Long‐Living Earthquake Swarm and Intermittent Seismicity in the Northeastern Tip of the Noto Peninsula, Japan

The factors controlling earthquake swarm duration are remain unclear, especially in the long‐living ones. A severe earthquake swarm struck the tip of the Noto peninsula, Japan. Ten M > 4.0 earthquakes occurred, and the sequence has continued more than 4 years. We investigated the spatiotemporal characteristics of the swarm using relocated hypocenters to elucidate the factors causing this long duration. The swarm consists of four seismic clusters—northern, northeastern, western, and southern—the latter of which began first. Diffusive hypocenter migrations were observed in the western, northern, and northeastern clusters with moderate to low diffusivities, implying a low‐permeability environment. Rapid diffusive migration associated with intermittent seismicity deep within the southern cluster suggests the presence of a highly pressurized fluid supply. We conclude that the nature of this fluid supply combined with intermittent seismicity from the southern cluster and a low‐permeability environment are the key causes of this long‐living swarm.

Understanding the causes of earthquake swarm longevity is an important step in elucidating the overall nature of earthquake swarms and assessing the risk to human life when a swarm area is close to anthropogenic activity.
In this study, we examined the driving mechanisms of a long-living earthquake swarm in the northeastern tip of the Noto Peninsula in central Japan (Figure 1). The swarm activity began in May 2018 and has continued for over 4 years. More than 20,000 earthquakes, including three M ≥ 5.0 events, were detected within a 15 km 2 area at the tip of the peninsula. The activity drastically increased in December 2020, and three novel seismic clusters formed in the western, northern, and northeastern areas adjacent to the initial cluster (hereafter referred to as the W, N, NE, and S clusters, respectively) ( Figure 1). The largest earthquake recorded during this timeframe (M5.4) occurred on 19 June 2022 at the west rim of the NE cluster. The focal mechanisms provided by the F-net moment tensor catalog (National Research Institute for Earth Science and Disaster Resilience, 2019a) indicate mostly reverse faults with northwest-southeast compression. These focal mechanisms are comparable to the regional reverse fault-dominated stress field (Terakawa & Matsu'ura, 2010). To reveal the mechanisms perpetuating this long-living swarm, we performed a detailed analysis of the spatiotemporal change in hypocenter distribution using a high-resolution relocated hypocenter catalog.

Hypocenter Relocation
We used the double-difference algorithm (Waldhauser & Ellsworth, 2000) to relocate the hypocenters of 20,542 events detected in the swarm area by the Japan Meteorological Agency (JMA) between May 2018 and June 2022. The magnitudes of the relocated events were greater than or equal to 0.0. We prepared differential-time data using both the travel-time data taken from the unified catalog of JMA and cross-correlation delay times. Calculations using the JMA catalog yielded 497,446 and 490,057 differential-time data for P and S wave, respectively. The number of differential-time data calculated using the P and S waveform cross-correlation delay times was 373,090 and 481,843, respectively. To calculate the cross-correlation, we gathered data on the vertical component waveforms from at least six stations around the swarm area and applied a bandpass filter between 5 and 10 Hz. The time window for P and S waves was before and after 1.0 s of the theoretical travel time. We calculated the cross-correlation function for all event pairs and adopted delay times with the maximum correlation as differential-times. The lower limit of the cross-correlation coefficient was 0.8. We used the JMA2001 1-D velocity model (Ueno et al., 2002), which is routinely used at the JMA for hypocenter determination in Japan. We performed 30 iterations of hypocenter relocation. In the first half of the iterations, the catalog data were weighted 100 times higher than the cross-correlation data to constrain the relative locations of the hypocenters. In the second half of the iterations, we weighted the cross-correlation data 100 times higher than the catalog data to constrain fine-scale structures.

Evaluation of Hypocenter Migration
To determine the hypocenter migration features for comparison with earthquake swarms in other regions, we estimated the diffusivity of hypocenter migration by fitting an isotropic pore-fluid pressure diffusion model proposed by Shapiro et al. (1997). According to this model, the front line of hypocenter migration can be represented as follows: where r [m] is the distance from the diffusion origin, t [s] is the elapsed time from the beginning of diffusion, and D [m 2 /s] is the hydraulic diffusivity. For model fitting, we followed the procedure of Amezawa et al. (2021), which stably estimated the diffusivity of multiple swarms in northeastern Japan using unified criteria. Using Equation 1, the diffusivity D was estimated by linear regression. To extract the front line of hypocenter migration for fitting, we calculated the 95th percentile distance for events that occurred in a 30-day moving time bin that overlapped by 5 days. During curve-fitting, we found that some hypocenter migrations ceased in the middle of the sequence (Figures 2a and 2c). To address this, we performed the theoretical curve fitting using the early-stage seismicity in each cluster that the hypocenter migration can be observed. We set the end-time of the fitting as the date when the cumulative number of events in each cluster reached 30% of the total.
For theoretical curve fitting, we needed to determine the spatial and temporal origins of hypocenter migration. Because the true diffusion origin was unknown, we employed a grid search algorithm to identify it. We separated the swarm area ( Figure 2) into 0.01° × 0.01° × 1.0 km spatial grid points, and prepared temporal origin candidates as the time before the origin time of the first event in each cluster. The temporal origin was searched in 5-day increments within the range of 0-15 days before the first event in each cluster. We then performed theoretical curve fitting on all diffusion origin candidates to identify the best-fitting result.

Results
We successfully relocated 99% of the initial hypocenters (20,399 events). The differential time residuals for the catalog data and cross-correlation data decreased from 134 to 53 ms and from 251 to 4 ms, respectively.  The relocated hypocenter locations revealed the spatiotemporal development of the swarm in detail (Figure 1, Movie S1). Seismic activity initiated deep within (10-15 km) the S cluster and continued for approximately 2 years in almost the same area. On 27-28 December 2020, numerous small earthquakes suddenly occurred deeper (15-20 km) within the S cluster, followed by three novel, swarm-like sequences in areas 5 km west, north, and northeast of the S cluster (W, N, and NE cluster, respectively). The novel activities began in the order of the W, N, and NE cluster ( Figure S1 in Supporting Information S1).
The seismicity characteristics between each cluster are quite different. In the S cluster, small earthquakes (M ≤ 2.0) were predominant (Figures S2a, S2e in Supporting Information S1), and seismic activity was intermittent. The notable features of the hypocenter distribution in this cluster were deep activity (10-20 km) and a corn-like shape (Figures 1c and 1d, and Movie S2). The W cluster was also composed of earthquakes of M ≤ 2.0 (Figures S2b, S2f in Supporting Information S1), but showed continuous seismic activity. The seismicity in the N cluster was consistently energetic, involving more than 10 earthquakes of M ≥ 4.0 ( Figures S2c, S2g in Supporting Information S1) The hypocenter distribution showed many parallel planes approximately 1 km in length striking northeast-southwest and dipping approximately 45° to the east side (Figures 1c and 1f, and Movie S3). Seismicity in the NE cluster was relatively quiet from January-July 2021 ( Diffusive hypocenter migrations were observed over the entire period in the W, N, and NE clusters ( Figure 2). The hypocenter migration diffusivities in the W, N, and NE clusters were estimated to be (9.8 × 10 −2 ± 5.3 × 10 −3 m 2 /s), (9.4 × 10 −2 ± 4.7 × 10 −3 m 2 /s), and (1.2 × 10 −1 ± 3.2 × 10 −3 m 2 /s), respectively. The locations of the diffusion origins are shown in Figures 2d-2f. The time origins were estimated to be 15 days before the first event in any cluster.
To confirm the robustness of the diffusivities and diffusion origins, we also calculated the diffusivity assigning the spatiotemporal origin of hypocenter migration to the first earthquake, showing that the results were not significantly different in both ways ( Figure S3 in Supporting Information S1). These results indicate that despite the trade-off between the spatial and temporal origin, the diffusivities are stably estimated.
Although we could not observe clear diffusive migration throughout the entire period of the S cluster, several intermittent activities with diffusive migration were observed (Figure 3). We roughly estimated the order of diffusivities of them from each first event using the diffusion model (Equation 1). Figure 3b-3i shows examples of intermittent seismic activities, and we found rapid diffusive migrations with very high diffusivity (e.g., D = 2.0 × 10 2 m 2 /s) (Figure 3e).

Discussion and Conclusions
We observed diffusive hypocenter migrations in the swarm. Because diffusive hypocenter migration often occurs in swarms associated with anthropogenic fluid injection (e.g., Shapiro et al., 1997Shapiro et al., , 2002, our observations suggest the presence of fluid in the swarm area. In addition, we found a corn-shaped hypocenter distribution in the deeper part of the S cluster (Figures 1c, 1d, and Movie S2). This characteristic distribution is often present beneath volcanoes and is commonly interpreted as a circular dyke or the collapse of the chamber roof (Acocella, 2007). Although no volcanism has occurred around the swarm area since the Neogene (Ishiyama et al., 2017), there are hot springs with high geothermal gradients (Tanaka et al., 2004) and one with a high 3 He/ 4 He ratio (Umeda et al., 2009) near the swarm area ( Figure S4 in Supporting Information S1). These facts support the inference that mantle-origin fluid exists beneath the swarm area. Recent findings in other studies on this swarm corroborate this suggestion; Nishimura, Nishikawa, et al. (2022) reported crustal deformation around the swarm-there has been 1.2 cm of horizontal displacement and 3.0 cm of uplift during the year since January 2021. They also reported an annual volumetric increase of approximately 2.5 × 10 7 m 3 at a depth of approximately 12 km, assuming a spherical inflation source. Nakajima (2022) performed seismic travel-time tomography around the swarm area and detected a low-velocity anomaly just beneath the S cluster. Considering these facts, we suggest that this swarm is plausibly driven by fluid stored beneath the S cluster migrating through the fractures created by Neogene volcanism.
The swarm was initiated in the S cluster and intensified after the end of December 2020 (Figure 1, Movie S1). We divided the swarm activity into two stages: precursor activity below 5 km depth of the S cluster (Figure 4a,  periods (1) and (2)), and subsequent intense activity involving novel seismicity in other clusters (Figure 4a, period (3)). Herein, we discuss a plausible mechanism for this two-stage activation. As mentioned prior, we believe that a main driving factor of this swarm is the decrease in effective normal stress due to the intrusion of over-pressurized fluid from depth below the S cluster. Figures 4b-4d shows the inferred principal stress profiles during the sequence and Mohr's circle diagrams at two representative depths (see Text S1 in Supporting Information S1 for detailed analysis). In the early stage of the precursor activity ((1) in Figure 4a), fluid supply from more than 15 km deep causes an increase in pore fluid pressure at a depth of approximately 15 km, initiating swarm activity. The stress conditions at this stage are shown in Figure 4b. Subsequent fluid supply further increases the pore fluid pressure within the S cluster, which changes the stress condition, as shown in Figure 4c, to that in Figure 4d (namely, the increase in the pore fluid pressure ratio, ). This model explains the migration of swarm activity to the shallower area (5-10 km) in the S cluster ((2) in Figure 4a). As time passes, the pore fluid pressure eventually exceeds the minimum principal stress ( 3 ) at depth (Figure 4d), which widens the pre-existing fractures.
The reverse fault-type focal mechanism solutions (Figure 1) suggest that the minimum principal stress axis is vertical. We infer that the open cracks both created the pathways of fluid supply and allowed additional supply between the S cluster and the surrounding areas, which enhanced the novel swarm activities in the other clusters ((3) in Figure 4a). Figure 4e shows a schematic diagram of the swarm activity with respect to the creation of fluid pathways and spatiotemporal swarm development. Sill-like horizontal cracks may have formed in the area due to the increased pore fluid pressure. Results from the geodetic analysis assuming a tensile crack source, also support the existence of sill-like structure between S cluster and northern clusters (Nishimura, Hiramatsu, & Ohta, 2022). In this stage, the fluid dissipated toward the other clusters, thus reducing the pore pressure and quiescing the seismic activity in the initial S cluster area (10-15 km depth) (Figures 4a and 4e). Approximately 50 days after the initiation of intense activity in the S cluster, novel seismic activities began in the W, N, and NE clusters beyond approximately 5 km of low-seismicity areas (Figures 1, Figure 4a). If fluid migrated through these low-seismicity areas, assuming density is 10 3 kg/m 3 and dynamic viscosity is 10 −3 Pa ⋅ s (e.g., Talwani et al., 2007), the permeability would be on the order of 10 −8 m 2 . This value is notable higher than the seismogenic permeability (5 × 10 −16 to 5 × 10 −14 m 2 ) estimated for injection-induced seismicity (Talwani et al., 2007). This high permeability implies that rapid, aseismic fluid flow is occurring in these areas.
The swarm exhibits diffusive hypocenter migrations with varying diffusivities. According to previous studies that compiled the diffusivities with earthquake swarms (Amezawa et al., 2021;Chen et al., 2012;Talwani et al., 2007), the diffusivities estimated for the W, N, and NE cluster are moderate to low. These values are smaller than the diffusivities estimated for swarms around active volcanoes (e.g., Shelly et al., 2016;Yukutake et al., 2011). This suggests that swarms in the W, N, and NE clusters have been driven by relatively slow pore fluid pressure diffusion in a low-permeability environment. Ross et al. (2020) imaged the fine 3-D spatiotemporal development of a long-living earthquake swarm in Cahuilla, California. They found strike-parallel channels of relatively high seismicity with hundreds of meters of vertical separation and suggested that a 3-D heterogeneous permeability structure with sub-horizontal permeability barriers in the fault zone controlled the slow spatiotemporal development of the swarm. We also found multiple clear planar hypocenter distributions, such as the one in the N cluster (Figure 1f and Movie S3). This situation is very similar to that in the Cahuilla swarm and suggests strong spatial heterogeneity in the permeability structure in this area. This may be one of the factors contributing to the longevity of the swarm. On the contrary, several intermittent seismic activities in the S cluster showed rapid hypocenter migration with high diffusivity (10 1 -10 2 m 2 /s) (Figures 3d, 3e, 3g, 3h). This is greater than the hypocenter migration associated with the common earthquake swarms described above (10 −3 -10 1 m 2 /s), and less than the diffusion speed of migration of slow earthquakes (10 3 -10 5 m 2 /s) observed at plate boundaries (e.g., Ide, 2010;Kato & Nakagawa, 2020). The former is thought to be related to spatiotemporal changes in pore fluid pressure, including fluid flow (e.g., Shelly et al., 2016;Yukutake et al., 2011), while the latter is thought to reflect stress diffusion (e.g., Ando et al., 2012). Thus, intermittent diffusive seismic activities in the S cluster may be a hybrid of both physical processes or simply the rapid fluid flow in a high-permeability environment. Quantitatively evaluating these processes and their interactions is open for the future work.
The intermittent seismic activity in the much deeper part of S cluster is critically important for understanding this long-living earthquake swarm. We observed rapid diffusive hypocenter migrations, especially after the activation of deep seismicity. Each burst of activity ceased within 10 minutes ( Figure 3). As mentioned above, these rapid diffusive migrations are related to not only diffusive spatiotemporal changes in the stress field, but also diffusive pore fluid pressure changes due to the release of highly pressurized fluid. Furthermore, the geothermal gradient of 80 K/km near the swarm area (Tanaka et al., 2004) and deep hypocenter distribution (Figure 1d) suggest that intermittent seismic activity occurs under a temperature and pressure environment on the order of 10 2 °C and 10 2 MPa, respectively. Thus, we propose two reasons for the intermittent seismic activity: the first is due to the high confining pressure around the deeper part of the S cluster (at least 350 MPa in 15-20 km); as soon as the fluid pressure diffuses, the effective normal stress reduction becomes inadequate for fault failure. The second is the rapid recovery of fault strength due to silica precipitation caused by abrupt depressurization when earthquakes occur (e.g., Amagai et al., 2019;Ujiie et al., 2018;Weatherley & Henley, 2013). These intermittent seismic activities cause the geyser-like fluid supply from the S cluster to diffuse toward the other clusters through the high-permeability (low-seismicity) areas discussed above. Upward hypocenter migrations in depth direction observed in the W, N, NE clusters ( Figure S5 in Supporting Information S1) also support the fluid supply from the deep of S cluster to other shallower clusters. In addition, the relatively small diffusivities observed in the W, N, and NE clusters suggests that once the supplied fluid reaches these areas, its dispersal is slowed by the relatively low permeability, allowing the pore fluid pressure to increase such that seismic activity escalates. Thus, the geyser-like fluid supply from beneath the S cluster coupled with the relatively low-permeability in the other cluster areas has made this swarm a long-living one.

Data Availability Statement
We used hypocenter catalog data provided by the Japan Meteorological Agency (available at https://www.data. jma.go.jp/eqev/data/daily_map/index.html) and the F-net (National Research Institute for Earth Science and Disaster Resilience, 2019a) CMT catalog (https://www.fnet.bosai.go.jp). We also used seismographs observed by the Hi-net (National Research Institute for Earth Science and Disaster Resilience, 2019b), the Japan Meteorological Agency, Kyoto University, and the University of Tokyo. The seismographs were downloaded from the Hi-net website (https://www.hinet.bosai.go.jp). The figures in this paper were generated using Generic Mapping Tools ; https://www.generic-mapping-tools.org). Topographic data used to construct figures were obtained from SRTM15+V2.1 (Tozer et al., 2019). The hypocenter catalog used in this study is available as Data Set S1.