Using the focal mechanisms of Imanishi et al. (2012), MIM reveals two normal-faulting stress states around Iwaki City before the 2011 Tohoku earthquake (Fig. 2). In this study, we discuss the temporal and spatial stress changes around Iwaki City to explain the stress heterogeneity.

### Temporal and spatial stress changes around Iwaki City

We attribute the variations in the stress field to temporal variations. Stress regime A can be seen to account for all the focal mechanisms derived from earthquakes that occurred before 2005. This implies that only stress regime A should be used as an appropriate solution before 2005 (Fig. 3). In contrast, stress regime B can be seen to account for all the focal mechanisms, except for no. 11, derived from earthquakes occurring after 2008 (Fig. 3). In the intervening period between 2005 and 2008, derived focal mechanisms can be related to both stress regimes A and B. Hence, one possible explanation of the stress heterogeneity is that the stress field around Iwaki City temporally changed from a NNW–SSE-trending triaxial extensional stress (regime A) to a NW–SE-trending axial tension (regime B), with the transition between the two occurring from 2005 to 2008. Hence, we define stress period I from 2003 to 2005 and stress period II from 2008 to 2010 (Fig. 3).

Next, we consider the dynamics for the stress changes around Iwaki City. The *σ*_{3} orientation of stress regime B is subparallel to the orientations of the co- and post-seismic displacements of large earthquakes (Mw ~ 7) that occurred during the period 2005–2010 (Fig. 2b; Suito et al. 2011). The post-seismic deformation determined from continuous GNSS monitoring reveals that the seismic moments released by transient slip following the M7 class earthquakes are much larger than the seismic moment estimates for the earthquakes themselves (Suito et al. 2011). Stress regime B may therefore be the result of accumulated extensional stress associated with co- and post-seismic deformation due to the M7 class earthquakes, which occur more frequently than M9 class earthquakes.

We focus on the location of the epicenter of the earthquakes to explain the stress heterogeneity around Iwaki City. Stress regime A accommodates all focal mechanisms derived from earthquakes in the western part of the study area around 140.8°E, except for no. 11. This implies that stress regime A is the most appropriate solution for this region (Fig. 4). On the other hand, stress regime B encompasses all focal mechanisms in the region around 141.0°E (Fig. 4). In the area between the two regions, the computed focal mechanisms could be related to either regime (Fig. 4). Hence, we infer that a series of M7 class earthquakes altered the stress regime only in the east of the study area.

### Estimation of differential stress around Iwaki City

Figure 5 shows the GNSS time series of the NW–SE component at sites near Iwaki City together with the occurrence times of five M7 interplate earthquakes. The time series show a deviation from a steady westward movement after the 2008 Mj 7.0 Ibaraki-ken Oki earthquake (label B). The timing of the transition toward eastward motion appears to correlate with the period during which stress regime B was dominant. The observation supports the hypothesis that the inferred change in stress field over time was due to extension associated with the co- and post-seismic deformation from the M7 class earthquakes.

We compared the stress changes caused by the co- and post-seismic deformation with the extensional stresses in stress periods I and II. The direction of extensional stresses induced by the co- and post-seismic deformation is almost parallel to the orientation of the *σ*_{3} axes, while it is perpendicular to the orientations of the *σ*_{1} and *σ*_{2} axes (Fig. 2b). Because *σ*_{1} is the overburden pressure, *σ*_{1} is almost constant during the co- and post-seismic deformation. Hence, the extensional stress induced by the co- and post-seismic deformation should only affect the magnitude of *σ*_{3} rather than those of *σ*_{1} and *σ*_{2}, and in order for the stress ratio to change from 0.54 (± 0.18) to 0.84 (± 0.10), *σ*_{3} must decrease. Here, the reduction in the magnitude of *σ*_{3} corresponds to a build-up of extensional stress.

The magnitude of the differential stress in the study area is estimated based on the temporal change in the stress field (Fig. 6). For convenience, in the following discussion, we define *σ*
^{A}_{1}
(*σ*
^{B}_{1}
), *σ*
^{A}_{2}
(*σ*
^{B}_{2}
), and *σ*
^{A}_{3}
(*σ*
^{B}_{3}
) as the maximum, intermediate, and minimum compressive principal stresses for stress A (and B), respectively. The differential stress for stress A (B) can be expressed by Δ*σ*^{A }= *σ*
^{A }_{1}
− *σ*
^{A}_{3}
(Δ*σ*^{B} = *σ*
^{B }_{1}
− *σ*
^{B}_{3}
). From the change in the stress ratio from 0.54 (± 0.18) to 0.84 (± 0.10), we obtain the following relationships: *σ*
^{B}_{3}
− *σ*
^{A }_{3}
~ 0.09 − 9.03Δ*σ*^{A} and Δ*σ*^{B }~ 1.08 – 10.03Δ*σ*^{A} (Fig. 6). The former relationship indicates that the extensional stress induced by the co- and post-seismic deformation is approximately 0.1 to 9 times as large as the differential stress for stress A. The latter relationship signifies that the extensional differential stress increases by a factor of almost 1.1 to 10 from stress A to stress B. Based on the amount of displacement from the co- and post-seismic deformation (~ 1–3 cm; Fig. 5), the resulting strain is estimated to be ~ 3 × 10^{−7} to 2 × 10^{−6} for the NW–SE component between the two sites near Iwaki City. Assuming that the crust is elastic with a Young’s modulus of 32 GPa, the induced stress, *σ*
^{B}_{3}
− *σ*
^{A}_{3}
, is estimated between 0.9 × 10^{−2} and 6.4 × 10^{−2} MPa. Inserting this estimated value into the relationships derived above, we obtain differential stresses for stress A, Δ*σ*^{A}, and stress B, Δ*σ*^{B}, of approximately 1.00 × 10^{−3} to 7.11 × 10^{−1} and 1.10 × 10^{−3} to 7.13 MPa, respectively. Hence, we propose that the differential stress is less than the order of 1 MPa around Iwaki City prior to the 2011 Tohoku earthquake.

### Background of the low differential stress around Iwaki City

We consider the generation of the 2011 Iwaki earthquake in the context of the low differential stress in the study area. We showed the stress heterogeneity around Iwaki City prior to the 2011 Tohoku earthquake as the spatial or temporal stress changes. In this study, we could not identify a possible explanation of the stress heterogeneity. In both cases, we suggest that the stress state around Iwaki City prior to the 2011 Tohoku earthquake might have been extensional with a low differential stress. A low differential stress prior to the 2011 Iwaki earthquake was reported by Yoshida et al. (2015), who estimated differential stress magnitudes ~10^{0}–10^{1} MPa by comparing the stress orientations in the post-Iwaki earthquake period with static stress changes due to the Iwaki earthquake and three nearby M5 class earthquakes. Tomographic studies have imaged low-velocity anomalies beneath the hypocenter of the 2011 Iwaki earthquake (Fig. 1; see also Kato et al. 2013), which may correspond to zones of high pore-fluid pressure. Zhao (2015) showed that a low-velocity zone is visible in the lower crust and mantle wedge, and that it extends beneath the hypocenter of the 2011 Iwaki earthquake, down to the subducting Pacific slab. The discharge of a large amount of thermal water after the 2011 Iwaki earthquake (Sato et al. 2011; Kazahaya et al. 2013) indicates that earthquakes in this region promote the upwelling of deep groundwater. The earthquakes themselves may be triggered by a decrease in effective normal stress and fault strength due to the increased pore-fluid pressure (e.g., Sibson 1990; Micklethwaite and Cox 2006; Terakawa et al. 2013). By examining the fault failure of the 2011 Iwaki earthquake with respect to the change in the state of stress in the Iwaki area produced by the 2011 Tohoku earthquake, Miyakawa and Otsubo (2015) showed that excess fluid pressure is required to explain the 2011 Iwaki earthquake. Therefore, we infer that high pore-fluid pressure could enable the generation of earthquakes under conditions of low differential stress (Sibson 1992).