A weak subducting slab at intermediate depths below northeast Japan

Abstract

Knowledge of the state of stress in subducting slabs is essential for understanding their mechanical behavior and the physical processes that generate earthquakes. Here, we develop a framework which uses a high-resolution focal mechanism catalog to determine the change in the position of the neutral plane before and after the M9 Tohoku-oki earthquake to determine that the deviatoric stress within the slab at intermediate depths must be very low (∼1 MPa). We show that by combining the static stress calculated from coseismic slip distributions with the stress orientations before and after the mainshock, we can determine the full deviatoric stress tensor within the subducting slab at intermediate depths. These results preclude earthquake source mechanisms that require large background driving stresses, favoring a mechanically weak subducting slab, thus providing quantitative constraints on the physical processes that generate intermediate-depth earthquakes.

The stress levels within the subducting slab at intermediate depths are notably low (≤2 MPa).

INTRODUCTION

On 11 March 2011, the devastating M9 Tohoku-oki Earthquake occurred on the interface between the subducting Pacific Plate, and the overriding continental plate. This event was the fourth largest earthquake ever recorded, and the rupture itself is the most-studied megathrust rupture event. The regions surrounding this event continue to exhibit enhanced seismicity rates and postseismic deformation over a decade later (1). However, we still lack a critical understanding of the basic physical and chemical processes controlling the occurrence and magnitude of subduction zone earthquakes, and in particular, we do not understand how stress accumulates over the course of the seismic cycle. Quantitative constraints on the current state of stress, and its accumulation history, are critical for seismic hazard assessment and mitigation.

At intermediate depths (60 to 200 km), interplate earthquakes on the megathrust are not observed because of the high temperatures and high confining pressures at the plate boundary, rather intraplate earthquakes beneath northeast (NE) Japan form two inclined parallel planes of seismicity separated by ∼35 km (Fig. 1), with the upper and lower planes in downdip compression and tension, respectively (2–4). The physical mechanisms controlling the generation and occurrence of these types of intermediate-depth earthquakes remain elusive because of a lack of direct observation of the composition and in situ stress state of the rock hosting them (5, 6).

Fig. 1. Locations of earthquake focal mechanisms and moment tensors used in this study (2002–2021).

The yellow star denotes the hypocenter of the M9 mainshock. (A) Map view of all earthquake focal mechanisms determined in this study and the coseismic slip distribution determined by Yamazaki et al. (69). The events located within the region used to compute the final shear stress inversions report in Table 1 are denoted by the filled circles where the purple and green colors denote events located within the upper and lower planes of seismicity, respectively. The open gray circles represent all of the intermediate depth focal mechanisms. (B) Transect view plot of the focal mechanisms used in this study. Moment tensors from F-NET are shown as black circles with white fill. (C) Histogram of event magnitudes determined in this study and NIED F-NET moment tensor magnitudes.

Mechanical models of subduction zones can be combined with observations of earthquake focal mechanism (7, 8) and observations of the morphology and structure of the accretionary wedge (9, 10) to interrogate the state of stress within the subduction zone throughout the megathrust earthquake cycle. These combinations of models and observations have been shown to be particularly well suited to estimate the frictional properties of the coupled seismogenic zone of large interplate earthquakes (11, 12). Spatiotemporal changes in intraplate earthquake activity are thought to reflect changes in the regional stress field caused by shear interactions between the subducting and over-riding plates throughout the seismic cycle (13) and are observed to modulate the intraplate earthquake activity throughout the subducting oceanic plate (14, 15). The rupture of large interplate earthquakes substantially alters the regional stress fields and are observable as rotations of the principle stress axes that can be derived from earthquake focal mechanisms (16). Further, the orientation of the principal stress axes relative to the plate interface following the rupture of a large earthquake can provide quantitative constraints on the stress state of the plate interface fault zone (11, 17).

Following the 2011 Tohoku-oki earthquake, numerous studies examined the interplate and intraplate earthquakes to explore the state of stress of the Pacific and North American Plates (18, 19). The rotation of the principal stress axes derived from earthquake focal mechanisms was used to infer the stress drop of the mainshock rupture (20), as well as the spatially variable deviatoric stress state in the crust of the continental lithosphere (21, 22). The temporal evolution of the crustal stress orientations were also shown to provide constraints on postseismic relaxation models (23).

In this study, we analyze the entire seismogenic zone of the subducting slab at intermediate depths. Because this region is directly below the densely instrumented mainland of Honshu, we can use well constrained focal mechanisms even for small earthquakes and generate a catalog of high spatiotemporal resolution. This dataset allows us to analyse the state of stress within the slab as a function of perpendicular distance from the plate interface (4), and additionally, to construct a nearly two-decades-long stress orientation time series with subyear temporal resolution. The unique spatial resolution of this dataset allows us to quantitatively examine interactions of the coseismic stress change with the background ambient stresses, such as those generated by plate bending and unbending. Compared to previous studies that focused on stress rotations nearer to the mainshock (24, 25), we are able to calculate reliable stress changes from slip distributions. The precise values of the stress field changes located near the regions of high coseismic slip are strongly dependent on the details of the slip distribution being used; however, at the intermediate depths examined in this study, the static stress calculated from different coseismic slip distributions qualitatively agree to within several percent. Using models of the static stress change to quantify the perturbation to the stress field, we are able to determine the full deviatoric stress tensor within the subducting slab. In addition, the temporal resolution of this dataset allows us to interrogate the subsequent temporal evolution of the observed stress orientations, associated with postseismic relaxations following the mainshock. Our results and analysis provide direct constraints on the absolute state of stress in the subducting lithosphere, the long-term rheological strength of the slab controlling its curvature, and the postseismic processes which alter the stress within the slab at intermediate depths.

RESULTS

To examine the spatiotemporal stress changes within the slab associated with the mainshock, we bin the focal mechanisms and then invert for optimally oriented stress orientations ${\widehat{\mathbf{\sigma }}}_{\mathrm{i}}$ and the stress ratio R between the principal values σ_i (see Methods), where σ_i is the ith eigenvalue of the stress tensor corresponding to the ith eigenvector ${\widehat{\mathbf{\sigma }}}_{\mathrm{i}}$ (i.e., principal stress direction).

The oceanic Pacific plate subducts beneath the Tohoku region of Honshu with a convergence rate of ∼10 cm/year and at angle parallel to the downdip direction of ∼30° (26). In contrast to other subduction zones which undergo oblique slip kinematics such as Cascadia (27), the convergence geometry in Tohoku results in dominant dip-slip deformation. If we assume that the absolute deviatoric stress field within the slab at intermediate depths is dominated by plate unbending, then we would expect the most compressional principal stress axis ${\widehat{\mathbf{\sigma }}}_{\mathrm{1}}$ in the upper plane to be aligned parallel with the plate interface tangent vector and pointing in the downdip direction (Fig. 2A). Similarly, we would expect the ${\widehat{\mathbf{\sigma }}}_{\mathrm{3}}$ in the upper plane to be parallel to the plate interface surface normal (Fig. 2A). If we further assume that the bending stress associated with along-strike variations are negligible, then ${\widehat{\mathbf{\sigma }}}_{\mathrm{2}}$ should be approximately horizontal and oriented along strike. We would expect a corresponding orientation in the lower plane as the upper plane with ${\widehat{\mathbf{\sigma }}}_{\mathrm{1}}$ and ${\widehat{\mathbf{\sigma }}}_{\mathrm{3}}$ swapped, because the unbending stress is tensile rather than compressional in the lower plane (Fig. 2A).

Fig. 2. Stress orientations and earthquake distribution with distance from plate interface 5 years before (2006–2011) and after (2011–2016) the M9 mainshock.

(A) Schematic of the stress orientations expected from unbending at intermediate depths. In the lower three panels (B to D), dotted and solid lines denote quantities before and after the mainshock, respectively. (B and C) Events are binned using overlapping 7-km-thick slices with 1-km steps. The plunges of the principal stress axes ( ${\widehat{\mathbf{\sigma }}}_i$ ) are given on the x axis and the centroid depth of the slice relative to the plate interface is shown on the y axis. The red and blue correspond to the largest ( ${\widehat{\mathbf{\sigma }}}_1$ ) and smallest ( ${\widehat{\mathbf{\sigma }}}_3$ ) principal stress orientations, respectively. The black vertical lines denote the average dip of the plate interface at these depths. (D) Number of earthquake focal mechanisms located in each overlapping depth bins before (dotted line) and after the M9 mainshock (solid line). (E) Similar to (B) and (C) but showing the change in plunge before and after the mainshock. The horizontal gray lines denote the depths of the inferred neutral plane before (21 km) and after (25 km) the M9 mainshock.

The focal mechanisms are first binned using overlapping 7-km-thick slices with 1-km steps in the interface-normal direction and separated by the time of the M9 mainshock (see Methods). We invert for the stress states within each bin and find that the plate can be separated into two distinct layers defined by their distances to the plate interface, which we refer to as the “upper” (7 to 23 km; containing 62 events before and 67 after), and “lower” (2 to 45 km; containing 51 events before and 34 after) planes, respectively (Fig. 2). Our stress inversion results before the mainshock are consistent with previous studies (4) and are consistent with stresses generated by plate unbending (Fig. 2). To avoid complications arising from possible downdip variations in the principal stress orientations (figs. S1 and S2), we only examine the seismicity within a region of the plate that is 100 km long in the dip direction.

Following the mainshock, ${\widehat{\mathrm{\sigma }}}_1$ in the upper plane is perturbed by ∼20° to a shallower plunge, while the plunge of ${\widehat{\mathbf{\sigma }}}_{\mathrm{3}}$ steepens (Fig. 2, B and C). The orientations in the lower plane were less strongly affected by the mainshock with changes in their plunges of less than 5° (Fig. 2, B and C). There is no substantial variation in the orientation of ${\widehat{\mathbf{\sigma }}}_{\mathrm{2}}$ in the interface-normal direction before or after the mainshock (fig. S3).

We see corresponding behavior in the relative sizes of the principal stresses (i.e., the stress ratio R). Before the mainshock, the stress ratio in the upper plane is nearly constant with a mean value of R = 0.6 and has a nearly constant value of 0.85 in the lower plane. Following the mainshock, we see a nearly constant increase in the upper plane (≤∼23 km) to a mean value of 0.82 and no notable change in the lower plane (fig. S4).

In subduction zones with pronounced double seismic zones, the neutral plane depth is defined as the depth below the plate interface where the downdip-oriented principal stress changes from the maximum to the minimum principal stress (Fig. 2). Following the M9 mainshock, the neutral plane is estimated to be about 4 km further from the plate interface than before the mainshock, indicating increased downdip compression in this portion of the slab (Fig. 3). This resulted in a change from down-dip extension to down-dip compression in the 21- to 25-km distance range (fig. S5). While there was anelastic damage reported offshore (28) which could artificially affect the event depths used in this study, because of the event-station geometry the raypaths do not pass through this region. Further, studies using repeating earthquakes to examine velocity changes caused by the Tohoku earthquake found that the P-wave velocities were unaffected (29). The event depth are thus unlikely to be affected by changes to the crustal velocity and cannot explain the observed shift in the location of the neutral plane. This change in the position of the neutral plane is robust to the choice of bin width, and consistent results are obtained if 4-km-thick slices with 0.5-km steps are used (fig. S6). The neutral plane is inherently a region of low deviatoric stress and thus a region of sparse seismicity, and correspondingly, we observe the location of the inferred neutral plane calculated from the stress orientations to coincide with the distance from the plate interface with the minimum number of events, both before and after the mainshock (Fig. 2D).

Fig. 3. Schematic illustrating the deepening of the neutral plane.

Unbending stresses ( ${\mathrm{\sigma }}_{\mathit{xx}}^{\mathrm{\text{before}}}$ ) contribute downdip deviatoric compression (s_xx > 0) in the upper seismic plane, and downdip tension (s_xx < 0) in the lower plane. The neutral plane is located between the upper and lower planes where the downdip deviatoric stress (σ_xx) is zero, shown schematically by the y-intercept (horizontal red line) of the downdip stress curve (black line). The contribution from the M9 mainshock (Δσ_xx) is downdip compressional in both planes. The linear superposition of these two stress fields ( ${\mathrm{\sigma }}_{\mathit{xx}}^{\text{after}}$ = ${\mathrm{\sigma }}_{\mathit{xx}}^{\text{before}}$ + Δσ_xx) causes the neutral plane to shift downwards further from the plate interface.

To further examine the temporal evolution of stress within the slab, we separately examine the upper and lower planes and divide them into 50% overlapping time bins each containing 40 focal mechanisms (see Methods). Because of the large scatter, and possible contamination by poorly located interface events which can extend down to 60-km depth (1), we restrict our analysis to events with depths greater than or equal to 65 km and located within the upper and lower planes (i.e., exclude all events within 7 km of the plate interface). The temporal evolution of the orientation of the principal axes in the upper plane (i.e., ${\widehat{\mathbf{\sigma }}}_{\mathrm{1}}$ and ${\widehat{\mathbf{\sigma }}}_{\mathrm{3}}$ ) reveals a marked change in their plunge at the time of the Tohoku mainshock (Fig. 4A). Note that because the principal axis associated with σ₃ in the upper plane is nearly perpendicular to Earth’s surface, small errors in the direction of the principal axis result in large, but insubstantial, variations in the azimuth. We do not expect to observe the previously predicted systematic rotations along strike (21), because the transect used in our calculations is symmetric about the mainshock centroid. We do not observe a notable temporal change in the orientation of ${\widehat{\mathbf{\sigma }}}_{\mathrm{2}}$ (fig. S7). These results are robust to choice of transect width, maximum downdip distance, and minimum depth (figs. S8 to S10). We note that the spatial sampling of the earthquakes is stationary throughout the observational time period, which ensures that each temporal bin is associated with the same region of the subducting slab (fig. S11).

Fig. 4. Stress orientations with time in the upper and lower planes.

The dashed vertical line denotes the time of the M9 mainshock. (A) The plunges of the upper plane principal axes ${\widehat{\mathbf{\sigma }}}_1$ (red) and ${\widehat{\mathbf{\sigma }}}_3$ (blue). The dotted horizontal line denotes the dip of the plate interface. (B) The azimuth of the upper plane principal axes ${\widehat{\mathbf{\sigma }}}_1$ (red) and ${\widehat{\mathbf{\sigma }}}_3$ (blue). The dotted horizontal lines denote the azimuth of the downdip direction. (C and D) Same as (A) and (B) but for the lower plane.

Inversion for the full deviatoric stress tensor

The focal mechanism inversions yield optimal stress orientations and a stress ratio but not stress tensors. To estimate the absolute levels of deviatoric stresses in the slab (i.e., the six components of the deviatoric stress tensor), we combine the inverted stress orientations before and after the mainshock together with the static stress tensor change produced by coseismic slip (Eq. 3). The stress change was calculated using elastic dislocation models of numerous existing coseismic slip distributions of the mainshock (see Methods). For all slip distributions examined, the static stress change is compressional in the downdip direction for both planes and smoothly varying within the regions of interest such that variations are on the order of order of a few megapascals (fig. S12). The orientation of the principal axes of the stress change tensors in the lower and upper plane are similar for all of the slip distributions examined (fig. S13), with the values of the principal stresses in the lower plane being slightly less because of further distance from the mainshock rupture area to the lower plane region. However, as indicated above, the upper and lower planes are treated separately due to their contrasting background stress states (Fig. 2).

The normalized deviatoric stress tensors representing the state of stress in the slab before and after the M9 were obtained from our inversions of sets of focal mechanisms before and after the M9 mainshock (see Fig. 5). The inversion for the full deviatoric stress tensors before and after the mainshock quantitatively confirms that the large stress rotation due to the mainshock slip requires that the background deviatoric stress values be less than or comparable in size to the static stress of the mainshock. Further, the contrasting behavior of the lower plane (wherein maximum shear stress drops due to the mainshock) with the upper plane (wherein maximum shear stress increases due to the mainshock) is consistent with the previously inferred pre-existing stress orientations of each plane (i.e., the upper and lower planes are in stress states of downdip compression and extension respectively). The resulting maximum shear stresses [i.e., (σ₁ − σ₃)/2] both before and after the M9 mainshock are small, below 2.0 MPa for all mainshock slip models (Fig. 6 and Table 1).

Fig. 5. Lower hemisphere projection of principal axes, and confidence bounds.

The symbols circle, x, and square and red, yellow, and blue dots represent the most, intermediate, and least compressional principal directions from stress inversion of sets of focal mechanisms without and with added noise, respectively. The ∗ and ⋆ symbols denote the plate convergence direction, and direction perpendicular to the plate interface, respectively. The number of events in each bin is reported in the upper left hand corner of each stereonet, and the plunge of each principal axes is shown by the colored numbers. Note that these results are robust to the choice of minimum depth (figs. S14 and S15).

Fig. 6. Maximum shear stresses and error ellipses for seven mainshock slip distributions.

Dots show the maximum possible shear stresses associated with the best-fit solutions to Eq. 4. Contours represent an estimation of 95% confidence regions. The misfit level that is contoured is derived by comparing the misfit surfaces to the range of best-fit noisy solutions obtained from noisy stress orientation inputs to calibrate the contoured misfit level (e.g., fig. S16). Purple and green dots and contours represent results for the upper and lower seismic planes, respectively. Note the small stress values and the separation of upper and lower planes. Slip distributions are numbered as in Table 1.

Table 1. Maximum shear values before and after the M9 mainshock in the upper and lower planes obtained for each coseismic slip model.

Slip model	Upper plane		Lower plane
	Before	After	Before	After
1 - Shao et al. (63)	0.29	1.33	1.19	0.64
2 - Wei et al. (64)	0.21	1.29	1.42	0.90
3 - Yue et al. (68)	0.85	1.24	0.77	0.39
4 - Yamazaki et al. (69)	0.63	1.25	0.83	0.39
5 - Yagi et al. (66)	0.95	1.45	1.58	1.45
6 - Hayes et al. (65)	0.66	1.56	0.91	0.79
7 - Hooper et al. (75)	0.24	1.08	0.98	0.66
Mean	0.55 ± 0.30	1.30 ± 0.16	1.09 ± 0.31	0.68 ± 0.23

DISCUSSION

The spatiotemporal stress inversion performed here provides quantitative constraints of the deviatoric stress tensor for all three portions of the megathrust cycle in the upper plane. Conceptually, the megathrust cycle can be divided into long-term tectonic loading, near-instantaneous coseismic rupture, and transient postseismic processes (30). Associated with the coseismic rupture, we observe a discontinuous change in the orientations of the plunges of the principal axes (Fig. 4), as well as an associated change in the relative size of the principal stresses themselves (fig. S17C) and a corresponding increase in the occurrence rate of earthquakes (fig. S17D). The postseismic relaxation processes are captured by the decay back toward the premainshock levels following the discontinuous changes (Fig. 4). The occurrence rate of earthquakes in the upper plane decays on the shortest timescales and is thought to be correlated with deep afterslip on the megathrust (31). A recent study (32) has challenged this interpretation and suggests that the occurrence rate of intermediate depth earthquakes is not affected by the static stress change of the M9 mainshock. However, there is a clear change in earthquake-occurrence rate observed in the upper plane for all analysis transects with widths less than ∼150 km regardless of the minimum depth cutoff considered (31). The earthquake-occurrence rate increase only becomes difficult to resolve when considering transects with along-strike widths beyond the peak slip zone of the coseismic rupture and zone of greatest coseismic stress increase such as the one in (32). Further, a template matching catalog that identifies six times the number of events contained within the Japanese Meteorological Agency (JMA) earthquake catalog finds compelling rate increases in both the upper and lower planes of seismicity (33). The rapid return toward premainshock stress orientations on timescales much shorter than the seismic cycle is consistent with numerous other observations of the temporal evolution of coseismic stress changes following earthquake mainshocks (17). However, this rapid rotation close to premainshock levels at intermediate depths following the Tohoku-oki mainshock is associated with a low-absolute stress state and consistent with estimates of 2 to 4% of the seismic cycle stress being reloaded at the plate interface by deep postseimic slip and/or viscous relaxation (25, 34). These results further suggest that b-value observations that report the rapid recovery of stresses following the Tohoku-oki earthquake likely reflect the state of stress within the lithosphere, rather than the plate interface itself (35).

This full stress inversion provides the level of shear stress available to drive seismic faulting at intermediate depths and can inform calculations of slab deformation and dynamics. The mean stresses at these depths will be mainly due to the overburden and are about 2800 and 4000 MPa, respectively, but we can infer an effective mean stress from our deviatoric stress tensors by assuming a level of sliding friction and shifting the Mohr circles over to just tangentially touch the associated failure envelope (Fig. 7). The effective mean stress inferred in this way is extremely small compared to the overburden stress, even for assumed friction values as small as 0.01 (see text S1 and fig. S18), implying near-lithostatic pore pressures are needed for faulting (36), or alternatively nonfrictional failure (e.g., a pressure-independent shear strength or plastic behavior).

Fig. 7. Interpretation of deviatoric stresses in a Mohr-Coulomb context.

In all panels, the brown and teal colors correspond to 3D stress states associated the periods of time before and after the mainshock, respectively. (A and B) The gray dotted half-circle depicts the average stress change due to the mainshock rupture (σ^MS). The half-circles drawn with dashed brown and teal lines correspond to the deviatoric stress tensors ( ${\tilde{\mathbf{s}}}^{\text{before}}$ and ${\tilde{\mathbf{s}}}^{\text{after}}$ ) obtained using Eq. 4. The colored dots on the x axis (i.e., shear stress = 0) indicate the principal values of the stress tensors. The solid half-circles indicate full absolute stress tensors ( ${\mathbf{\sigma }}_{\mathit{CF}}^{\text{before}}$ and ${\mathbf{\sigma }}_{\mathit{CF}}^{\text{after}}$ ) estimated using the deviatoric stress tensors ( ${\tilde{\mathbf{s}}}^{\text{before}}$ and ${\tilde{\mathbf{s}}}^{\text{after}}$ ) and a maximum effective mean normal stress that still allows frictional failure to occur (i.e., the Mohr circle tangentially touches the associated failure envelope). This process is indicated schematically by black arrows which show how the Mohr circles were shifted. The inner Mohr circles associated with the intermediate principal stresses (i.e., s₂ and σ₂) are omitted for clarity, but small dots show their values. (C) The color-filled circles denote the maximum shear stresses estimated using the Mohr circles drawn with solid lines in (A) and (B). Small brown and teal x’s show the maximum available shear stresses (Mohr circle radii) based on inversions of sets of focal mechanisms with noise added ( ${\tilde{\mathbf{s}}}^{\text{before}}$ and ${\tilde{\mathbf{s}}}^{\text{after}}$ , respectively) and color-filled squares show the medians obtained from 200 noisy inversions.

The shear stress levels (which are unaffected by pore pressure) are close to, but smaller than, typical earthquake stress drops (37–39). The stresses estimated here apply over broad regions of tens to hundreds of kilometers in scale, whereas smaller scale stresses that concentrate on asperities within individual fault planes may produce higher-stress-drop earthquakes. However, physical mechanisms of seismogenesis that require large background or driving shear stresses to operate, such as shear heating of highly localized shear zones (40–42), can be ruled out by our results.

Similarly, we can use the deepening of the neutral plane and the modeled coseismic stress change to provide an independent estimate of the deviatoric stresses that can be supported in the slab. At the depths considered in this study (≥65 km), and at the long-term timescales associated with changes in plate curvature, we are able to neglect the elasticity of the slab when calculating the stresses associated with bending because the elastic stresses well exceed those that would drive brittle and plastic deformation. This theoretical consideration is also supported by analysis of gravity-topography admittance (43). If we assume that the slab material is incompressible and can be described by an “effective strength parameter” η, we can derive an expression which relates the change in downdip compression across the entire width of the slab Δσ_xx (caused by the coseismic stress change from the M9 mainshock) to the change in the position of the neutral plane Δy

$$\mathrm{\Delta }{\mathrm{\sigma }}_{\mathit{xx}}\approx \frac{4\mathrm{\eta }{u}_0}{R_{\text{min}}^2}\mathrm{\Delta }y$$ (1)

where R_min is the minimum radius of curvature and u₀ is the plate subduction rate (see Methods for full derivation). Thus, using our observed deepening of the neutral plane and our modeled downdip compressional stress change due to the mainshock, we can estimate the rheological properties of the subducting slab at depth that control slab topology on geological timescales. For the Pacific Plate at intermediate depths, down dip of the M9 Tohoku-oki Earthquake, R_min ≈ 200 km (44), u₀ ≈ 10 cm/year, Δy ≈ 4 km (Fig. 2) and Δσ_xx ≈ 0.5 MPa. Using these values, we estimate an effective rheological parameter of η ≈ 10¹⁵⁻¹⁶ Pa s. This rheological parameter is related to the strength of the slab and should be interpreted as a parameter which controls the maximum shear stress that can be supported by the deforming slab. For reference, (45) construct a composite rheology of the subducting oceanic plate using Byerlee’s law together with laboratory-based models for creep in olivine (46) and estimate an effective rheology of η = 5.5 × 10²² Pa s. Our results suggest that the plate is failing at shear stresses much lower than those predicted by Byerlee’s law or viscous flow, requiring a weakening mechanism such as high-pore fluid pressures or mechanisms that vastly reduce the slope of the frictional failure envelope. Observations of low shear wave velocities throughout the upper plane in this region (47) support low effective normal stress being the source of slab weakness. This analysis is consistent with the Mohr stress analysis, and both results suggest that low effective-friction controls earthquake failure in the upper plane of the subducting slab at intermediate depths.

Absolute stress levels within the subducting slab at intermediate depths

In this study, we analyzed first-motion focal mechanisms determined by the National Research Institute for Earth Science and Disaster Prevention (NIED) using Hi-net stations at depths of 60 to 200 km with magnitudes as low as M2.8. We present the first combined analysis of stress orientation information from numerous earthquakes at intermediate depths in the slab downdip of the M9 Tohoku-oki earthquake with seismically and geodetically informed model estimates of the absolute static stress change induced by the M9 mainshock itself. We report stress orientations, inferred absolute deviatoric stress levels, and the rapid temporal evolution of stresses and seismicity within the subducting slab at intermediate depths following the mainshock. Stress orientations within the upper plane of the slab downdip of the mainshock rotated abruptly by ∼20° at the time of the event, and the stress ratio increased by a factor of ∼1.5. We inverted the stress orientations and ratios just before and after the mainshock, together with the static stress tensor imposed by existing mainshock slip distributions, to determine ambient deviatoric stress tensors in the slab before and after the mainshock. This framework allowed us to determine the absolute level of deviatoric stress deep within the subducting slab, a quantity that is difficult to obtain. The stress levels that we find are notably low (<2.0 MPa), which means that the slab is weak and cannot support much shear stress. This result is supported by an independent analysis that combines the observed change in the position of the neutral plane with modeled bending stresses to estimate the rheological strength of the slab. These two estimates of a weak slab, paired with the observed rapid return to premainshock orientations on timescales of several years, suggest that the slab may participate more in postseismic deformation than previously assumed (48, 49). Further, given the very low deviatoric stresses determined here, even with very low friction values, pore pressure must be very high and effectively lithostatic. Our results provide constraints on the proposed physical processes that generate intermediate-depth earthquakes, a long-standing puzzle in seismology, lending support to the process of dehydration embrittlement and ruling out shear heating mechanisms that require large background driving stresses.

METHODS

First-motion focal mechanism determination

We use waveform data from F-net (50) and Hi-Net (51) to analyze moment tensor solutions, hypocenters, and first-motion focal mechanisms of intraplate earthquakes occurring in NE Japan (36.5 ≤ lat ≤ 42.5 and 138.5 ≤ lon ≤ 142.5) from 2008 to 2021. The NIED focal mechanisms were constrained using the methods, P-wave polarity observations, and hypocentral information of the NIED catalog and the Monitoring of Waves on Land and Seafloor (MOWLAS) system (52). This catalog of 3852 focal mechanisms is combined with 632 mechanisms (2002–2008, M > 2.8) from Kita et al. (3) to constrain the state of stress within the deep subducting Pacific plate from 2002 to 2021 (depths ≥60 km). We then select ∼2200 focal mechanisms for analysis that occur within the subducting slab downdip of and near the mainshock rupture area, (i.e., within a 150-km-wide transect centered on the epicenter and parallel to the slab dip at depths ≥65 and ≤200 km; Fig. 1). This dataset greatly increases the spatial and temporal sampling of the region compared to the existing NIED F-NET focal mechanisms (black circles with white fill; Fig. 1, A and B). In addition, these focal mechanisms extend to much lower magnitudes (Fig. 1C), with approximately 60% of the events being located in the upper plane, and 90% of the catalog occurring after the mainshock.

Inversion of focal mechanisms for principal stress orientations

In all stress inversions, we restrict our analysis to focal mechanism with depths greater than 65 km and less than 200 km, and mechanisms that are contained within the 150-km-wide analysis transect centered on the M9 hypocenter with an azimuth aligned with the downdip direction of the subducting plate (Fig. 1). To avoid complications arising from possible downdip variations in the principal stress orientations (figs. S1 and S2), we only examine a 100 km of seismicity in the dip direction. Mechanisms are further binned by distance from the plate interface, which is calculated as the distance along the normal between the mechanisms and the nearest point on the plate interface. These inversions seek to identify a single ambient stress state (i.e., ${\widehat{\mathbf{\sigma }}}_1,{\widehat{\mathbf{\sigma }}}_2,{\widehat{\mathbf{\sigma }}}_3,R$ ) that is consistent with the observed set of diverse focal mechanisms.

The inversion for the principal stress orientations and stress ratios were obtained following the approach of Vavryčuk et al. (53). The inversion of principal stresses has from earthquake focal mechanisms has been used to examine the state of stress of the lithosphere globally and shown to provide results consistent with those from other geophysical methods (54). This technique has also previously been applied to subduction zones globally and used to qualitatively infer the strength of megathrust faults (55). The methodology has seen extensive development and application (16, 17, 56, 57); Vavryčuk et al. (53) follow the inversion scheme and assumptions of Michael’s approach but add a Coulomb criterion to choose the best-fitting nodal plane for each input focal mechanism. This iterative procedure, which uses the so-called “fault-instability constraint” (58), requires a value for the friction μ in the Coulomb failure criterion, which we fix to be 0.7. We observe that the inversion results are largely insensitive to the numerical value μ. New stress inversion methods relax the assumption of a constant shear stress on all of the faults and show that in most instances, reliable stress orientations are obtained from the inversion of focal mechanisms assuming constant shear stress (59). Stress inversions of focal mechanisms are capable of constraining four parameters, the three orientations of the principal deviatoric stresses ( ${\widehat{\mathbf{\sigma }}}_1$ , ${\widehat{\mathbf{\sigma }}}_2$ , and ${\widehat{\mathbf{\sigma }}}_3$ ) and a stress ratio (R) (60). For each inversion, we estimate the confidence limits using a “noise-injection” procedure following the approach of Vavryčuk et al. (53) that generates 200 random noise realizations assuming conservative errors of 20° in the angles that describe the fault orientation corresponding to a given focal mechanism. These noise-injection methods typically result in confidence intervals which are similar to, but slightly smaller than, those obtained using the bootstrapping procedure of Michael (56). The bootstrapping methods tend to estimate confidence regions which are too large (61), likely because a wide distribution of P- and T-axes can still be consistent with small confidence limits on the resulting inverted stress orientations (53).

While this inversion alone cannot fully determine the principal stresses themselves, the stress ratio R, which is constrained in these inversions, does provide a constraint on the relationship between the principal stresses, namely

$$R=\frac{{\mathrm{\sigma }}_1-{\mathrm{\sigma }}_2}{{\mathrm{\sigma }}_1-{\mathrm{\sigma }}_3}$$ (2)

where σ_i is the ith eigenvalue corresponding to the ith eigenvector ${\widehat{\mathbf{\sigma }}}_i$ . Here, we use the convention in which σ₁ is the most compressive stress (i.e., σ₁ < 0 corresponds to compression), and σ₃ is the least compressive stress (i.e., the largest tensile stress for deviatoric tensors).

To analyze the state of stress as a function of “depth” within the subducting slab (Fig. 2, we used overlapping bins with 7-km width in the direction perpendicular to the plate interface and 1-km step size [i.e., (0 to 7 km), (1 to 8 km), (2 to 9 km), ...]. To analyze the temporal evolution, we used the results from the depth inversions to separate the seismicity into two nearly homogeneous bands of seismicity defined by their distance from the plate interface, the upper plane (7 to 21 km) and the lower plane (25 to 45 km).

To analyze the state of stress as a function of time, we first separate the focal mechanisms spatially into the upper and lower planes that define regions of near constant stress state. Then, for each layer, we separately bin events in time such that each bin contains 40 events and overlap by 50%. Note that the results shown here are not strongly dependent on the choice of the number of mechanisms. The choice of 40 events is consistent with the minimum number of events required (53).

We do not analyze the first 30 days following the M9 mainshock to avoid the reduced network performance, during which the magnitude of completeness is estimated to have increased from M1.5 to M3 (31). However, the inversion results do not change substantially if these events are included, presumably because most of the focal mechanisms in our catalog have magnitudes above this temporary elevated magnitude of completeness.

Modeled coseismic tensor stress change

To compute the full stress tensor due to mainshock slip, we applied a calculation for deformation and stress in a halfspace (62) using previously determined mainshock slip distributions. For all calculations, we assumed a Poisson’s ratio of 0.25 and a Young’s modulus of 70 GPa.

We investigated the slip distributions from several body-wave, surface wave, geodetic, and/or tsunami inversions of the Tohoku earthquake (63–71). The value at the center of each of the two analysis regions is reasonably representative of the entire spatial region (fig. S13).

Inversion for full deviatoric stress tensors before and after mainshock

We adapt the general approach of Wesson and Boyd (72) and seek to determine the scalar constants which fit the generalized equation

$${\mathbf{s}}^{\text{ms}}=c^{\text{after}}{\tilde{\mathbf{s}}}^{\text{after}}-c^{\text{before}}{\tilde{\mathbf{s}}}^{\text{after}}+\mathbf{ϵ}({\mathbf{\sigma }}^{MS},{\tilde{\mathbf{s}}}^{\text{after}},{\tilde{\mathbf{s}}}^{\text{before}})$$ (3)

where σ^MS is a tensor describing the static stress change due to mainshock slip with deviatoric component S^MS; ${\tilde{\mathbf{s}}}^{\text{after}}$ and ${\tilde{\mathbf{s}}}^{\text{after}}$ are normalized deviatoric stress tensors (constructed from orientations of the three principal axes and the stress ratio) for the states of stress before and after the M9 mainshock, respectively; unknowns c^before and c^after are scalars representing the absolute stress level before and after the mainshock with units of Pa (72); and ϵ is a general term describing the total collective errors. The calculation of the static stress change tensor σ^MS results in errors due to imperfect knowledge of both the coseismic slip distribution and the elastic structure of the subduction zone. Additional errors arise in the determination of both ${\tilde{\mathbf{s}}}^{\text{before}}$ and ${\tilde{\mathbf{s}}}^{\text{after}}$ from the inversion of noisy focal mechanisms.

Note that throughout this manuscript bold symbols denote tensors (e.g., s), a tilde (e.g., $\tilde{\mathbf{s}}$ ) is used to denote a normalized quantity, and we further use a convention where “sigma” denotes the full stress tensor (e.g., σ) and “s” denotes a deviatoric stress tensor (e.g., s) such that σⁱ = sⁱ + PI, where $P=\text{Tr}({\mathbf{\sigma }}^i)={\mathrm{\sigma }}_{11}^i+{\mathrm{\sigma }}_{22}^i+{\mathrm{\sigma }}_{33}^i$ is the isotropic static pressure, or volumetric stress, and I is the identity matrix. Although the static stress change tensors calculated for the mainshock coseismic slip σ^ms include an isotropic component (i.e., change in static pressure), the normalized stress tensors from the focal mechanism inversions ${\tilde{\mathbf{s}}}_{\text{before}}$ and ${\tilde{\mathbf{s}}}_{\text{after}}$ (right-hand side of Eq. 3) are deviatoric (i.e., do not constrain static pressure), and thus, we can only use s^ms to constrain c^before and c^after.

In practice, the errors associated with ϵ cannot be explicitly determined and are implicitly included in the estimated values for the tensors s^MS, s^before, and s^after, and thus, Eq. 3 can be represented as an overdetermined inconsistent system of six equations and two unknowns which may be written in the form “Ax = b”. Expressed in component form, the equation we invert is

$$\left[\begin{array}{c}{s}_{\mathit{xx}}^{\text{ms}}\\ s_{\mathit{yy}}^{\text{ms}}\\ s_{\mathit{zz}}^{\text{ms}}\\ s_{\mathit{xy}}^{\text{ms}}\\ s_{\mathit{xz}}^{\text{ms}}\\ s_{\mathit{yz}}^{\text{ms}}\end{array}\right]=c^{\text{after}}\left[\begin{array}{c}{s}_{\mathit{xx}}^{\text{after}}\\ s_{\mathit{yy}}^{\text{after}}\\ s_{\mathit{zz}}^{\text{after}}\\ s_{\mathit{xy}}^{\text{after}}\\ s_{\mathit{xz}}^{\text{after}}\\ s_{\mathit{yz}}^{\text{after}}\end{array}\right]-c^{\text{before}}\left[\begin{array}{c}{s}_{\mathit{xx}}^{\text{before}}\\ s_{\mathit{yy}}^{\text{before}}\\ s_{\mathit{zz}}^{\text{before}}\\ s_{\mathit{xy}}^{\text{before}}\\ s_{\mathit{xz}}^{\text{before}}\\ s_{\mathit{yz}}^{\text{before}}\end{array}\right]=\left[\begin{array}{cc}{s}_{\mathit{xx}}^{\text{after}},& -s_{\mathit{xx}}^{\text{before}}\\ s_{\mathit{yy}}^{\text{after}},& -s_{\mathit{yy}}^{\text{before}}\\ s_{\mathit{zz}}^{\text{after}},& -s_{\mathit{zz}}^{\text{before}}\\ s_{\mathit{xy}}^{\text{after}},& -s_{\mathit{xy}}^{\text{before}}\\ s_{\mathit{xz}}^{\text{after}},& -s_{\mathit{xz}}^{\text{before}}\\ s_{\mathit{yz}}^{\text{after}},& -s_{\mathit{yz}}^{\text{before}}\end{array}\right] \left[\begin{array}{c}{c}^{\text{after}}\\ c^{\text{before}}\end{array}\right]$$ (4)

We determined the values of c^before and c^after by minimizing the L2-norm difference between the two sides of Eq. 4 using a simple grid search. Wesson and Boyd (72) and Hardebeck and Okada (17) suggest using a non-negative least-squares inversion; however, because we are only inverting two parameters we perform an exhaustive gird search that allows us to better explore the entire solution space and better characterizes the uncertainties associated with the values determined for c_before and c_after. Multiplication of the normalized tensors s^before and s^after by c^before and c^after then gives the (spartially averaged) full devatoric stress tensors in the slab estimated for both the upper and lower planes, before and after the M9 mainshock (i.e., ${\mathbf{s}}^i=c^i{\tilde{\mathbf{s}}}^i$ ). Errors and confidence limits are estimated in two ways: (i) by assessing the ranges of c_before and c_after, and (ii) determining c_before and c_after using stress orientations and ratios from 200 inversions of sets of focal mechanisms with random perturbations added (see Fig. 7C).

Note that Eq. 4 is not the same as the equation inverted in Wesson and Boyd (72). We include all six equations, whereas Wesson and Boyd (72) choose to eliminate the equation associated with the “zz” tensor components. They choose to reduce their system of equations to only five equations by assuming that the “zz” equation was redundant because the stress tensors are all deviatoric and thus $s_{\mathit{zz}}^i=-s_{\mathit{xx}}^i-s_{\mathit{yy}}^i$ for each tensor i. However, this condition does not in fact give justification for eliminting an equation. If this system of equations was being inverted directly for the components of the stress tensor (i.e., ${\mathit{s}}_{\mathit{xx}}^{\mathit{i}}$ , ${\mathit{s}}_{\mathit{xx}}^{\mathit{i}}$ , ...), for which the six tensor elements were the unknown and dependent variables, then this condition would justify eliminating one of the equations, because in that case one of the diagonal tensor elements would be directly dependent on the other two components, and the resulting system of linear equations would be linearly dependent. However, because we are inverting for two coefficients that when multiplied by two known tensors match a third known tensor [i.e., Eq. 3, and equation 2 in the study by Wesson and Boyd (72)], rather than directly for the components, the deviatoric condition would only result in a linearly dependent equation if all quantities were error-free (i.e., ϵ = 0) and thus the equations formed a “consistent” set of equations. Because the tensor elements used in these inversions are derived from noisy observations, and imperfect calculations, the system of equations is not consistent. Instead, we obtain an overdetermined, inconsistent system for which the equation associated with “zz” is not linearly dependent. If we consider the case of a consistent set of equations, then it would be the case that any subset of two equations could be used to solve for the two unknowns (c^before and c^after) and identical results would be obtained. In practice, eliminating one of the equations does affect the results of the inversion, and further, the choice of eliminating “zz” over “xx” or “yy” is arbitrary and not necessary or appropriate for this inversion scheme.

Order-of-magnitude estimates from the change in the position of the neutral plane

The upper and lower planes of the double seismic zone in the subducting Pacific slab are in downdip deviatoric compression and extension (4), respectively, presumably due to the unbending of the slab (Fig. 2). To make an order-of-magnitude estimate of the strength of the slab, we assume that the stress within the slab at these intermediate depths is generated by the superposition of a static stress field generated by bending/unbending, slab-pull (i.e., gravity), viscous resistance of the mantle, and the dynamic stresses generated by processes such as the time-varying locking/frictional resistance of the plate interface, pore-fluid pressure fluctuations, and the stress change from earthquakes (7, 8, 73, 74).

We assume that the deformation of the plate is pure bending (i.e., no thinning or buckling), and because the plate curvature K(x, t) does not appreciably vary over timescales associated with the mega-thrust earthquakes cycle (i.e., $\frac{\mathrm{\partial }K}{\mathrm{\partial }t}\ll u\frac{\mathrm{\partial }K}{\mathrm{\partial }x}$ ) then the strain-rate can be approximated as

$${\dot{\mathrm{ϵ}}}_{\mathit{xx}}=-\mathit{yu}\frac{\mathrm{\partial }K}{\mathrm{\partial }x}$$ (5)

where x is the coordinate along the dip direction, y is the coordinate perpendicular to the neutral-plane that transects the slab, and u is the plate subduction rate (45).

We assume that the material is incompressible and can be described by a generic powerlaw rheology from the Levy-Mises equation

$${\dot{\mathrm{ϵ}}}_{\mathit{ij}}=\frac{1}{2\mathrm{\eta }}({\mathrm{\sigma }}_{\mathit{II}}^{n-1}){\mathrm{\sigma }\prime }_{\mathit{ij}}$$ (6)

where ${\dot{\mathrm{ϵ}}}_{\mathit{ij}}$ is the strain rate, ${\mathrm{\sigma }\prime }_{\mathit{ij}}$ is the deviatoric stress-tensor, ${\mathrm{\sigma }}_{\mathit{II}}=\sqrt{J_2}$ is related to the second-invariant of the stress tensor $J_2={\mathrm{\sigma }\prime }_{\mathit{ij}}{\mathrm{\sigma }\prime }_{\mathit{ij}}/2$ and η is a material constant (i.e., an effective viscosity for n = 1). Buffett and Becker (45) show that

$${\mathrm{\sigma }}_{\mathit{xx}}(y)=2s(2\mathrm{\eta }\mid {\dot{\mathrm{ϵ}}}_{\mathit{xx}}(y)\mid )1/n$$ (7)

where s is the sign of ${\dot{\mathrm{ϵ}}}_{\mathit{xx}}$ , ${\dot{\mathrm{ϵ}}}_{\mathit{xx}}(y)$ is the downdip strain rate and σ_xx(y) is the total downdip stress (i.e., not just the deviatoric component). Using this effective viscosity (with n = 1) allows us to relate the change in downdip stress (Δσ_xx) to the change in the neutral plane (Δy) by plugging in our expression for the strain as a function of curvature (Eq. 5) into our stress-strain relation (Eq. 6)

$$\begin{array}{c}\mathrm{\Delta }{\mathrm{\sigma }}_{\mathit{xx}}=4\mathrm{\eta }{\dot{\mathrm{ϵ}}}_{\mathit{xx}}\\ =-4\mathrm{\eta }\mathrm{\Delta }{\mathit{yu}}_0\frac{\mathrm{\partial }K}{\mathrm{\partial }x}\\ \approx \frac{4\mathrm{\eta }{u}_0}{R_{\text{min}}^2}\mathrm{\Delta }y\end{array}$$ (8)

where we used the approximation $\mathrm{\partial }K/\mathrm{\partial }x\approx R_{\min }^{-2}$ (44). Note that we were able to neglect the overburden pressure because this does not change before and after the mainshock, and we assumed a linear rheology (i.e., n = 1). The equation derived above (i.e., Eq. 1) allows us to relate the total downdip compression, not just the deviatoric stress, resulting from the static stress change associated with the mainshock to the change in the position of the neutral plane (Fig. 3).

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S18

References