Temporal changes in sealing time
Fluid inclusion analysis revealed a large fluid pressure change during each crack-seal event (Fig. 4). This may also be indicated by the wide variation in the homogenization temperatures (150–280 °C) across multiple solid inclusion bands in the shear veins from the same vein concentration zone in the Makimine mélange (Nishiyama et al. 2020). To estimate the time for each crack-seal event, we considered fluid advection through the cracked shear vein, during which fluid pressure dropped from lithostatic to hydrostatic (235 MPa at a depth of 15 km). The kinetic equation of quartz precipitation driven by a fluid pressure drop in an advecting fluid is given as (Rimstidt and Barnes 1980):
$$\frac{{\partial C_{{SiO_{2} }} }}{\partial t} = k\frac{{A_{{{\text{H}}_{2} {\text{O}}}} }}{{M_{{{\text{H}}_{2} {\text{O}}}} }}\left( {C_{{{\text{SiO}}_{2} ,{\text{eq}}}} - C_{{{\text{SiO}}_{2} }} } \right)$$
(2)
where CSiO2 is the concentration of SiO2 in the fluid, CSiO2,eq is the solubility of quartz in the fluid at hydrostatic pressure, t is the time, MH2O is the mass of H2O in the crack, and AH2O is the reactive surface area. k is the precipitation rate of quartz, which is empirically determined by log10k = − 0.0886–2638/T, where T is the temperature (Okamoto et al. 2010). Following Ujiie et al. (2018), the model considered inclusion band spacing, a typical length of shear veins (1 m), a temperature of 330 °C, and fluid pressure drop from lithostatic to hydrostatic values. We assumed that the precipitation rate of quartz remained constant regardless of the band spacing. The SiO2 concentration at t = 0 was equal to the quartz solubility at lithostatic fluid pressure and dropped to CSiO2,eq + 0.001 mg kg−1 through the crack. Quartz solubility was calculated using LonerAP, developed by Akinfiev and Diamond (2009).
Figure 3 shows the temporal changes in sealing time between individual thrusting events. The sealing time cyclically changed between 0.16 ± 0.04 and 2.7 ± 0.8 years, with a mean value of 1.1 years. Based on the results, we estimated the durations of the decrease and increase in the sealing time. In the estimations for transect 4 of sample R2 and transects 1 and 2 of sample R1, we assumed that the decrease in sealing time continued until the sealing time reached its minimum value (Figs. 3d–f). The estimated durations of temporal decrease and increase in the sealing time ranged from 11 ± 1 to 51 ± 2 years and from 16 ± 1 to 42 ± 3 years, respectively.
Relating temporal changes in sealing time to SST recurrence intervals
Assuming complete crack healing during crack-sealing by fluid advection, the estimated sealing time of ~ 0.16–2.7 years between each crack-seal event gives the minimum time interval of repeated brittle fracturing events. Crack-seal events can also occur through the local transport of silica by diffusion (Renard et al. 2000; Fisher and Brantley 2014). Fisher et al. (2019) considered that the diffusive distribution of silica in mélange shear zones was promoted by a transient drop in fluid pressure or a difference in mean stress between blocks and matrix in the mélange. The latter is unlikely for the shear veins in the Makimine mélange as the vein concentration zone is poor in blocks, while shear veins mostly developed in the mudstone matrix (Fig. 1c). When crack-seal events take place by local diffusion of silica driven by the fluid pressure difference between the wall rock and crack, the sealing time (t) can be expressed as (Fisher and Brantley 2014)
$$t = \frac{{k_{d} l^{2} + 2V_{q} \phi \tau D_{f} F_{d} C_{2} l}}{{2k_{d} lV_{q} \phi \tau D_{f} F_{d} \left( {C_{{{\text{SiO}}_{2} ,1}} - C_{{{\text{SiO}}_{2} ,2}} } \right)}}{ }$$
(3)
where kd is the dissolution rate constant of quartz, l is the inclusion band spacing, Vq is the molar volume of quartz, ϕ is the porosity of the wall rock, τ is the tortuosity, Df is the diffusion coefficient of silica through the grain boundary, \(C_{{{\text{SiO}}_{2} ,1}}\) and \(C_{{{\text{SiO}}_{2} ,2}}\) are the quartz solubility at the site of dissolution (wall rock) and growth (crack), respectively, and Fd is the volume fraction of dissolved quartz in the wall rock. kd was obtained from the kinetic equation proposed by Tester et al. (1994). ϕ was assumed to be 0.01, based on the porosities of metasediments metamorphosed at depths of 10–15 km (Bray and Karig 1985). Df and τ were 1 × 10−10 m2 s−1 and 1, respectively (Fisher and Brantley 1992; Gratier et al. 2009). The Fd value of 0.11 was obtained from the difference in SiO2 concentration between mudstone in the vicinity of the shear vein and mudstone far from the vein. SiO2 concentrations were estimated from the results of inductively coupled plasma mass spectrometry measurements. \(C_{{{\text{SiO}}_{2} ,1}}\) and \(C_{{{\text{SiO}}_{2} ,2}}\) were calculated using the LonerAP software. Figure 5a shows the relationship between the fluid pressure difference and the sealing time estimated from Eq. (3). When the fluid pressure changes from lithostatic to hydrostatic values at the depth of 15 km, the sealing time ranged from 0.04 ± 0.02 to 4 ± 2 years, comparable to the time of crack-sealing by fluid advection (Fig. 5). Thus, irrespective of whether the crack sealing occurred by fluid advection or local diffusion, the minimum time interval of individual brittle thrusting was in the range of 0.04–4 years when the fluid pressure changed from lithostatic to hydrostatic values. Considering the infiltration of mantle-derived fluids into the Makimine mélange (Nishiyama et al. 2020) and the fault–fracture mesh geometry in the vein concentration zone, rapid sealing by fluid advection rather than local diffusion of silica is likely to be the dominant mechanism of crack sealing.
The spacing of crack-seal bands may also reflect the local stress field or rock physical properties, as the crack aperture (d) is expressed as \(d \approx 2\sigma L/E\), where σ is the driving stress, L is the crack length, and E is the Young’s modulus of the wall rock (Renard et al. 2005; Gudmundsson 2011; Fisher et al. 2019). Fisher et al. (1995) suggested that E might progressively increase with an increase in quartz content due to vein growth, leading to a decrease in d. However, this is unlikely for the shear veins in the Makimine mélange as the band spacing not only decreased but also increased with time (Fig. 3). Alternatively, if E and L remain constant, the spatial change in the band spacing might reflect the temporal variation in σ (Renard et al. 2005). Assuming E = 10–70 GPa for mudstones (Turcotte and Schubert 2002), d = 4–65 μm, and L = 1 m, the spatial changes in band spacing may reflect temporal variations in \(\sigma\) in the range of 0.31–2.1 MPa. These small values of σ are consistent with the inferred elevated fluid pressure in the vein concentration zones in the Makimine mélange.
The kinematics of low-angle thrust faulting, 0.1–0.2 mm slip increments, and brittle fracturing under near-lithostatic fluid pressures recorded in the shear veins may be comparable to conditions of LFEs (Shelly et al. 2006, 2007; Bostock et al. 2012, 2015). However, the length of individual shear veins is ~ 1–10 m, which is smaller than the dimensions of individual LFEs, ranging from 100 to 1000 m (Bostock et al. 2015). On the other hand, the length scales of the vein concentration zones are > 100 m, similar to those of the LFEs. The estimated sealing time of ~ 0.16–2.7 years is longer than the recurrence interval of LFEs (seconds to days, Frank et al. 2015) but is comparable to that of the SST (months to years, Behr and Bürgmann 2021). Considering that the shear veins constitute fault–fracture meshes in the subducting mélange, brittle fracturing at individual shear veins may represent a small component of tremor composed of LFEs, which occurred in different locations within the ~ 10–60 m thick vein concentration zones.
The lithostatic to hydrostatic pressure changes (222–280 MPa) recorded in the crack-seal shear veins appear to be much larger than the small stress drop (1–100 kPa) and the small fluid pressure change (1–10 MPa) observed in the SST source area (Rubinstein et al. 2007; Bostock et al. 2015; Gosselin et al. 2020). The stress drop can be large when the shear strength (τ) is described by the effective normal stress, τ = C + μ(σn − Pf), where C is the cohesive strength, μ is the friction coefficient, σn is the normal stress, and Pf is the fluid pressure. However, the shear veins in the Makimine mélange formed as dilational shear fractures, as indicated by the shear veins at a very small angle (5.5°) to σ1 and the opening of shear veins at high angles to the vein margin (Ujiie et al. 2018 and Fig. 2). In this case, τ can be written as τ2 − 4T0σn − 4T02 = 0, where T0 is the tensile strength. Therefore, the stress drop may remain very small even if fluid pressure changes were large. Indeed, the stress drop, estimated from slip increments (0.1–0.2 mm), vein length (1–10 m), and shear modulus (3 GPa, Takahashi et al. 2002), was in the order of tens to hundreds of kPa, which is consistent with the estimated small stress drops during SST (cf. Fagereng et al. 2011; Ujiie et al. 2018).
Large discrepancies in fluid pressure changes between geophysical and geological observations may arise from the large differences in spatial resolution. While large fluid pressure changes were derived from the fluid inclusions between volumetrically minor crack-seal bands of several tens of microns in thickness, small fluid pressure changes were estimated from receiver function data at vertical scale lengths of 1–10 km, which could represent averaged fluid pressure changes in the low-velocity layer (LVL) (Gosselin et al. 2020). Thus, while large fluid pressure changes could occur in narrow cracks, the entire fluid pressure changes in the subduction mélange (or LVL) may be small.
The analyzed shear veins recorded two cycles of temporal decrease and increase in sealing time, with one cycle lasting ≥ 27 ± 2 to 93 ± 5 years. The range of one cycle duration is within the recurrence intervals of megathrust earthquakes larger than Mw 7 in subduction zones. Historical documents, historical earthquakes, and geological records of tectonic subsidence and tsunami over the last ≤ 8000 years indicate that the recurrence intervals of megathrust earthquakes in the Nankai, Sumatra, and Chile subduction zones were 90–200, 63–157, and 128–300 years, respectively (Additional file 1: Table S2; Lomnitz 1970; Ando 1975; Bilham et al. 2005; Cisternas et al. 2005; Malik et al. 2019). Therefore, if the inclusion band spacing in the analyzed shear veins represents the SST recurrence interval, our results suggest that the SST recurrence interval may temporally decrease and increase during megathrust earthquake cycles.