Decadal seafloor geodesy reveals changes in the slip deficit rate along the Nankai Trough

Decadal seafloor geodesy reveals changes in the slip deficit rate along the Nankai Trough | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Decadal seafloor geodesy reveals changes in the slip deficit rate along the Nankai Trough Yusuke Yokota, Shun-ichi Watanabe, Koya Nagae, Yuto Nakamura, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8151000/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Identifying the frictionally locked area of a plate boundary is an important geodetic issue in mitigating earthquake disasters. However, recent long-term geodetic observations have revealed that actual geodetic data contain transient behaviors due to slow slip events or changes in slip deficit rates. Therefore, the use of a snapshot of temporally averaged geodetic data is far insufficient to understand the accurate frictional state. This problem is particularly serious at sub-seafloor plate boundaries, where continuous or periodic geodetic observations for a long time are rarely realized. Here, we evaluated long-term slip deficit rate variations in the Nankai Trough, the only area in the world for which high-density data on horizontal and vertical components have been accumulated via seafloor observations with a sufficient frequency on the decadal scale. Consequently, we constrained the constantly locked areas and found that it was limited mainly to a depth of 10 – 20 km, with slip deficit rate changes occurring throughout the entire shallow side adjacent to the locked area. GNSS-A Nankai trough slip deficit rate SSE Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction The frictional state of plate boundaries in subduction zones varies from locked or unstable to creeping or stable (Savage, 1983 ; Scholz, 2004; Wang and Dixon, 2004 ; Almeida et al., 2018 ) and knowing the frictional and stress states on plate boundaries is necessary for simulating earthquake cycles and constructing earthquake and tsunami scenarios. The actual states can be estimated from the distribution of slip deficit rate (SDR) as extracted basically from geodetic observations (Wallace et al., 2004 ; Hashimoto et al., 2009 ; Lindsey et al., 2021 ). Global Navigation Satellite System – Acoustic ranging combination (GNSS-A) observations can detect horizontal crustal movements directly on the seafloor, providing key data for determining the distribution of slip deficits at plate boundaries. In recent years, advances in signal compensation technology have made them effective for detecting long-term vertical movements (Yokota et al., 2024 ). Since Yokota et al. ( 2016 ) had showed the distribution of SDR in the Nankai Trough using horizontal displacement rates obtained by GNSS-A, it has been studied using various methods, including the influence of viscoelastic relaxation and estimation of stress distribution (Saito and Noda, 2022 ; Sherill et al., 2024 ; Li and Chen, 2024). On the other hand, as shown in Yokota and Ishikawa ( 2020 ), GNSS-A displacement rates in the Nankai Trough vary with time. These are caused by temporal changes in SDR, which can be interpreted as shallow slow slip events (SSEs) (Obara and Kato, 2016 ) occurred near the trench axis. Sub-seafloor SSEs are observed frequently by modern seafloor geodetic techniques, such as ocean bottom pressure gauges and pore pressure gauges observations (e.g., Wallace et al., 2016 ; Araki et al., 2017 ). Yokota and Ishikawa ( 2020 ) had investigated steady-state and non-steady-state and detected centimeter-scale transient horizontal crustal deformation. However, as shown in Section 2 in this paper, examination of long-term data up to 2023 revealed that the temporal changes were diverse, making it difficult to distinguish between steady and transient states. Such fluctuations in the crustal deformation rate over time can be interpreted as frequent changes in the SDR at shallow plate boundaries. So far, the temporal change of SDR has been estimated only by terrestrial GNSS (Nishimura et al, 2004 ; Ochi, 2015 ). In this paper, we investigated the recent SDR behavior in the Nankai Trough using both horizontal and vertical components of GNSS-A data. 2 Data We used the Seafloor Geodetic Observation-Array (SGO-A) GNSS-A observation network, which has been operated by the Japan Coast Guard (JCG) (Ishikawa et al., 2020 ; Fig. 1 ) in the Nankai Trough constantly for over 10 years. According to the empirical slow slip scaling law (Gao et al., 2012 ), slow slips of magnitude (M) 6 or greater have an impact of crustal deformation of more than 1 cm/year on the seafloor in ranges of about 50 km. Such amount of displacement rate change can be detected with the current site density of SGO-A. Although vertical motions were not used in previous studies because of the low accuracy of vertical positioning, the recently developed Acoustic Ambiguity Reduction (AAR) method (Yokota et al., 2024 ) has brought the accuracy of vertical positioning closer to the horizontal positioning (1 – 2 cm). Herein, we use the horizontal and vertical displacement rates of the seafloor GNSS-A data of SGO-A and terrestrial GNSS data of GEONET (Takamatsu et al., 2023 ) from January 2013 to December 2023 shown in Fig. 1 to discuss the temporal variations of SDR. The locations of terrestrial GNSS sites and observation period were selected to reduce the influences of the 2011 Tohoku-oki earthquake, the 2016 Kumamoto earthquake, and the Median Tectonic Line. We used the GNSS-A seafloor position data processed with GARPOS version 1.0.1 (Watanabe et al., 2020 ; Watanabe et al., 2022 ) for the period from January 2013 to December 2023 observed by SGO-A. To discuss the velocity variation of less than 1 cm/year for each time window, we calculated the 4-year average velocity; this was because a numerical investigation of the accuracy of velocity variations in long-term observation data (Fig. 2 in Yokota et al. ( 2021 )) has indicated that the current observation frequency (approximately four times per year) of SGO-A permits discussion of variations in velocity of about 0.5 – 0.8 cm/year. The left and right sides of Fig. 2 are the obtained GNSS-A time series and the velocities estimated in 4-year moving windows for eight periods, from 2013.01 – 2016.12, 2014.01 – 2017.12 …, respectively. The 95% confidence intervals for the estimated velocity were often less than 0.5 cm/year. Although the AAR method has improved the accuracy of vertical displacement considerably, it may still remain synchronized biases at different observation sites during the same period for reasons such as replacement of seafloor stations. For example, the latest 2 years for sites 4, 6, and 9 have similar bias errors in the vertical components. In the future, as more data are accumulated at these sites, bias corrections will become possible using the AAR method. The coordinates at the SGO-A sites were taken based on ITRF2020 (Altamimi et al., 2023 ). The displacements shown in the left panels of Fig. 2 (Data S1) indicate the internal plate deformation calculated by excluding the rigid motion of the Amur plate modeled in MORVEL (DeMets et al., 2010 ). The right panels (Data S2) show velocities estimated in 4-year moving windows. The long-term vertical motions in Fig. 2 were almost zero or slightly negative, which is consistent with the elastic crustal deformation expected from the shape of the plate boundary in the Nankai Trough (i.e., low dip angle). Many sites, e.g., sites 5 and 13, showed variations in horizontal velocity of more than 2 cm/year, indicating large SDR variations in the middle of the observation period. At site 5, for example, different rates were observed every 3–4 years during the early, middle, and late periods, which cannot be simply interpreted as SSEs of the same magnitude occurring at the same location. There is no period of constant SDR (steady state) throughout the Nankai Trough, and it is believed that the state is constantly changing. In this paper, we calculate the time evolution of the SDR to understand these variations. 3 Method We here used the surface velocity data calculated from SGO-A and GEONET for eight time windows over 4 years, e.g., from 2013.01 – 2016.12 (2015), 2014.01 – 2017.12 (2016) .... The range of time window was determined considering the estimation accuracy. The data before 2012 were not used to avoid the influence of the 2011 Tohoku-oki earthquake, and the spatial range of GEONET observation sites were limited to avoid the influences of the Median Tectonic Zone and the 2016 Kumamoto earthquake (Kato et al., 2016 ). Considering that the horizontal components have less variance than the vertical components, they were given twice the weighting. Estimation of SDR for large spatial coverage with topographic variation depends strongly on the Earth’s shape and heterogenous velocity structure. We used the Green’s function library for subduction zones (GLFSZ; Hori et al. ( 2021 )) to calculate the surface displacement due to a plate boundary slip deficit. This library was calculated considering the three-dimensional heterogeneous velocity structure, surface topography, and the ellipsoidal shape of the Earth (for more detail, see Hori et al. ( 2021 )). The plate boundary is divided into 459 grids with 20-km intervals, and a slip is expressed by placing a cubic B-spline basis function on each grid. A slip is decomposed into two directions: the plate convergence direction (“02”: N305E) and the perpendicular direction (“03”). The Green’s function represents the surface displacement for a unit slip of the basis function, and the displacement of the surface observation site is calculated by $$\:{\varvec{d}}^{\text{c}\text{a}\text{l}\text{c}}\left({\varvec{\theta\:}}_{02},{\varvec{\theta\:}}_{03}\right)={\varvec{G}}_{02}{\varvec{\theta\:}}_{02}+{\varvec{G}}_{03}{\varvec{\theta\:}}_{03},$$ 1 where \(\:{\varvec{d}}^{\text{c}\text{a}\text{l}\text{c}}\) is a vector listing the displacements at each site, \(\:{\varvec{G}}_{02}\) and \(\:{\varvec{G}}_{03}\) are Green’s function matrices for slips in the “02” and “03” directions, and \(\:{\varvec{\theta\:}}_{02}\) and \(\:{\varvec{\theta\:}}_{03}\) are vectors listing the coefficients of 459 basis functions for slips in the “02” and “03” directions, respectively. We estimated the optimal parameters of \(\:\varvec{\theta\:}\) = ( \(\:{\varvec{\theta\:}}_{02}\) , \(\:{\varvec{\theta\:}}_{03}\) ) for the observed data using Bayesian inference. Assuming that the observed surface displacement varies normally around the calculated value, the conditional probability of the observed value \(\:{\varvec{d}}^{\text{o}\text{b}\text{s}}\) under the given parameters \(\:\varvec{\theta\:}\) is expressed as $$\:p\left({\varvec{d}}^{\text{o}\text{b}\text{s}}|\varvec{\theta\:},{\sigma\:}_{m}\right)\propto\:\text{exp}\left(-\frac{1}{2}{\left({\varvec{d}}^{\text{o}\text{b}\text{s}}-{\varvec{d}}^{\text{c}\text{a}\text{l}\text{c}}\left(\varvec{\theta\:}\right)\right)}^{T}{{\Sigma\:}}^{-1}\left({\varvec{d}}^{\text{o}\text{b}\text{s}}-{\varvec{d}}^{\text{c}\text{a}\text{l}\text{c}}\left(\varvec{\theta\:}\right)\right)\right),$$ 2 where the covariance matrix \(\:{\Sigma\:}\) is a diagonal matrix with a common variance \(\:{{\sigma\:}_{m}}^{2}\) in the diagonal elements. Particularly in the offshore areas, where the number of grids is greater than the number of observation sites, a physically unnatural slip distribution may be estimated. Therefore, we gave a prior distribution that reduces the second-order difference of the coefficients of the basis functions, so that the final calculated slip distribution is spatially smooth. This prior distribution is given as $$\:p\left(\varvec{\theta\:}|{\rho\:}_{m}\right)\propto\:\text{exp}\left(-\frac{1}{2{{\rho\:}_{m}}^{2}}{\left(\varvec{L}\varvec{\theta\:}\right)}^{T}\left(\varvec{L}\varvec{\theta\:}\right)\right),$$ 3 where \(\:\varvec{L}\) is the Laplacian operator representing the second-order difference, and \(\:{\rho\:}_{m}\) is a hyperparameter representing the strength of the constraint. Based on Bayes’ theorem, we calculated the posterior distribution of the parameters given by $$\:p\left(\varvec{\theta\:},{\sigma\:}_{m},{\rho\:}_{m}|{\varvec{d}}^{obs}\right)\propto\:p\left({\varvec{d}}^{\text{o}\text{b}\text{s}}\right|\varvec{\theta\:},{\sigma\:}_{m}\left)\:p\left(\varvec{\theta\:}|{\rho\:}_{m}\right)p\right({\sigma\:}_{m}\left)p\right({\rho\:}_{m}),$$ 4 where \(\:p\left({\sigma\:}_{m}\right)\) and \(\:p\left({\rho\:}_{m}\right)\) are the prior distributions of the hyperparameters, and sufficiently wide distributions were adopted. In this study, we used the Markov-Chain Monte Carlo (MCMC) method to efficiently evaluate the posterior distribution and the Metropolis–Hastings method to concretely obtain the samples. Because the hyperparameter \(\:{\rho\:}_{m}\) varies by several orders of magnitude, we stabilized the estimation of other parameters by obtaining the optimal value from the marginal distribution of the hyperparameter obtained in a prior calculation and recalculating the parameters by fixing the hyperparameter to the optimal value. The distribution of the obtained parameters can be regarded as a sampling from the posterior distribution. Since the distribution is roughly close to a normal distribution, we adopted the average value of the distribution as the obtained optimal \(\:\varvec{\theta\:}\) . The map of standard deviation (σ) of SDR estimation calculated based on the distribution of coefficient values (Fig. 3 , Data S3) represents the spatial resolution of the SDR estimation. Using the obtained optimal \(\:\varvec{\theta\:}\) , the final SDR distribution was calculated from a linear combination of basis functions provided in the GFLSZ library. Eight snapshots of SDR distribution for 4-year moving time windows (Fig. 4 , Data S4) were estimated. The observed and calculated velocities are compared in Fig. 5 (Data S5). In this paper, considering the estimation accuracy of SDR, we discuss the area in which the average of standard deviation of SDR estimation for each time window (Fig. 3 ) is smaller than 1.25 cm/year, or approximately 20%–25% of the convergence rate. 4 Result Figure 6 shows the temporal variation of SDR and the accumulated slip deficits for the points selected from deep (A–C) and shallow (D–F) parts in three along-trough segments, i.e., the southern areas of Enshu-Nada, Kumano-Nada, and Tosa Bay. There is little difference between the maximum SDR values of the shallow and deep points in each segment, though it depends on the segments. The results from shallow points (D–F) show a decrease in SDR greater than 1σ. To discuss the spatial distribution of frictional states of the plate boundary, we extracted the statistical SDR distributions as follows: by picking the minimum SDR values from each time window, as “min SDR”; by taking the average over the time windows, as “average SDR”; and by taking the difference of them, as “diff SDR.” The statistical SDR distributions are shown in Fig. 7 . 5 Discussion 5.1 Green’s functions SDR models in many past studies had been calculated using simple topographic and velocity structure models. Figure 8 shows the ”average SDR” results obtained using the Green’s functions of a semi-infinite homogeneous elastic medium (Okada, 1992 ) and the average of standard deviation. In the western area, the SDR became larger than the plate convergence rate \(\:{V}_{pl}\) of the Philippine Sea plate under the Amur plate calculated using MORVEL (DeMets et al., 2010 ) (e.g., 6.5 cm/year) when estimated using the homogeneous model, but the estimated SDR became smaller when using GFLSZ. On the other hand, in the eastern area, they were larger for the GFLSZ case, indicating the complex influence of three-dimensional structure. In GFLSZ, the surface displacement is larger directly above and smaller at a distance due to the influence of the shallow structure. This effect also improves the standard deviation distribution around the seafloor site compared to the case using the homogeneous medium (Figs. 3 and 8 b). 5.2 Interpretation Around the locked interface, the SDR becomes large and approaches the plate subduction rate \(\:{V}_{pl}\) (Fig. 9 ). A large crustal deformation in the direction of plate convergence occurs on the surface above the high SDR area. In plate subduction zones such as the Nankai Trough, where plates subduct from the seafloor beneath the land, terrestrial GNSS measures such crustal deformation, allowing us to grasp the existence of deep locked areas directly below the inland. If the shallow area is locked and stress is occasionally released by slow slips (Fig. 9 c), then the SDR should be moderate on average, fluctuate in time, and have a small minimum. Even if the shallow part is temporarily or even constantly unlocked, the deeper locked area drags the shallower side, so the SDR does not fall to zero and a crustal deformation occurs \(\:\:\) (Fig. 9 b). Known as stress shadow, this phenomenon causes the high-SDR area to be wider than the mechanically locked area. High-precision and continuous GNSS-A, such as the current SGO-A, makes it possible to distinguish between these states. The area of high “min SDR” (Fig. 7 ) primarily indicates the constantly locked area (Figs. 9 a and 9 b) where no large slow slip occurred in this 11 years. For example, around A–C have less time variation and the minimum SDR is higher than that in the surrounding areas. The constantly frictionally locked area is limited within this high “min SDR” area in the deeper portion. Because of the shortage of observation period, i.e., 11 years, more fluctuation of the SDR may be observed in the future and the constantly locked area could be further constrained. For example, the area west of F is the only area in the shallow side with small SDR variation (high “min SDR” value), but there is a possibility that the SDR in this area may fluctuate in the future. Around A, this high “min SDR” area is wide in the dip direction, compared to around B. The “min SDR” values around D and E (shallower part of A and B, respectively) show a correlation with the range of high “min SDR” area in the deeper sides. This indicates that the width or upper limit of the constantly locked area controls the magnitude of the stress shadow, and therefore the “min SDR” values on the shallower side. Empirically, there is a spatial and temporal correlation between low frequency tremors (LFTs), very low frequency earthquake (VLFs), and slow slips (Obara and Kato, 2016 ). The shallow areas of low “min SDR” coincide roughly with the areas of high “diff SDR” which suggests the occurrence of slow slips, and they include the high activity areas of LFTs and VLFs (Yamashita et al., 2015 ; Nakano et al., 2018 ; Yamashita et al., 2021 ; Takemura et al., 2022 ; Tamaribuchi et al., 2022 ; Yamamoto et al., 2022 ; Takemura et al., 2023 ). For example, synchronous activities of LFT and VLF with SDR variations off the Kii Channel around 2018 were estimated (Fig. 4 ) around a subducted seamount (Kodaira et al., 2000 ). The only shallow area with a low “average SDR,” meaning constantly low SDR, is in the south of Kumano-Nada, where short-term slow slips have occurred with LFTs and VLFs (Araki et al., 2017 ; Edgington et al., 2025 ), which is not an area that is always unlocked, but rather an area where slow slips occur frequently. Additionally, in the results of this study, the area of high “diff SDR” extends to areas without LFT and VLF activities, i.e., the southeast of Enshu-Nada where the subducted paleo-Zenisu ridge is located (Park et al., 2004 ) and the south of Tosa Bay. It has been pointed out that SSEs may be occurring from land in the northeast around point F (Kikuchi et al., 2025 ), and the long-term decrease in SDR in this area may be a major event that extends to land. Therefore, the distribution of shallow slow slips shown in this study is not necessarily correlated with other slow earthquakes or subducting seamounts and ridges, but rather spreads across almost the entire shallow side. It may be a feature of this plate subduction zone itself. 6 Conclusion GNSS-A observations in SGO-A over about 10 years constrained the extent of the constantly locked area and further revealed that almost the shallowest part of the Nankai Trough plate boundary does not always remain in the state of Fig. 9 a or Fig. 9 b. SGO-A is a seafloor geodetic observation network that has continued stable observation for the longest period in the world, yet it is only possible to evaluate the frictional state of the plate boundary for about one decade. It is necessary to continue accumulating data and to evaluate the degree of time variation and stability in both shallow and deep areas. Long-term and frequent seafloor geodetic observations in many more subduction zones are needed to verify the generality of the frictional conditions at shallow plate boundaries revealed in this study across other subduction zones. In the future, it will also be necessary to further discuss changes in the stress state at the plate boundary based on the stress change distribution calculated considering three-dimensional heterogeneous velocity structure. Abbreviations GNSS Global Navigation Satellite System GNSS-A Global Navigation Satellite System – Acoustic combination technique SGO-A Seafloor Geodetic Observation – Array SDR Slip Deficit Rate Declarations Competing interests The authors declare no competing interests. Funding This study was supported by ERI JURP 2024-Y-KOBO12 in Earthquake Research Institute, the University of Tokyo, by SECOM science and technology foundation, and by JSPS KAKENHI Grant Number JP21H05200 in Grant-in-Aid for Transformative Research Areas (A) “Science of Slow-to-Fast Earthquakes.” Authors' contributions YY and TI proposed the concept and managed the project. TI constructed the method. KN, SW, and YY analyzed GNSS-A data and SDR. SW, TI, and YY visualized the results. YY, SW, KN, YN, and TI read and approved the final manuscript. Acknowledgements We thank F. Tomita and T. Iinuma for helpful comments on the initial consideration. In-situ observations were performed by the survey vessels operated by the Japan Coast Guard. Availability of data and materials The GNSS and GNSS-A datasets used in the current study are available at https://doi.org/10.57499/GSI_GNSS_2025_001 (Geodetic Observation Center, GSI, 2025) and https://doi.org/10.57553/2024001 (Japan Coast Guard, 2024 ). The GNSS-A analysis software GARPOS v1.0.1 (Watanabe et al., 2020 ; Watanabe et al., 2022 ) is available at Zenodo ( https://doi.org/10.5281/zenodo.6414642 ). The Green's function library ( https://www.jamstec.go.jp/feat/gflsz/ ) for subduction zones by Hori et al. ( 2021 ) was used, which was created by JAMSTEC's own modification of a computer program under development by Earthquake Research Institute, The University of Tokyo. The library includes data modified from Japan Integrated Velocity Structure Model version 1 (JIVSM) (Koketsu et al., 2009 ; Koketsu et al., 2012 ) and the Earth Gravitational Model 2008 (Pavlis et al., 2012 ). References Almeida R et al (2018) Can the updip Limit of frictional locking on megathrusts be detected geodetically? Quantifying the effect of stress shadows on near-trench coupling. Geophys Res Lett 45:4754–4763. 10.1029/2018GL077785 Altamimi Z, Rebischung P, Collilieux X, Métivier L, Chanard K (2023) ITRF2020: an augmented reference frame refining the modeling of nonlinear station motions. J Geod 97:47. 10.1007/s00190-023-01738-w Araki E et al (2017) Recurring and triggered slow-slip events near the trench at the Nankai Trough subduction megathrust. Science 356:1157–1160. 10.1126/science.aan3120 DeMets C, Gordon RG, Argus DF (2010) Geologically current plate motions. Geophys J Int 181:1–80. 10.1111/j.1365-246X.2009.04491.x Edgington JR, Saffer DM, Williams CA (2025) Migrating shallow slow slip on the Nankai Trough megathrust captured by borehole observations. Science 388:6754, 1396–1400. 10.1126/science.ads9715 Gao H, Schmidt DA, Weldon IIRJ (2012) Scaling relationships of source parameters for slow slip events. Bull Seismol Soc Am 102:352–360. 10.1785/0120110096 Geodetic O, Center GSI (2025) GNSS data. 10.57499/GSI_GNSS_2025_001 Hashimoto C, Noda A, Sagiya T, Matsu’ura M (2009) Interplate seismogenic zones along the Kuril-Japan trench inferred from GPS data inversion. Nat Geosci 2:141–144. 10.1038/NGEO421 Hori T et al (2021) High-fidelity elastic Green’s functions for subduction zone models consistent with the global standard geodetic reference system. Earth Planet Space 73:41. 10.1186/s40623-021-01370-y Ishikawa T, Yokota Y, Watanabe S, Nakamura Y (2020) History of on-board equipment improvement for GNSS-A observation with focus on observation frequency. Front Earth Sci 8:150. 10.3389/feart.2020.00150 Japan Coast Guard (2024) GNSS-A observation data in GARPOS format obtained at the SGO-A sites. 10.57553/2024001 Kato A, Nakamura K, Hiyama Y (2016) The 2016 Kumamoto earthquake sequence. Prog Jpn Acad Ser B 92:8. 10.2183/pjab.92.359 Kikuchi Y, Mitsui Y, Kano M (2025) Detection of slow slip event lasting several months in the shallow region of the Suruga Trough, the eastern end of the Nankai Trough, Japan. Prog Earth Planet Sci 12:58. 10.1186/s40645-025-00737-z Kobayashi A (2017) Objective detection of long-term slow slip events along the Nankai Trough using GNSS data (1996–2016). Earth Planet Space 69:171. 10.1186/s40623-017-0755-7 Kodaira S, Takahashi N, Nakanishi A, Miura S, Kaneda Y (2000) Subducted seamount imaged in the rupture zone of the 1946 Nankaido earthquake. Science 289:104–106. 10.1126/science.289.5476.104 Koketsu K, Miyake H, Tanaka Y (2009) A proposal for a standard procedure of modeling 3-D velocity structures and its application to the Tokyo metropolitan area, Japan. Tectonophysics 472:290–300. 10.1016/j.tecto.2008.05.037 Koketsu K, Miyake H, Suzuki H (2012) Japan integrated velocity structure model version 1. Proceedings of the 15th World Conference on Earthquake Engineering (1773), Lisbon Lindsey EO et al (2021) Slip rate deficit and earthquake potential on shallow megathrusts. Nat Geosci 14:321–326. 10.1038/s41561-021-00736-x Nakano M, Hori T, Araki E, Kodaira S, Ide S (2018) Shallow very-low-frequency earthquakes accompany slow slip events in the Nankai subduction zone. Nat Comm 9:984. 10.1038/s41467-018-03431-5 Nishimura T et al (2004) Temporal change of interplate coupling in northeastern Japan during 1995–2002 estimated from continuous GPS observations. Geophys J Int 157:901–916. 10.1111/j.1365-246X.2004.02159.x Obara K (2002) Nonvolcanic deep tremor associated with subduction in southwest Japan. Science 296:1679–1681. 10.1126/science.10703 Obara K, Tanaka S, Maeda T, Matsuzawa T (2010) Depth-dependent activity of non-volcanic tremor in southwest Japan. Geophys Res Lett 37:L13306. 10.1029/2010GL043679 Ozawa S (2017) Long-term slow slip events along the Nankai trough subduction zone after the 2011 Tohoku earthquake in Japan. Earth Planet Space 69:56. 10.1186/s40623-017-0640-4 Obara K, Kato A (2016) Connecting slow earthquakes to huge earthquakes. Science 353:6296, 253–257. 10.1126/science.aaf1512 Ochi T (2015) Temporal change in plate coupling and long-term slow slip events in southwestern Japan. Earth Planet Sci Lett 431:8–14. 10.1016/j.epsl.2015.09.012 Okada Y (1992) Internal deformation due to shear and tensile faults in a half-space. Bull Seismol Soc Am 82:1018–1040. 10.1785/BSSA0820021018 Ozawa S, Munekane H, Suito H (2024) Time-dependent modeling of slow-slip events along the Nankai Trough subduction zone, Japan, within the 2018–2023 period. Earth Planet Space 76:23. 10.1186/s40623-024-01970-4 Yamamoto Y et al (2013) Imaging of the subducted Kyushu-Palau Ridge in the Hyuga-nada region, western Nankai Trough subduction zone. Tectonophysics 589:90–102. 10.1016/j.tecto.2012.12.028 Park J-O, Moore GF, Tsuru T, Kodaira S, Kaneda Y (2004) A subducted oceanic ridge influencing the Nankai megathrust earthquake rupture. Earth Planet Sci Lett 217:77–84. 10.1016/S0012-821X(03)00553-3 Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Res 117:B04406. 10.1029/2011JB008916 Saito T, Noda A (2022) Mechanically coupled areas on the plate interface in the Nankai trough, Japan and a possible seismic and aseismic rupture scenario for megathrust earthquakes. J. Geophys. Res. Solid Earth 127, e2022JB023992. 10.1029/2022JB023992 Savage JC (1983) A dislocation model of strain accumulation and release at a subduction zone. J Geophys Res 88:4984–4996. 10.1029/JB088iB06p04984 Scholz CH (1998) Earthquakes and friction laws. Nature 391:37–42. 10.1038/34097 Sherill EM, Johnson KM, Jackson NM (2024) Locating boundaries between locked and creeping regions at Nankai and Cascadia subduction zones. J Geophys Res Solid Earth 129:e2024JB029346. 10.1029/2024JB029346 Takamatsu N et al (2023) New GEONET analysis strategy at GSI: daily coordinates of over 1300 GNSS CORS in Japan throughout the last quarter century. Earth Planet Space 75(1):49. 10.1186/s40623-023-01787-7 Takemura S, Obara K, Shiomi K, Baba S (2022) Spatiotemporal variations of shallow very low frequency earthquake activity southeast off the Kii Peninsula, along the Nankai Trough, Japan. J. Geophys. Res. Solid Earth 127, e2021JB023073. 10.1029/2021JB023073 Takemura S et al (2023) A review of shallow slow earthquakes along Nankai Trough. Earth Planet Space 75:164. 10.1186/s40623-023-01920-6 Tamaribuchi K, Ogiso M, Noda A (2022) Spatiotemporal distribution of shallow tremors along the Nankai Trough, southwest Japan, as determined from waveform amplitudes and cross-correlations. J. Geophys. Res. Solid Earth 127, e2022JB024403. 10.1029/2022JB024403 Wallace LM, Beavan J, McCaffrey R, Darby D (2004) Subduction zone coupling and tectonic block rotations in the North Island, New Zealand. J Geophys Res 109:B12406. 10.1129/2004JB003241 Wallace LM et al (2016) Slow slip near the trench at the Hikurangi subduction zone, New Zealand. Science 352:701–704. 10.1126/science.aaf2349 Wang K, Dixon T (2004) Coupling semantics and science in earthquake research. Eos 85(18):180–181. 10.1029/2004EO180005 Watanabe S, Ishikawa T, Nakamura Y, Yokota Y (2020) GARPOS: analysis software for the GNSS-A seafloor positioning with simultaneous estimation of sound speed structure. Front Earth Sci 8:597532. 10.3389/feart.2020.597532 Watanabe S, Ishikawa T, Nakamura Y, Yokota Y (2022) GARPOS: Analysis tool for GNSS-Acoustic seafloor positioning (1.0.1). Zenodo. 10.5281/zenodo.6414642 Yamamoto Y, Ariyoshi K, Yada S, Nakano M, Hori T (2022) Spatio-temporal distribution of shallow very-low-frequency earthquakes between December 2020 and January 2021 in Kumano-nada, Nankai subduction zone, detected by a permanent seafloor seismic network. Earth Planet Space 74:14. 10.1186/s40623-022-01573-x Yamashita Y et al (2015) Migrating tremor off southern Kyushu as evidence for slow slip of a shallow subduction interface. Science 348:6235, 676–679. 10.1126/science.aaa4242 Yamashita Y, Shinohara M, Yamada T (2021) Shallow tectonic tremor activities in Hyuga-nada, Nankai subduction zone, based on long-term broadband ocean bottom seismic observations. Earth Planet Space 73:196. 10.1186/s40623-021-01533-x Yokota Y, Ishikawa T, Watanabe S, Tashiro T, Asada A (2016) Seafloor geodetic constraint for interplate coupling along the Nankai Trough megathrust zone. Nature 534:374–377. 10.1038/nature17632 Yokota Y, Ishikawa T (2020) Shallow slow slip events along the Nankai Trough detected by GNSS-A. Sci Adv 6:eaay5786. 10.1126/sciadv.aay5786 Yokota Y, Ishikawa T, Watanabe S, Nakamura Y (2021) Crustal deformation detection capability of the GNSS-A seafloor geodetic observation array (SGO-A), provided by Japan Coast Guard. Prog Earth Planet Sci 8:63. 10.1186/s40645-021-00453-4 Yokota Y et al (2024) Acoustic ambiguity reduction (AAR) method: an acoustic signal identification method for GNSS-A observation considering instrumental signal distortion. Earth Planet Space 76:97. 10.1186/s40623-024-02050-3 Supplementary Files GAv2.png Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major Revision 26 Jan, 2026 Reviewers agreed at journal 18 Dec, 2025 Reviewers invited by journal 10 Dec, 2025 Editor assigned by journal 20 Nov, 2025 First submitted to journal 18 Nov, 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8151000","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":558576739,"identity":"d93fc7ec-51ce-4852-b79f-0bb154eed09a","order_by":0,"name":"Yusuke Yokota","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYHACZhAhx8YM5UogC+PWksBgDNViQLyWxAYGNC04gcGN5MMGH3/Ypfexsz9g5mH4Iyc5I/kAw48aBnZznFrSkhNnJCTntjHzGAC1GBhLS6QlMPYcY2C2bMClJcf4ME8CM0gLAzPvP4PEeRI5Bgy8DQzMBgfwaqlPZ2MGOwyihfEvAS3JPAmHE4AhBnZY4mygFmZ8tkieeZZsOCPtuCHILwfnMBgbS/Y8Szgsc0wCp1/4jicflvhgUy0v33/84YM3DHJyEseTDz58U2OTjCvEFC4kIDgQlwgkgBgSyQY4tMj3Y7iYHyJih0vLKBgFo2AUjDgAAMdfTduGAm7vAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-2969-9110","institution":"The University of Tokyo Institute of Industrial Science: Tokyo Daigaku Seisan Gijutsu Kenkyujo","correspondingAuthor":true,"prefix":"","firstName":"Yusuke","middleName":"","lastName":"Yokota","suffix":""},{"id":558576740,"identity":"5a0f5013-d3d9-4d18-9ed6-b3512e3b24e2","order_by":1,"name":"Shun-ichi Watanabe","email":"","orcid":"","institution":"Hydrograpihc and Oceanographic Department, Japan Coast Guard","correspondingAuthor":false,"prefix":"","firstName":"Shun-ichi","middleName":"","lastName":"Watanabe","suffix":""},{"id":558576741,"identity":"82c18113-465c-4082-a825-b780b58e51d7","order_by":2,"name":"Koya Nagae","email":"","orcid":"","institution":"Hydrographic and Oceanpgraphic Department, Japan Cuast Guard","correspondingAuthor":false,"prefix":"","firstName":"Koya","middleName":"","lastName":"Nagae","suffix":""},{"id":558576742,"identity":"1b875d92-2397-4525-9c39-27826b43ceea","order_by":3,"name":"Yuto Nakamura","email":"","orcid":"","institution":"Hydrographic and Oceanographic Department, Japan Coast Guard","correspondingAuthor":false,"prefix":"","firstName":"Yuto","middleName":"","lastName":"Nakamura","suffix":""},{"id":558576743,"identity":"efbde8ff-bb19-48d4-a263-a14005c2f0ce","order_by":4,"name":"Tadashi Ishikawa","email":"","orcid":"","institution":"Japan Coast Guard Academy","correspondingAuthor":false,"prefix":"","firstName":"Tadashi","middleName":"","lastName":"Ishikawa","suffix":""}],"badges":[],"createdAt":"2025-11-19 05:16:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8151000/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8151000/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98438550,"identity":"06f927ac-b2b2-401b-ab78-3743fc761db7","added_by":"auto","created_at":"2025-12-17 16:59:30","extension":"xml","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":9390,"visible":true,"origin":"","legend":"","description":"","filename":"epspEPSPD2500380.xml","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/d2c5047b39a90d1405f6cd40.xml"},{"id":98328518,"identity":"9b7c647c-aff0-440d-b97d-9bc479bf9182","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1057,"visible":true,"origin":"","legend":"","description":"","filename":"EPSPD250038011578.go.xml","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/a690106b0f59622ab79b2c6b.xml"},{"id":98328521,"identity":"06e58a96-b76b-4c1b-ba3b-119471354702","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"xml","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":805,"visible":true,"origin":"","legend":"","description":"","filename":"EPSPD2500380Import.xml","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/afb0ceb7908af1d2fe4fa0e2.xml"},{"id":98438229,"identity":"095b8bb3-0ac9-4b88-8cd9-5aac19e39d2c","added_by":"auto","created_at":"2025-12-17 16:58:50","extension":"xml","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":110472,"visible":true,"origin":"","legend":"","description":"","filename":"EPSPD25003800enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/ece661a5d9bb145f0c4962b8.xml"},{"id":98436929,"identity":"9a99c71b-738d-4a45-bc78-b0af05958c5f","added_by":"auto","created_at":"2025-12-17 16:56:28","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":377458,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/d1f558f83d45b358a4339b04.png"},{"id":98328532,"identity":"2da77968-b0c8-432d-9f5c-658f35f7fef0","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":94182,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/7e12f1625fde9e54369bc302.png"},{"id":98328531,"identity":"a4ded43f-285c-4f94-a8bc-3c8c2191c66e","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"jpeg","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":291541,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/10ba558c365df8efbb59a799.jpeg"},{"id":98436936,"identity":"ac9b5050-5305-441c-8396-af7a50d12a7c","added_by":"auto","created_at":"2025-12-17 16:56:28","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1068911,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/a71c2f245082d4b0cf9dfbeb.png"},{"id":98328533,"identity":"eba858dd-bf81-4c3c-82ba-8795b6b67c52","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":617722,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/ae10004b5e9cd752746d274d.png"},{"id":98438221,"identity":"21155005-0517-4cad-8a60-e5ee1abeadbb","added_by":"auto","created_at":"2025-12-17 16:58:49","extension":"png","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2127529,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/aa3245c931d7f104b3e9522b.png"},{"id":98328536,"identity":"38bb1d8d-377f-400f-9efc-3389e05eb496","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2158725,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/152201067d892cbe1c6b6cd2.png"},{"id":98328535,"identity":"04142328-3a92-4cc1-9b45-4df0a139e546","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":16,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2111694,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/5b00d506d5b58b2683b2c373.png"},{"id":98437118,"identity":"823ffe85-fcb1-4849-9695-8d461376e616","added_by":"auto","created_at":"2025-12-17 16:57:00","extension":"png","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1887128,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/4d3a846ef4ffc0aeb34e4980.png"},{"id":98437059,"identity":"fab77071-16af-4eca-b7c3-38047a1cc9a6","added_by":"auto","created_at":"2025-12-17 16:56:51","extension":"jpeg","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1058452,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/1d768cf12cc00c95b29a96a9.jpeg"},{"id":98328546,"identity":"90e4a913-b420-44bd-aa81-1da2d8635aaf","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"jpeg","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1243594,"visible":true,"origin":"","legend":"","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/20fc35b48c2f0c32bc1aa1aa.jpeg"},{"id":98437238,"identity":"f2e835f2-2f89-4d68-91b6-8cb557569e78","added_by":"auto","created_at":"2025-12-17 16:57:09","extension":"jpeg","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":113329,"visible":true,"origin":"","legend":"","description":"","filename":"groupimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/2e09e7b5b15cfa5534f4c838.jpeg"},{"id":98328551,"identity":"ba12cebc-39d8-4efb-92aa-52b76fd2b74e","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"jpeg","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":98768,"visible":true,"origin":"","legend":"","description":"","filename":"groupimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/1787b0efcdab22feb7b3032d.jpeg"},{"id":98437726,"identity":"dddd5991-825f-479a-b933-1af58bfd29e6","added_by":"auto","created_at":"2025-12-17 16:57:36","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":49824,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/fda653426a7762732b3b761c.png"},{"id":98328541,"identity":"ff852794-3e72-4430-94e3-be3ece495355","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":27681,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/ef7650e8f2eb37300ae14bf0.png"},{"id":98437373,"identity":"4cf7a602-6dca-41b5-8a62-446dcc7e3f71","added_by":"auto","created_at":"2025-12-17 16:57:15","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":49981,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/5afe6ffbde20df3fbd013755.png"},{"id":98438625,"identity":"2da3c99d-85fd-4c8f-b956-16c5147813d6","added_by":"auto","created_at":"2025-12-17 16:59:40","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":364364,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/6b89165617b6137b065602de.png"},{"id":98328548,"identity":"adeca095-13a0-4e2b-b988-f9709f92d3e3","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":101343,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/e11a694256780b86ec58ae4d.png"},{"id":98436615,"identity":"4ae388cc-5fd0-442c-a3ad-9097baa6d28b","added_by":"auto","created_at":"2025-12-17 16:55:59","extension":"png","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":309962,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/2506c5b1b5839a1baf1edcdb.png"},{"id":98328559,"identity":"1d0e2483-1719-4512-b115-3686c6e40694","added_by":"auto","created_at":"2025-12-16 15:05:14","extension":"png","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":312267,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/7898829525bcf190f32edc05.png"},{"id":98438581,"identity":"7f6b2fc7-e2e1-4c9e-8155-1fcc57bf7118","added_by":"auto","created_at":"2025-12-17 16:59:33","extension":"png","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":304921,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/86a8cf48c8511bce20346852.png"},{"id":98328553,"identity":"39f1e96d-3cc7-4cc3-bb1e-d6d769350f6f","added_by":"auto","created_at":"2025-12-16 15:05:14","extension":"png","order_by":30,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":276932,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/d852d9deac445bdac9fb70a1.png"},{"id":98437341,"identity":"29ea7544-6283-4e37-b7c0-a85b33f3bda8","added_by":"auto","created_at":"2025-12-17 16:57:13","extension":"png","order_by":31,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":261405,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/9792a2f5037307609c32e43c.png"},{"id":98328557,"identity":"0b24e094-55ce-4bd9-ab8c-6f18d1c3b333","added_by":"auto","created_at":"2025-12-16 15:05:14","extension":"png","order_by":32,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":278229,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/3948efdf3d5dee9835d18cbf.png"},{"id":98328555,"identity":"b5470e38-6635-4d0e-9479-57da77c4b9a6","added_by":"auto","created_at":"2025-12-16 15:05:14","extension":"png","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":73411,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinegroupimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/13ddcb8e5cc92578791b1f83.png"},{"id":98328549,"identity":"8ecf1e57-2edd-4067-abb1-c2b7204315a6","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":34,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":57303,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinegroupimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/18f859ce3a7bc7fe8664b7d2.png"},{"id":98328558,"identity":"5b18b3e5-1ee6-4354-89cd-91062dd32d92","added_by":"auto","created_at":"2025-12-16 15:05:14","extension":"xml","order_by":35,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":108423,"visible":true,"origin":"","legend":"","description":"","filename":"EPSPD25003800structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/ab724c31077dc41ef7db1577.xml"},{"id":98328556,"identity":"6621ac9f-2105-4575-bad1-9917a24fc9c7","added_by":"auto","created_at":"2025-12-16 15:05:14","extension":"html","order_by":36,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":121369,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/79cc1a2f9cb57ae9b563635a.html"},{"id":98436782,"identity":"713abfa2-cae1-4300-94ce-b2ea46eafd0b","added_by":"auto","created_at":"2025-12-17 16:56:14","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1874631,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of observation sites (inland: GEONET, offshore: SGO-A) used in this study. The area surrounded by the gray lines indicate the area calculated by the Green’s function library by Hori et al. (2021). The area with a standard deviation of 1.25 cm/yearor less in Fig. 3 is surrounded by the blue line. The gray dashed line and the gray circle indicate the Median Tectonic Zone and the epicenter of the 2016 Kumamoto earthquake (Kato et al., 2016).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/062f76863afea469ab23f13e.png"},{"id":98437370,"identity":"a9494110-cbd6-4f8d-8649-ad0b79f640c5","added_by":"auto","created_at":"2025-12-17 16:57:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":531565,"visible":true,"origin":"","legend":"\u003cp\u003eTime series of N35E, N305E, and vertical components of (left) position and (right) velocity. On the left, the estimated velocities for eight periods, from 2013.01\u003cem\u003e–\u003c/em\u003e2016.12, 2014.01\u003cem\u003e–\u003c/em\u003e2017.12 …, are also drawn as red lines. The rightpanel shows the obtained velocities for eight periods.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/2081171fa588c519a63a52a4.png"},{"id":98437939,"identity":"bee6be22-ed93-4846-9a51-067322d9be36","added_by":"auto","created_at":"2025-12-17 16:58:15","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1083086,"visible":true,"origin":"","legend":"\u003cp\u003eThe average of standard deviation of slip deficit rate (SDR) estimation for each period.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/7c05940630f890fdc34b1e55.png"},{"id":98437545,"identity":"2a209282-70e0-4b0a-80b4-0cf316391be7","added_by":"auto","created_at":"2025-12-17 16:57:27","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1085989,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of SDRs over eight time windows. ”2015”indicates the period from January 2013 to December 2016, and similarly for other periods. The direction of N305E is defined as positive. The yellow and light-blue areas are those of deep low-frequency tremor (LFT) activity and the distribution of deep slow slips from 2013 (Obara, 2002; Obara et al., 2010; Ozawa et al., 2017; Kobayashi, 2017; Obara et al., 2024). The light-green and green dots show LFT and very low frequency event (VLF) activity during each period (Yamashita et al., 2015; Nakano et al., 2018; Yamashita et al., 2021; Takemura et al., 2022; Tamaribuchi et al., 2022; Yamamoto et al., 2022; Takemura et al., 2023). The gray lines indicate the depth contours of the plate boundary in Hori et al. (2021). The area with a standard deviation of 1.25 cm/yearor less in Fig. 3 is surrounded by a blue line. Marks A to F indicate the locations of points whose graphs of the SDR time variations are shown in Fig. 6.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/5ea1b3a916209d21310ba5f5.png"},{"id":98438433,"identity":"d967d31a-3fc3-48c3-9974-afbaf54e118b","added_by":"auto","created_at":"2025-12-17 16:59:14","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1018983,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity comparison for each time window. Red vectors are observedvelocities and black vectors are calculated velocities.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/4e3a2a160d7fa5e92002d4eb.png"},{"id":98328528,"identity":"556b1e0b-4e5a-4e2e-8488-21d5254de871","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":142739,"visible":true,"origin":"","legend":"\u003cp\u003eTemporal variation of SDR for each point in Fig. 4. The columns with bars and line graphs show the SDR with estimated ±1σ for each period (left vertical axis) and their accumulation (right vertical axis), respectively.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/f852366c20911638e2916192.png"},{"id":98436958,"identity":"51372046-bde2-4655-b42f-71bc54eae39c","added_by":"auto","created_at":"2025-12-17 16:56:30","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2753499,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of minimum SDR values (min SDR), average SDR values (average SDR), and their differences (diff SDR). The subducting seamounts (Kodaira et al., 2000; Park et al., 2024; Yamamoto et al., 2013) areshown in purple. Other drawn marks are the same as in Fig. 4.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/12219dd5c5e5ba579b25e111.png"},{"id":98437046,"identity":"93013d6e-8a9c-4c2b-93b0-93c86b35b69f","added_by":"auto","created_at":"2025-12-17 16:56:51","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":2778404,"visible":true,"origin":"","legend":"\u003cp\u003e(a) The “average SDR” result obtained using the Green’s functions calculated assuming a semi-infinite homogeneous medium and considering only the depth (Okada, 1992) . (b) The distribution of average standard deviation.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/f1687a467f1e19be302920ec.png"},{"id":98328526,"identity":"96ab7c42-3c39-4383-a941-f010a1de2bc4","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":165956,"visible":true,"origin":"","legend":"\u003cp\u003eSchematics of frictional properties of shallow megathrust based on Wang and Dixon (2004) and Almeida et al. (2018). (a) Shallow part is frictionally locked. (b) Shallow part is unlocked but the deeper side is frictionally locked. The bottom part is a schematic of the ratio of SDR on the plate boundary to plate subduction rate \u003cem\u003e\u003cstrong\u003eV\u003c/strong\u003e\u003c/em\u003e\u003csub\u003e\u003cem\u003epl\u003c/em\u003e\u003c/sub\u003e. (c) Enlarged view of assumed SDR ratio in the shallower part. When slow slips occur, SDR fluctuates between the states of (a) and (b).\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/7519243d742325e3f009f1d5.png"},{"id":98774569,"identity":"822cbd50-1aa8-48a3-ac23-03c180450adb","added_by":"auto","created_at":"2025-12-22 12:01:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":12248704,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/8a2d03b3-a3a1-4fde-aa30-6c2d6979db85.pdf"},{"id":98328524,"identity":"5f0bcbf9-e407-418d-b88c-e39ea794e594","added_by":"auto","created_at":"2025-12-16 15:05:13","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":325970,"visible":true,"origin":"","legend":"","description":"","filename":"GAv2.png","url":"https://assets-eu.researchsquare.com/files/rs-8151000/v1/1606772ae8c292566c3ee7bf.png"}],"financialInterests":"","formattedTitle":"Decadal seafloor geodesy reveals changes in the slip deficit rate along the Nankai Trough","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe frictional state of plate boundaries in subduction zones varies from locked or unstable to creeping or stable (Savage, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1983\u003c/span\u003e; Scholz, 2004; Wang and Dixon, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Almeida et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) and knowing the frictional and stress states on plate boundaries is necessary for simulating earthquake cycles and constructing earthquake and tsunami scenarios. The actual states can be estimated from the distribution of slip deficit rate (SDR) as extracted basically from geodetic observations (Wallace et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Hashimoto et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Lindsey et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eGlobal Navigation Satellite System \u0026ndash; Acoustic ranging combination (GNSS-A) observations can detect horizontal crustal movements directly on the seafloor, providing key data for determining the distribution of slip deficits at plate boundaries. In recent years, advances in signal compensation technology have made them effective for detecting long-term vertical movements (Yokota et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eSince Yokota et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) had showed the distribution of SDR in the Nankai Trough using horizontal displacement rates obtained by GNSS-A, it has been studied using various methods, including the influence of viscoelastic relaxation and estimation of stress distribution (Saito and Noda, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Sherill et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Li and Chen, 2024). On the other hand, as shown in Yokota and Ishikawa (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), GNSS-A displacement rates in the Nankai Trough vary with time. These are caused by temporal changes in SDR, which can be interpreted as shallow slow slip events (SSEs) (Obara and Kato, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) occurred near the trench axis. Sub-seafloor SSEs are observed frequently by modern seafloor geodetic techniques, such as ocean bottom pressure gauges and pore pressure gauges observations (e.g., Wallace et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Araki et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eYokota and Ishikawa (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) had investigated steady-state and non-steady-state and detected centimeter-scale transient horizontal crustal deformation. However, as shown in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e in this paper, examination of long-term data up to 2023 revealed that the temporal changes were diverse, making it difficult to distinguish between steady and transient states. Such fluctuations in the crustal deformation rate over time can be interpreted as frequent changes in the SDR at shallow plate boundaries. So far, the temporal change of SDR has been estimated only by terrestrial GNSS (Nishimura et al, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Ochi, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In this paper, we investigated the recent SDR behavior in the Nankai Trough using both horizontal and vertical components of GNSS-A data.\u003c/p\u003e"},{"header":"2 Data","content":"\u003cp\u003eWe used the Seafloor Geodetic Observation-Array (SGO-A) GNSS-A observation network, which has been operated by the Japan Coast Guard (JCG) (Ishikawa et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) in the Nankai Trough constantly for over 10 years. According to the empirical slow slip scaling law (Gao et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), slow slips of magnitude (M) 6 or greater have an impact of crustal deformation of more than 1 cm/year on the seafloor in ranges of about 50 km. Such amount of displacement rate change can be detected with the current site density of SGO-A.\u003c/p\u003e \u003cp\u003eAlthough vertical motions were not used in previous studies because of the low accuracy of vertical positioning, the recently developed Acoustic Ambiguity Reduction (AAR) method (Yokota et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) has brought the accuracy of vertical positioning closer to the horizontal positioning (1\u003cem\u003e\u0026ndash;\u003c/em\u003e2 cm). Herein, we use the horizontal and vertical displacement rates of the seafloor GNSS-A data of SGO-A and terrestrial GNSS data of GEONET (Takamatsu et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) from January 2013 to December 2023 shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e to discuss the temporal variations of SDR. The locations of terrestrial GNSS sites and observation period were selected to reduce the influences of the 2011 Tohoku-oki earthquake, the 2016 Kumamoto earthquake, and the Median Tectonic Line.\u003c/p\u003e \u003cp\u003eWe used the GNSS-A seafloor position data processed with GARPOS version 1.0.1 (Watanabe et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Watanabe et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) for the period from January 2013 to December 2023 observed by SGO-A. To discuss the velocity variation of less than 1 cm/year for each time window, we calculated the 4-year average velocity; this was because a numerical investigation of the accuracy of velocity variations in long-term observation data (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e in Yokota et al. (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)) has indicated that the current observation frequency (approximately four times per year) of SGO-A permits discussion of variations in velocity of about 0.5\u003cem\u003e\u0026ndash;\u003c/em\u003e0.8 cm/year. The left and right sides of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e are the obtained GNSS-A time series and the velocities estimated in 4-year moving windows for eight periods, from 2013.01\u003cem\u003e\u0026ndash;\u003c/em\u003e2016.12, 2014.01\u003cem\u003e\u0026ndash;\u003c/em\u003e2017.12 \u0026hellip;, respectively. The 95% confidence intervals for the estimated velocity were often less than 0.5 cm/year. Although the AAR method has improved the accuracy of vertical displacement considerably, it may still remain synchronized biases at different observation sites during the same period for reasons such as replacement of seafloor stations. For example, the latest 2 years for sites 4, 6, and 9 have similar bias errors in the vertical components. In the future, as more data are accumulated at these sites, bias corrections will become possible using the AAR method.\u003c/p\u003e \u003cp\u003eThe coordinates at the SGO-A sites were taken based on ITRF2020 (Altamimi et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The displacements shown in the left panels of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e (Data S1) indicate the internal plate deformation calculated by excluding the rigid motion of the Amur plate modeled in MORVEL (DeMets et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). The right panels (Data S2) show velocities estimated in 4-year moving windows. The long-term vertical motions in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e were almost zero or slightly negative, which is consistent with the elastic crustal deformation expected from the shape of the plate boundary in the Nankai Trough (i.e., low dip angle).\u003c/p\u003e \u003cp\u003eMany sites, e.g., sites 5 and 13, showed variations in horizontal velocity of more than 2 cm/year, indicating large SDR variations in the middle of the observation period. At site 5, for example, different rates were observed every 3\u0026ndash;4 years during the early, middle, and late periods, which cannot be simply interpreted as SSEs of the same magnitude occurring at the same location. There is no period of constant SDR (steady state) throughout the Nankai Trough, and it is believed that the state is constantly changing. In this paper, we calculate the time evolution of the SDR to understand these variations.\u003c/p\u003e"},{"header":"3 Method","content":"\u003cp\u003eWe here used the surface velocity data calculated from SGO-A and GEONET for eight time windows over 4 years, e.g., from 2013.01\u003cem\u003e\u0026ndash;\u003c/em\u003e2016.12 (2015), 2014.01\u003cem\u003e\u0026ndash;\u003c/em\u003e2017.12 (2016) .... The range of time window was determined considering the estimation accuracy. The data before 2012 were not used to avoid the influence of the 2011 Tohoku-oki earthquake, and the spatial range of GEONET observation sites were limited to avoid the influences of the Median Tectonic Zone and the 2016 Kumamoto earthquake (Kato et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Considering that the horizontal components have less variance than the vertical components, they were given twice the weighting.\u003c/p\u003e \u003cp\u003eEstimation of SDR for large spatial coverage with topographic variation depends strongly on the Earth\u0026rsquo;s shape and heterogenous velocity structure. We used the Green\u0026rsquo;s function library for subduction zones (GLFSZ; Hori et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)) to calculate the surface displacement due to a plate boundary slip deficit. This library was calculated considering the three-dimensional heterogeneous velocity structure, surface topography, and the ellipsoidal shape of the Earth (for more detail, see Hori et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)). The plate boundary is divided into 459 grids with 20-km intervals, and a slip is expressed by placing a cubic B-spline basis function on each grid. A slip is decomposed into two directions: the plate convergence direction (\u0026ldquo;02\u0026rdquo;: N305E) and the perpendicular direction (\u0026ldquo;03\u0026rdquo;). The Green\u0026rsquo;s function represents the surface displacement for a unit slip of the basis function, and the displacement of the surface observation site is calculated by\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\varvec{d}}^{\\text{c}\\text{a}\\text{l}\\text{c}}\\left({\\varvec{\\theta\\:}}_{02},{\\varvec{\\theta\\:}}_{03}\\right)={\\varvec{G}}_{02}{\\varvec{\\theta\\:}}_{02}+{\\varvec{G}}_{03}{\\varvec{\\theta\\:}}_{03},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{d}}^{\\text{c}\\text{a}\\text{l}\\text{c}}\\)\u003c/span\u003e\u003c/span\u003e is a vector listing the displacements at each site, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}}_{02}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{G}}_{03}\\)\u003c/span\u003e\u003c/span\u003e are Green\u0026rsquo;s function matrices for slips in the \u0026ldquo;02\u0026rdquo; and \u0026ldquo;03\u0026rdquo; directions, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{\\theta\\:}}_{02}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{\\theta\\:}}_{03}\\)\u003c/span\u003e\u003c/span\u003e are vectors listing the coefficients of 459 basis functions for slips in the \u0026ldquo;02\u0026rdquo; and \u0026ldquo;03\u0026rdquo; directions, respectively.\u003c/p\u003e \u003cp\u003eWe estimated the optimal parameters of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\theta\\:}\\)\u003c/span\u003e\u003c/span\u003e = (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{\\theta\\:}}_{02}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{\\theta\\:}}_{03}\\)\u003c/span\u003e\u003c/span\u003e) for the observed data using Bayesian inference. Assuming that the observed surface displacement varies normally around the calculated value, the conditional probability of the observed value \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{d}}^{\\text{o}\\text{b}\\text{s}}\\)\u003c/span\u003e\u003c/span\u003e under the given parameters \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\theta\\:}\\)\u003c/span\u003e\u003c/span\u003e is expressed as\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:p\\left({\\varvec{d}}^{\\text{o}\\text{b}\\text{s}}|\\varvec{\\theta\\:},{\\sigma\\:}_{m}\\right)\\propto\\:\\text{exp}\\left(-\\frac{1}{2}{\\left({\\varvec{d}}^{\\text{o}\\text{b}\\text{s}}-{\\varvec{d}}^{\\text{c}\\text{a}\\text{l}\\text{c}}\\left(\\varvec{\\theta\\:}\\right)\\right)}^{T}{{\\Sigma\\:}}^{-1}\\left({\\varvec{d}}^{\\text{o}\\text{b}\\text{s}}-{\\varvec{d}}^{\\text{c}\\text{a}\\text{l}\\text{c}}\\left(\\varvec{\\theta\\:}\\right)\\right)\\right),$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere the covariance matrix \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\Sigma\\:}\\)\u003c/span\u003e\u003c/span\u003e is a diagonal matrix with a common variance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\sigma\\:}_{m}}^{2}\\)\u003c/span\u003e\u003c/span\u003e in the diagonal elements. Particularly in the offshore areas, where the number of grids is greater than the number of observation sites, a physically unnatural slip distribution may be estimated. Therefore, we gave a prior distribution that reduces the second-order difference of the coefficients of the basis functions, so that the final calculated slip distribution is spatially smooth. This prior distribution is given as\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:p\\left(\\varvec{\\theta\\:}|{\\rho\\:}_{m}\\right)\\propto\\:\\text{exp}\\left(-\\frac{1}{2{{\\rho\\:}_{m}}^{2}}{\\left(\\varvec{L}\\varvec{\\theta\\:}\\right)}^{T}\\left(\\varvec{L}\\varvec{\\theta\\:}\\right)\\right),$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{L}\\)\u003c/span\u003e\u003c/span\u003e is the Laplacian operator representing the second-order difference, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{m}\\)\u003c/span\u003e\u003c/span\u003e is a hyperparameter representing the strength of the constraint. Based on Bayes\u0026rsquo; theorem, we calculated the posterior distribution of the parameters given by\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:p\\left(\\varvec{\\theta\\:},{\\sigma\\:}_{m},{\\rho\\:}_{m}|{\\varvec{d}}^{obs}\\right)\\propto\\:p\\left({\\varvec{d}}^{\\text{o}\\text{b}\\text{s}}\\right|\\varvec{\\theta\\:},{\\sigma\\:}_{m}\\left)\\:p\\left(\\varvec{\\theta\\:}|{\\rho\\:}_{m}\\right)p\\right({\\sigma\\:}_{m}\\left)p\\right({\\rho\\:}_{m}),$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left({\\sigma\\:}_{m}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:p\\left({\\rho\\:}_{m}\\right)\\)\u003c/span\u003e\u003c/span\u003e are the prior distributions of the hyperparameters, and sufficiently wide distributions were adopted. In this study, we used the Markov-Chain Monte Carlo (MCMC) method to efficiently evaluate the posterior distribution and the Metropolis\u0026ndash;Hastings method to concretely obtain the samples. Because the hyperparameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\rho\\:}_{m}\\)\u003c/span\u003e\u003c/span\u003e varies by several orders of magnitude, we stabilized the estimation of other parameters by obtaining the optimal value from the marginal distribution of the hyperparameter obtained in a prior calculation and recalculating the parameters by fixing the hyperparameter to the optimal value.\u003c/p\u003e \u003cp\u003eThe distribution of the obtained parameters can be regarded as a sampling from the posterior distribution. Since the distribution is roughly close to a normal distribution, we adopted the average value of the distribution as the obtained optimal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\theta\\:}\\)\u003c/span\u003e\u003c/span\u003e. The map of standard deviation (σ) of SDR estimation calculated based on the distribution of coefficient values (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, Data S3) represents the spatial resolution of the SDR estimation. Using the obtained optimal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\theta\\:}\\)\u003c/span\u003e\u003c/span\u003e, the final SDR distribution was calculated from a linear combination of basis functions provided in the GFLSZ library.\u003c/p\u003e \u003cp\u003eEight snapshots of SDR distribution for 4-year moving time windows (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, Data S4) were estimated. The observed and calculated velocities are compared in Fig.\u0026nbsp;5 (Data S5). In this paper, considering the estimation accuracy of SDR, we discuss the area in which the average of standard deviation of SDR estimation for each time window (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) is smaller than 1.25 cm/year, or approximately 20%\u0026ndash;25% of the convergence rate.\u003c/p\u003e"},{"header":"4 Result","content":"\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the temporal variation of SDR and the accumulated slip deficits for the points selected from deep (A\u0026ndash;C) and shallow (D\u0026ndash;F) parts in three along-trough segments, i.e., the southern areas of Enshu-Nada, Kumano-Nada, and Tosa Bay. There is little difference between the maximum SDR values of the shallow and deep points in each segment, though it depends on the segments. The results from shallow points (D\u0026ndash;F) show a decrease in SDR greater than 1σ. To discuss the spatial distribution of frictional states of the plate boundary, we extracted the statistical SDR distributions as follows: by picking the minimum SDR values from each time window, as \u0026ldquo;min SDR\u0026rdquo;; by taking the average over the time windows, as \u0026ldquo;average SDR\u0026rdquo;; and by taking the difference of them, as \u0026ldquo;diff SDR.\u0026rdquo; The statistical SDR distributions are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e"},{"header":"5 Discussion","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Green\u0026rsquo;s functions\u003c/h2\u003e \u003cp\u003eSDR models in many past studies had been calculated using simple topographic and velocity structure models. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the \u0026rdquo;average SDR\u0026rdquo; results obtained using the Green\u0026rsquo;s functions of a semi-infinite homogeneous elastic medium (Okada, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1992\u003c/span\u003e) and the average of standard deviation. In the western area, the SDR became larger than the plate convergence rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{pl}\\)\u003c/span\u003e\u003c/span\u003e of the Philippine Sea plate under the Amur plate calculated using MORVEL (DeMets et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) (e.g., 6.5 cm/year) when estimated using the homogeneous model, but the estimated SDR became smaller when using GFLSZ. On the other hand, in the eastern area, they were larger for the GFLSZ case, indicating the complex influence of three-dimensional structure. In GFLSZ, the surface displacement is larger directly above and smaller at a distance due to the influence of the shallow structure. This effect also improves the standard deviation distribution around the seafloor site compared to the case using the homogeneous medium (Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003eb).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Interpretation\u003c/h2\u003e \u003cp\u003eAround the locked interface, the SDR becomes large and approaches the plate subduction rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{pl}\\)\u003c/span\u003e\u003c/span\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e). A large crustal deformation in the direction of plate convergence occurs on the surface above the high SDR area. In plate subduction zones such as the Nankai Trough, where plates subduct from the seafloor beneath the land, terrestrial GNSS measures such crustal deformation, allowing us to grasp the existence of deep locked areas directly below the inland. If the shallow area is locked and stress is occasionally released by slow slips (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003ec), then the SDR should be moderate on average, fluctuate in time, and have a small minimum. Even if the shallow part is temporarily or even constantly unlocked, the deeper locked area drags the shallower side, so the SDR does not fall to zero and a crustal deformation occurs\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\:\\)\u003c/span\u003e\u003c/span\u003e(Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003eb). Known as stress shadow, this phenomenon causes the high-SDR area to be wider than the mechanically locked area. High-precision and continuous GNSS-A, such as the current SGO-A, makes it possible to distinguish between these states.\u003c/p\u003e \u003cp\u003eThe area of high \u0026ldquo;min SDR\u0026rdquo; (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e) primarily indicates the constantly locked area (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003ea and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003eb) where no large slow slip occurred in this 11 years. For example, around A\u0026ndash;C have less time variation and the minimum SDR is higher than that in the surrounding areas. The constantly frictionally locked area is limited within this high \u0026ldquo;min SDR\u0026rdquo; area in the deeper portion. Because of the shortage of observation period, i.e., 11 years, more fluctuation of the SDR may be observed in the future and the constantly locked area could be further constrained. For example, the area west of F is the only area in the shallow side with small SDR variation (high \u0026ldquo;min SDR\u0026rdquo; value), but there is a possibility that the SDR in this area may fluctuate in the future. Around A, this high \u0026ldquo;min SDR\u0026rdquo; area is wide in the dip direction, compared to around B. The \u0026ldquo;min SDR\u0026rdquo; values around D and E (shallower part of A and B, respectively) show a correlation with the range of high \u0026ldquo;min SDR\u0026rdquo; area in the deeper sides. This indicates that the width or upper limit of the constantly locked area controls the magnitude of the stress shadow, and therefore the \u0026ldquo;min SDR\u0026rdquo; values on the shallower side.\u003c/p\u003e \u003cp\u003eEmpirically, there is a spatial and temporal correlation between low frequency tremors (LFTs), very low frequency earthquake (VLFs), and slow slips (Obara and Kato, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The shallow areas of low \u0026ldquo;min SDR\u0026rdquo; coincide roughly with the areas of high \u0026ldquo;diff SDR\u0026rdquo; which suggests the occurrence of slow slips, and they include the high activity areas of LFTs and VLFs (Yamashita et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Nakano et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Yamashita et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Takemura et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Tamaribuchi et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yamamoto et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Takemura et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). For example, synchronous activities of LFT and VLF with SDR variations off the Kii Channel around 2018 were estimated (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) around a subducted seamount (Kodaira et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). The only shallow area with a low \u0026ldquo;average SDR,\u0026rdquo; meaning constantly low SDR, is in the south of Kumano-Nada, where short-term slow slips have occurred with LFTs and VLFs (Araki et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Edgington et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), which is not an area that is always unlocked, but rather an area where slow slips occur frequently. Additionally, in the results of this study, the area of high \u0026ldquo;diff SDR\u0026rdquo; extends to areas without LFT and VLF activities, i.e., the southeast of Enshu-Nada where the subducted paleo-Zenisu ridge is located (Park et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2004\u003c/span\u003e) and the south of Tosa Bay. It has been pointed out that SSEs may be occurring from land in the northeast around point F (Kikuchi et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), and the long-term decrease in SDR in this area may be a major event that extends to land. Therefore, the distribution of shallow slow slips shown in this study is not necessarily correlated with other slow earthquakes or subducting seamounts and ridges, but rather spreads across almost the entire shallow side. It may be a feature of this plate subduction zone itself.\u003c/p\u003e \u003c/div\u003e"},{"header":"6 Conclusion","content":"\u003cp\u003eGNSS-A observations in SGO-A over about 10 years constrained the extent of the constantly locked area and further revealed that almost the shallowest part of the Nankai Trough plate boundary does not always remain in the state of Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003ea or Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003eb. SGO-A is a seafloor geodetic observation network that has continued stable observation for the longest period in the world, yet it is only possible to evaluate the frictional state of the plate boundary for about one decade. It is necessary to continue accumulating data and to evaluate the degree of time variation and stability in both shallow and deep areas. Long-term and frequent seafloor geodetic observations in many more subduction zones are needed to verify the generality of the frictional conditions at shallow plate boundaries revealed in this study across other subduction zones. In the future, it will also be necessary to further discuss changes in the stress state at the plate boundary based on the stress change distribution calculated considering three-dimensional heterogeneous velocity structure.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eGNSS\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eGlobal Navigation Satellite System\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eGNSS-A\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eGlobal Navigation Satellite System \u0026ndash; Acoustic combination technique\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSGO-A\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSeafloor Geodetic Observation \u0026ndash; Array\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv class=\"DefinitionListEntry\"\u003e \u003cdiv class=\"Term\"\u003eSDR\u003c/div\u003e \u003cdiv class=\"Description\"\u003e \u003cp\u003eSlip Deficit Rate\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis study was supported by ERI JURP 2024-Y-KOBO12 in Earthquake Research Institute, the University of Tokyo, by SECOM science and technology foundation, and by JSPS KAKENHI Grant Number JP21H05200 in Grant-in-Aid for Transformative Research Areas (A) \u0026ldquo;Science of Slow-to-Fast Earthquakes.\u0026rdquo;\u003c/p\u003e\u003ch2\u003eAuthors' contributions\u003c/h2\u003e \u003cp\u003eYY and TI proposed the concept and managed the project. TI constructed the method. KN, SW, and YY analyzed GNSS-A data and SDR. SW, TI, and YY visualized the results. YY, SW, KN, YN, and TI read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eWe thank F. Tomita and T. Iinuma for helpful comments on the initial consideration. In-situ observations were performed by the survey vessels operated by the Japan Coast Guard.\u003c/p\u003e\u003ch2\u003eAvailability of data and materials\u003c/h2\u003e \u003cp\u003eThe GNSS and GNSS-A datasets used in the current study are available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.57499/GSI_GNSS_2025_001\u003c/span\u003e\u003cspan address=\"10.57499/GSI_GNSS_2025_001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (Geodetic Observation Center, GSI, 2025) and \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.57553/2024001\u003c/span\u003e\u003cspan address=\"10.57553/2024001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (Japan Coast Guard, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The GNSS-A analysis software GARPOS v1.0.1 (Watanabe et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Watanabe et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) is available at Zenodo (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5281/zenodo.6414642\u003c/span\u003e\u003cspan address=\"10.5281/zenodo.6414642\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The Green's function library (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.jamstec.go.jp/feat/gflsz/\u003c/span\u003e\u003cspan address=\"https://www.jamstec.go.jp/feat/gflsz/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) for subduction zones by Hori et al. (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) was used, which was created by JAMSTEC's own modification of a computer program under development by Earthquake Research Institute, The University of Tokyo. The library includes data modified from Japan Integrated Velocity Structure Model version 1 (JIVSM) (Koketsu et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Koketsu et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and the Earth Gravitational Model 2008 (Pavlis et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlmeida R et al (2018) Can the updip Limit of frictional locking on megathrusts be detected geodetically? Quantifying the effect of stress shadows on near-trench coupling. Geophys Res Lett 45:4754\u0026ndash;4763. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2018GL077785\u003c/span\u003e\u003cspan address=\"10.1029/2018GL077785\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAltamimi Z, Rebischung P, Collilieux X, M\u0026eacute;tivier L, Chanard K (2023) ITRF2020: an augmented reference frame refining the modeling of nonlinear station motions. J Geod 97:47. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s00190-023-01738-w\u003c/span\u003e\u003cspan address=\"10.1007/s00190-023-01738-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAraki E et al (2017) Recurring and triggered slow-slip events near the trench at the Nankai Trough subduction megathrust. Science 356:1157\u0026ndash;1160. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.aan3120\u003c/span\u003e\u003cspan address=\"10.1126/science.aan3120\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeMets C, Gordon RG, Argus DF (2010) Geologically current plate motions. Geophys J Int 181:1\u0026ndash;80. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1111/j.1365-246X.2009.04491.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1365-246X.2009.04491.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEdgington JR, Saffer DM, Williams CA (2025) Migrating shallow slow slip on the Nankai Trough megathrust captured by borehole observations. Science 388:6754, 1396\u0026ndash;1400. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.ads9715\u003c/span\u003e\u003cspan address=\"10.1126/science.ads9715\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGao H, Schmidt DA, Weldon IIRJ (2012) Scaling relationships of source parameters for slow slip events. Bull Seismol Soc Am 102:352\u0026ndash;360. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1785/0120110096\u003c/span\u003e\u003cspan address=\"10.1785/0120110096\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGeodetic O, Center GSI (2025) GNSS data. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.57499/GSI_GNSS_2025_001\u003c/span\u003e\u003cspan address=\"10.57499/GSI_GNSS_2025_001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHashimoto C, Noda A, Sagiya T, Matsu\u0026rsquo;ura M (2009) Interplate seismogenic zones along the Kuril-Japan trench inferred from GPS data inversion. Nat Geosci 2:141\u0026ndash;144. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/NGEO421\u003c/span\u003e\u003cspan address=\"10.1038/NGEO421\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHori T et al (2021) High-fidelity elastic Green\u0026rsquo;s functions for subduction zone models consistent with the global standard geodetic reference system. Earth Planet Space 73:41. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-021-01370-y\u003c/span\u003e\u003cspan address=\"10.1186/s40623-021-01370-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIshikawa T, Yokota Y, Watanabe S, Nakamura Y (2020) History of on-board equipment improvement for GNSS-A observation with focus on observation frequency. Front Earth Sci 8:150. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3389/feart.2020.00150\u003c/span\u003e\u003cspan address=\"10.3389/feart.2020.00150\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJapan Coast Guard (2024) GNSS-A observation data in GARPOS format obtained at the SGO-A sites. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.57553/2024001\u003c/span\u003e\u003cspan address=\"10.57553/2024001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKato A, Nakamura K, Hiyama Y (2016) The 2016 Kumamoto earthquake sequence. Prog Jpn Acad Ser B 92:8. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.2183/pjab.92.359\u003c/span\u003e\u003cspan address=\"10.2183/pjab.92.359\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKikuchi Y, Mitsui Y, Kano M (2025) Detection of slow slip event lasting several months in the shallow region of the Suruga Trough, the eastern end of the Nankai Trough, Japan. Prog Earth Planet Sci 12:58. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40645-025-00737-z\u003c/span\u003e\u003cspan address=\"10.1186/s40645-025-00737-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKobayashi A (2017) Objective detection of long-term slow slip events along the Nankai Trough using GNSS data (1996\u0026ndash;2016). Earth Planet Space 69:171. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-017-0755-7\u003c/span\u003e\u003cspan address=\"10.1186/s40623-017-0755-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKodaira S, Takahashi N, Nakanishi A, Miura S, Kaneda Y (2000) Subducted seamount imaged in the rupture zone of the 1946 Nankaido earthquake. Science 289:104\u0026ndash;106. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.289.5476.104\u003c/span\u003e\u003cspan address=\"10.1126/science.289.5476.104\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKoketsu K, Miyake H, Tanaka Y (2009) A proposal for a standard procedure of modeling 3-D velocity structures and its application to the Tokyo metropolitan area, Japan. Tectonophysics 472:290\u0026ndash;300. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.tecto.2008.05.037\u003c/span\u003e\u003cspan address=\"10.1016/j.tecto.2008.05.037\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKoketsu K, Miyake H, Suzuki H (2012) Japan integrated velocity structure model version 1. Proceedings of the 15th World Conference on Earthquake Engineering (1773), Lisbon\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLindsey EO et al (2021) Slip rate deficit and earthquake potential on shallow megathrusts. Nat Geosci 14:321\u0026ndash;326. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/s41561-021-00736-x\u003c/span\u003e\u003cspan address=\"10.1038/s41561-021-00736-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNakano M, Hori T, Araki E, Kodaira S, Ide S (2018) Shallow very-low-frequency earthquakes accompany slow slip events in the Nankai subduction zone. Nat Comm 9:984. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/s41467-018-03431-5\u003c/span\u003e\u003cspan address=\"10.1038/s41467-018-03431-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNishimura T et al (2004) Temporal change of interplate coupling in northeastern Japan during 1995\u0026ndash;2002 estimated from continuous GPS observations. Geophys J Int 157:901\u0026ndash;916. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1111/j.1365-246X.2004.02159.x\u003c/span\u003e\u003cspan address=\"10.1111/j.1365-246X.2004.02159.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eObara K (2002) Nonvolcanic deep tremor associated with subduction in southwest Japan. Science 296:1679\u0026ndash;1681. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.10703\u003c/span\u003e\u003cspan address=\"10.1126/science.10703\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eObara K, Tanaka S, Maeda T, Matsuzawa T (2010) Depth-dependent activity of non-volcanic tremor in southwest Japan. Geophys Res Lett 37:L13306. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2010GL043679\u003c/span\u003e\u003cspan address=\"10.1029/2010GL043679\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOzawa S (2017) Long-term slow slip events along the Nankai trough subduction zone after the 2011 Tohoku earthquake in Japan. Earth Planet Space 69:56. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-017-0640-4\u003c/span\u003e\u003cspan address=\"10.1186/s40623-017-0640-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eObara K, Kato A (2016) Connecting slow earthquakes to huge earthquakes. Science 353:6296, 253\u0026ndash;257. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.aaf1512\u003c/span\u003e\u003cspan address=\"10.1126/science.aaf1512\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOchi T (2015) Temporal change in plate coupling and long-term slow slip events in southwestern Japan. Earth Planet Sci Lett 431:8\u0026ndash;14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.epsl.2015.09.012\u003c/span\u003e\u003cspan address=\"10.1016/j.epsl.2015.09.012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOkada Y (1992) Internal deformation due to shear and tensile faults in a half-space. Bull Seismol Soc Am 82:1018\u0026ndash;1040. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1785/BSSA0820021018\u003c/span\u003e\u003cspan address=\"10.1785/BSSA0820021018\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOzawa S, Munekane H, Suito H (2024) Time-dependent modeling of slow-slip events along the Nankai Trough subduction zone, Japan, within the 2018\u0026ndash;2023 period. Earth Planet Space 76:23. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-024-01970-4\u003c/span\u003e\u003cspan address=\"10.1186/s40623-024-01970-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYamamoto Y et al (2013) Imaging of the subducted Kyushu-Palau Ridge in the Hyuga-nada region, western Nankai Trough subduction zone. Tectonophysics 589:90\u0026ndash;102. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.tecto.2012.12.028\u003c/span\u003e\u003cspan address=\"10.1016/j.tecto.2012.12.028\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePark J-O, Moore GF, Tsuru T, Kodaira S, Kaneda Y (2004) A subducted oceanic ridge influencing the Nankai megathrust earthquake rupture. Earth Planet Sci Lett 217:77\u0026ndash;84. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/S0012-821X(03)00553-3\u003c/span\u003e\u003cspan address=\"10.1016/S0012-821X(03)00553-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J Geophys Res 117:B04406. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2011JB008916\u003c/span\u003e\u003cspan address=\"10.1029/2011JB008916\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaito T, Noda A (2022) Mechanically coupled areas on the plate interface in the Nankai trough, Japan and a possible seismic and aseismic rupture scenario for megathrust earthquakes. \u003cem\u003eJ. Geophys. Res. Solid Earth\u003c/em\u003e 127, e2022JB023992. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2022JB023992\u003c/span\u003e\u003cspan address=\"10.1029/2022JB023992\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSavage JC (1983) A dislocation model of strain accumulation and release at a subduction zone. J Geophys Res 88:4984\u0026ndash;4996. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/JB088iB06p04984\u003c/span\u003e\u003cspan address=\"10.1029/JB088iB06p04984\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScholz CH (1998) Earthquakes and friction laws. Nature 391:37\u0026ndash;42. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/34097\u003c/span\u003e\u003cspan address=\"10.1038/34097\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSherill EM, Johnson KM, Jackson NM (2024) Locating boundaries between locked and creeping regions at Nankai and Cascadia subduction zones. J Geophys Res Solid Earth 129:e2024JB029346. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2024JB029346\u003c/span\u003e\u003cspan address=\"10.1029/2024JB029346\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTakamatsu N et al (2023) New GEONET analysis strategy at GSI: daily coordinates of over 1300 GNSS CORS in Japan throughout the last quarter century. Earth Planet Space 75(1):49. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-023-01787-7\u003c/span\u003e\u003cspan address=\"10.1186/s40623-023-01787-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTakemura S, Obara K, Shiomi K, Baba S (2022) Spatiotemporal variations of shallow very low frequency earthquake activity southeast off the Kii Peninsula, along the Nankai Trough, Japan. \u003cem\u003eJ. Geophys. Res. Solid Earth\u003c/em\u003e 127, e2021JB023073. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2021JB023073\u003c/span\u003e\u003cspan address=\"10.1029/2021JB023073\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTakemura S et al (2023) A review of shallow slow earthquakes along Nankai Trough. Earth Planet Space 75:164. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-023-01920-6\u003c/span\u003e\u003cspan address=\"10.1186/s40623-023-01920-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTamaribuchi K, Ogiso M, Noda A (2022) Spatiotemporal distribution of shallow tremors along the Nankai Trough, southwest Japan, as determined from waveform amplitudes and cross-correlations. \u003cem\u003eJ. Geophys. Res. Solid Earth\u003c/em\u003e 127, e2022JB024403. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2022JB024403\u003c/span\u003e\u003cspan address=\"10.1029/2022JB024403\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWallace LM, Beavan J, McCaffrey R, Darby D (2004) Subduction zone coupling and tectonic block rotations in the North Island, New Zealand. J Geophys Res 109:B12406. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1129/2004JB003241\u003c/span\u003e\u003cspan address=\"10.1129/2004JB003241\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWallace LM et al (2016) Slow slip near the trench at the Hikurangi subduction zone, New Zealand. Science 352:701\u0026ndash;704. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.aaf2349\u003c/span\u003e\u003cspan address=\"10.1126/science.aaf2349\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang K, Dixon T (2004) Coupling semantics and science in earthquake research. Eos 85(18):180\u0026ndash;181. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2004EO180005\u003c/span\u003e\u003cspan address=\"10.1029/2004EO180005\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWatanabe S, Ishikawa T, Nakamura Y, Yokota Y (2020) GARPOS: analysis software for the GNSS-A seafloor positioning with simultaneous estimation of sound speed structure. Front Earth Sci 8:597532. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.3389/feart.2020.597532\u003c/span\u003e\u003cspan address=\"10.3389/feart.2020.597532\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWatanabe S, Ishikawa T, Nakamura Y, Yokota Y (2022) GARPOS: Analysis tool for GNSS-Acoustic seafloor positioning (1.0.1). Zenodo. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.5281/zenodo.6414642\u003c/span\u003e\u003cspan address=\"10.5281/zenodo.6414642\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYamamoto Y, Ariyoshi K, Yada S, Nakano M, Hori T (2022) Spatio-temporal distribution of shallow very-low-frequency earthquakes between December 2020 and January 2021 in Kumano-nada, Nankai subduction zone, detected by a permanent seafloor seismic network. Earth Planet Space 74:14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-022-01573-x\u003c/span\u003e\u003cspan address=\"10.1186/s40623-022-01573-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYamashita Y et al (2015) Migrating tremor off southern Kyushu as evidence for slow slip of a shallow subduction interface. Science 348:6235, 676\u0026ndash;679. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/science.aaa4242\u003c/span\u003e\u003cspan address=\"10.1126/science.aaa4242\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYamashita Y, Shinohara M, Yamada T (2021) Shallow tectonic tremor activities in Hyuga-nada, Nankai subduction zone, based on long-term broadband ocean bottom seismic observations. Earth Planet Space 73:196. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-021-01533-x\u003c/span\u003e\u003cspan address=\"10.1186/s40623-021-01533-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYokota Y, Ishikawa T, Watanabe S, Tashiro T, Asada A (2016) Seafloor geodetic constraint for interplate coupling along the Nankai Trough megathrust zone. Nature 534:374\u0026ndash;377. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/nature17632\u003c/span\u003e\u003cspan address=\"10.1038/nature17632\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYokota Y, Ishikawa T (2020) Shallow slow slip events along the Nankai Trough detected by GNSS-A. Sci Adv 6:eaay5786. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1126/sciadv.aay5786\u003c/span\u003e\u003cspan address=\"10.1126/sciadv.aay5786\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYokota Y, Ishikawa T, Watanabe S, Nakamura Y (2021) Crustal deformation detection capability of the GNSS-A seafloor geodetic observation array (SGO-A), provided by Japan Coast Guard. Prog Earth Planet Sci 8:63. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40645-021-00453-4\u003c/span\u003e\u003cspan address=\"10.1186/s40645-021-00453-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYokota Y et al (2024) Acoustic ambiguity reduction (AAR) method: an acoustic signal identification method for GNSS-A observation considering instrumental signal distortion. Earth Planet Space 76:97. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-024-02050-3\u003c/span\u003e\u003cspan address=\"10.1186/s40623-024-02050-3\" 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":"GNSS-A, Nankai trough, slip deficit rate, SSE","lastPublishedDoi":"10.21203/rs.3.rs-8151000/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8151000/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIdentifying the frictionally locked area of a plate boundary is an important geodetic issue in mitigating earthquake disasters. However, recent long-term geodetic observations have revealed that actual geodetic data contain transient behaviors due to slow slip events or changes in slip deficit rates. Therefore, the use of a snapshot of temporally averaged geodetic data is far insufficient to understand the accurate frictional state. This problem is particularly serious at sub-seafloor plate boundaries, where continuous or periodic geodetic observations for a long time are rarely realized. Here, we evaluated long-term slip deficit rate variations in the Nankai Trough, the only area in the world for which high-density data on horizontal and vertical components have been accumulated via seafloor observations with a sufficient frequency on the decadal scale. Consequently, we constrained the constantly locked areas and found that it was limited mainly to a depth of 10\u003cem\u003e\u0026ndash;\u003c/em\u003e20 km, with slip deficit rate changes occurring throughout the entire shallow side adjacent to the locked area.\u003c/p\u003e","manuscriptTitle":"Decadal seafloor geodesy reveals changes in the slip deficit rate along the Nankai Trough","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-16 15:05:04","doi":"10.21203/rs.3.rs-8151000/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revision","date":"2026-01-26T05:41:26+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-12-19T00:51:55+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-11T04:53:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-20T07:22:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth, Planets and Space","date":"2025-11-19T00:15:47+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":"e28bc628-2509-430e-ac65-f67120359b2b","owner":[],"postedDate":"December 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-17T02:24:27+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-16 15:05:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8151000","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8151000","identity":"rs-8151000","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}