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In this study, we developed a regional likelihood model for crustal earthquakes using geodetic strain-rate data from southwest Japan. First, the smoothed strain-rate distributions were estimated from continuous Global Navigation Satellite System (GNSS) measurements. Second, we removed the elastic strain rate attributed to interplate coupling on the subducting plate boundary, including the observed strain rate, under the assumption that it is not attributed to permanent loading on crustal faults. We then converted the geodetic strain rates to seismic moment rates and calculated the 30-year probability for M ≥ 6 earthquakes in 0.2 × 0.2° cells, using a truncated Gutenberg–Richter law and time-independent Poisson process. Likelihood models developed using different conversion equations, seismogenic thicknesses, and rigidities were validated using the epicenters and moment distribution of historical earthquakes. The average seismic moment rate of crustal earthquakes recorded during 1586–2020 was only 13–20% of the seismic moment rate converted from the geodetic data, which suggests that the observed geodetic strain rate includes considerable inelastic strain. Therefore, we introduced an empirical coefficient to calibrate the moment rate converted from geodetic data with the moment rate of the earthquakes. Several statistical scores and the Molchan diagram showed all models could predict real earthquakes better than the reference model, in which earthquakes occur uniformly in space. Models using principal horizontal strain rates exhibited better predictive skill than those using the maximum horizontal shear strain rate. There were no significant differences in predictive skill between uniform and variable distributions for seismogenic thickness and rigidity. The preferred models suggested high 30-year probability in the Niigata–Kobe Tectonic Zone and central Kyushu, exceeding 1% in more than half of the analyzed region. The model predictive skill was also verified by a prospective test using earthquakes recorded during 2010–2020. This study suggests that the proposed forecast model based on geodetic data can improve the regional likelihood model for crustal earthquakes in Japan in combination with other forecast models based on active faults and seismicity.

In this study, short-term slow slip events (SSEs) along the Ryukyu Trench, southwestern Japan were systematically examined using continuous global navigation satellite system (GNSS) data. In total, 130 probable and 93 possible short-term SSEs in the moment magnitude ( M w ) range of 5.6 to 6.8 were identified from January 1997 to November 2013 by GNSS time series offset monitoring and elastic dislocation modeling with a rectangular fault located on the subducting Philippine Sea Plate. The detected short-term SSEs were found to have a variety of characteristic recurrence intervals, magnitudes, durations, and coincidental seismic activities. Short-term SSEs without identified low-frequency earthquakes (LFEs) and low-frequency tremors (LFTs) were found to be common along the Ryukyu Trench. The total slip distributions and SSE numbers were heterogeneous and mostly between 10 and 60 km in depth. Although shallow (depth ≤20 km) short-term SSEs have never been detected along the Nankai Trough, it was notable that such SSEs often occur on the shallow plate interface along the Ryukyu Trench. This may be related to the incomplete interplate locking estimated by various geodetic studies. A band of short-term SSEs in the 20 to 40 km depth range extends from west Shikoku through the Bungo Channel to mid-Kyushu and then fades away around the subducted Kyushu-Palau Ridge. SSEs with accompanying LFEs and LFTs were found to be limited to western Shikoku and the Bungo Channel. We found several distinctive clusters of short-term SSEs, in addition to a cluster previously identified in the Yaeyama Islands. The study also identified a cluster northeast of Kikaijima consisting of 20 repeated SSEs at depths in the vicinity of 10 km near the trench where the Amami Plateau subducts, as well as another cluster southeast of Okinawa Island consisting of 29 M w  ≤ 6.0 SSEs. The results suggest that the distribution of short-term SSEs, as well as that of large earthquakes, is affected by the topography of the subducting plate.

Since November 30, 2020, an intense seismic swarm and transient deformation have been continuously observed in the Noto Peninsula, central Japan, which is a non-volcanic/geothermal area far from major plate boundaries. We modeled transient deformation based on a combined analysis of multiple Global Navigation Satellite System (GNSS) observation networks, including one operated by a private sector company (SoftBank Corp.), relocated earthquake hypocenters, and tectonic settings. Our analysis showed a total displacement pattern over 2 years shows horizontal inflation and uplift of up to ~ 70 mm around the source of the earthquake swarm. In the first 3 months, the opening of the shallow-dipping tensile crack had an estimated volumetric increase of ~ 1.4 × 10 7  m 3 at a depth of ~ 16 km. Over the next 15 months, the observed deformation was well reproduced by shear-tensile sources, which represent an aseismic reverse-type slip and the opening of a southeast-dipping fault zone at a depth of 14–16 km. We suggest that the upwelling fluid spread at a depth of ~ 16 km through an existing shallow-dipping permeable fault zone and then diffused into the fault zone, triggering a long-lasting sub-meter aseismic slip below the seismogenic depth. The aseismic slip further triggered intense earthquake swarms at the updip.

Present day crustal displacement rates can be accurately observed at stations of global navigation satellite system (GNSS), and crustal deformation has been investigated by estimating strain-rate fields from discrete GNSS data. For this purpose, a modified least-square inversion method was proposed by Shen et al. (J Geophys Res 101:27957–27980, 1996). This method offers a simple formulation for simultaneously estimating smooth velocity and strain-rate fields from GNSS data, and it has contributed to clarify crustal deformation fields in many regions all over the world. However, we notice three theoretical points to be examined when we apply the method: mathematical inconsistency between estimated velocity and strain-rate fields, difficulty in objectively determining the optimal value of a hyperparameter that controls smoothness, and inappropriate estimation of uncertainty. In this study, we propose a method of basis function expansion with Akaike’s Bayesian information criterion (ABIC), which overcomes the above difficulties. Application of the two methods to GNSS data in Japan reveals that the inconsistency in the method of Shen et al. is generally insignificant, but could be clear in regions with sparser observation stations such as in islet areas. The method of basis function expansion with ABIC shows a significantly better performance than the method of Shen et al. in terms of the trade-off curve between the residual of fitting and the roughness of velocity field. The estimated strain-rate field with the basis function expansion clearly exhibits a low strain-rate zone in the forearc from the southern Tohoku district to central Japan. We also find that the Ou Backbone Range has several contractive spots around active volcanoes and that these locations well correspond to the subsidence areas detected by InSAR after the 2011 Tohoku-oki earthquake. Thus, the method of basis function expansion with ABIC would serve as an effective tool for estimating strain-rate fields from GNSS data.

Since their discovery over 25 years ago, slow slip events (SSEs) have been regarded as key phenomena for better understanding the characteristics and kinematics of faults. Although ordinary and seismic slow earthquake activities indicate numerous SSE occurrences, the number of SSEs detected by geodetic measurements remains limited in northeast Japan, where the Pacific plate subducts beneath the Okhotsk and Philippine Sea plates. In this study, we focus on short-term SSEs ( S -SSEs) with a duration of several days to weeks and investigate their activity by a systematic detection method and a time series stacking technique using data from Global Navigation Satellite System (GNSS). By applying the systematic detection method to ~ 27-year data, we identified 71 S -SSEs. Most of them are located in the southernmost part of the analyzed region. These isolated distributions are likely attributable to the GNSS station distribution and the subduction of the Philippine Sea plate. In addition, we elucidate the Sanriku and Tokachi-Oki SSEs, which are synchronized with repeating and slow earthquake activities, respectively. We conduct the time series stacking with reference to very low-frequency earthquakes in Tokachi-Oki and average fault model estimation using displacements obtained from the stacked series to discuss their possible location range with their uncertainty. The average displacement field exhibits southeastward displacements in the coastal area, which indicates the occurrence of interplate slip. Although the estimated fault size has a large uncertainty, the average fault model is located offshore Hokkaido and overlaps with the source area of very low-frequency earthquakes, tectonic tremors, and the afterslip of the 2003 Tokachi-Oki earthquake. Our scrupulous data processing and techniques to emphasize deformation signals demonstrate the overlap between the source area of the SSEs and those of other interplate slip phenomena including repeating earthquakes, seismic slow earthquakes, and afterslip. Graphical abstract

The Tohoku-Oki earthquake Detailed analysis of Global Positioning System data from Japan's Geospatial Information Authority network provides a record of coseismic and postseismic slip distribution on the megathrust fault where the magnitude-9.0 Tohoku-Oki earthquake occurred on 11 March 2011. The coseismic slip area stretches some 400 kilometres along the Japan trench, matching the area of the preseismic locked zone. Afterslip is now overlapping the coseismic slip area and expanding into the surrounding regions. The authors conclude that such geodetic data could help to improve the forecasting of earthquake potential along other subduction zones. In the accompanying News & Views, Jean-Philippe Avouac discusses current models for assessing seismic hazard. Most large earthquakes occur along an oceanic trench, where an oceanic plate subducts beneath a continental plate. Massive earthquakes with a moment magnitude, M w , of nine have been known to occur in only a few areas, including Chile, Alaska, Kamchatka and Sumatra. No historical records exist of a M w = 9 earthquake along the Japan trench, where the Pacific plate subducts beneath the Okhotsk plate, with the possible exception of the ad 869 Jogan earthquake 1 , the magnitude of which has not been well constrained. However, the strain accumulation rate estimated there from recent geodetic observations is much higher than the average strain rate released in previous interplate earthquakes 2 , 3 , 4 , 5 , 6 . This finding raises the question of how such areas release the accumulated strain. A megathrust earthquake with M w = 9.0 (hereafter referred to as the Tohoku-Oki earthquake) occurred on 11 March 2011, rupturing the plate boundary off the Pacific coast of northeastern Japan. Here we report the distributions of the coseismic slip and postseismic slip as determined from ground displacement detected using a network based on the Global Positioning System. The coseismic slip area extends approximately 400 km along the Japan trench, matching the area of the pre-seismic locked zone 4 . The afterslip has begun to overlap the coseismic slip area and extends into the surrounding region. In particular, the afterslip area reached a depth of approximately 100 km, with M w = 8.3, on 25 March 2011. Because the Tohoku-Oki earthquake released the strain accumulated for several hundred years, the paradox of the strain budget imbalance may be partly resolved. This earthquake reminds us of the potential for M w  ≈ 9 earthquakes to occur along other trench systems, even if no past evidence of such events exists. Therefore, it is imperative that strain accumulation be monitored using a space geodetic technique to assess earthquake potential.

Using global navigation satellite system (GNSS) data to detect millimeter-order signals of short-term slow slip events (S-SSEs) and to estimate their source parameters, especially duration, is challenging because of low signal-to-noise ratio. Although the duration of S-SSEs in the Nankai subduction zone has been estimated using tiltmeters, its regional variation has never been quantitatively studied. We developed an S-SSE detection method to estimate both the fault model and duration with their errors based on the detection methods developed by previous studies and applied it to a 23-year period of GNSS data in the Nankai subduction zone. We extracted S-SSE signals by calculating correlation coefficients between the GNSS time series and a synthetic template representing the time evolution of an S-SSE and by computing the average of correlation coefficients weighted by the predicted S-SSE signals. We enhanced the signals for duration estimation by stacking GNSS time series weighted by displacements calculated from the estimated fault model. By applying the developed method, we detected 284 S-SSEs from 1997 to 2020 in the Nankai subduction zone from Tokai to Kyushu and discussed their regional characteristics. The results include some newly detected S-SSEs, including events accompanying very low-frequency earthquakes and repeating earthquakes in offshore Kyushu. Our study provides the first geodetic evidence for synchronization of S-SSEs and other seismic phenomena in offshore Kyushu. We estimated the cumulative slip and duration, and their error carefully. We also estimated the average slip rate by dividing the cumulative slip by the cumulative duration. This study clarified that the average slip rate in western Shikoku was approximately twice as that in eastern Shikoku and Kyushu. These regional differences were statistically significant at the 95% confidence interval. Multiple factors can influence the regional characteristics of S-SSEs, and we speculate that the subducting plate interface geometry is one of the dominant factors.

A bstract We study three-point functions of operators on the 1/2 BPS Wilson loop in planar N = 4 super Yang-Mills theory. The operators we consider are \"defect changing operators\", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the S L 2 ℝ symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.

Over the past decade, short-term slow slip events (S-SSEs) have been detected along the entire Nankai Trough using Global Navigation Satellite System (GNSS) data. To enhance the detection of S-SSEs, we focused on the spatial and temporal coincidence of tremors and S-SSEs, a phenomenon known as episodic tremor and slip. We developed a machine learning-based method to detect S-SSEs directly from continuous seismic waveforms and applied it to seismic and geodetic data in western Shikoku, Japan. We trained a random forest regression model using statistical features extracted from continuous seismic waveforms as input variables and GNSS-derived displacement rates as target outputs. We predicted the GNSS displacement rate over a period of ~ 6 years and defined S-SSEs as periods when the predicted GNSS displacement rate increased sharply. We then estimated fault models for each detected S-SSE. The predicted displacement rates were correlated strongly with the observed displacement rates, and we identified a total of 23 S-SSEs, including 5 previously unrecognized events. The results demonstrate the effectiveness of machine learning using continuous seismic waveforms for improving S-SSE detection along the Nankai Trough. Graphical Abstract

Slow earthquakes are episodic slow fault slips. They form a fundamental component of interplate deformation processes, along with fast, regular earthquakes. Recent seismological and geodetic observations have revealed detailed slow earthquake activity along the Japan Trench—the subduction zone where the March 11, 2011, moment magnitude (Mw) 9.0 Tohoku-Oki earthquake occurred. In this paper, we review observational, experimental, and simulation studies on slow earthquakes along the Japan Trench and their research history. By compiling the observations of slow earthquakes (e.g., tectonic tremors, very-low-frequency earthquakes, and slow slip events) and related fault slip phenomena (e.g., small repeating earthquakes, earthquake swarms, and foreshocks of large interplate earthquakes), we present an integrated slow earthquake distribution along the Japan Trench. Slow and megathrust earthquakes are spatially complementary in distribution, and slow earthquakes sometimes trigger fast earthquakes in their vicinities. An approximately 200-km-long along-strike gap of seismic slow earthquakes (i.e., tectonic tremors and very-low-frequency earthquakes) corresponds with the huge interplate locked zone of the central Japan Trench. The Mw 9.0 Tohoku-Oki earthquake ruptured this locked zone, but the rupture terminated without propagating deep into the slow-earthquake-genic regions in the northern and southern Japan Trench. Slow earthquakes are involved in both the rupture initiation and termination processes of megathrust earthquakes in the Japan Trench. We then compared the integrated slow earthquake distribution with the crustal structure of the Japan Trench (e.g., interplate sedimentary units, subducting seamounts, petit-spot volcanoes, horst and graben structures, residual gravity, seismic velocity structure, and plate boundary reflection intensity) and described the geological environment of the slow-earthquake-genic regions (e.g., water sources, pressure–temperature conditions, and metamorphism). The integrated slow earthquake distribution enabled us to comprehensively discuss the role of slow earthquakes in the occurrence process of the Tohoku-Oki earthquake. The correspondences of the slow earthquake distribution with the crustal structure and geological environment provide insights into the slow-earthquake-genesis in the Japan Trench and imply that highly overpressured fluids are key to understanding the complex slow earthquake distribution. Furthermore, we propose that detailed monitoring of slow earthquake activity can improve the forecasts of interplate seismicity along the Japan Trench.