Modeling of seismic activity modulated by stress changes during the interplate earthquake cycle along the Sagami Trough, central Japan

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However, the role of static stress changes in driving this pattern remains poorly understood. Therefore, to examine whether static stress changes from the Sagami Trough earthquake cycle could be responsible for this pattern, we simulated stress evolution using a layered elastic-viscoelastic model. The receiver faults were defined based on the focal mechanisms of earthquakes observed between 1997 and 2023. Additional intrinsic stress loading was also applied with a CFS accumulation rate of 1.0 kPa per year to all receiver faults for permanent stress accumulation. We assumed the earthquake occurrence rate at each receiver fault to be proportional to the increase in the Coulomb failure stress (CFS) from its previous maximum value, and set it to zero when CFS decreased. The spatial and temporal distributions of earthquake occurrence rates were then assessed by aggregating them across the study region. The spatial distribution of earthquake occurrence rates calculated by our optimal model closely matches the distribution of earthquakes observed between 1997 and 2023, supporting the validity of our modeling approach. Although our model could not fully explain the locations of several M7-class earthquakes that occurred before the 1923 Kanto earthquake, we found that these events tended to occur during periods when the modeled earthquake occurrence rate at each location was estimated to be high within the earthquake cycle. We discovered that interplate earthquakes in the transition zone from full coupling to no coupling are likely to increase as the next M8-class interplate earthquake along the Sagami Trough approaches. The results suggest that a physics-based framework for constructing earthquake activity scenarios in the Kanto region can improve seismic hazard assessments and contribute to disaster risk reduction. Coulomb failure stress Earthquake occurrence rate Interplate earthquake cycle Modeling Viscoelasticity Sagami Trough Kanto region Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction The Kanto region in central Japan has a complex tectonic setting in which two oceanic plates subduct beneath the continental plate from the south and east, resulting in high seismic activity (Fig. 1 ). The Philippine Sea Plate subducts beneath the North American Plate at a rate of a few centimeters per year, and geological, geomorphological, and historical studies have suggested that M8-class interplate earthquakes repeatedly occur along the Sagami Trough (Shishikura, 1999 , 2001 ; Shishikura et al., 2005 ; Satake, 2023 ). In particular, the 1703 M8.1 Genroku Kanto earthquake and the 1923 M7.9 Taisho Kanto earthquake have been the subjects of numerous studies, including estimation of their source models and other related research (e.g., Sato et al., 2005 ). In addition, both interplate and intraplate M7-class earthquakes, including the 1855 M7.0 Ansei Edo and the 1987 M6.8 Chiba-ken-toho-oki earthquakes (e.g., Bakun, 2005 ), have damaged the Kanto region throughout history. The Earthquake Research Committee ( 2004 ) of the Japanese government published a long-term forecast that the probability of such earthquakes within the next 30 years is estimated to be approximately 70%. It also pointed out that the seismicity of M7-class earthquakes was not constant over the interseismic period between the 1703 and 1923 M8-class interplate earthquakes. Seven of the eight M7-class earthquakes occurred during the latter 70 years of the interseismic period. Okada ( 2001 ) suggested that the interseismic period can be divided into periods of enhanced seismicity (so-called an active period) and reduced seismicity (so-called a quiescent period). Such phenomena, in which large earthquakes on major faults representative of the region influence the timing of the surrounding intereismic activities, are also known in regions such as the San Francisco Bay area and southwestern Japan (Bakun, 1999 ; Utsu, 1974 ). Therefore, to evaluate seismic hazards in the Kanto region, it is essential to assess temporal changes not only for M8-class interplate earthquakes along the Sagami Trough but also for M7-class earthquakes in surrounding areas. The phenomenon of triggering, in which one earthquake influences the occurrence of another, includes static and dynamic triggers (Pollitz and Johnston, 2006 ). Dynamic triggering is the mechanism by which earthquakes are induced by transient stress perturbations caused by the passage of seismic waves (e.g., Harris, 1998 ; Stein, 1999 ). Dynamic triggering can induce seismic activity even in distant locations where static stress changes are minimal (e.g., Kilb et al., 2000 ; Freed, 2005 ), but its effects are often transient and do not contribute to long-term seismic activity. In contrast, static triggering is a mechanism in which static stress changes due to coseismic slip promote or delay the failure of surrounding faults. The static stress increase or reduction is not a temporary alteration but remains permanent. This can influence long-term seismic activity. In southwest Japan, where long-term earthquake history has been clarified in the last millennium, the surrounding areas are known to have entered an active period from 50 years before to 10 years after repeated M8-class interplate earthquakes along the Nankai Trough (Utsu, 1974 ). Many previous studies have shown that long-term temporal changes in seismic activity can be explained by static triggering using the Coulomb failure stress ( \(\:\text{CFS}\) ) (e.g., Hori and Oike, 1996 ; Hashima et al., 2024 ; Mitogawa and Nishimura, 2020 ; Pollitz and Sacks, 1997 ; Shikakura et al., 2014). Some suggest that not only an instantaneous elastic stress change but also transient stress relaxation due to the viscoelastic asthenosphere can have an impact on stress evolution during the megathrust earthquake cycle. Similarly, long-term temporal changes in seismic activity in the Kanto region can be evaluated based on stress evolution driven by periodic large interplate earthquakes along the Sagami Trough. In this study, we simulated transient viscoelastic stress changes during a megathrust earthquake cycle along the Sagami Trough to examine temporal changes in seismicity in the Kanto region. We constructed a model based on the hypocenter distribution and focal mechanism of current seismic activity. We then discuss the characteristics of elevated seismicity in the Kanto region over the coming century, as predicted by the constructed model. 2 Methods In this study, we focused on the Kanto region and its surroundings (longitude 138.4°E to 142°E, latitude 34.4°N to 36.6°N, depth 0 to 85 km) and calculated the stress changes induced by slip and locking of the subducting plate interface (i.e., megathrust fault) along the Sagami Trough and other stress sources in a simplified viscoelastic subsurface structure. The geometry of the receiver faults subjected to stress changes was based on the focal mechanisms of recent earthquakes, and the temporal changes in Coulomb failure stress ( \(\:\text{CFS}\) ) were calculated. Furthermore, we evaluated the earthquake occurrence rate by calculating the rate of \(\:\text{CFS}\) increase over time. In the following sections, we describe the model structure, stress sources, and receiver faults used to calculate the Coulomb failure stress and earthquake occurrence rates. 2.1 Model structure We assumed a subsurface structure in which an elastic layer overlies a Maxwell viscoelastic half-space to account for the stress changes owing to viscoelastic relaxation. The stress changes were calculated using a semi-analytical solution for the viscoelastic response considering gravity (Fukahata and Matsu’ura, 2006). The model parameters of the structure were assumed to be an elastic layer thickness of 60 km and a viscosity of 1.0×10 19 Pa s (hereafter referred to as the reference model). The Maxwell relaxation time of the reference model was approximately 5.28 years. In addition to the reference model, we also constructed nine models with different parameters—elastic layer thicknesses of 40 km or 80 km and viscosities of 5.0×10 18 Pa s or 2.0×10 19 Pa s. The Maxwell relaxation times for viscosities of 5.0×10 18 Pa s and 2.0×10 19 Pa s are approximately 2.64 years and 10.56 years, respectively. For all the models, the density, rigidity, and bulk modulus were set to be uniform for each layer, as listed in Table 1 . Table 1 Elastic parameters in each layer. Layer Density Rigidity Bulk modulus Elastic 2800 kg/m 3 35 GPa 65 GPa Viscoelastic 3400 kg/m 3 60 GPa 125 GPa 2.2 Stress sources The assumed stress sources include periodic coseismic slip and interseismic locking on the megathrust fault along the Sagami Trough. The resulting stress evolution on each receiver fault was also purely periodic, with a megathrust earthquake cycle, in a linear viscoelastic medium, and did not increase in the long term. Therefore, we assume a constant rate of additional intrinsic stress loading at each receiver fault. We also calculated the impact of the 2011 M w 9.0 Tohoku-oki earthquake, including its largest aftershock off the coast of Ibaraki Prefecture (M w 7.9), because of its significant influence on the Kanto region. The details of the calculation methods for each stress source are as follows: 2.2.1 Earthquake cycle along the Sagami Trough It is hypothesized that two types of megathrust earthquakes with different source areas and magnitudes have occurred repeatedly along the Sagami Trough. One is analogous to the 1923 Taisho Kanto earthquake (hereafter, the Taisho-type earthquake), and the other is analogous to the 1707 Genroku Kanto Earthquake (hereafter, the Genroku-type earthquake). According to the Earthquake Research Committee ( 2004 ), the recurrence intervals for Taisho-type and Genroku-type earthquakes were estimated to be 200–400 years and 2300 years, respectively. However, several recent studies have suggested that the recurrence intervals of Genroku-type earthquakes may be shorter (Komori et al., 2017 ; Sato et al., 2016 ). For simplicity, this study assumes that Taisho-type and Genroku-type earthquakes occur every 200 and 1800 years, respectively, with no Taisho-type earthquakes occurring when Genroku-type earthquakes occur. We assumed dislocation sources on the megathrust fault along the Sagami Trough to calculate stress changes. The geometry of the megathrust fault and the distribution of the slip deficit rate were derived from the model of Nishimura et al. ( 2018 ), who estimated them based on onshore and offshore geodetic data. However, we assigned null slip deficit rates at depths deeper than 30 km because of the large uncertainties in the estimated slip deficit rate in some deep regions of the megathrust fault in Nishimura et al. ’s (2018) model. The source faults for the Taisho-type and Genroku-type earthquakes were set as presented in Figs. 2 b and 2 c, based on fault models estimated in previous studies (e.g., Murakami and Tsuji, 2002 ). The maximum coseismic slip for the Taisho-type and Genroku-type earthquakes, assuming that all the slip deficit accumulated during the interseismic period is released during an earthquake, is approximately 5.4 m and 49.7 m, respectively. However, the coseismic slip was unrealistically large on the eastern side of the Genroku-type earthquake-slip area. This is because, while the slip deficit in the western part of the Genroku-type earthquake slip area is released every 200 years by Taisho-type earthquakes, that in the eastern part has accumulated for 1800 years. Since the tsunami and coseismic deformation of the Genroku-type earthquake suggests that the coseismic slip of the 1707 Genroku Kanto earthquake was at most approximately 10–12 m (Satake et al., 2008 ), we reduced the slip deficit rates by multiplying the Nishimura et al. ’s (2018) slip deficit rate by 0.2 in the area that slips only during the Genroku-type earthquake (Fig. 2 a), and adjusted the maximum slip amount to approximately 10 m (Fig. 2 c). The stress loading rate due to steady locking can be expressed as the complete relaxed response to an instantaneous slip deficit in a viscoelastic medium (Matsu’ura and Sato 1989). We applied the response after 10,000 years of slip deficit as a constant stress rate owing to steady locking. In a megathrust earthquake cycle, interseismic locking and coseismic slip occur repeatedly. Considering the assumed recurrence intervals of the two earthquake types, eight Taisho-type earthquakes occurred within a cycle of the Genroku-type earthquake. Because we considered the viscoelastic stress evolution of past megathrust earthquakes, the stress evolution in some cycles differed from that in the previous cycle owing to the initial conditions. Therefore, we repeated the cycle 24 times to achieve a nearly stable stress evolution during the earthquake cycle and obtained a solution in the limit cycle. The final cycle was then treated as a temporal change in stress caused by the earthquake cycle along the Sagami Trough. 2.2.2 Intrinsic stress loading In this model, the earthquake cycle along the Sagami Trough alone did not lead to permanent stress accumulation on each receiver fault. This is because it is assumed to fully compensate for the stress caused by the slip deficit rate during the interseismic period due to coseismic slip. Although mechanisms of permanent stress accumulation, including aseismic slip at the deep extension of the crustal fault, are proposed (e.g., Iio and Kobayashi, 2002 ), we simply assume a constant stress accumulation rate that results in a \(\:\text{CFS}\) rate of 1.0 kPa/year on each receiver fault without any assumption of specific mechanisms of stress accumulation. Kaizuka and Imaizumi ( 1984 ) studied the active fault around the Kanto region and estimated 1.4 to 1.8 × 10 − 8 /year of a permanent crustal strain rate. This strain rate corresponds to a stress rate of 1.6 kPa/year with the elastic parameters in our model. Therefore, the stress loading rate assumed in this study is generally considered reasonable. 2.2.3 The 2011 Tohoku-oki earthquake The 2011 Tohoku-oki earthquake (M w 9.0) occurred along the Japan Trench 88 years after the 1923 Taisho Kanto earthquake. This earthquake is believed to have caused significant stress changes in the interplate and intraplate faults in and around the Kanto region (Toda and Stein, 2011). In this model, to account for stress changes caused by the Tohoku-oki earthquake sequences, four rectangular faults for the mainshock and the largest aftershock off the coast of Ibaraki Prefecture were defined, as shown in Table 2 . In the calculations, a uniform slip was applied to four rectangular fault models 88 years after the first Taisho-type earthquake, following the Genroku-type earthquake. The stress changes due to this slip are considered not only the coseismic changes but also the postseismic viscoelastic relaxation, whereas the stress loading due to interseismic locking is not considered. Table 2 Fault parameters of the coseismic slip for the 2011 Tohoku-oki earthquake including the largest aftershock. Latitude Longitude Depth Width Length Strike Dip Rake Slip 38.99°N 143.82°E 8.0 km 75.9 km 90.3 km 204.0° 16.1° 118.7° 40.89 m 38.30°N 143.49°E 7.9 km 122.6 km 129.6 km 204.0° 16.9° 90.0° 17.36 m 37.29°N 142.68°E 7.9 km 104.3 km 146.6 km 204.0° 15.8° 84.0° 4.72 m 36.106°N 141.777°E 8.7 km 61.0 km 59.0 km 211.0° 26.0° 104.0° 3.76 m 2.3 Receiver faults and Coulomb failure stress Receiver faults were inferred from the focal mechanisms of recent earthquakes to investigate future changes in seismic activity for earthquakes occurring within the current stress field. The focal mechanisms of earthquakes were obtained from the Full Range Seismograph Network of Japan (F-net) catalog of the National Research Institute for Earth Science and Disaster Resilience (NIED), specifically for earthquakes with a magnitude of four or greater from 1997 to 2023. It is impractical to calculate the viscoelastic response for all earthquake sources within the model area owing to computational cost constraints. Therefore, stress tensor calculation points were assigned at intervals of 0.2° horizontally and 10 km vertically within the model area. We use the calculated stress tensor at these grid points closest to each earthquake source for Coulomb failure stress changes ( \(\:\varDelta\:\text{C}\text{F}\text{S}\) ). \(\:\varDelta\:\text{C}\text{F}\text{S}\) is defined as $$\:\text{∆CFS}={\text{∆}\tau\:}_{s}+\mu\:{\prime\:}{\text{∆}\sigma\:}_{n}$$ where \(\:{\text{∆}\tau\:}_{s}\) , \(\:{\text{∆}\sigma\:}_{n}\) , and \(\:\mu\:{\prime\:}\) are the shear stress change, normal stress change (positive in extension) on the receiver fault plane, and the apparent friction coefficient, respectively. The apparent friction coefficient includes the effects of pore fluids and the material properties of the fault zone (Harris, 1998 ). When we determine a fault plane from the best double-couple focal mechanism of the F-net, there are two orthogonal nodal planes as possible fault planes. \(\:\varDelta\:\text{C}\text{F}\text{S}\) differed across these nodal planes. However, the shear stresses on the two nodal planes are always equal in an isotropic medium because conjugate shear stresses act on the orthogonal planes. To avoid ambiguity of the receiver fault plane, we set the apparent coefficient of friction to 0, allowing us to calculate a unique \(\:\varDelta\:\text{C}\text{F}\text{S}\) for each focal mechanism. 2.4 Earthquake occurrence rate Assuming that numerous faults with the same fault strength and initial stress are uniformly distributed between 0 and the fault strength, the number of earthquakes per unit time (i.e., the earthquake occurrence rate) is proportional to the rate of increase in \(\:\text{CFS}\) (e.g., Ader et al., 2014 ). However, if \(\:\text{CFS}\) decreases at any point, the earthquake occurrence rate becomes zero until \(\:\text{CFS}\) returns to its previous maximum value, because the fault cannot reach its strength. In other words, the earthquake occurrence rate is proportional to the increment from the past maximum \(\:\text{CFS}\) (hereafter referred to as CFR) (Fig. 3 ). In this model, the initial stress was set to zero, and a Genroku-type earthquake was generated. We calculated the temporal variation in the CFR over the subsequent 1800 years at one-year intervals. However, to investigate the recent seismic activity, we focused on the 200 years following the 1923 Taisho Kanto Earthquake. Specifically, we calculated the CFR for 200 years from the first occurrence of the Taisho-type earthquake to the second occurrence in the simulation. This corresponds to the years 1923–2123. 3 Earthquake occurrence rates in the reference model and differences due to the viscoelastic structure The CFR for all earthquakes was calculated using the stress tensor at the calculation points on the nearby three-dimensional grid points. Their sums were then calculated at each three-dimensional grid point. To examine long-term trends in seismicity, we divided the 200-year interseismic period between the first and second occurrences of the Taisho-type earthquake into 50-year intervals. The integral of the yearly CFR over each 50-year period was called CFR50. Hereafter, the four divided periods during the interseismic period are referred to as Periods I, II, III, and IV, in chronological order. These periods correspond to 1923–1973, 1973–2023, 2023–2073, and 2073–2123, respectively. Period II included the observation period of the earthquake sources used as receiver faults. Therefore, we evaluated the validity of CFR50 in Period II using the number of earthquakes at the grid points. In the case of the medium reference model, CFR50 was larger in areas with a higher number of earthquakes, which demonstrates that the model can generally reproduce the observed seismicity (Fig. 4 ). However, discrepancies were observed between the actual number of earthquakes and the CFR50 in some areas, including at depths of ~ 0 km off the eastern coast of the Izu Peninsula (Area A in Fig. 4 ) and ~ 70 km off the northwestern Chiba Prefecture (Area B in Fig. 4 ). These discrepancies may depend on parameters such as the thickness of the elastic layer and the viscosity assumed in this model. Therefore, to determine the optimal combination of elastic thickness and viscosity in the model, we calculated the correlation coefficients ( \(\:\text{CC}\) ) between the number of earthquakes and CFR50 at each grid point for different calculation depths. The correlation coefficient (CC) is expressed by the following equation: $$\:{\text{CC}}_{d}=\frac{{\sum\:}_{lat,lng}\left({\text{CFR}\text{50}}_{lat,lng,d}-\stackrel{-}{{\text{CFR}\text{50}}_{d}}\right)\left({\text{N}}_{lat,lng,d}-\stackrel{-}{{\text{N}}_{d}}\right)}{\sqrt{{\sum\:}_{lat,lng}{\left({\text{CFR}\text{50}}_{lat,lng,d}-\stackrel{-}{{\text{CFR}\text{50}}_{d}}\right)}^{2}{\sum\:}_{lat,lng}{\left({\text{N}}_{lat,lng,d}-\stackrel{-}{{\text{N}}_{d}}\right)}^{2}}}$$ where \(\:{\text{CC}}_{d}\) represents the correlation coefficient at depth of \(\:d\) , \(\:{\text{CFR}\text{50}}_{lat,lng,d}\) and \(\:{\text{N}}_{lat,lng,d}\) represent CFR50 and the number of earthquakes at depth for a given latitude and longitude, respectively. \(\:\stackrel{-}{{\text{CFR}\text{50}}_{d}}\) and \(\:\stackrel{-}{{\text{N}}_{d}}\) represent the average values of all CFR50 values and the number of earthquakes at depth, respectively. Table 3 lists the \(\:\text{CC}\) at different depths for each model medium. The model with an elastic thickness of 40 km showed a slightly higher correlation between CFR50 and the number of earthquakes at depths from 0 to 20 km compared to the other models, indicating that it better explains shallow regions. However, the model with an elastic thickness of 80 km showed a much higher correlation at depths greater than 40 km compared to the other models, indicating that it better explains the deeper regions. These comparisons suggest the importance of a three-dimensional viscoelastic structure for reproducing the observed seismicity distribution in the model. We found that the correlation decreased substantially when the calculation depth was within the viscoelastic layer, and that the total correlation deteriorated significantly when the elastic layer was thin. In fact, the model with an elastic thickness of 80 km and a viscosity of 2.0 × 10 19 Pa s yielded the highest total \(\:\text{CC}\) for all depths. Therefore, we regarded this model as optimal. However, viscosity cannot be uniquely constrained because seismic activity over 50-year intervals shows little sensitivity to changes in viscosity (Tables 3 and 4 ). This result indicates that, in this model, the influence of viscoelastic relaxation on the simulated seismicity is extremely limited. Table 3 Correlation coefficients at each calculation depth for each model. Calculation point depth Model parameters(Elastic layer Thickness [km], Viscosity [10 19 Pa s]) (40, 0.5) (40, 1.0) (40, 2.0) (60, 0.5) (60, 1.0) (60, 2.0) (80, 0.5) (80, 1.0) (80, 2.0) 0 km 0.41 0.41 0.41 0.40 0.41 0.41 0.40 0.41 0.41 10 km 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.45 0.45 20 km 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 30 km 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 40 km 0.79 0.78 0.78 0.80 0.80 0.80 0.80 0.80 0.80 50 km 0.45 0.40 0.42 0.87 0.87 0.87 0.86 0.87 0.87 60 km 0.72 0.73 0.74 0.84 0.83 0.83 0.89 0.88 0.88 70 km 0.53 0.59 0.54 0.58 0.64 0.71 0.97 0.97 0.97 80 km 0.50 0.63 0.70 0.50 0.56 0.72 0.91 0.92 0.92 Table 4 Correlation coefficients at each calculation depth, excluding the impact of the 2011 Tohoku-oki earthquake. Calculation point depth Model parameters(Elastic layer Thickness [km], Viscosity [10 19 Pa s]) (40, 0.5) (40, 1.0) (40, 2.0) (60, 0.5) (60, 1.0) (60, 2.0) (80, 0.5) (80, 1.0) (80, 2.0) 0 km 0.59 0.57 0.53 0.50 0.50 0.49 0.51 0.51 0.51 10 km 0.68 0.73 0.75 0.65 0.68 0.71 0.68 0.69 0.69 20 km 0.97 0.97 0.97 0.98 0.98 0.98 0.98 0.98 0.98 30 km 0.89 0.90 0.90 0.95 0.96 0.96 0.96 0.96 0.96 40 km 0.96 0.96 0.96 0.99 0.99 0.99 0.98 0.98 0.98 50 km 0.60 0.61 0.53 0.98 0.99 0.99 0.99 0.99 0.99 60 km 0.39 0.44 0.55 0.86 0.87 0.89 0.97 0.97 0.98 70 km 0.33 0.51 0.69 0.20 0.53 0.70 0.99 0.99 1.00 80 km 0.36 0.58 0.63 0.28 0.48 0.62 0.97 0.97 0.97 To investigate the impact of the 2011 Tohoku-oki earthquake, we calculated CFR50 without the Tohoku-oki earthquake as a stress source and presented the \(\:\text{CC}\) at various depths for each model medium (Table 4 ). In this scenario, the focal mechanisms of the earthquakes used to calculate \(\:\text{CFS}\) excluded those occurring after March 11, 2011, the date of the Tohoku-oki earthquake. When the impact of the Tohoku-oki earthquake was examined, the \(\:\text{CC}\) at a depth of 20 km with the Tohoku-oki earthquake was significantly lower than that without the earthquake regardless of the viscoelastic structural models (Table 3 ). It is likely that the distribution of many aftershocks from the Tohoku-oki earthquake cannot be explained by the simple rectangular fault model used in this study. Therefore, \(\:\text{CFS}\) and CFR near the rectangular fault model of the Tohoku-oki earthquake should be interpreted with caution. 4. Earthquake occurrence rate in the optimal model Figure 5 shows the CFR50 at the three-dimensional grid points for Periods I–IV in the optimal model. In Period II, the impact of the 2011 Tohoku-oki Earthquake caused a sharp increase in CFR50 off the coast of the Ibaraki Prefecture, followed by a gradual decrease. In Period II of the optimal model, CFR50 increased to 70 km in northwestern Chiba Prefecture (Area B in Fig. 4 ), thereby reducing the discrepancy between CFR50 and the number of earthquakes observed in the reference model. This suggests that the discrepancy between CFR50 and the number of earthquakes observed in the northwestern Chiba Prefecture in the reference model was due to the calculation points being in the viscoelastic layer. In contrast, the CFR in the regions of intense seismicity off the eastern coast of the Izu Peninsula was not significantly large, even in the optimal model. Although Area A in Fig. 4 is relatively shallow (depth ≤ 20 km), variations in parameters such as elastic layer thickness and viscosity have little impact on CFR50 values in this seismic zone (Table 3 ). The area off the eastern coast of the Izu Peninsula is adjacent to the Izu Microplate, where the stress loading rate may be very high because of the high slip rates of the megathrust fault (Nishimura et al., 2018 ). In this model, a constant stress loading rate of 1.0 kPa/year was assumed for all receiver faults; however, this assumption deviates from reality. Although our assumption of a uniform stress rate across all earthquake sources is oversimplified, the high correlation between the CFR and the number of observed seismic events suggests that our model reproduces this observation as a first approximation. However, in the future, it will be necessary to consider a more detailed stress field to evaluate localized seismic activity. 5. Comparison with historical earthquake activity in the Kanto Region We investigated whether the optimal model could reproduce the seismicity enhancement in the latter part of the interplate earthquake cycle in the Kanto region, as described by Okada ( 2001 ). To explore this, we focus on CFR50 for the 50 years starting 150 years after the Genroku-type earthquake, that is, 50 years before the occurrence of the first Taisho-type earthquake. In this period, multiple M7-class earthquakes are known to have occurred (Earthquake Research Committee, 2021 ). To exclude the influence of the 2011 Tohoku-oki earthquake, only the focal mechanisms used for the receiver fault were considered for the period prior to the occurrence of the earthquake. At all three-dimensional grid points, we calculated the ratio of CFR50 for each 50-year period to the total CFR50 over 200 years during the interplate earthquake cycle. Hereafter, this ratio is referred to as the CFR50 ratio. The CFR50 ratio represents the proportion of seismicity that occurred during each 50-year window relative to the long-term total at that location. When the rate of \(\:\text{CFS}\) is constant with time, the CFR50 ratio will always be 0.25, and a CFR50 ratio exceeding 0.25 indicates that a grid point is in an active period where earthquakes are relatively likely to occur in the total 200-year period. The CFR50 value indicates the relative spatial likelihood of earthquake occurrence (Fig. 6 a), and the CFR50 ratio indicates the relative temporal likelihood of earthquake occurrence at each grid point (Fig. 6 b). To evaluate the consistency between the model results and historical seismicity, we extracted M ≥ 6.8 earthquakes in the studied area in the 50 years preceding the 1923 Taisho Kanto earthquake (Table 5 and Fig. 6 ) from the Utsu earthquake catalog (Utsu, 1990 , 2002 , 2004 ). For earthquakes whose hypocentral depth is described as “shallow” in the Utsu catalog, we plotted them across all depths from 20 to 50 km in Fig. 6 . Table 5 M7-class earthquakes occurred in 50 years before the 1923 Taisho Kanto earthquake. ID Name Magnitude latitude ( \(\:^\circ\:\) ) longitude ( \(\:^\circ\:\) ) Depth (km) 1 1894 Meiji Tokyo earthquake 7.0 35.7 139.8 ~ 80 km 2 1895 southern Ibaraki earthquake 7.2 36.1 140.4 Shallow 3 1896 Ibaraki-oki earthquake 7.3 36.5 141.0 Shallow 4 1909 Boso-oki earthquake 7.5 34.5 141.5 Shallow 5 1916 Boso-oki earthquake 7.0 34.4 141.2 Shallow 6 1921 southwestern Ibaraki earthquake 7.0 36.0 140.2 53 km 7 1922 Uraga Channel earthquake 6.8 35.2 139.8 71 km For CFR50, the 1896 Ibaraki-oki earthquake occurred at a point with a relatively higher CFR50 than the surrounding areas, whereas the other earthquakes did not show such high values (Fig. 6 a). Next, focusing on the CFR50 ratio, the 1894 Meiji Tokyo earthquake occurred near the grid point with a CFR50 ratio of ~ 0.79, indicating that it occurred during a period of relatively high seismic potential in the model (Fig. 6 d). For the other events, considering uncertainties in hypocenter locations and evaluating not only the nearest grid point, but also adjacent grid points (spaced at 0.2°horizontally and 10 km vertically), the CFR50 ratio ranged from ~ 0.31 to ~ 1. These results suggest that the model captured the temporal clustering of historical seismicity reasonably well. 6. Focal mechanisms of future earthquakes in the Kanto region To explore the potential for future seismic activation, we focused on 200 years following the first Taisho-type earthquake. This analysis employed the CFR50 ratio introduced in Section 5 , which incorporated the influence of the 2011 Tohoku-oki earthquake (Fig. 7 ). This metric enabled the evaluation of the relative concentration of seismic activity during each 50-year interval. Similar to the approach in Section 3 , we divided the 200-year span from 200 to 400 years after the Genroku-type earthquake into four 50-year intervals, referred to as Periods I–IV. In Period I, the CFR50 ratio was particularly high for the 50 years following the Genroku-type earthquake, especially near the megathrust fault (Fig. 7 ). This indicates that the seismicity was temporally concentrated in the early postseismic period at many grid points, suggesting a strong coseismic influence on the stress rates immediately after the earthquake. This trend is further illustrated in Figs. 8 a–c, which show examples of the temporal CFR evolution at the selected grid points. As shown in Fig. 8 c, most of the elevated CFR values during this period were associated with the instantaneous increase in elastic stress due to coseismic slip. This coseismic activation can be recognized as an aftershock, consistent with the intense aftershock activity observed after the 1923 Taisho Kanto earthquake, including six M7-class earthquakes (e.g., Takemura, 1994 ). During Period II, which included the timing of the 2011 Tohoku-oki earthquake, the CFR50 ratio increased in the northeastern part of the study region near the source area of the Tohoku-oki earthquake (Fig. 7 ). This is consistent with the observed activation of earthquakes in the region following the Tohoku-oki earthquake reported by the Earthquake Research Committee (2011). In Period III, the overall CFR50 ratio decreased. However, in Period IV, it increased again at several grid points, indicating a trend toward seismic activation in the later stages of the interplate earthquake cycle. Figures 8 d–f present an example of a CFR time series that exhibits a late-stage increase in CFR50. This example suggests that the CFS exceeded its past maximum only in the later part of the seismic cycle, potentially leading to the next major rupture. In particular, the increase in seismic potential during the later stages of the cycle was primarily attributed to negative coseismic stress changes on the megathrust fault along the Sagami Trough (Fig. 8 c). In addition, since the 2011 Tohoku-oki earthquake occurred during Period II, its associated stress shadow has contributed to similar effects in some regions. Although the high CFR50 ratio in Fig. 7 does not directly indicate the number of earthquakes, it highlights the periods and locations in which high seismicity is expected from the simulation. We further investigated the spatial and temporal trends of potential earthquakes based on the simulation results. We focus on the region where the CFR increases by 0.2 MPa/year or more from Period II to Period IV. As the region of high CFR increase is concentrated near the western part of the Sagami Trough (Fig. 9 a), more attention should be provided to future earthquake hazards in this region. An examination of the focal mechanisms in the region revealed regional characteristics. In the area north of 35.3°N (hereafter referred to as Kanagawa Prefecture), 10 of the 12 receiver focal mechanisms have similar fault geometries, in which one of the conjugate planes is a northwest-dipping low-angle reverse fault (Fig. 9 b). These receiver faults are located at depths of 20–40 km near the megathrust fault along the Sagami Trough. Considering these characteristics and the slip deficit distribution (Fig. 2 a), the interplate earthquakes in the down-dip transition zone from full coupling to no coupling increased as the next Taisho-type earthquake approached. In the area south of 35.3°N, which is off the eastern coast of the Izu Peninsula region, the overlaid beach ball diagrams for 113 receiver focal mechanisms suggest N-S or E-W trending strike-slip faults (Fig. 9 c). Several M7-class earthquakes, including the 1978 M6.9 Izu-oshima earthquake and the 1980 M6.7 east of the Izu Peninsula, have occurred in this region. In addition to these tectonic earthquakes, volcano-tectonic earthquake swarms associated with the intrusion of volcanic fluids were intermittently observed during the 1980s–2000s (e.g., Aoki et al., 1999 ). Such volcanic stress sources were not considered in this model, and it is possible that the model was unable to adequately reproduce temporal changes in seismic activity in this region. As described in Section 4 , the assumed stress loading rate in this region may be underestimated. If the loading rate is higher, temporal changes in the stress rate and its modulation of local seismicity become relatively small during the interseismic period. Note that the receiver faults used in this study were only from the F-net catalog, and the mechanisms currently quiescent owing to the influence of the earthquake cycle along the Sagami Trough and other factors may not have been sufficiently evaluated. 7. Conclusions This research unveiled significant insights into seismic activity along the Sagami Trough by modeling the interplate earthquake cycle using CFS changes. By constructing and validating a model that assumed an elastic layer overlying a Maxwell viscoelastic half-space, we compared calculated earthquake occurrence rates with those observed in recent seismic activity. The optimal model, characterized by an elastic layer thickness of 80 km and a viscosity of 2.0×10 19 Pa s, provided the best explanation for past seismic activity. Our findings suggest that most earthquakes occur within the elastic layer to reproduce the observed seismic activity in the Kanto region. When earthquakes occur within the viscoelastic layer, the correlation between predicted and observed seismicity decreases significantly. No model with an assumed two-dimensional viscoelastic structure could explain the distribution of the observed seismicity across all depths. This highlights the need to incorporate a three-dimensional viscoelastic structure to reproduce depth-dependent variations in earthquake enhancement and quiescence, as well as the observed earthquake distribution. Furthermore, the model reveals that receiver faults experiencing negative coseismic stress changes during the M8-class interplate earthquakes tend to delay rupture, leading to increased seismic activity in the later stages of the earthquake cycle. This behavior is consistent with the historical clustering of M7-class earthquakes in the Kanto region and highlights the importance of stress history in modulating long-term seismicity. This model can also predict the focal mechanisms of future activated earthquakes. For example, a northwest-dipping low-angle reverse fault earthquake is expected to increase around Kanagawa Prefecture from 2073 to 2123. This model offers valuable information for forecasting the timing, location, and mechanisms of the increased seismic activity in the Kanto region. In summary, this study provides a simple framework for understanding and predicting seismic activity in the Kanto region of Japan. This simulation to predict the timing, location, and mechanisms of increased seismic activity enabled us to construct specific earthquake activity scenarios based on physical mechanisms in the Kanto region. This advancement is expected to enhance seismic hazard prediction and contribute to disaster risk reduction. Abbreviations AMR Amurian Plate \(\:\text{CFS}\) Coulomb Failure Stress CFR Coulomb Failure Rate \(\:\text{CC}\) Correlation Coefficient \(\:\varDelta\:\text{CFS}\) Coulomb Failure Stress Change NA North American Plate PAC Pacific Plate PHS Philippine Sea Plate Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Competing interests The authors declare that they have no competing interests. Authors' information Digital Services Division, Pacific Consultants Co. Ltd., 3–22 Kanda-Nishikicho, Chiyoda-ku, Tokyo, Japan Tsukasa Mitogawa Disaster Prevention Research Institute, Kyoto University, Uji, 611 − 0011, Japan Takuya Nishimura Funding This study was supported by a joint research project between Kyoto University, Tokyo Polytechnic University, Shimizu Corporation, and Osaki Research Institute entitled "Building Performance Evaluation Considering Resilience and Sustainability”. Authors' contributions TM conducted all calculations for this study and wrote the manuscript. TN conceived the initial ideas and supervised manuscript revisions. Both authors read and approved the final version of the manuscript. Acknowledgements We thank Dr. Yukitoshi Fukahata for providing the numerical code for the viscoelastic response owing to a dislocation source in a layered medium. Figures were drawn using General Mapping Tools (Wessel et al. 2013). The F-net catalog was provided by the National Research Institute for Earth Science and Disaster Resilience (NIED). 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Geochem Geophys Geosyst 20:5556–5564. 10.1029/2019GC008515 Supplementary Files GraphicalAbstract.png Cite Share Download PDF Status: Published Journal Publication published 07 Apr, 2026 Read the published version in Earth, Planets and Space → Version 1 posted Reviewers agreed at journal 09 Dec, 2025 Reviewers invited by journal 09 Dec, 2025 Editor assigned by journal 04 Dec, 2025 First submitted to journal 03 Dec, 2025 Editorial decision: Major Revision 01 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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16:50:42","extension":"html","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":161472,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/739181b4c08f6924c1d76b6e.html"},{"id":98214581,"identity":"1064dfe2-6233-4977-b9e9-1f7a41bf6b68","added_by":"auto","created_at":"2025-12-15 10:10:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1103141,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSeismicity in the Kanto Region, central Japan.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea \u003c/strong\u003eLocation of the study area on a tectonic map. The solid red rectangle indicates the study area. PHS, PAC, NA, and AMR represent the Philippine Sea, Pacific, North American, and Amurian plates, respectively. The blue arrows near the plate boundaries indicate the approximate direction of the relative plate movement, based on Bird (2003). \u003cstrong\u003eb\u003c/strong\u003e Seismicity in the study area from 1994 to 2023. Circles indicate earthquake epicenters, with the size of the circles representing the magnitude and the color of the circles representing the depth of the hypocenter. The light blue solid line and light blue dashed line indicate the isodepthsof the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009). The earthquake data were sourced from the F-net catalog. \u003cstrong\u003ec\u003c/strong\u003e Magnitude-time diagram of M ≥ 6 earthquakes within the area shown in Figure 1b. The data were based on the Utsu earthquake catalog (Utsu, 1990, 2002, 2004).\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/11b38a92a207c98905dc881b.png"},{"id":98214606,"identity":"e8c791d8-b543-43fb-9640-98c88866be71","added_by":"auto","created_at":"2025-12-15 10:10:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":420615,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAssumed slip distribution on the megathrust fault along the Sagami Trough.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e Distribution of the assumed slip deficit rates at the subducting plate interface (i.e., megathrust fault) along the Sagami Trough during the interseismic period. The slip deficit rates were based on the results of Nishimura et al. (2018) with modifications. The area enclosed by the light blue line indicates the region in which the slip deficit rate is reduced to 20% of the original rate (see text). \u003cstrong\u003eb\u003c/strong\u003e Slip distribution of Taisho-type earthquakes. The slip is compensated by the slip deficit for 200 years in the area beyond the light blue polygon in \u003cstrong\u003ea\u003c/strong\u003e. \u003cstrong\u003ec\u003c/strong\u003e Slip distribution of the Genroku-type earthquake. The slip compensated for the slip deficit for 1800 years.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/7c37be11383609b42b30ffe9.png"},{"id":98214603,"identity":"e5026294-dd1f-4a2f-8371-102289ee4ed1","added_by":"auto","created_at":"2025-12-15 10:10:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":80484,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic diagram of the Coulomb failure stress (CFS) and Coulomb failure rate (CFR) in megathrust earthquake cycles.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe blue dashed and solid blue lines indicate the temporal evolution of the CFS and the maximum CFS up to that time, respectively. The dashed red line indicates the CFS rate and the solid red line indicates the rate of maximum CFS, which is defined as the Coulomb failure rate (CFR) in this study.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/ef4c731d7f6e418434f079af.png"},{"id":98214591,"identity":"f5952976-5bd1-4301-87d2-7f2a61b4767d","added_by":"auto","created_at":"2025-12-15 10:10:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":857595,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCFR50 in Period II for the reference model and the number of earthquakes during 1994–2023.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea \u003c/strong\u003eCFR50 in Period II for the reference model at intervals of 10 km depth. The reference model has an elastic thickness of 60 km and a viscosity of 1.0×10\u003csup\u003e19 \u003c/sup\u003ePa s. White and gray areas represent areas for 0 CFR and no receiver fault in the model, respectively. \u003cstrong\u003eb\u003c/strong\u003e The number of earthquakes with a magnitude of 3.5 or greater from 1994 to 2023. Areas A and B are off the eastern coast of the Izu Peninsula region and northwestern Chiba Prefecture, respectively (see text). The light blue solid line and light blue dashed line indicate the isodepths of the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009).\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/9e81f8c55e8a9d29f8b83d8d.png"},{"id":98214613,"identity":"54de3557-fc07-4fac-8340-84cfadf306d7","added_by":"auto","created_at":"2025-12-15 10:10:20","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1548908,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCFR50 in Periods I to IV for the optimal model.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe CFR50 values are shown at 10 km depth intervals for each 50-year period following the first Taisho-type earthquake: (a) Period I (200–250 years), (b) Period II (250–300 years), (c) Period III (300–350 years), and (d) Period IV (350–400 years). The color scale is the same as that shown in Figure 4a. The optimal model has an elastic thickness of 80 km and a viscosity of 2.0×10\u003csup\u003e19 \u003c/sup\u003ePa s. The light blue solid line and light blue dashed line indicate the isodepths of the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009).\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/2b88ea8c2da6c17811a4460d.png"},{"id":98214592,"identity":"b05501a8-8a90-4662-8f4c-f874302ecd70","added_by":"auto","created_at":"2025-12-15 10:10:15","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":804908,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCFR50 and CFR50 ratio for the 50 years before the Taisho-type earthquake.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e CFR50 from 150 to 200 years after the Genroku-type earthquake. \u003cstrong\u003eb\u003c/strong\u003e CFR50 ratio from 150 to 200 years after the Genroku-type earthquake. Each subfigure displays the CFR50 distribution at depths of 0–80 km. The hypocenters of M ≥ 6.8 earthquakes that occurred within the 50 years preceding the 1923 Taisho Kanto earthquake were also plotted. The numbers in the figure correspond to the earthquake IDs listed in Table 5. The light blue solid line and light blue dashed line indicate the isodepths of the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009).\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/bc92dee79fa0a5da3a718884.png"},{"id":98432233,"identity":"adfa3d34-7cd1-415c-b1a2-bd436c58a970","added_by":"auto","created_at":"2025-12-17 16:49:15","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1445558,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCFR50 ratio over the 200 years since the first Taisho-type earthquake.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe CFR50 ratios are shown at 10 km depth intervals for each 50-year period following the first Taisho-type earthquake: \u003cstrong\u003ea\u003c/strong\u003e Period I (0–50 years), \u003cstrong\u003eb\u003c/strong\u003e Period II (50–100 years), \u003cstrong\u003ec\u003c/strong\u003e Period III (100–150 years), and \u003cstrong\u003ed\u003c/strong\u003e Period IV (150–200 years). The CFR50 ratio is defined as the CFR50 over a 50-year period normalized by the total CFR over a 400-year span. The color scale is the same as that shown in Figure 4a. The optimal model used has an elastic thickness of 80 km and a viscosity of 2.0 × 10¹⁹ Pa·s. The green solid line and green dashed line indicate the isodepths of the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009).\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/d6373884de46dbabc3284816.png"},{"id":98431702,"identity":"d318a43f-fad8-4841-9718-8991bd4e8924","added_by":"auto","created_at":"2025-12-17 16:48:11","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":777462,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTemporal evolution of CFS and CFR for selected receiver faults.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e, \u003cstrong\u003ed\u003c/strong\u003e Focal mechanisms of receiver faults. The green solid and dashed lines indicate the isodepth contours of the subducting Philippine Sea and Pacific plates, respectively. \u003cstrong\u003eb, e\u003c/strong\u003e Time evolution of CFS with (solid line) and without (dashed line) the 2011 Tohoku-oki earthquake. \u003cstrong\u003ec\u003c/strong\u003e, \u003cstrong\u003ef\u003c/strong\u003eCorresponding CFR evolution. In subfigure \u003cstrong\u003ec\u003c/strong\u003e, the CFS at the time of a megathrust earthquake is explicitly labeled as the coseismicCFS because it becomes positive, causing an instantaneous increase in the CFR.The light blue solid line and light blue dashed line indicate the isodepthsof the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009).\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/8ee2da31a26e8c0e18d60c20.png"},{"id":98433382,"identity":"f0a128b0-7255-4656-b219-1a48c290e99c","added_by":"auto","created_at":"2025-12-17 16:50:41","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":337582,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDistribution of notable CFR50 increments from Period II to Period IV and major focal mechanisms in the CFR increased zone\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e Cumulative Coulomb failure rate (CFR) increment from Period II to Period IV. The CFR50 increments are plotted only in areas where the increment is 0.2 MPa/year or greater. The CFR50 increments were calculated by adding the CFR50 values overall depths. The area enclosed by the solid blue line is the area around Kanagawa Prefecture, and the area enclosed by the blue dashed line is off the Eastern Coast of the Izu Peninsula region. The thick light-blue solid line indicates the trench axis. The light blue solid line and light blue dashed line indicate the isodepths of the subducting Philippine Sea Plate and subducting Pacific Plate, respectively (Hirose et al. 2007; 2008a; b; Kita et al. 2010; Nakajima and Hasegawa 2006; 2007; Nakajima et al. 2009). \u003cstrong\u003eb\u003c/strong\u003e Overlaid beach balls for the focal mechanisms of the receiver faults around Kanagawa Prefecture in \u003cstrong\u003ea\u003c/strong\u003e. They were classified into two groups based on significantly different strike directions. Subfigure \u003cstrong\u003ec\u003c/strong\u003e is the same as subfigure \u003cstrong\u003eb\u003c/strong\u003e, but is off the eastern coast of the Izu Peninsula region.\u003c/p\u003e","description":"","filename":"Figure9.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/ca97f85e910f6cce025c4b6e.png"},{"id":106809358,"identity":"0908fdf5-2889-4612-a211-ef4b54e74be0","added_by":"auto","created_at":"2026-04-13 16:10:05","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8355826,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/555dd233-f2b5-4738-a7ca-2d3f1f2a0763.pdf"},{"id":98214596,"identity":"f04300cd-ec4f-457c-a632-0c707e7b776b","added_by":"auto","created_at":"2025-12-15 10:10:18","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"supplement","size":101252,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstract.png","url":"https://assets-eu.researchsquare.com/files/rs-8216970/v1/66bfb13c34c96bb956154f47.png"}],"financialInterests":"","formattedTitle":"Modeling of seismic activity modulated by stress changes during the interplate earthquake cycle along the Sagami Trough, central Japan","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe Kanto region in central Japan has a complex tectonic setting in which two oceanic plates subduct beneath the continental plate from the south and east, resulting in high seismic activity (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The Philippine Sea Plate subducts beneath the North American Plate at a rate of a few centimeters per year, and geological, geomorphological, and historical studies have suggested that M8-class interplate earthquakes repeatedly occur along the Sagami Trough (Shishikura, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1999\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Shishikura et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Satake, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In particular, the 1703 M8.1 Genroku Kanto earthquake and the 1923 M7.9 Taisho Kanto earthquake have been the subjects of numerous studies, including estimation of their source models and other related research (e.g., Sato et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2005\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn addition, both interplate and intraplate M7-class earthquakes, including the 1855 M7.0 Ansei Edo and the 1987 M6.8 Chiba-ken-toho-oki earthquakes (e.g., Bakun, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), have damaged the Kanto region throughout history. The Earthquake Research Committee (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) of the Japanese government published a long-term forecast that the probability of such earthquakes within the next 30 years is estimated to be approximately 70%. It also pointed out that the seismicity of M7-class earthquakes was not constant over the interseismic period between the 1703 and 1923 M8-class interplate earthquakes. Seven of the eight M7-class earthquakes occurred during the latter 70 years of the interseismic period. Okada (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) suggested that the interseismic period can be divided into periods of enhanced seismicity (so-called an active period) and reduced seismicity (so-called a quiescent period). Such phenomena, in which large earthquakes on major faults representative of the region influence the timing of the surrounding intereismic activities, are also known in regions such as the San Francisco Bay area and southwestern Japan (Bakun, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Utsu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1974\u003c/span\u003e). Therefore, to evaluate seismic hazards in the Kanto region, it is essential to assess temporal changes not only for M8-class interplate earthquakes along the Sagami Trough but also for M7-class earthquakes in surrounding areas.\u003c/p\u003e\u003cp\u003eThe phenomenon of triggering, in which one earthquake influences the occurrence of another, includes static and dynamic triggers (Pollitz and Johnston, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Dynamic triggering is the mechanism by which earthquakes are induced by transient stress perturbations caused by the passage of seismic waves (e.g., Harris, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Stein, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Dynamic triggering can induce seismic activity even in distant locations where static stress changes are minimal (e.g., Kilb et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Freed, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), but its effects are often transient and do not contribute to long-term seismic activity.\u003c/p\u003e\u003cp\u003eIn contrast, static triggering is a mechanism in which static stress changes due to coseismic slip promote or delay the failure of surrounding faults. The static stress increase or reduction is not a temporary alteration but remains permanent. This can influence long-term seismic activity. In southwest Japan, where long-term earthquake history has been clarified in the last millennium, the surrounding areas are known to have entered an active period from 50 years before to 10 years after repeated M8-class interplate earthquakes along the Nankai Trough (Utsu, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1974\u003c/span\u003e). Many previous studies have shown that long-term temporal changes in seismic activity can be explained by static triggering using the Coulomb failure stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e) (e.g., Hori and Oike, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Hashima et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Mitogawa and Nishimura, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Pollitz and Sacks, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Shikakura et al., 2014). Some suggest that not only an instantaneous elastic stress change but also transient stress relaxation due to the viscoelastic asthenosphere can have an impact on stress evolution during the megathrust earthquake cycle. Similarly, long-term temporal changes in seismic activity in the Kanto region can be evaluated based on stress evolution driven by periodic large interplate earthquakes along the Sagami Trough.\u003c/p\u003e\u003cp\u003eIn this study, we simulated transient viscoelastic stress changes during a megathrust earthquake cycle along the Sagami Trough to examine temporal changes in seismicity in the Kanto region. We constructed a model based on the hypocenter distribution and focal mechanism of current seismic activity. We then discuss the characteristics of elevated seismicity in the Kanto region over the coming century, as predicted by the constructed model.\u003c/p\u003e"},{"header":"2 Methods","content":"\u003cp\u003eIn this study, we focused on the Kanto region and its surroundings (longitude 138.4\u0026deg;E to 142\u0026deg;E, latitude 34.4\u0026deg;N to 36.6\u0026deg;N, depth 0 to 85 km) and calculated the stress changes induced by slip and locking of the subducting plate interface (i.e., megathrust fault) along the Sagami Trough and other stress sources in a simplified viscoelastic subsurface structure. The geometry of the receiver faults subjected to stress changes was based on the focal mechanisms of recent earthquakes, and the temporal changes in Coulomb failure stress (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e) were calculated. Furthermore, we evaluated the earthquake occurrence rate by calculating the rate of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e increase over time. In the following sections, we describe the model structure, stress sources, and receiver faults used to calculate the Coulomb failure stress and earthquake occurrence rates.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Model structure\u003c/h2\u003e\u003cp\u003eWe assumed a subsurface structure in which an elastic layer overlies a Maxwell viscoelastic half-space to account for the stress changes owing to viscoelastic relaxation. The stress changes were calculated using a semi-analytical solution for the viscoelastic response considering gravity (Fukahata and Matsu\u0026rsquo;ura, 2006). The model parameters of the structure were assumed to be an elastic layer thickness of 60 km and a viscosity of 1.0\u0026times;10\u003csup\u003e19\u003c/sup\u003e Pa s (hereafter referred to as the reference model). The Maxwell relaxation time of the reference model was approximately 5.28 years.\u003c/p\u003e\u003cp\u003eIn addition to the reference model, we also constructed nine models with different parameters\u0026mdash;elastic layer thicknesses of 40 km or 80 km and viscosities of 5.0\u0026times;10\u003csup\u003e18\u003c/sup\u003e Pa s or 2.0\u0026times;10\u003csup\u003e19\u003c/sup\u003e Pa s. The Maxwell relaxation times for viscosities of 5.0\u0026times;10\u003csup\u003e18\u003c/sup\u003e Pa s and 2.0\u0026times;10\u003csup\u003e19\u003c/sup\u003e Pa s are approximately 2.64 years and 10.56 years, respectively. For all the models, the density, rigidity, and bulk modulus were set to be uniform for each layer, as listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eElastic parameters in each layer.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLayer\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDensity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRigidity\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBulk modulus\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eElastic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2800 kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e35 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e65 GPa\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eViscoelastic\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3400 kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e60 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e125 GPa\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Stress sources\u003c/h2\u003e\u003cp\u003eThe assumed stress sources include periodic coseismic slip and interseismic locking on the megathrust fault along the Sagami Trough. The resulting stress evolution on each receiver fault was also purely periodic, with a megathrust earthquake cycle, in a linear viscoelastic medium, and did not increase in the long term. Therefore, we assume a constant rate of additional intrinsic stress loading at each receiver fault. We also calculated the impact of the 2011 M\u003csub\u003ew\u003c/sub\u003e 9.0 Tohoku-oki earthquake, including its largest aftershock off the coast of Ibaraki Prefecture (M\u003csub\u003ew\u003c/sub\u003e 7.9), because of its significant influence on the Kanto region. The details of the calculation methods for each stress source are as follows:\u003c/p\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e2.2.1 Earthquake cycle along the Sagami Trough\u003c/h2\u003e\u003cp\u003eIt is hypothesized that two types of megathrust earthquakes with different source areas and magnitudes have occurred repeatedly along the Sagami Trough. One is analogous to the 1923 Taisho Kanto earthquake (hereafter, the Taisho-type earthquake), and the other is analogous to the 1707 Genroku Kanto Earthquake (hereafter, the Genroku-type earthquake). According to the Earthquake Research Committee (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), the recurrence intervals for Taisho-type and Genroku-type earthquakes were estimated to be 200\u0026ndash;400 years and 2300 years, respectively. However, several recent studies have suggested that the recurrence intervals of Genroku-type earthquakes may be shorter (Komori et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Sato et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). For simplicity, this study assumes that Taisho-type and Genroku-type earthquakes occur every 200 and 1800 years, respectively, with no Taisho-type earthquakes occurring when Genroku-type earthquakes occur.\u003c/p\u003e\u003cp\u003eWe assumed dislocation sources on the megathrust fault along the Sagami Trough to calculate stress changes. The geometry of the megathrust fault and the distribution of the slip deficit rate were derived from the model of Nishimura et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), who estimated them based on onshore and offshore geodetic data. However, we assigned null slip deficit rates at depths deeper than 30 km because of the large uncertainties in the estimated slip deficit rate in some deep regions of the megathrust fault in Nishimura et al. \u0026rsquo;s (2018) model. The source faults for the Taisho-type and Genroku-type earthquakes were set as presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, based on fault models estimated in previous studies (e.g., Murakami and Tsuji, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). The maximum coseismic slip for the Taisho-type and Genroku-type earthquakes, assuming that all the slip deficit accumulated during the interseismic period is released during an earthquake, is approximately 5.4 m and 49.7 m, respectively. However, the coseismic slip was unrealistically large on the eastern side of the Genroku-type earthquake-slip area. This is because, while the slip deficit in the western part of the Genroku-type earthquake slip area is released every 200 years by Taisho-type earthquakes, that in the eastern part has accumulated for 1800 years. Since the tsunami and coseismic deformation of the Genroku-type earthquake suggests that the coseismic slip of the 1707 Genroku Kanto earthquake was at most approximately 10\u0026ndash;12 m (Satake et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), we reduced the slip deficit rates by multiplying the Nishimura et al. \u0026rsquo;s (2018) slip deficit rate by 0.2 in the area that slips only during the Genroku-type earthquake (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea), and adjusted the maximum slip amount to approximately 10 m (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe stress loading rate due to steady locking can be expressed as the complete relaxed response to an instantaneous slip deficit in a viscoelastic medium (Matsu\u0026rsquo;ura and Sato 1989). We applied the response after 10,000 years of slip deficit as a constant stress rate owing to steady locking.\u003c/p\u003e\u003cp\u003eIn a megathrust earthquake cycle, interseismic locking and coseismic slip occur repeatedly. Considering the assumed recurrence intervals of the two earthquake types, eight Taisho-type earthquakes occurred within a cycle of the Genroku-type earthquake. Because we considered the viscoelastic stress evolution of past megathrust earthquakes, the stress evolution in some cycles differed from that in the previous cycle owing to the initial conditions. Therefore, we repeated the cycle 24 times to achieve a nearly stable stress evolution during the earthquake cycle and obtained a solution in the limit cycle. The final cycle was then treated as a temporal change in stress caused by the earthquake cycle along the Sagami Trough.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e2.2.2 Intrinsic stress loading\u003c/h2\u003e\u003cp\u003eIn this model, the earthquake cycle along the Sagami Trough alone did not lead to permanent stress accumulation on each receiver fault. This is because it is assumed to fully compensate for the stress caused by the slip deficit rate during the interseismic period due to coseismic slip. Although mechanisms of permanent stress accumulation, including aseismic slip at the deep extension of the crustal fault, are proposed (e.g., Iio and Kobayashi, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), we simply assume a constant stress accumulation rate that results in a \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e rate of 1.0 kPa/year on each receiver fault without any assumption of specific mechanisms of stress accumulation.\u003c/p\u003e\u003cp\u003eKaizuka and Imaizumi (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1984\u003c/span\u003e) studied the active fault around the Kanto region and estimated 1.4 to 1.8 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e /year of a permanent crustal strain rate. This strain rate corresponds to a stress rate of 1.6 kPa/year with the elastic parameters in our model. Therefore, the stress loading rate assumed in this study is generally considered reasonable.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.2.3 The 2011 Tohoku-oki earthquake\u003c/h2\u003e\u003cp\u003eThe 2011 Tohoku-oki earthquake (M\u003csub\u003ew\u003c/sub\u003e 9.0) occurred along the Japan Trench 88 years after the 1923 Taisho Kanto earthquake. This earthquake is believed to have caused significant stress changes in the interplate and intraplate faults in and around the Kanto region (Toda and Stein, 2011). In this model, to account for stress changes caused by the Tohoku-oki earthquake sequences, four rectangular faults for the mainshock and the largest aftershock off the coast of Ibaraki Prefecture were defined, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. In the calculations, a uniform slip was applied to four rectangular fault models 88 years after the first Taisho-type earthquake, following the Genroku-type earthquake. The stress changes due to this slip are considered not only the coseismic changes but also the postseismic viscoelastic relaxation, whereas the stress loading due to interseismic locking is not considered.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFault parameters of the coseismic slip for the 2011 Tohoku-oki earthquake including the largest aftershock.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLatitude\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLongitude\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDepth\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eWidth\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLength\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eStrike\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eDip\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eRake\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003eSlip\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e38.99\u0026deg;N\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e143.82\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.0 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e75.9 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e90.3 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e204.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e16.1\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e118.7\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e40.89 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e38.30\u0026deg;N\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e143.49\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7.9 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e122.6 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e129.6 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e204.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e16.9\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e90.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e17.36 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e37.29\u0026deg;N\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e142.68\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7.9 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e104.3 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e146.6 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e204.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e15.8\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e84.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e4.72 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e36.106\u0026deg;N\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e141.777\u0026deg;E\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.7 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e61.0 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e59.0 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e211.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e26.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e104.0\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e3.76 m\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Receiver faults and Coulomb failure stress\u003c/h2\u003e\u003cp\u003eReceiver faults were inferred from the focal mechanisms of recent earthquakes to investigate future changes in seismic activity for earthquakes occurring within the current stress field. The focal mechanisms of earthquakes were obtained from the Full Range Seismograph Network of Japan (F-net) catalog of the National Research Institute for Earth Science and Disaster Resilience (NIED), specifically for earthquakes with a magnitude of four or greater from 1997 to 2023. It is impractical to calculate the viscoelastic response for all earthquake sources within the model area owing to computational cost constraints. Therefore, stress tensor calculation points were assigned at intervals of 0.2\u0026deg; horizontally and 10 km vertically within the model area. We use the calculated stress tensor at these grid points closest to each earthquake source for Coulomb failure stress changes (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{C}\\text{F}\\text{S}\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{C}\\text{F}\\text{S}\\)\u003c/span\u003e\u003c/span\u003e is defined as\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{∆CFS}={\\text{∆}\\tau\\:}_{s}+\\mu\\:{\\prime\\:}{\\text{∆}\\sigma\\:}_{n}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{∆}\\tau\\:}_{s}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{∆}\\sigma\\:}_{n}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:{\\prime\\:}\\)\u003c/span\u003e\u003c/span\u003e are the shear stress change, normal stress change (positive in extension) on the receiver fault plane, and the apparent friction coefficient, respectively. The apparent friction coefficient includes the effects of pore fluids and the material properties of the fault zone (Harris, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1998\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eWhen we determine a fault plane from the best double-couple focal mechanism of the F-net, there are two orthogonal nodal planes as possible fault planes. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{C}\\text{F}\\text{S}\\)\u003c/span\u003e\u003c/span\u003e differed across these nodal planes. However, the shear stresses on the two nodal planes are always equal in an isotropic medium because conjugate shear stresses act on the orthogonal planes. To avoid ambiguity of the receiver fault plane, we set the apparent coefficient of friction to 0, allowing us to calculate a unique \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{C}\\text{F}\\text{S}\\)\u003c/span\u003e\u003c/span\u003e for each focal mechanism.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Earthquake occurrence rate\u003c/h2\u003e\u003cp\u003eAssuming that numerous faults with the same fault strength and initial stress are uniformly distributed between 0 and the fault strength, the number of earthquakes per unit time (i.e., the earthquake occurrence rate) is proportional to the rate of increase in \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e (e.g., Ader et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). However, if \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e decreases at any point, the earthquake occurrence rate becomes zero until \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e returns to its previous maximum value, because the fault cannot reach its strength. In other words, the earthquake occurrence rate is proportional to the increment from the past maximum \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e (hereafter referred to as CFR) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn this model, the initial stress was set to zero, and a Genroku-type earthquake was generated. We calculated the temporal variation in the CFR over the subsequent 1800 years at one-year intervals. However, to investigate the recent seismic activity, we focused on the 200 years following the 1923 Taisho Kanto Earthquake. Specifically, we calculated the CFR for 200 years from the first occurrence of the Taisho-type earthquake to the second occurrence in the simulation. This corresponds to the years 1923\u0026ndash;2123.\u003c/p\u003e\u003c/div\u003e"},{"header":"3 Earthquake occurrence rates in the reference model and differences due to the viscoelastic structure","content":"\u003cp\u003eThe CFR for all earthquakes was calculated using the stress tensor at the calculation points on the nearby three-dimensional grid points. Their sums were then calculated at each three-dimensional grid point. To examine long-term trends in seismicity, we divided the 200-year interseismic period between the first and second occurrences of the Taisho-type earthquake into 50-year intervals. The integral of the yearly CFR over each 50-year period was called CFR50. Hereafter, the four divided periods during the interseismic period are referred to as Periods I, II, III, and IV, in chronological order. These periods correspond to 1923\u0026ndash;1973, 1973\u0026ndash;2023, 2023\u0026ndash;2073, and 2073\u0026ndash;2123, respectively.\u003c/p\u003e\u003cp\u003ePeriod II included the observation period of the earthquake sources used as receiver faults. Therefore, we evaluated the validity of CFR50 in Period II using the number of earthquakes at the grid points. In the case of the medium reference model, CFR50 was larger in areas with a higher number of earthquakes, which demonstrates that the model can generally reproduce the observed seismicity (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). However, discrepancies were observed between the actual number of earthquakes and the CFR50 in some areas, including at depths of ~\u0026thinsp;0 km off the eastern coast of the Izu Peninsula (Area A in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) and ~\u0026thinsp;70 km off the northwestern Chiba Prefecture (Area B in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). These discrepancies may depend on parameters such as the thickness of the elastic layer and the viscosity assumed in this model. Therefore, to determine the optimal combination of elastic thickness and viscosity in the model, we calculated the correlation coefficients (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CC}\\)\u003c/span\u003e\u003c/span\u003e) between the number of earthquakes and CFR50 at each grid point for different calculation depths. The correlation coefficient (CC) is expressed by the following equation:\u003c/p\u003e\u003cp\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{\\text{CC}}_{d}=\\frac{{\\sum\\:}_{lat,lng}\\left({\\text{CFR}\\text{50}}_{lat,lng,d}-\\stackrel{-}{{\\text{CFR}\\text{50}}_{d}}\\right)\\left({\\text{N}}_{lat,lng,d}-\\stackrel{-}{{\\text{N}}_{d}}\\right)}{\\sqrt{{\\sum\\:}_{lat,lng}{\\left({\\text{CFR}\\text{50}}_{lat,lng,d}-\\stackrel{-}{{\\text{CFR}\\text{50}}_{d}}\\right)}^{2}{\\sum\\:}_{lat,lng}{\\left({\\text{N}}_{lat,lng,d}-\\stackrel{-}{{\\text{N}}_{d}}\\right)}^{2}}}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{CC}}_{d}\\)\u003c/span\u003e\u003c/span\u003e represents the correlation coefficient at depth of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:d\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{CFR}\\text{50}}_{lat,lng,d}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{lat,lng,d}\\)\u003c/span\u003e\u003c/span\u003e represent CFR50 and the number of earthquakes at depth for a given latitude and longitude, respectively. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{\\text{CFR}\\text{50}}_{d}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{{\\text{N}}_{d}}\\)\u003c/span\u003e\u003c/span\u003e represent the average values of all CFR50 values and the number of earthquakes at depth, respectively.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e lists the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CC}\\)\u003c/span\u003e\u003c/span\u003e at different depths for each model medium. The model with an elastic thickness of 40 km showed a slightly higher correlation between CFR50 and the number of earthquakes at depths from 0 to 20 km compared to the other models, indicating that it better explains shallow regions. However, the model with an elastic thickness of 80 km showed a much higher correlation at depths greater than 40 km compared to the other models, indicating that it better explains the deeper regions. These comparisons suggest the importance of a three-dimensional viscoelastic structure for reproducing the observed seismicity distribution in the model. We found that the correlation decreased substantially when the calculation depth was within the viscoelastic layer, and that the total correlation deteriorated significantly when the elastic layer was thin. In fact, the model with an elastic thickness of 80 km and a viscosity of 2.0 \u0026times; 10\u003csup\u003e19\u003c/sup\u003e Pa s yielded the highest total \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CC}\\)\u003c/span\u003e\u003c/span\u003e for all depths. Therefore, we regarded this model as optimal. However, viscosity cannot be uniquely constrained because seismic activity over 50-year intervals shows little sensitivity to changes in viscosity (Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). This result indicates that, in this model, the influence of viscoelastic relaxation on the simulated seismicity is extremely limited.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCorrelation coefficients at each calculation depth for each model.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"10\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eCalculation point depth\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e\u003cp\u003eModel parameters(Elastic layer Thickness [km], Viscosity [10\u003csup\u003e19\u003c/sup\u003e Pa s])\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(40, 0.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(40, 1.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(40, 2.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(60, 0.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(60, 1.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(60, 2.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(80, 0.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(80, 1.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003e(80, 2.0)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e20 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e30 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e40 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.79\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e50 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e60 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.74\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e70 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e80 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCorrelation coefficients at each calculation depth, excluding the impact of the 2011 Tohoku-oki earthquake.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"10\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eCalculation point depth\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"9\" nameend=\"c10\" namest=\"c2\"\u003e\u003cp\u003eModel parameters(Elastic layer Thickness [km], Viscosity [10\u003csup\u003e19\u003c/sup\u003e Pa s])\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(40, 0.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e(40, 1.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e(40, 2.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e(60, 0.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003e(60, 1.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e(60, 2.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003e(80, 0.5)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003e(80, 1.0)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003e(80, 2.0)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e0 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e20 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e30 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e40 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e50 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e60 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e70 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e80 km\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eTo investigate the impact of the 2011 Tohoku-oki earthquake, we calculated CFR50 without the Tohoku-oki earthquake as a stress source and presented the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CC}\\)\u003c/span\u003e\u003c/span\u003e at various depths for each model medium (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). In this scenario, the focal mechanisms of the earthquakes used to calculate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e excluded those occurring after March 11, 2011, the date of the Tohoku-oki earthquake. When the impact of the Tohoku-oki earthquake was examined, the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CC}\\)\u003c/span\u003e\u003c/span\u003e at a depth of 20 km with the Tohoku-oki earthquake was significantly lower than that without the earthquake regardless of the viscoelastic structural models (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). It is likely that the distribution of many aftershocks from the Tohoku-oki earthquake cannot be explained by the simple rectangular fault model used in this study. Therefore, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e and CFR near the rectangular fault model of the Tohoku-oki earthquake should be interpreted with caution.\u003c/p\u003e"},{"header":"4. Earthquake occurrence rate in the optimal model","content":"\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the CFR50 at the three-dimensional grid points for Periods I\u0026ndash;IV in the optimal model. In Period II, the impact of the 2011 Tohoku-oki Earthquake caused a sharp increase in CFR50 off the coast of the Ibaraki Prefecture, followed by a gradual decrease. In Period II of the optimal model, CFR50 increased to 70 km in northwestern Chiba Prefecture (Area B in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), thereby reducing the discrepancy between CFR50 and the number of earthquakes observed in the reference model. This suggests that the discrepancy between CFR50 and the number of earthquakes observed in the northwestern Chiba Prefecture in the reference model was due to the calculation points being in the viscoelastic layer.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn contrast, the CFR in the regions of intense seismicity off the eastern coast of the Izu Peninsula was not significantly large, even in the optimal model. Although Area A in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e is relatively shallow (depth\u0026thinsp;\u0026le;\u0026thinsp;20 km), variations in parameters such as elastic layer thickness and viscosity have little impact on CFR50 values in this seismic zone (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The area off the eastern coast of the Izu Peninsula is adjacent to the Izu Microplate, where the stress loading rate may be very high because of the high slip rates of the megathrust fault (Nishimura et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). In this model, a constant stress loading rate of 1.0 kPa/year was assumed for all receiver faults; however, this assumption deviates from reality. Although our assumption of a uniform stress rate across all earthquake sources is oversimplified, the high correlation between the CFR and the number of observed seismic events suggests that our model reproduces this observation as a first approximation. However, in the future, it will be necessary to consider a more detailed stress field to evaluate localized seismic activity.\u003c/p\u003e"},{"header":"5. Comparison with historical earthquake activity in the Kanto Region","content":"\u003cp\u003eWe investigated whether the optimal model could reproduce the seismicity enhancement in the latter part of the interplate earthquake cycle in the Kanto region, as described by Okada (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). To explore this, we focus on CFR50 for the 50 years starting 150 years after the Genroku-type earthquake, that is, 50 years before the occurrence of the first Taisho-type earthquake. In this period, multiple M7-class earthquakes are known to have occurred (Earthquake Research Committee, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). To exclude the influence of the 2011 Tohoku-oki earthquake, only the focal mechanisms used for the receiver fault were considered for the period prior to the occurrence of the earthquake.\u003c/p\u003e\u003cp\u003eAt all three-dimensional grid points, we calculated the ratio of CFR50 for each 50-year period to the total CFR50 over 200 years during the interplate earthquake cycle. Hereafter, this ratio is referred to as the CFR50 ratio. The CFR50 ratio represents the proportion of seismicity that occurred during each 50-year window relative to the long-term total at that location. When the rate of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e is constant with time, the CFR50 ratio will always be 0.25, and a CFR50 ratio exceeding 0.25 indicates that a grid point is in an active period where earthquakes are relatively likely to occur in the total 200-year period. The CFR50 value indicates the relative spatial likelihood of earthquake occurrence (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea), and the CFR50 ratio indicates the relative temporal likelihood of earthquake occurrence at each grid point (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb). To evaluate the consistency between the model results and historical seismicity, we extracted M\u0026thinsp;\u0026ge;\u0026thinsp;6.8 earthquakes in the studied area in the 50 years preceding the 1923 Taisho Kanto earthquake (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) from the Utsu earthquake catalog (Utsu, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1990\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2002\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). For earthquakes whose hypocentral depth is described as \u0026ldquo;shallow\u0026rdquo; in the Utsu catalog, we plotted them across all depths from 20 to 50 km in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eM7-class earthquakes occurred in 50 years before the 1923 Taisho Kanto earthquake.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eID\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eName\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMagnitude\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003elatitude (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003elongitude (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:^\\circ\\:\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eDepth (km)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1894 Meiji Tokyo earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e35.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e139.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e~\u0026thinsp;80 km\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1895 southern Ibaraki earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e36.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e140.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eShallow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1896 Ibaraki-oki earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e36.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e141.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eShallow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1909 Boso-oki earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e34.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e141.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eShallow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1916 Boso-oki earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e34.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e141.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eShallow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1921 southwestern Ibaraki earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e36.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e140.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e53 km\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1922 Uraga Channel earthquake\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e35.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e139.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e71 km\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eFor CFR50, the 1896 Ibaraki-oki earthquake occurred at a point with a relatively higher CFR50 than the surrounding areas, whereas the other earthquakes did not show such high values (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea). Next, focusing on the CFR50 ratio, the 1894 Meiji Tokyo earthquake occurred near the grid point with a CFR50 ratio of ~\u0026thinsp;0.79, indicating that it occurred during a period of relatively high seismic potential in the model (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed). For the other events, considering uncertainties in hypocenter locations and evaluating not only the nearest grid point, but also adjacent grid points (spaced at 0.2\u0026deg;horizontally and 10 km vertically), the CFR50 ratio ranged from ~\u0026thinsp;0.31 to ~\u0026thinsp;1. These results suggest that the model captured the temporal clustering of historical seismicity reasonably well.\u003c/p\u003e"},{"header":"6. Focal mechanisms of future earthquakes in the Kanto region","content":"\u003cp\u003eTo explore the potential for future seismic activation, we focused on 200 years following the first Taisho-type earthquake. This analysis employed the CFR50 ratio introduced in Section \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e5\u003c/span\u003e, which incorporated the influence of the 2011 Tohoku-oki earthquake (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). This metric enabled the evaluation of the relative concentration of seismic activity during each 50-year interval.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eSimilar to the approach in Section \u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we divided the 200-year span from 200 to 400 years after the Genroku-type earthquake into four 50-year intervals, referred to as Periods I\u0026ndash;IV. In Period I, the CFR50 ratio was particularly high for the 50 years following the Genroku-type earthquake, especially near the megathrust fault (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). This indicates that the seismicity was temporally concentrated in the early postseismic period at many grid points, suggesting a strong coseismic influence on the stress rates immediately after the earthquake. This trend is further illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea\u0026ndash;c, which show examples of the temporal CFR evolution at the selected grid points. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec, most of the elevated CFR values during this period were associated with the instantaneous increase in elastic stress due to coseismic slip. This coseismic activation can be recognized as an aftershock, consistent with the intense aftershock activity observed after the 1923 Taisho Kanto earthquake, including six M7-class earthquakes (e.g., Takemura, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1994\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eDuring Period II, which included the timing of the 2011 Tohoku-oki earthquake, the CFR50 ratio increased in the northeastern part of the study region near the source area of the Tohoku-oki earthquake (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). This is consistent with the observed activation of earthquakes in the region following the Tohoku-oki earthquake reported by the Earthquake Research Committee (2011). In Period III, the overall CFR50 ratio decreased. However, in Period IV, it increased again at several grid points, indicating a trend toward seismic activation in the later stages of the interplate earthquake cycle. Figures\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ed\u0026ndash;f present an example of a CFR time series that exhibits a late-stage increase in CFR50. This example suggests that the CFS exceeded its past maximum only in the later part of the seismic cycle, potentially leading to the next major rupture. In particular, the increase in seismic potential during the later stages of the cycle was primarily attributed to negative coseismic stress changes on the megathrust fault along the Sagami Trough (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec). In addition, since the 2011 Tohoku-oki earthquake occurred during Period II, its associated stress shadow has contributed to similar effects in some regions.\u003c/p\u003e\u003cp\u003eAlthough the high CFR50 ratio in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e does not directly indicate the number of earthquakes, it highlights the periods and locations in which high seismicity is expected from the simulation. We further investigated the spatial and temporal trends of potential earthquakes based on the simulation results. We focus on the region where the CFR increases by 0.2 MPa/year or more from Period II to Period IV. As the region of high CFR increase is concentrated near the western part of the Sagami Trough (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea), more attention should be provided to future earthquake hazards in this region. An examination of the focal mechanisms in the region revealed regional characteristics. In the area north of 35.3\u0026deg;N (hereafter referred to as Kanagawa Prefecture), 10 of the 12 receiver focal mechanisms have similar fault geometries, in which one of the conjugate planes is a northwest-dipping low-angle reverse fault (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb). These receiver faults are located at depths of 20\u0026ndash;40 km near the megathrust fault along the Sagami Trough. Considering these characteristics and the slip deficit distribution (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea), the interplate earthquakes in the down-dip transition zone from full coupling to no coupling increased as the next Taisho-type earthquake approached.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn the area south of 35.3\u0026deg;N, which is off the eastern coast of the Izu Peninsula region, the overlaid beach ball diagrams for 113 receiver focal mechanisms suggest N-S or E-W trending strike-slip faults (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ec). Several M7-class earthquakes, including the 1978 M6.9 Izu-oshima earthquake and the 1980 M6.7 east of the Izu Peninsula, have occurred in this region. In addition to these tectonic earthquakes, volcano-tectonic earthquake swarms associated with the intrusion of volcanic fluids were intermittently observed during the 1980s\u0026ndash;2000s (e.g., Aoki et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Such volcanic stress sources were not considered in this model, and it is possible that the model was unable to adequately reproduce temporal changes in seismic activity in this region. As described in Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the assumed stress loading rate in this region may be underestimated. If the loading rate is higher, temporal changes in the stress rate and its modulation of local seismicity become relatively small during the interseismic period. Note that the receiver faults used in this study were only from the F-net catalog, and the mechanisms currently quiescent owing to the influence of the earthquake cycle along the Sagami Trough and other factors may not have been sufficiently evaluated.\u003c/p\u003e"},{"header":"7. Conclusions","content":"\u003cp\u003eThis research unveiled significant insights into seismic activity along the Sagami Trough by modeling the interplate earthquake cycle using CFS changes. By constructing and validating a model that assumed an elastic layer overlying a Maxwell viscoelastic half-space, we compared calculated earthquake occurrence rates with those observed in recent seismic activity. The optimal model, characterized by an elastic layer thickness of 80 km and a viscosity of 2.0\u0026times;10\u003csup\u003e19\u003c/sup\u003e Pa s, provided the best explanation for past seismic activity.\u003c/p\u003e\u003cp\u003eOur findings suggest that most earthquakes occur within the elastic layer to reproduce the observed seismic activity in the Kanto region. When earthquakes occur within the viscoelastic layer, the correlation between predicted and observed seismicity decreases significantly. No model with an assumed two-dimensional viscoelastic structure could explain the distribution of the observed seismicity across all depths. This highlights the need to incorporate a three-dimensional viscoelastic structure to reproduce depth-dependent variations in earthquake enhancement and quiescence, as well as the observed earthquake distribution.\u003c/p\u003e\u003cp\u003eFurthermore, the model reveals that receiver faults experiencing negative coseismic stress changes during the M8-class interplate earthquakes tend to delay rupture, leading to increased seismic activity in the later stages of the earthquake cycle. This behavior is consistent with the historical clustering of M7-class earthquakes in the Kanto region and highlights the importance of stress history in modulating long-term seismicity.\u003c/p\u003e\u003cp\u003eThis model can also predict the focal mechanisms of future activated earthquakes. For example, a northwest-dipping low-angle reverse fault earthquake is expected to increase around Kanagawa Prefecture from 2073 to 2123. This model offers valuable information for forecasting the timing, location, and mechanisms of the increased seismic activity in the Kanto region.\u003c/p\u003e\u003cp\u003eIn summary, this study provides a simple framework for understanding and predicting seismic activity in the Kanto region of Japan. This simulation to predict the timing, location, and mechanisms of increased seismic activity enabled us to construct specific earthquake activity scenarios based on physical mechanisms in the Kanto region. This advancement is expected to enhance seismic hazard prediction and contribute to disaster risk reduction.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eAMR\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eAmurian Plate\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eCoulomb Failure Stress\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eCFR\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eCoulomb Failure Rate\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{CC}\\)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eCorrelation Coefficient\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varDelta\\:\\text{CFS}\\)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eCoulomb Failure Stress Change\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003eNA\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003eNorth American Plate\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003ePAC\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003ePacific Plate\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003ePHS\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003ePhilippine Sea Plate\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003cp\u003eNot applicable\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003cp\u003eNot applicable\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003ch2\u003eCompeting interests\u003c/h2\u003e\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\u003c/p\u003e\u003cp\u003e\u003ch2\u003eAuthors' information\u003c/h2\u003e\u003cp\u003eDigital Services Division, Pacific Consultants Co. Ltd., 3\u0026ndash;22 Kanda-Nishikicho, Chiyoda-ku, Tokyo, Japan\u003c/p\u003e\u003cp\u003eTsukasa Mitogawa\u003c/p\u003e\u003cp\u003eDisaster Prevention Research Institute, Kyoto University, Uji, 611\u0026thinsp;\u0026minus;\u0026thinsp;0011, Japan\u003c/p\u003e\u003cp\u003eTakuya Nishimura\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis study was supported by a joint research project between Kyoto University, Tokyo Polytechnic University, Shimizu Corporation, and Osaki Research Institute entitled \"Building Performance Evaluation Considering Resilience and Sustainability\u0026rdquo;.\u003c/p\u003e\u003ch2\u003eAuthors' contributions\u003c/h2\u003e\u003cp\u003eTM conducted all calculations for this study and wrote the manuscript. TN conceived the initial ideas and supervised manuscript revisions. Both authors read and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\u003cp\u003eWe thank Dr. Yukitoshi Fukahata for providing the numerical code for the viscoelastic response owing to a dislocation source in a layered medium. Figures were drawn using General Mapping Tools (Wessel et al. 2013). The F-net catalog was provided by the National Research Institute for Earth Science and Disaster Resilience (NIED).\u003c/p\u003e\u003ch2\u003eAvailability of data and materials\u003c/h2\u003e\u003cp\u003eWe used focal mechanism parameters from the F-net catalog. (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.fnet.bosai.go.jp/event/search.php?LANG=en\u003c/span\u003e\u003cspan address=\"https://www.fnet.bosai.go.jp/event/search.php?LANG=en\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAoki Y, Segall P, Kato T, Cervelli P, Shimada S (1999) Imaging Magma Transport During the 1997 Seismic Swarm off the Izu Peninsula, Japan. 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Geochem Geophys Geosyst 20:5556\u0026ndash;5564. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2019GC008515\u003c/span\u003e\u003cspan address=\"10.1029/2019GC008515\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Coulomb failure stress, Earthquake occurrence rate, Interplate earthquake cycle, Modeling, Viscoelasticity, Sagami Trough, Kanto region","lastPublishedDoi":"10.21203/rs.3.rs-8216970/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8216970/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe Kanto region of central Japan has experienced temporal clustering of M7-class earthquakes, particularly during the later stages of the large interplate earthquake cycle along the Sagami Trough. However, the role of static stress changes in driving this pattern remains poorly understood. Therefore, to examine whether static stress changes from the Sagami Trough earthquake cycle could be responsible for this pattern, we simulated stress evolution using a layered elastic-viscoelastic model. The receiver faults were defined based on the focal mechanisms of earthquakes observed between 1997 and 2023. Additional intrinsic stress loading was also applied with a CFS accumulation rate of 1.0 kPa per year to all receiver faults for permanent stress accumulation. We assumed the earthquake occurrence rate at each receiver fault to be proportional to the increase in the Coulomb failure stress (CFS) from its previous maximum value, and set it to zero when CFS decreased. The spatial and temporal distributions of earthquake occurrence rates were then assessed by aggregating them across the study region. The spatial distribution of earthquake occurrence rates calculated by our optimal model closely matches the distribution of earthquakes observed between 1997 and 2023, supporting the validity of our modeling approach. Although our model could not fully explain the locations of several M7-class earthquakes that occurred before the 1923 Kanto earthquake, we found that these events tended to occur during periods when the modeled earthquake occurrence rate at each location was estimated to be high within the earthquake cycle. We discovered that interplate earthquakes in the transition zone from full coupling to no coupling are likely to increase as the next M8-class interplate earthquake along the Sagami Trough approaches. The results suggest that a physics-based framework for constructing earthquake activity scenarios in the Kanto region can improve seismic hazard assessments and contribute to disaster risk reduction.\u003c/p\u003e","manuscriptTitle":"Modeling of seismic activity modulated by stress changes during the interplate earthquake cycle along the Sagami Trough, central Japan","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-15 10:09:01","doi":"10.21203/rs.3.rs-8216970/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2025-12-10T00:25:20+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-09T17:14:56+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-04T08:15:05+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth, Planets and Space","date":"2025-12-03T18:37:03+00:00","index":"","fulltext":""},{"type":"decision","content":"Major Revision","date":"2025-12-01T23:48:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"62bc1240-4d13-4e9f-9803-762b3cfe3faf","owner":[],"postedDate":"December 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-13T16:05:55+00:00","versionOfRecord":{"articleIdentity":"rs-8216970","link":"https://doi.org/10.1186/s40623-026-02422-x","journal":{"identity":"earth-planets-and-space","isVorOnly":false,"title":"Earth, Planets and Space"},"publishedOn":"2026-04-07 15:59:01","publishedOnDateReadable":"April 7th, 2026"},"versionCreatedAt":"2025-12-15 10:09:01","video":"","vorDoi":"10.1186/s40623-026-02422-x","vorDoiUrl":"https://doi.org/10.1186/s40623-026-02422-x","workflowStages":[]},"version":"v1","identity":"rs-8216970","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8216970","identity":"rs-8216970","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}