitory diminishing rapidly through the aftershock period as a consequence of fracture healing and cementation in the active hydrothermal environment (cf. Bosl and Nur 2002).

A potentially important additional source of silica-saturated fluid comes from serpentinization of the forearc mantle (Hyndman et al. 2015), with fluid channelled along the SISZ to create low-permeability silicification caps along the SISZ hanging wall at depths of 25–40 km characterized by high V P/V S from silica enrichment (Audet and Bürgmann 2014). In combination with the effects of solution transfer within SISZ, silicification arising from serpentinization has multiple effects—restoring cohesive strength to existing fractures, reducing porosity, precipitating low-permeability seals, and promoting overpressuring in areas of fluid release.

Association with anomalous slip behaviour

Along northern portions of the Hikurangi subduction margin offshore from Gisborne, New Zealand, Bell et al. (2010) have demonstrated an association between low-dipping (0°–9°) areas of the subduction interface at shallow depth (c. 10 ± 5 km) that are undergoing periodic slow-slip with anomalously high seismic reflectivity in regions where the interface is locally upwarped by subducting seamounts. The anomalous reflectivity is attributed to overpressured fluid-rich sediments. At depths of 25–25 km along the Tokai segment of the Nankai Trough subduction system, immediately northeast of the 1944 Mw8.1 Tonankai megathrust rupture, Kodaira et al. (2004) find an association between the 60 km × 60 km areal extent of a slow-slip event on the interface locally dipping c. 16° and a highly reflective portion of the plate interface directly overlying subducted oceanic crust with anomalously high Poisson’s ratio denoting strong fluid overpressuring. The down-dip limit to seismogenic activity in the Nankai subduction system is defined by a belt of non-volcanic tremor [NVT—equivalent to episodic tremor and slip (ETS) in Cascadia] at depths of c. 35–45 km (Obara 2002). Very-low-frequency earthquakes with extremely low stress drops located in the Nankai accretionary prism are likewise attributed to rupturing of fluid-saturated rock under extreme overpressure (Ito and Obara 2006). A high-resolution study of this belt by Shelly et al. (2006) reveals a band of low-frequency earthquakes (LFEs) along the subduction interface dipping 10° NNW overlying a band of microearthquakes within the oceanic crust of the subducting lithosphere which, from its V P/V S signature, appears to be fluid-rich from metamorphic dewatering and highly overpressured.

Discussion and conclusions

The hypothesis advanced here is that local attainment of the tensile overpressure state (P f > σ 3) is associated with formation and activation of distributed fault–fracture meshes that are capable of giving rise to a variety of anomalous slow-slip phenomena (LFEs, VLFEs, NVT, etc.). A great deal of circumstantial evidence supports this hypothesis, but further testing is clearly needed for full substantiation.

Geological and geophysical field evidence suggests that the tensile overpressure state (creating tensile overpressure compartments where σ 3′ = (σ 3 − P f) < 0, and hydraulic fracturing is widespread) is locally developed in both sub-greenschist and greenschist metamorphic assemblages. An association with active low-angle thrust faults (dips mostly <15°) in compressional regimes (including continental thrusts and subduction thrust interfaces) is sometimes evident from inferred geophysical characteristics (high seismic reflectivity, anomalously high V P/V S, and high electrical conductivity), suggesting that ~lithostatic levels of fluid overpressuring (i.e. P f ~ σ v) are locally achieved. In some instances, a relationship between potential tensile overpressure compartments and different varieties of anomalous slip phenomena (slow-slip events, LFEs, VLFEs, NVT, etc.) is apparent.

Circumstances contributing to the development of distributed fault–fracture meshes in tensile overpressure compartments include: (1) varying competence within the rock mass (e.g. in a mélange formation) inducing diverse modes of brittle failure (Fagereng and Sibson 2010; Fagereng 2011; Kimura et al. 2012); (2) extensive solution transfer of silica and other hydrothermal materials following dissolution along foliation which serves to reduce existing porosity, helps form low-permeability seals promoting development of overpressure, and restores cohesion across existing fractures preventing shear localization (Kawabata et al. 2007; Rowe et al. 2009). For example, the intensely veined Rodeo Cove thrust zone at Marin Headlands within the Franciscan Complex of California has many of the hallmarks of a subduction fault–fracture mesh assemblage (Meneghini and Moore 2007).

Incremental shear displacement across fault–fracture meshes necessarily involves dilatation of extension fractures coupled to increments of shear displacement so that they have a tendency to act as viscous ‘dashpots’ slowing down slip transfer (Fig. 11). This allows a spectrum of time-dependent behaviour depending on the proportion of shear to extensional fractures, fluid viscosity, rate of overpressure generation, etc. Such structures may plausibly be responsible for the range of observed slow-slip behaviour including LFEs, VLFEs, NVT (or ETS). Maintenance of near-lithostatic fluid overpressures is precarious, and it is likely that fault–fracture meshes overpressured to near-lithostatic levels are extremely unstable. Loss of fluid from an overpressured mesh will cause frictional strengthening and a change in slip behaviour.

Fig. 11
figure 11

Possible ‘volumetric’ source model for anomalous slow-slip (LFEs, VLFEs, NVT, etc.). Local development of a thrust fault–fracture mesh within a ‘log-jam’ of competent boudins developed within a SISZ. Thrust ruptures tend to follow anisotropy from oblique shear zone foliation. Slip transfer involves dilatational opening of linking extension fractures and associated fluid diffusion. Equivalent rheological model whereby rate-and-state frictional instability is damped by viscous dashpot

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