An inhomogeneous across-slab conduit controlled by intraslab stress heterogeneity in the Nankai subduction zone

Nonvolcanic, deep low-frequency tremors and slow-slip events occur simultaneously in the transition zone from locked to continuously creeping fault in the down-dip portion of the Nankai Trough subduction zone, southwestern Japan. The occurrence of these slow earthquakes is discontinuous along the trench and attributed to the effect of high pore pressures at the plate boundary. Here, we show that spatial variations in intraslab stress may control fluid migration from the subducted Philippine Sea slab to the plate boundary. The triaxial normal faulting stress, detected by stress tensor inversion using focal mechanisms in the slab, controls anisotropically permeability that trends NNW–SSE subhorizontally from the subducted Philippine Sea slab to the plate boundary. The inhomogeneous permeability controlled by spatial stress heterogeneities in the subducted Philippine Sea slab controls the intraslab fluid pathway. This hypothesis is consistent with the spatial heterogeneity of slow earthquakes and 3He/4He ratio distributions.

Scientific RepoRts | (2019) 9:994 | https://doi.org/10.1038/s41598-018-38142-w multiple inverse method (MIM) 7 to separate stresses derived from earthquake focal mechanism data from the spatially variable state of stress. Figure 1 shows focal mechanism data of seismic events in the Philippine Sea slab beneath Shikoku and the Kii Peninsula, which are made publicly available by the National Research Institute for Earth Science and Disaster Prevention (NIED), Japan. The data correspond to 188 seismic events that occurred between 1 January 1997 and 31 December 2010. All the foci were located in the depth range of 35-70 km, and all the events had magnitudes exceeding 3.2 (Fig. 1a). The P-and T-axes of the focal mechanisms are illustrated in Fig. 1b. Most of the events represent normal and strike-slip faulting with NE-SW-to E-W-trending T-axes (Fig. 1b).
separating stresses from heterogeneous focal mechanism data. Three stresses, labelled A, B, and C, were detected by the MIM (Fig. 2a). Stress A has σ 1 and σ 3 orientations (strike/dip) of 153°/55° and 245°/2°, respectively, and a stress ratio Φ (Φ = (σ 2 -σ 3 )/(σ 1 -σ 3 )) of 0.92 (Fig. 2a) where σ 1 , σ 2 , and σ 3 are the maximum, intermediate, and minimum principal stress magnitudes, respectively. The second solution, Stress B, has σ 1 and σ 3 orientations of 337°/13° and 70°/12°, respectively, and a stress ratio Φ of 0.86 (Fig. 2a). The third solution, Stress C, has σ 1 and σ 3 orientations of 170°/76° and 62°/4°, respectively, with a stress ratio Φ of 0.34 (Fig. 2a). The σ 1 and σ 3 orientations of the stresses do not overlap at 95% confidence intervals of the stresses. To judge a stress as fitting a datum, the stress must explain slip vectors on either nodal plane for all 188 events. When a stress with an angular misfit of <30° is judged to be compatible with a fault-slip datum 8 , either or both of the stresses explain slip vectors on one of the nodal planes for 164 of the 188 events. The thresholds of the angular misfit were determined here based on the uncertainties of the strike, dip, and rake 9,10 . When the angular misfits are smaller than the uncertainties of the focal mechanisms, the observed slip directions agree with theoretical directions to within the estimated the uncertainties. Of the 164 events, only 36 are compatible only with a single principal stress, as the stress tensor inversion based on the Wallace-Bott hypothesis 11,12 provides rather loose constraints on the fit of a stress to a fault-slip datum 13 . Estimation of pore fluid pressure in the Philippine Sea slab. We next estimated the spatial distribution of pore fluid pressure in the Philippine Sea slab. The normal and shear stresses acting on a fault of any orientation (i.e., fault strike and dip-angle) within a stress regime are represented by Mohr circles 14 . The variation in the orientations of the focal mechanisms is attributed to fault strength heterogeneity caused by variation in the effective friction coefficient, μ′ which is represented by the ratio of normal stress to shear stress for each focal mechanism. In accordance with the principle of the law of effective stress, the effective friction coefficient μ′ can be defined as μ′ = μ(1 -λ) 15 , where μ is the friction coefficient and λ is the pore fluid pressure ratio. We classified the 36 earthquake events into three groups as F1, F2, and F3 to estimate μ′ for each fault group compatible only with the stress. Assuming a constant friction coefficient μ = 0.6 16 , the effective friction coefficients of groups F1, F2, and F3 were calculated as 0.02, 0.01, and 0.08, respectively (Fig. 2b). The coefficients show that the pore fluid pressure ratio λ is 0.85-0.97 in the Philippine Sea slab. Figure 3 shows spatial changes in the stress field obtained from the focal mechanisms for which observed slip directions are consistent with a single stress solution among the stresses. The focal mechanisms activated by Stress C dominate in the slab beneath the western and central regions of Shikoku, and the Kii Peninsula, whereas a wide region including the Kii channel includes focal mechanisms activated by Stresses A and B (Fig. 3). Beneath the Kii Peninsula and western and central parts of Shikoku, the gently dipping slab with a NW-SE strike has a convex-upwards shape (Fig. 1), as inferred from the distribution of intraslab earthquakes 17,18 and from seismic tomography 19 . The intraslab earthquakes activated by the normal faulting stress (Stress C) are dominant in the region of convex-shaped slab (Convex slab point, CSP in Fig. 3). The resistance of the mantle to the margin-parallel component of oblique plate subduction controls the distribution of stress in the Philippine Sea slab 18 . Therefore, the heterogeneous stress distribution we obtained may be a function of the shape of the Philippine Sea slab. Future work will focus on spatial heterogeneities of stresses in the Philippine Sea slab by the detail seismicity study.

Discussion
The results of our stress tensor inversion yield three major findings. First, the stress state in the Philippine Sea slab is spatially heterogeneous. Second, the triaxial normal faulting stress regime (Stress C) is confined to a limited part of the slab. Third, the pore fluid pressure ratio is high in the slab. We propose that the significant stress contrasts in the Philippine Sea slab cause regional variations in fluid migration within the slab. The permeability of rocks may be related to the σ 2 -axis direction 20,21 . True triaxial compression tests indicate that the σ 2 -axis direction is associated with the maximum permeability of rocks 22 . When the maximum permeability is dominant in the direction of σ 2 and the hydraulic gradient has a component in the σ 2 direction, fluids flow selectively in the σ 2 direction 23 . Given this, we determined that Stress C, which has the intermediate stress ratio, gives rise to rocks with the greatest anisotropy of permeability. For Stresses A and B, there is a NNW-SSE-trending girdle of σ 1 -axes in a stereogram (Fig. 2a). The states of stress indicate a high stress ratio and thus σ 1 ≈ σ 2 . Thus, the states of stress for Stresses A and B cause little anisotropy of permeability. The relationship between Stress C and The anisotropy of intraslab permeability causes regional variations in fluid migration in the Philippine Sea slab. This inference is consistent with the 3 He/ 4 He ratio distribution in the Kii Peninsula and western and central parts of Shikoku, which are regions of anomalous 3 He/ 4 He ratios. Recent studies [24][25][26][27] have reported that the 3 He/ 4 He ratios in these regions show anomalously high values despite the fore-arc location, and the high ratios may be attributable to mantle helium derived from a magma source 28 . The inferred anisotropy of permeability in the region underlying the Kii Peninsula and western and central Shikoku is associated with high 3 He/ 4 He ratios.
We are now able to explain, in terms of the heterogeneous distribution of stresses in the slab, why the region with a high 3 He/ 4 He ratios occur not only along the Kii Peninsula but also across the entire peninsula and western and central parts of Shikoku. Hence, the characteristic fluid migration mechanisms associated with Stress C are more favourable for generating fractures, which in turn facilitate the migration of mantle-derived helium.
The anisotropy of permeability caused by Stress C promotes fluid migration trending NNW-SSE subhorizontally. The high pore fluid pressure ratio (λ = 0.85-0.97) inferred by the present study is equivalent to a pore fluid pressure ratio λ = 0.95 29 under the conditions of stress and temperature at depths where intraslab earthquakes occur. In the Nankai subduction zone, the fluids are liberated from the subducting slab at depth of 30-60 km 30 . This depth almost overlaps the depth of the earthquakes in the slab crust and mantle we used. If the spatial heterogeneity in fluid migration from the slab produces regional variations in the fluid volume, the accumulation of fluid and the build-up of high pore fluid pressure in the corner of the mantle wedge vary spatially along the slab. A relatively low value (λ = 0.85) of pore fluid pressure ratio in the slab with Stress C may support a large amount of dehydration to mantle wedge compared to the slab with Stresses A and B. We infer that slow earthquakes linked   (Fig. 3). The region stretches ~10 km from ENE to SWS and ~20 km from NNW to SSE (See Low permeable anisotropy zone, LPZ in Fig. 3). In the region, the dehydration in Stresses A and B is not promoted only in a specific direction. The inhomogeneous conduit controlled by spatial heterogeneity in stress in the subducted Philippine Sea slab represents an intraslab fluid pathway, and is a plausible cause of the observed spatial heterogeneities in slow earthquake activity and 3 He/ 4 He ratio distribution (Fig. 4).

Method
We applied the MIM 7 to the data shown in Fig. 1. The MIM uses stress tensor inversions 15 with a resampling technique for separating stresses from heterogeneous focal mechanism data 7 . Significant stresses are represented as clusters of reduced stress tensors and are identified by k-means clustering 31 .

Data Availability
The datasets generated during the current study are available from the corresponding author on meaning request.