japan volcano case study

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• Published: 03 May 2016

2014 Mount Ontake eruption: characteristics of the phreatic eruption as inferred from aerial observations

• Takayuki Kaneko   ORCID: orcid.org/0000-0001-8499-8354 1 ,
• Fukashi Maeno 1 &
• Setsuya Nakada 1  

Earth, Planets and Space volume  68 , Article number:  72 ( 2016 ) Cite this article

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The sudden eruption of Mount Ontake on September 27, 2014, led to a tragedy that caused more than 60 fatalities including missing persons. In order to mitigate the potential risks posed by similar volcano-related disasters, it is vital to have a clear understanding of the activity status and progression of eruptions. Because the erupted material was largely disturbed while access was strictly prohibited for a month, we analyzed the aerial photographs taken on September 28. The results showed that there were three large vents in the bottom of the Jigokudani valley on September 28. The vent in the center was considered to have been the main vent involved in the eruption, and the vents on either side were considered to have been formed by non-explosive processes. The pyroclastic flows extended approximately 2.5 km along the valley at an average speed of 32 km/h. The absence of burned or fallen trees in this area indicated that the temperatures and destructive forces associated with the pyroclastic flow were both low. The distribution of ballistics was categorized into four zones based on the number of impact craters per unit area, and the furthest impact crater was located 950 m from the vents. Based on ballistic models, the maximum initial velocity of the ejecta was estimated to be 111 m/s. Just after the beginning of the eruption, very few ballistic ejecta had arrived at the summit, even though the eruption plume had risen above the summit, which suggested that a large amount of ballistic ejecta was expelled from the volcano several tens-of-seconds after the beginning of the eruption. This initial period was characterized by the escape of a vapor phase from the vents, which then caused the explosive eruption phase that generated large amounts of ballistic ejecta via sudden decompression of a hydrothermal reservoir.

Mount Ontake in central Japan erupted on September 27, 2014 (Fig.  1 ). The sudden eruption led to a tragedy in which more than 60 hikers on the mountain were killed or went missing. Since the eruption was small and terminated within a short period, details of the mechanisms responsible for hazardous eruptions such as this remain unknown. However, in order to mitigate such volcano-related disasters, we need a thorough understanding of the activity status and stages of progression of volcanic activity.

a Location of Mount Ontake. PAC Pacific plate, PHS Philippine Sea plate, NA North America plate, EUR Eurasian plate. b Topography of Mount Ontake. Kengamine is the summit of Mount Ontake (3067 m ASL). The topographic base map was produced using a GSI map issued by the Geospatial Information Authority of Japan

Mount Ontake erupted for the first time in recorded history in 1979 (Kobayashi 1980 ), and since then, small phreatic eruptions occurred in 1991 and 2007 (Oikawa 2008 ; Oikawa et al. 2014 ). On September 10 and 11, 2014, the frequency of tremors under the volcano increased before subsiding again on September 12 (Japan Metrological Agency (JMA) 2014 ). Then, at 11:52 on September 27, the volcano erupted suddenly from a vent in the Jigokudani valley on the southern side of the summit (JMA 2014 ). The volcanic tremors that began 11 min before the eruption were followed by rapid inflation of the edifice 4 min later (JMA 2014 ). The eruption plume, which resembled cumulonimbus clouds, finally reached a height of approximately 11 km above sea level (ASL; Sato et al. 2015 ), and pyroclastic flows flowed down the slopes. The ballistic ejecta that were generated were considered to be the main cause of the many casualties, according to comments from the local hospital (Nagano Prefectural Kiso Hospital). Metrological radar observations indicated that the explosive phase ceased around 12:40 (Sato et al. 2015 ). As with previous eruptions, the 2014 eruption was considered to be a phreatic eruption, as no fresh magma was contained (Oikawa et al. 2015 ).

This paper attempted to interpret the status and progression of the volcanic activity associated with the 2014 Mount Ontake eruption through aerial observations and to analyze the eruptive processes and mechanisms associated with the phreatic eruption that resulted in the disaster on Mount Ontake.

In this study, analyses of the eruption processes based on erupted materials were complicated by the extensive disturbance and disruption of the original structure of the deposits that were due to the extensive rescue operations and rainfall following the eruption. Specifically, rescue efforts involved extensive excavation of the deposits near the summit, and the rains disrupted large amounts of tephra and ejected materials during the one-month period when access to the site by volcanologists was strictly prohibited. We therefore focused our analysis on aerial photographs taken immediately after the eruption, as these preserved the original situation and structure of the erupted materials and topography, both of which are important for elucidating eruption processes. On September 28, the day following the eruption, between 13:54 and 15:15, one of us (TK) surveyed the volcano from a media helicopter (Chunichi/Tokyo Shimbun Newspaper Co.) and took more than 350 images of the areas affected by the eruption with a digital camera (SONY DSC-RX100M2). In addition to these photographs, we also used many images and videos of the eruption that were captured by hikers and members of the mass media. Together with the eyewitness testimonies, the image information was useful for inferring and refining the temporal relationships among the events associated with the eruption.

Results: characteristics of vents and depositional areas inferred from aerial observations

Distribution and characteristics of the eruption vents.

The eruption vents produced by the 2014 eruption were located on the southwestern side of the summit and oriented along a west-northwest to east-southeast axis (Figs.  1 b, 2 a). The three vent areas included the W1 vent and fissures on the western slope of the Ichinoike cone, the J1–J7 vents in the Jigokudani valley, and the E1 vent west of Ohtakisancho peak. Although the location and general orientation of the vents were similar to those for the 1979 eruption, they had shifted 200–300 m to the south-southwest and had extended by about 300 m to the west-northwest.

a Distribution of the eruption vents on September 28, 2014. b Eruption vents in the Jigokudani valley at 14:13 on September 27 and c at 16:44 on September 27. The topographic base map was produced using a GSI map issued by the Geospatial Information Authority of Japan

Three large, adjacent vents (J3–J5) that appeared to be connected were located on the floor of the Jigokudani valley. On September 28, three smaller vents (J1–J2 and J6) were observed on the valley wall (Figs.  2 a, 3 e; the J7 vent was inactive on the 28th). The large vents were associated with piles of pyroclastic materials and formed a pyroclastic cone on the southern slope of the valley. In the photograph taken at 14:13 on September 27 (Figs.  2 b, 3 a), the J4 vent appeared as it was on September 28 (Figs.  2 a, 3 e); however, the J3 vent appeared somewhat smaller in size, and the J5 vent could not be identified. In the photograph taken at 15:11 (Fig.  3 b), the J3 vent was larger in size, reaching its final shape in the photographs taken at 16:02 (Fig.  3 c), and parts of the J5 vent could be recognized near the eastern side of the valley wall (Fig.  3 c). Thus, these two vents are considered to have formed between 14:13 and 16:02 on September 27. Because no explosive eruption occurred during that time, they are considered to have been generated by non-explosive processes such as the collapse of a part of the vent area into the conduit. Thus, it is likely that the J4 vent was the main vent involved in the eruption on September 27. In the photograph taken at 16:44 (Figs.  2 c, 3 d), a mudflow was observed on the slope of the pyroclastic cone. The mudflow appeared to have effused between 16:02 and 16:44. In the image taken on September 28, the interior of the J4 vent appeared dark, suggesting that it was filled with mud or water. In addition, a rill-like structure formed on the slope of the pyroclastic cone (Fig.  3 e, f), probably due to erosion caused by repeated mudflows from the vent. Small-scale mudflows were also observed, which probably effused from other very small vents and fractures (Fig.  3 a, b).

Photographs of the eruption vents in the Jigokudani valley at a 14:13 on September 27 (Asahi Shimbun), b 15:11 on September 27 (The Mainichi), c 16:02 on September 27 (Asahi Shimbun), d 16:44 on September 27 (Asahi Shimbun), and e 14:46 on September 28 (J2 and J6 are not visible in this photograph). f Close-up of a rill-like structure that originated from the J4 vent

On the western slope of the Ichinoike cone, the fissures generated were arranged along an east–west trending axis, with the W1 vent in the center (Fig.  2 a). Although the W1 vent was not surrounded by a pile of pyroclastic materials, it ejected a fine brownish ash layer that covered the surrounding areas, particularly to the north. In addition, a mudflow was observed to have effused from the vent (Fig.  4 ). All of the fissures emitted fumarolic gas. The E1 vent located 400 m west of Ohtakisancho peak (Fig.  2 a) may have ejected ballistic materials over the surrounding areas, but pyroclastic materials did not appear to have collected around it.

Photographs of the eruption vents and fissures on the western slope of the Ichinoike cone, taken at 14:53 on September 28

Distribution and characteristics of the pyroclastic flows

Pyroclastic flow-like units occurred during this eruption. Although no examples of pyroclastic flow typical of magmatic eruptions were observed, flows comprising a mixture of ash and gas moved down the slope by gravity (Yamamoto 2014 ). We referred to these as “pyroclastic flows.”

Based on images captured by hikers (e.g., Asahi 2014 ), when the initial eruption plume reached an altitude of several hundred meters above the summit, the plume began to expand laterally before flowing down the volcano slopes as pyroclastic flow in almost all directions. Because the temperature of the plume was relatively low, the entire plume may not have been able to rise very high above the volcano. Based on the time at which the dense ashy plume that covered the cottage at the summit had disappeared (Kaito 2014 ), pyroclastic flows are considered to have been generated intermittently until around 12:20 on September 27. Video footage taken by a hiker who was caught in moving pyroclastic flow ( https://www.youtube.com/watch?v=GGTp0bNb608 ) revealed that the flow consisted of aggregated ash particles blowing laterally as in a snow storm. The majority of the pyroclastic flow deposits were distributed within approximately 1 km of the vents, except in the area southwest of the vent (Fig.  5 a).

a Distribution of pyroclastic flow deposits and air-fall ash. b , c , d , f , g with small arrows show the direction or location where b , c , d , f , g were taken, respectively. b The Jigokudani valley viewed from the southwest on September 28. c Distribution axis of air-fall ash extending to the north-northeast, viewed from above the Ninoike cone on September 28. d Close-up of the depositional area of the pyroclastic flow on September 28. e Air-fall ash deposited on a leaf, taken on the evening of September 27 (120 m east-northeast of Shikano-yu ropeway station). f Impact craters and sun cracks (representative cracks are suggested by arrows ) that developed on the ash deposits in Ichinoike on September 28. g Impact craters on the inner wall of the Ichinoike cone, most of which contained water at the bottom and appear to be glistening white because of reflected sunlight. The topographic base map was produced using a GSI map issued by the Geospatial Information Authority of Japan

The pyroclastic flow moved away from the vent in a southwesterly direction along the Jigokudani valley for approximately 2.5 km, as this area was lower than the surrounding areas (Fig.  5 a, b). Areas affected by the pyroclastic flow appeared whitish because of the presence of ash on vegetation (Fig.  5 d). The absence of burned or fallen trees implied that the temperatures and forces associated with the pyroclastic flow events were both low.

Camera footage recorded by the Ministry of Land, Infrastructure, Transport and Tourism, taken from near Takigoshi village on the southern foot of the volcano ( http://www.cbr.mlit.go.jp/tajimi/sabo/ontake/ , https://www.youtube.com/watch?v=jt36uloZ3oI ), revealed that the pyroclastic flow reached a distance of 2.5 km away from the vent at 11:57 about 5 min after the beginning of the eruption. The front of the pyroclastic flow passed through the point of an altitude of 2500 m of the Jigokudani valley around 11:53; thus, it traveled 2.1 km in 4 min. This means that the pyroclastic flow in this area moved at an average speed of 32 km/h (8.8 m/s), which is considered slow for pyroclastic flow (see Cas and Wright 1987 ). Indeed, the pyroclastic flows observed in this study could be considered a kind of pyroclastic surge that is characterized by low speed and low temperature. Similar pyroclastic flows were also observed in the phreatic eruption of Miyakejima on August 29, 2000 (Nakada et al. 2005 ), indicating that this kind of pyroclastic flow might be typical of low-temperature, phreatic eruptions with no magmatic material in the ejecta.

Distribution and characteristics of the air-fall deposits

The height of the eruption plume increased over time and, based on metrological radar observations, was inferred to have reached an altitude of approximately 11 km around 12:10 (Sato et al. 2015 ). Although the plume, precipitating ash over an extensive area, tilted toward the northeast at low altitudes, it moved east-northeast at high altitudes. A mixture of air-fall and pyroclastic flow deposits appears to have settled in the vicinity of the summit.

The depositional axis of the air-fall ash, indicated by a whitish color on the ground, extended to the east-northeast (Fig.  5 a, c). The arrow labeled “e” in Fig.  5 c indicates air-fall ash deposits comprising fine ash particles aggregated with accretionary lapilli (Fig.  5 e); the thickness of this layer was 2–3 mm, and the size of the particles was 1–2 mm.

At the summit of Ichinoike, which was covered by a thick layer of ashy deposits, sun cracks developed on the surface (Fig.  5 f), and water collected in the bottom of the impact craters on the day after eruption, even in those on part of the inner wall of the Ichinoike cone (Fig.  5 g). These findings reveal that the ash (air-fall/pyroclastic flow) was enriched with water components, corroborating the observation of accretionary lapilli. According to a hiker at the summit, although the ash was initially dry, it became wetter, taking on the form of “mud rain” in the final stages (Kaito 2014 ). In video footage taken immediately after the eruption ( https://www.youtube.com/watch?v=ODiqlpUwcVM ), the top 1–2 cm of the few tens-of-centimeters of ash that was deposited near the summit appeared wet and semisolid, looking dark in color. This water is considered to have been derived from the precipitation of water vapor contained in the eruption plume.

Distribution of ballistic ejecta

The phreatic eruption of Mount Ontake generated large amounts of ballistic ejecta. According to a hiker who sought shelter in the cottage at the summit, the generation of ejecta continued intermittently for about 1 h (Kato 2014 ). This report is concordant with the morphological variation observed in the impact craters produced by the ballistic ejecta, which included craters with both well-defined and indistinct outlines (Fig.  5 f).

Instead of actual ballistic ejecta, which are difficult to identify directly, the distribution of ballistic ejecta was inferred based on the distribution of impact craters in the photographs taken on September 28 (Figs.  6 , 7 ). Impact craters were identified based on the outline and concave topography suggested by the effect of shading in the photographs. In each photograph, the scale of the scene was estimated by matching characteristic topographic features including large rocks to the locations on topographic map using Google Maps/Google Earth and GSI Maps (Geospatial Information Authority of Japan— http://maps.gsi.go.jp ). Based on the estimated scales, 5 × 5 m areas were selected on each photograph to count the number of impact craters (Fig.  7 ). The size of impact craters and ballistics was also estimated based on the scale obtained here and characteristic objects in the same scene, such as statues, monuments, stone stairs, or rescue workers.

Distribution of impact craters generated by ballistic ejecta. Zone A : N  ≥ 10 impact craters per 5 × 5 m, Zone B : 9 ≥  N  ≥ 3, Zone C : 2 ≥  N  > 0, Zone D : N  = 0. The dotted line in the middle shows the long axis of the distribution of impact craters. The topographic base map was produced using a GSI map issued by the Geospatial Information Authority of Japan

Appearance of impact craters in each zone. Numbers in circles show the location of the areas in Fig.  6

The diameters of impact craters ranged between several tens-of-centimeters to 1 m, while those of ballistic ejecta ranged from 10 cm to several tens-of-centimeters (maximum c. 1 m). The distribution density was classified into four zones, based on the number of craters per unit area (5 × 5 m); these zones were called Zones A, B, C, and D, with Zone A having the highest density of impact craters and Zone D having no impact craters. Because the distribution density of craters decreased with increasing distance from the vents, the distribution density was very high between Kengamine and Ichinoike (Fig.  7 , Zone A ➀ – ➂ ). The furthest impact crater was located at Ninoike pond, 950 m from the vents in the Jigokudani valley (Fig. 7 , Zone C ➈ ). We were unable to survey the distribution of impact craters in the area to the south of the vents because they were obscured by the volcanic plume at the time the observations were made, and the deposition of ash layer was too thin to leave clear crater structures by impact.

The distribution of craters was not isotropic but slightly extended in a north-northeasterly direction (dotted line in Fig.  6 ). Because the Jigokudani valley extends along a north-northeast to south-southwest axis, and because the vents are located on the valley floor, it is possible that the valley walls acted as barriers to ejecta, preventing ballistics from being ejected far beyond the valley walls along both sides of the valley.

Discussion: occurrence of ballistic ejecta and mechanism of phreatic eruption

Estimation of the initial velocity of ballistic ejecta.

Initial velocity estimates for ballistic ejecta were made based on their distribution. The furthest impact crater was located 950 m from the J4 vent in the Jigokudani valley; however, it was reported that ballistic ejecta reached the Ninoike-Honkan cottage approximately 1000 m north-northeast of the vents. Assuming an ejection angle of 45° and a horizontal travel distance of 1000 m, the initial velocity was estimated to be 99 m/s based on a simple ballistic trajectory calculation without air resistance and vertical dip. Assuming that the ejection angles were random, this estimate is considered to reflect the maximum initial ejecta velocity. More precisely, because the J4 vent was located at an altitude of 2750 m and the point of impact—the Ninoike-Honkan cottage—was at 2900 m, the maximum initial velocity was estimated to be 111 m/s with an ejection angle of 49° (Fig.  8 a) using the ballistic calculator software “Eject!” (Mastin 2008 ). In this calculation, the following conditions were used: block shape, sphere; density, 2500 kg/m 3 ; diameter, 0.2 m; speed of tailwind, 0 m/s; extent of zone of reduced drag, 0 m; temperature at sea level, 25 °C; and thermal lapse rate, 6.5 °C/km. The value for the diameter was adopted in reference to the size of the ballistic that hit the Ninoike-Honkan cottage (17 cm, Cabinet Office 2015 ). Here, even if we assumed the diameter to be 1 m, the estimated initial velocity would be 108 m/s. Compared to some magmatic eruptions, the maximum initial velocity and the maximum distance estimates associated with this eruption are relatively small. For example, ballistic ejecta generated by the 2011 Shinmoedake eruption traveled 3.4 km and had initial velocities of 240–290 m/s (Maeno et al. 2013 ).

Schematic illustrations showing the estimation of velocity and flight duration of ballistic ejecta based on the ballistic calculator software, “Eject!” (Mastin 2008 ). a Estimation of the initial velocity of ejecta that traveled the furthest. b Estimation of initial and final velocities and minimum and maximum flight durations of ballistic ejecta that traveled to Kengamine, where many people were killed on impact

Relationship between the occurrence of the eruption plume and impacts of ballistic ejecta

The eruption plume increased in size shortly after the eruption and reached a height of several hundred meters above the summit (Kengamine; Fig.  9 a). In that time, very little ballistic ejecta landed near the summit, where many people were killed on impact. Based on the time taken to reach a maximum height of approximately 11 km at 12:10 (Sato et al. 2015 ), the average upward speed of the eruption plume was estimated to be 400–500 m/min. If we assume that the altitude of the top of the eruption plume in the photograph shown in Fig.  9 a was 3200 m, then this photograph is considered to have been taken about 1 min after the beginning of the eruption. Ballistic ejecta with the shortest flight durations are estimated to have landed on the summit (elevation: 3000 m; travel distance: 450 m) with a final velocity of 58 m/s about 7.7 s after ejection from the vent at an initial velocity of 93 m/s with an ejection angle 50° (Fig.  8 b, case A). Ballistic ejecta with a maximum velocity of 111 m/s are estimated to have landed on the summit 18.5 s after ejection (ejection angle: 76°) with a final velocity of 79 m/s (Fig.  8 b, case B), which is considered to represent the maximum flight duration. This means that large amounts of ballistic ejecta likely occurred several tens-of-seconds after the beginning of the eruption and that initially the eruption plume comprised a mixture of ash and gas that was ejected from the vents. This corroborates the eyewitness accounts of hikers at the summit who stated that the eruption plume rose soundlessly and that an explosion was only heard about 1 min after the beginning of the eruption (e.g., Tsuno 2014 ). The cluster of ballistic ejecta shown in Fig.  9 b would have been the first cluster to land on the summit several seconds after this photograph was taken.

a Growing eruption plume photographed immediately after the beginning of eruption. This photograph was taken by the late Noguchi I from Kengamine at the summit of Mt Ontake. b Close-up of the photograph. Arrows indicate a cluster of ballistics

The volcanic tremor and inflation of the edifice that occurred 11 and 7 min before the eruption, respectively, are considered to have been caused by the sudden migration of the vapor phase, comprising water vapor and other gasses, to shallower depths (Kato et al. 2015 ). The initial phase of the eruption may therefore have been caused by the ejection of this vapor phase to the surface at 11:52 on September 27; however, the ejection of this gas phase did not generate large amounts of ballistic ejecta, probably because the intensity of the resulting explosion was too low. The removal of a large amount of the vapor phase from a hydrothermal reservoir in which the water–vapor system is in equilibrium can cause rapid boiling (bumping) of water due to a decrease in the boiling temperature via sudden decompression of the system (Taniguchi and Ueki 2014 ). This likely caused the explosive phase of the eruption, which then generated a cluster of ballistic ejecta, several tens-of-seconds after the initial phase of the eruption. The occurrence of rapid boiling and the accompanying explosions may have gradually propagated to the deeper parts of the hydrothermal system, resulting in the intermittent generation of ballistic ejecta during the explosive phase of the eruption, which continued for approximately 1 h.

Concluding remarks

We clarified the eruptive processes and mechanisms associated with the 2014 Mount Ontake eruption using aerial photographs taken the day after the eruption as well as other information. The conclusions of the study can be summarized as follows:

The vents involved in the eruption on the southwestern side of the summit are arranged along a west-northwest to east-southeast axis, which is sub-parallel to the axis of the vents involved in the 1979 eruption.

Among the three major vents on the floor of the Jigokudani valley, the vent at the center (J4) was the main vent involved in the eruption on September 27, with the other vents likely forming as a result of non-explosive processes on the following day.

The pyroclastic flow travelled about 2.5 km along the Jigokudani valley at an average speed of 32 km/h. Since no burned or fallen trees were observed in this region, it appears that the temperature and destructive force associated with the pyroclastic flow were low.

The distribution of ballistic ejecta was inferred from impact craters, and the furthest impact crater was located 950 m from the vents, although the furthest ballistic was found at the mountain cottage, located 1000 m from the summit. Based on ballistic models, the maximum initial velocity of the ejecta was estimated to be 111 m/s.

Immediately after the beginning of the eruption, very few ballistic ejecta were observed around the summit, even though the eruption plume had risen above the summit. Based on this observation and the relationship between the speed of upward expansion of the eruption plume and the minimum flight duration of ballistic ejecta that landed on the summit, the generation of large amounts of ballistic ejecta is considered to have occurred several tens-of-seconds after the beginning of the eruption, probably in relation to the explosion mechanism of the hydrothermal reservoir deep under the volcano.

The results of this study show that, in the case of phreatic eruptions, there is a window of several tens-of-seconds before the first cluster of ballistic ejecta arrives. In the Mount Ontake 2014 eruption, ballistic analysis revealed that the final velocity of ejecta at the time of landing ranged between 58 and 79 m/s (209 and 284 km/h) near the summit. Anyone struck by such ejecta could be seriously injured. Thus, when hiking on volcanoes that have undergone repeated phreatic eruptions, it is important to minimize the amount of time spent near vents and to be aware of structures that can be used for protection, such as mountain cottages, large rocks, or shelters. Furthermore, in the event of an eruption, it is important to avoid centers of volcanic activity and to seek shelter during the time window before ballistic ejecta are generated.

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Authors’ contributions

TK took aerial photographs and analyzed them with FM. SN helped draft the manuscript. All authors read and approved the final manuscript.

Acknowledgements

We thank the Chunichi/Tokyo Shimbun Newspaper Co. and Usami A for the opportunity to observe the volcano from a helicopter and Noguchi H for permitting us to use photographs of the eruption that were taken by her husband, the late Noguchi I. We are also very grateful to the reviewers, Yoshimoto M, and an anonymous reviewer, whose comments were useful for improving the manuscript. This work was supported in part by a Grant-in-Aid for Scientific Research (A) from the Japan Society for the Promotion of Science KAKENHI (Grant No. 23241055 to TK).

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Kaneko, T., Maeno, F. & Nakada, S. 2014 Mount Ontake eruption: characteristics of the phreatic eruption as inferred from aerial observations. Earth Planet Sp 68 , 72 (2016). https://doi.org/10.1186/s40623-016-0452-y

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Received : 20 November 2015

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DOI : https://doi.org/10.1186/s40623-016-0452-y

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• Y. Yukutake   ORCID: orcid.org/0000-0002-1533-4885 5 &
• T. Kumazawa   ORCID: orcid.org/0000-0003-2435-640X 3  

Scientific Reports volume  13 , Article number:  10562 ( 2023 ) Cite this article

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• Environmental sciences
• Natural hazards
• Solid Earth sciences

The relation between earthquakes and volcanic eruptions, each of which is manifested by large-scale tectonic plate and mantle motions, has been widely discussed. Mount Fuji, in Japan, last erupted in 1707, paired with a magnitude ( M )-9-class earthquake 49 days prior. Motivated by this pairing, previous studies investigated its effect on Mount Fuji after both the 2011 M 9 Tohoku megaquake and a triggered M 5.9 Shizuoka earthquake 4 days later at the foot of the volcano, but reported no potential to erupt. More than 300 years have already passed since the 1707 eruption, and even though consequences to society caused by the next eruption are already being considered, the implications for future volcanism remain uncertain. This study shows how volcanic low-frequency earthquakes (LFEs) in the deep part of the volcano revealed unrecognized activation after the Shizuoka earthquake. Our analyses also show that despite an increase in the rate of occurrence of LFEs, these did not return to pre-earthquake levels, indicating a change in the magma system. Our results demonstrate that the volcanism of Mount Fuji was reactivated by the Shizuoka earthquake, implying that this volcano is sufficiently sensitive to external events that are considered to be enough to trigger eruptions.

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Introduction.

When earthquakes accompany volcanic eruptions, there is the possibility of a causal relationship between them 1 , 2 . Many researchers studied how volcanic eruptions are triggered by earthquakes 3 , 4 , 5 , 6 , 7 , 8 , motivated by a physical viewpoint in which the stress 7 and/or strain 8 of an eruption needs to change, with earthquakes causing rapid and sometimes large changes in that stress and/or strain. We draw on a specific case in California, where the 1992 Landers earthquake triggered seismicity at very large distances, including the magmatically active Long Valley caldera region, which also experienced a significant coincident deformation transient 5 , 6 . Another case 1 complements the search for direct evidence of the pairing of earthquakes and eruptions, having examined the historical record of large earthquakes and explosive eruptions to show that eruptions occurred in the vicinity of a large earthquake more often than is expected by chance 7 . In contrast, many large earthquakes have no immediate effect on volcanoes.

The March 11, 2011 magnitude ( M ) 9.0 Tohoku, Japan earthquake and the following large earthquakes that occurred in eastern Japan caused large changes in stress/strain (Fig.  1 a). The Japan Meteorological Agency (JMA) 9 reported active seismicity in about 20 volcanoes after this earthquake, although no eruptions occurred. Recent studies 10 , 11 , 12 that examined seismic waveforms revealed the detailed behavior of seismic activation beneath the Zao volcano and quiescence beneath the Azuma and Nasudake volcanoes in northeastern Japan after the Tohoku earthquake. Another study 13 , which also examined seismic waveforms, showed remotely-triggered and unrecognized seismicity in the Hakone volcano in central Japan at an epicentral distance of 450 km from the Tohoku earthquake.

Mount Fuji and Japanese earthquakes. ( a ) Map showing Mount Fuji (red triangle) and the source area of the Tohoku earthquake (rectangular area surrounded by broken lines) 70 . Active volcanoes are indicated by black triangles. Grey dots indicate LFEs in the JMA catalog. ( b ) Left panel shows LFEs (grey circles) around Mount Fuji (summit is indicated by a triangle). Black circles indicate 87 template LFEs. The source area of the Shizuoka earthquake is indicated by a rectangular area 19 . Right panel shows a cross-sectional view of the LFEs and the source area. ( c ) M -time diagram of LFEs (y-axis on the left side). Overlapped is the cumulative number of LFEs as a function of time since 2003 (y-axis on the right side). Vertical line indicates the moments of the Tohoku and Shizuoka earthquakes, which overlap. ( d ) Same as ( c ) for a zoom-in plot at times before and after both earthquakes from 2011.1, as a decimal year (Feb. 6, 2011, 12:00:00) to 2011.3, as a decimal year (Apr. 20, 2011, 12:00:00).

Mount Fuji is the Japan’s highest mountain and is also an active volcano. In addition, it has repeatedly erupted, causing lava flows into its vicinity several times. In 1707, the large Hoei eruption during the Hoei era also deposited volcanic ash in Tokyo on the east side of Mount Fuji 14 , 15 , 16 . In the approximately 300 years since that eruption, Mount Fuji has not erupted and volcanic activity has been low, so the risks of eruption-related disasters caused by Mount Fuji have been neglected. However, a swarm of volcanic low-frequency earthquakes (LFEs) from the fall of 2000 to the spring of 2001 17 changed this situation completely, and the possibility of eruption-related disasters by Mount Fuji has been reassumed while disaster response plans have been developed to counter them 18 . Therefore, it can be stated that the importance of monitoring the volcanic activity of Mount Fuji is increasing.

Mount Fuji exhibited increased seismicity, culminating in the triggered M 5.9 earthquake that occurred in Shizuoka prefecture 4 days after the Tohoku earthquake. This volcano experienced the 1707 M 9-class Hoei earthquake 49 days prior to its eruption. This unique experience led to an evaluation of the Tohoku and Shizuoka earthquakes 19 , revealing that crustal deformation due to these earthquakes induced changes in stress of Mount Fuji’s magma reservoir in the order of 0.001–1 MPa. The values are considered to be sufficient to trigger an eruption, if that magma is ready to erupt 20 , 21 . However, no LFEs were reportedly activated, suggesting that Mount Fuji did not have the potential to erupt 9 , 19 . It is not easy to characterize LFEs that are ubiquitous and indicative of seismic activities in the deep parts of volcanoes due to their low signal-to-noise ratio 22 .

This study was motivated by previous studies 10 , 11 , 12 , 13 , which suggested that the source mechanism of LFEs was quite important to interpret the impact of large earthquakes on the activity of LFEs and deep magmatic processes. We examined if no LFEs beneath Mount Fuji were indeed activated immediately following the Tohoku and Shizuoka earthquakes. A seismic catalog produced in this study revealed that there were LFEs just after the Shizuoka earthquake. Moreover, seismic activation due to this earthquake continued for at least the next eight years, confirmed by using data until 2019. Evidence was shown that the Shizuoka earthquake and crustal deformation 19 triggered reactivation of the volcano. Given that Mount Fuji is sensitive to such external influences, it is important to carefully monitor its development, especially when events external to the volcano might cause a disturbance.

In this section, we examine the temporal change in the activity of LFEs beneath Mount Fuji, Japan, and discuss the possibility of an increase in magmatic activities in the lower crust which was triggered by the 2011 Tohoku and Shizuoka earthquakes. We first obtain new catalogs of LFEs, and then apply statistical analyses to examine the temporal changes in LFE activity. Based on the results of these analyses, we conclude that the change in stress caused by the 2011 Shizuoka earthquake enhanced the creation of fractures and resultant change in activity of LFEs around the deep magma reservoir in the lower crust. We also suggest that the activation of LFEs may reflect the sensitivity of Mount Fuji to external disturbances and that the volcano may have the potential to erupt after a 300-year quiescent period.

First, we show the influence of the 2011 Japanese earthquakes on LFEs manifested in the magma system of Mount Fuji. Second, we offer support that this magma system was disturbed due to such events, which played a role on activated LFEs. For inference on volcanic hazards of Mount Fuji, implications for future volcanism based on our observations will be discussed later.

Influence on LFE activity after the 2011 Japanese earthquakes

To resolve the difficulty in detecting LFEs by conventional event‐detection methods, we produced seismicity catalogs using the matched-filter (MF) method, which cross-correlated a template to continuous seismic signals 22 , 23 , 24 , 25 , 26 (details of the “ MF method ” in “ Methods ” and Supplementary Figs. S1 – S4 ). In this method, which considers a continuum of seismic signals, an LFE is identified when the timing of a seismic signal and the timing of a template signal overlap. Our resultant catalog includes ~ 16,000 LFEs (Supplementary Fig. S1 ) whose correlation coefficients ( CC ) to quantify signal similarity range from 0.1 (poor correlation) to 1 (strong correlation and most likely a template LFE). Histograms of CC -values show a tall peak at CC  ~ 0.2 (Supplementary Fig. S1 ). The minimum threshold for CC ( CC th ), above which LFEs are used for subsequent analysis, should be above the upper noise limit. A low CC th would result in a large number of false detections while a high CC th would result in a reduced number of available LFEs. We selected CC th  = 0.25, at the 2-sigma level of a normal distribution, as is expected for the random correlation between signal and noise 27 , 28 , 29 . Higher values of CC th  = 0.3, 0.35, and 0.5 above the 3-sigma level were also considered to examine the dependence of the result on CC th . Mainly the results for CC th  = 0.25 are shown in the text.

The number of LFEs in our catalog of CC th  = 0.25 is about three times larger than in the JMA catalog, which lists about 2,000 LFEs detected in 2003–2019 by a conventional method that is not based on CC (Figs. 1 c and 2 a). Our catalogs of CC th  = 0.25, 0.3, and 0.35 include LFEs immediately after the Shizuoka earthquake (Fig.  2 a and Supplementary Fig. S1 ) while the JMA catalog does not (Fig.  1 d). One may see that there are just a handful of LFEs next to the line that indicates the timing of the Shizuoka earthquake (Fig.  2 b). There may be doubts as to whether high-frequency (ordinary) aftershocks were mis-detected as LFEs, since the source area of the Shizuoka earthquake and the occurrence area of LFEs were close to each other (Fig.  1 b). If CC th was selected to be below the upper noise limit, there would be a chance that our catalogs inadvertently included many non-volcanic seismic events. However, our choice of CC th (= 0.25, 0.3, 0.35) indicates that events with low-frequency signals truly occurred immediately after the Shizuoka earthquake. Given that the number of LFEs in our CC th  = 0.5 catalog is about one-fourth of that in the JMA catalog (Supplementary Fig. S1 ), there were no LFEs immediately after the Shizuoka earthquake.

MF method of LFEs. ( a ) Same as Fig.  1 c,d for LFEs in the MF catalog ( CC  > 0.25). ( b ) Top panel: ΔAIC = AIC single  − AIC 2stage as a function of T c since 2003, where LFEs ( M  ≥ 0.3) in the MF catalog ( CC  > 0.25) (black) and LFEs ( M  ≥ 0.5) in the JMA catalog (grey) were used. The minimum magnitudes ( M th  = 0.3 and 0.5) for the MF and JMA catalogs, respectively, were used, taking homogeneity of seismicity recordings of both catalogs into consideration (details of catalog quality evaluation in “ Methods ”). Small points show that the model-fitting analysis did not converge when assuming the corresponding T c . As a reference, thin vertical lines indicate Jan. 1 for 2004–2019. The timings of the Tohoku and Shizuoka earthquakes overlap, showing a single thick vertical line. Horizontal dashed lines representing 2 q for the MF and JMA catalogs overlap, where q is the degree of freedom imposed when searching T c based on the data over the entire period (see “ Methods ” for details of the ETAS model). Bottom panel: same as the top panel for zoom-in from Feb. 6, 2011, 12:00:00 to Apr. 20, 2011, 12:00:00.

The cumulative number of LFEs as a function of time in Fig.  2 a shows that the rates of occurrence changed around the moments of the Tohoku and Shizuoka earthquakes. To support the observation that either earthquake very likely played a role in reactivation, a statistical analysis was conducted. We introduced the epidemic type aftershock sequence (ETAS) model 30 , assuming that this model, which was originally developed for ordinary earthquakes, was applicable to LFEs (details of the ETAS model in “ Methods ”). Even though the ETAS model provides a good fit to standard earthquake occurrence, it is known that transient non-standard cases are poorly fitted by the standard ETAS model 31 , 32 , 33 . We focused on differences between the standard ETAS model and an extended two-stage ETAS model, which covers non-standard cases in fitting LFE timeseries, whereas the two-stage ETAS model is the simplest alternative to the standard model 32 , 33 . This two-stage model assumes different parameter values in subperiods before and after a particular time (change point, T c ), and the whole period is divided into two adjoining periods to fit the ETAS models separately. This is best applied to cases where there is a clear-cut time instant across which ETAS parameter values change 32 , 33 . To test whether or not there are changes in seismicity pattern at T c in a given period, the problem of model selection is reduced by using AIC (Akaike Information Criterion) 34 . We compared AIC single (AIC for a single ETAS fitting) with AIC 2stage (AIC for a two-stage ETAS fitting) to select the model with the smaller value, where AIC 2stage  = AIC 1  + AIC 2 (AIC 1 and AIC 2 for fitting to the 1st and 2nd subperiods, respectively).

ΔAIC (= AIC single  − AIC 2stage ), as a function of T c during 2003–2019 (Fig.  2 b), shows that the two-stage ETAS model was much better than the single ETAS model, indicating that the most significant T c was around the time of the Tohoku and Shizuoka earthquakes. This feature was observed regardless of the CC th value (Supplementary Fig. S5 ). There was a pronounced discontinuation in smoothing at the time of the Shizuoka earthquake due to triggered LFEs for CC th  = 0.25 (Fig.  2 b), 0.3, and 0.35, but this was not the case for CC th  = 0.5 due to few LFEs around the time of the Shizuoka earthquake. AIC when the JMA catalog was used (grey data in Fig.  2 b) also showed a better (but insignificant) outcome when the two-stage ETAS model, rather than the single ETAS model, was used (Supplementary Fig. S5 ). Namely, ΔAIC was higher than 0 (ΔAIC > 0) when T c was around the time of the Shizuoka earthquake, but it was below the horizontal dashed line in Fig.  2 b. This line indicates a hurdle to the selection of the two-stage ETAS model, given that T c was searched from the data during 2003–2019 32 , 33 .

Visual inspection of T c immediately before the Shizuoka earthquake confirmed that fitting by the two-stage ETAS model (Fig.  3 a,b) was better than that by the single ETAS model (Fig.  3 c). An AIC 1 of 216.7, when seismicity since 2003 until immediately before the Shizuoka earthquake was fitted, shows that the occurrence rates (black) were significantly larger than the extrapolated rates (red) after the Shizuoka earthquake (Fig.  3 a). This significant difference continued until more recent times (until 2019). This continuation (AIC 2  = − 4234.6) (Fig.  3 b) was confirmed by switching fitting and extrapolating periods. The fitting of the single ETAS model to seismicity during the entire period (AIC single  = − 3969.4) was visually poor (Fig.  3 c), with ΔAIC = 48.5 {= − 3969.4–(216.7–4234.6)}.

Change point analysis of LFEs. ( a ) Cumulative function of M  ≥ 0.3 LFEs is plotted against ordinary time (left panel) and transformed time (right panel), showing the ETAS fitting in the target interval from 2003 until immediately before the Shizuoka earthquake and then extrapolated until July 2019. The parabola represents the 95% confidence intervals of the extrapolation. Note that K 0  = 4.51 × 10 –5 for M  = 2 (details in the ETAS model in “ Methods ”), although “ K 0  = 0.00” is shown in the graph. The smaller panel below each larger panel indicates an M -time diagram. ( b ) As in ( a ) except that the target is the later time interval after the Shizuoka earthquake. Because K 0  = 6.16 × 10 –5 obtained is too small, it is shown as “ K 0  = 0.00” in the graph. ( c ) As in ( a ) except that the target is the entire time interval.

Disturbed magma system plays a role on activated LFEs

A challenge in exploring the reason for the changes in the rate of occurrence of LFEs (Figs. 2 and 3 ) is that the magma system, which is underground, i.e., beneath Mount Fuji, and directly unobservable, results in highly clustered and heterogeneous occurrence times of LFEs. A solution to this problem is to take a reductionism approach, by decomposing LFEs into primary LFEs and secondary-triggered LFEs. Measuring the occurrence rate of the former LFEs (indicative of Poisson background activity) and the latter LFEs (indicative of aftershock activity), allows the magma system and the interactions (triggering) among LFEs to be inferred. The ETAS model can be applied to offer a solution 30 , 31 , 32 , 33 . In the ETAS model 30 , seismic activity is expressed by two terms, one for Poisson background activity and another for aftershock activity, assuming that each earthquake (including the aftershocks of another earthquake) is followed by aftershocks (details of the ETAS model in “ Methods ”).

As a preliminary analysis, we examined whether decomposing the LFE sequence was really meaningful, i.e., if secondary triggering played a role in the LFE sequence. Using AIC for the two-stage ETAS model (same model as for Fig.  2 b and Supplementary Fig. S5 ) and the two-stage Poisson model (same as the two-stage ETAS model except that the aftershock activity term was ignored), we compared the goodness-of-fits between them applied to the same dataset. For this comparison, the same procedure as for Fig.  2 b and Supplementary Fig. S5 was used except that the single ETAS model was replaced by the two-stage Poisson model. The difference in AIC between the ETAS and Poisson models shows that the former model is superior to the latter one (Supplementary Fig. S6 ), indicating that the aftershock activity term is not negligible. This result allowed us to examine whether or not the changes in occurrence rate were due to enhanced Poisson background and aftershock activities (Fig.  4 and Supplementary Table S1 ).

Background and aftershock seismicity. ( a , b ) μ and K 0 as a function of CC th , calculated for two time-windows before Jan. 1, 2011 (solid line) and after Dec. 31 2011 (broken line). We considered the minimum magnitudes M th  = 0.2 (blue), 0.3 (red), and 0.4 (green). Other ETAS parameters ( c , p , and α) are constants irrespective of different values for time windows, M th , and CC th : ( c , p , α) = (0.0015, 2.80, 0.5). Open circles indicate that the model-fitting analysis did not converge well, resulting in large errors. See “ Methods ” for details of time-dependent μ and K 0 and Supplementary Table S1 .

We used μ (a solo parameter of the Poisson background activity term of the ETAS model) and K 0 (a parameter representing clustering aftershock productivity and one of the four parameters of the aftershock activity term), while the other three parameters were constants. For details of these parameters, see the ETAS model in “ Methods ”. In Fig.  4 , μ and K 0 were significantly larger after than before 2011 (details of time-dependent μ and K 0 in “ Methods ” and Supplementary Table S1 ). Moreover, μ and K 0 increased with decreasing CC th for both periods, before and after 2011. This indicates that small- CC LFEs identified by relaxing the event identification protocol contributed to both the Poisson background activity and the aftershock activity. The μ-pattern was not sensitive to switching from K 0 (Fig.  4 and Supplementary Table S1 ) to other parameters (details of time-dependent μ and K 0 in “ Methods ” and Supplementary Fig. S7 and Tables S2 and S3 ). Our results show the contribution of enhanced background and aftershock activities to the increase in occurrence rate of LFEs, and support the possibility of changes in the magma system due to the Shizuoka earthquake.

The bottom panel of Fig.  2 a shows that the high rate of LFEs after the Shizuoka event decreased as a function of time, implying that LFEs behaved as aftershocks of the Shizuoka event. Therefore, it may be considered that the background rate of LFEs was globally similar to what was observed before 2011. However, this is not true because μ before 2011 was smaller than after 2011 (Fig.  4 a) and because the two-stage ETAS model performed better than the single ETAS model, which included the Shizuoka earthquake (Fig.  2 b). A clear change in LFE activity during the occurrence of the Shizuoka earthquake indicates the contribution of the changes in both aftershock and background activities.

If there was to be a disturbance in the magma system, it might induce differences in template LFEs between pre- and post-Shizuoka-quake sequences, allowing differences in detected LFEs between them. A simple test (top panel of Fig.  5 ) was conducted to assess this possibility, revealing that templates in the pre- (post-) Shizuoka-quake sequence were likely applicable for detecting LFEs in the same sequence. Figure  5 (bottom panels), which shows examples from two individual template LFEs, highlights this difference. The feature was not sensitive to CC  > 0.25, 0.3, 0.35 and 0.5 (Supplementary Fig. S8 ). LFEs before/after 2011 were mostly detected by templates in the same time periods.

Temporal changes of LFE pattern. Top panel: same as Fig.  2 a except for the separation between LFEs (orange dots) detected by a correlation with waveforms of template LFEs (orange cross) listed in the JMA catalog before the Tohoku earthquake and LFEs (blue dots) by a correlation with waveforms of template LFEs (blue cross) after the Shizuoka earthquake. Bottom left panel: same as the top panel for highlighting LFEs detected by using an exemplified template LFE before the Tohoku and Shizuoka earthquakes (vertical line). Bottom right panel: same as the bottom left panel, but after these earthquakes.

In this test (top panel of Fig.  5 ), the two time-windows before and after the Shizuoka earthquake were chosen. It is quite usual for detections to be temporally clustered with template LFEs, so there may be curiosity about the time-windows that were selected. However, the statement that LFEs before/after 2011 were mostly detected by templates in the same time periods is insensitive to selection bias of the time-windows (Supplementary Fig. S9 ).

A seismic survery 35 , 36 that elucidated the 3D structures of the P-wave velocity ( V P ), S-wave velocity ( V S ) as well as V P / V S beneath Mount Fuji, revealed a low- V P , low- V S and low- V P / V S anomaly at depths of 7–17 km, corresponding with the locations of LFEs. The coincidence of the velocity anomaly and the locations of LFEs suggests that supercritical volatile fluids, such as H 2 O and CO 2 , may be abundant in the low- V P / V S area and may play an important role in generating LFEs.

Two possible processes leading to an eruption are currently considered for Mount Fuji 19 : the promotion of bubbling due to pressurization, and changes in stress in surrounding rocks. The first process promotes exsolving volatile components (H 2 O and CO 2 ) from liquid to gas 37 , 38 , 39 , 40 , 41 . If the magma plumbing system is open or has weak walls that are easily expanded or fractured, increased pressure creates paths for the magma to migrate, so magma pressure will be further reduced and bubbling will be accelerated. In the second process, cracks close to the magma system would be unstable due to stress perturbation. These failures can become paths through which magma flows up, leading to an eruption. Disturbances caused by external fractures, such as the Shizuoka earthquake, may be a key to initiating both processes.

Nakamichi et al. 35 suggested that a complex process occurred beneath Mount Fuji in which the characteristics of its LFEs were due to a variety of focal processes, and where the source mechanism of the largest LFE ( M 2.3) was explained by non-double-couple components. Among variable LFEs, only those associated with newly-created fractures and reactivated fractures pushed closer to failure by stress changes due to the Shizuoka earthquake, may have become active. The reader might note alternative source processes. LFEs might not always be generated by magma movement. Hydrothermal fluids, as well as the attenuation of higher frequency earthquakes, can create apparent LFEs 42 , 43 .

Schematic cross-sections beneath Mount Fuji 17 , 44 before and after the Shizuoka earthquake (Fig.  6 ) show how newly created fractures 19 and activated LFEs are associated with changes in the magma system and fluid- and gas-rich area 35 , 36 . However, based on our result, it remains unsolved if the Shizuoka earthquake triggered an increase in the supply of magmatic fluid to the magma reservoir. Furthermore, there was no evidence that the amount of rising magma increased because clear near-surface deformation around Mount Fuji was not observed before and after the Shizuoka earthquake.

Schematic cross sections. Relationship between LFEs and the magma system beneath Mount Fuji, before and after the Shizuoka earthquake, is shown in ( a ) and ( b ), respectively. ( a ) is based on previous studies 17 , 35 , 36 , 44 . New fractures and magma injection due to the earthquake were suggested 19 , shown in ( b ). We proposed activated LFEs in ( b ).

Stress changes on the magma system beneath Mount Fuji of 0.001–0.01 and 0.1–1 MPa were caused by the Tohoku and Shizuoka earthquakes, respectively 19 . The latter change is considered to be sufficient to trigger earthquakes 20 , 21 , implying the excitement of the magma system and triggering an eruption through either or both processes described above 19 . Our results (Figs. 2 , 3 , 4 , 5 ) demonstrate that the Shizuoka earthquake played a role in the magma system’s excitation, but not enough to trigger an eruption. We conclude that Mount Fuji was sensitive to disturbances due to this earthquake. This is consistent with a previous study in which it was implied that the crust in the area near Mount Fuji is quite sensitive to transient stress perturbation and that the level of pressurization of the hydrothermal and/or magmatic fluids is high in the Mount Fuji area 45 .

In 1703, four years before the 1707 Hoei eruption, seismic swarms were observed 35 days after the M 8-class Genroku Kanto earthquake, about 100 km east of Mount Fuji, but no eruption occurred 14 , 15 , 16 . The 1707 eruption was also preceded by the M 9-class Hoei earthquake, about 200 km to the southwest, on October 7, 49 days before the eruption. Beginning on November 28, 1707, earthquake swarms were observed several times and dozens of earthquakes were felt from December 15, 1707. Mount Fuji then began to erupt on December 16, 1707.

In 2000–2001, LFE swarms occurred, starting in August 2000, two months after the eruption of Miyakejima volcano, which lies 160 km to the south of Mount Fuji, although the change in stress was 10 –4 MPa 19 , 46 , or 0.001 ~ 0.0001 of that caused by the Shizuoka earthquake. This change in stress is considered to be too small to trigger an eruption. The experience of Mount Fuji described above implies that it tends to be influenced by external disturbances such as large earthquakes and active volcanoes. Our observation of activated LFEs due to the Shizuoka earthquake and a previous theory of an increase in stress imparted by this earthquake 19 support this tendency, although the volcano has not yet erupted (June 2023). While this study presents a case for the interaction of the Mount Fuji volcanic system with tectonic earthquakes, it remains possible that considerable volcano-seismic activity took place without any influence by tectonics for some cases.

Over 300 years after the 1707 Hoei eruption, the Japanese government has started to consider preparations for the next eruption, citing a worst-case scenario that inflicts catastrophic damage on humans and society 18 . Whether the increase in occurrence rate of LFEs (Fig.  2 ) will continue or subside absent external events remains unknown, and it is impossible to draw conclusions about the timing of the next eruption. However, our detailed study demonstrates that LFE activity is an important indicator of Mount Fuji’s subsurface magma system 17 , 35 , 36 , 44 . Given that this study covered data up to 2019, additional analyses for more recent LFEs in future research may be useful for identifying the current state of Mount Fuji. Thus, together with seismological and geodetic observations, it is worthwhile monitoring LFEs to contribute to the prevention and mitigation of Mount Fuji’s volcanic hazard. Our arguments for the use of monitoring LFEs are applicable to active volcanoes around the world that have not yet erupted but are considered to have the potential to erupt.

When studying LFEs associated with volcanic phenomena, researchers may want to use a catalog that consists of a complete list of LFEs. However, due to their low signal-to-noise ratio, LFE signals are difficult to detect by conventional event-detection methods. We used an MF method that correlates waveforms of continuous signals with those of a template and allows the detection of seismic sequences with a low signal-to-noise ratio 22 , 23 , 24 , 25 , 26 . In this study, the MF system used for detecting LFEs beneath the Hakone volcano, Japan 22 was modified so that it was applicable to Mount Fuji.

Waveforms of continuous signals that were used in this study covered the Jan. 2003-Jul. 2019 period, as recorded by 16 seismic stations (Supplementary Fig. S1 ) with a three-component velocity seismometer around Mount Fuji. These were obtained from the Earthquake Research Institute at the University of Tokyo.

All stations used in this study (Supplementary Fig. S1 ) host borehole seismometers (eigen frequency of 1 Hz), except for the stations OMZ (35.434332°N, 139.012649°E, 503 m above sea level), FJO (35.3666°N, 138.9102°E, 490 m above sea level), EV.FJZ (35.4487°N, 138.7525°E, 1090 m above sea level), and EV.SBSR (35.36582°N, 138.77818°E, 1980 m above sea level), installed on the surface of the ground. OMZ, FJO, and EV.FJZ host Lennartz seismometers (1 Hz) and EV.SBSR hosts a Nanometrics Trillium seismometer (1/120 Hz).

To prepare template LFEs, we used the JMA catalog, which includes ordinary earthquakes and LFEs observed in Japan. Although ordinary earthquakes are distributed all over Japan, LFEs tend to concentrate beneath active volcanoes (Fig.  1 a), along the boundary between the Philippine Sea plate and the continental plate in western Japan 47 , and as several isolated clusters in the intraplate regions 48 . Each event in the JMA catalog is classified based on subsidiary information: natural (ordinary) earthquake, LFE, artificial event, etc. The spatial map of events classified as LFEs shows that the area of LFEs around Mount Fuji was separated from other areas of LFEs (Fig.  1 a). We only selected LFEs around Mount Fuji and defined the catalog including these LFEs (Fig.  1 b–d). The source area of the Shizuoka earthquake and the occurrence area of LFEs are close to each other (Fig.  1 b). However, due to subsidiary information, there is no doubt that the LFE catalog we used eliminated aftershocks (ordinary earthquakes) of the Shizuoka earthquake.

This study relied on statistical analyses of the LFE catalog, which required the use of a complete LFE catalog that covered the study region and time period. It should be carefully considered that the catalog may be controlled by the selection of template earthquakes in the MF analysis. To ensure the completeness of the catalog, it is critical to use a well-chosen set of template LFEs. Careful consideration was needed to make a set of template LFEs, as explained below.

First, large LFEs were selected as templates in order to allow template waveforms to include more information on signals than on noise. Using the JMA catalog, we investigated an M -time graph of LFEs around Mount Fuji during the Jan. 2003–Jul. 2019 period (Fig.  1 c), and found that the majority was M  = 0 ~ 1, regardless of the date. Visual inspection shows that LFEs of M  > 1 were rare with no particular tendency such as LFEs of M  > 1 which occurred more frequently or less frequently over time. If smaller magnitude criteria were selected to increase the number of template LFEs, then more LFEs would be detected. However, since implementation of the MF system was computationally more intensive when using a large number of template LFEs than when using a small number of template LFEs, so an implementation trial was conducted by using different magnitude criteria under our computing environment. We found that the most feasible was to use M  ≥ 0.9 LFEs as templates. Thus, irrespective of time, LFEs with M  ≥ 0.9 in Jan. 2003-Jul. 2019 were selected as templates. Then, among them, LFEs that were recorded by six stations with a minimum signal-to-noise-ratio of 2, were selected 22 .

Second, we verified whether a chosen-set of LFEs ( M  ≥ 0.9) showed appropriate spatiotemporal coverage. This becomes particularly important when the source mechanism changes over time. Map and cross-sectional views around Mount Fuji (Fig.  1 b) show that selected LFEs ( M  ≥ 0.9) were mostly distributed within the cluster of LFEs, with all magnitudes between Jan. 2003 and Jul. 2019. A consistent spatial coverage of LFEs ( M  ≥ 0.9) was found between the pre- and post-Shizuoka-quake periods: the coverage of LFEs ( M  ≥ 0.9) before the Shizuoka earthquake was observed in the area where LFEs ( M  ≥ 0.9) had already occurred thus far (Supplementary Fig. S1 ).

It appears that there were more template LFEs from the post-Shizuoka-quake period than from the pre-Shizuoka-quake period (Fig.  5 and Supplementary Fig. S8 ), which could potentially result in an overrepresentation of detected earthquakes in the post-Shizuoka-quake period relative to the pre-Shizuoka-quake period. However, as described above, this bias was not intentionally included. Thus, we did not distort to select template LFEs for making a template LFE catalog, which would be used for a subsequent MF procedure.

The MF procedure to identify LFEs, briefly described in this paragraph, is the same as that of Yukutake et al. 22 . Three-component waveform records for each template LFE were used, applying a six-second time window beginning two seconds before the onset time of the theoretical S-wave arrivals. Both templates and continuous waveforms were bandpass-filtered for 1–6 Hz and decimated at 20 Hz to reduce the calculation cost. This band was selected because Yukutake et al. 22 was followed, although other studies used a slightly narrower band (e.g., 1–4 Hz 49 ). The CC between a template and continuous waveform at each sampling time for every component at each station was calculated. After subtracting the hypocenter-to-station travel time of the theoretical S-wave, the time sequences of the correlation function throughout all channels were stacked (Supplementary Figs. S2 and S3 ). When the peak of the stacked correlation function exceeded a threshold level of nine times the median absolute deviation, an event was identified as a candidate LFE. It would be beneficial to show examples of detected LFE waveforms (Supplementary Figs. S2 and S3 ) in order to verify the earthquake detection process that could enhance the reliability of this study. After removing multiple counts, the location of the candidate was assigned to the hypocenter of the matched template LFE determined by JMA (also see the “ Catalog quality evaluation ” section in “ Methods ”). Magnitude was determined as the mean of the maximum amplitude ratios of the template with respect to the candidate. The MF procedure described above was applied to all waveform records in the Jan. 2003–Jul. 2019 period, and a preliminary catalog, including candidate LFEs, was created, but LFEs identified by five or less stations were not included in this catalog 22 .

Less reliable LFEs were removed from this preliminary catalog to create a finalized catalog, as follows. Among candidate LFEs, false detection occasionally occurred due to contamination by other seismic signals such as teleseismic earthquakes. This contamination led to the detection of LFEs with a large M , so we visually inspected whether each template LFE was used to detect many candidate LFEs with M  > 2, a magnitude above which few LFEs have been recorded beneath Mount Fuji in the JMA catalog since 2003. We considered that such template LFEs had a feature similar to teleseismic earthquakes and decided to eliminate them from the list of template LFEs. Thus, candidate LFEs detected by using the eliminated template LFEs were removed from the preliminary catalog, resulting in the finalized catalog that included ~ 16,000 LFEs. A total of 87 template LFEs were used for the finalized catalog. The locations of template LFEs and seismic stations are indicated in Fig.  1 b and Supplementary Fig. S1 . Despite this primary quality test, an additional test was conducted, as described in the next paragraphs and in the “ Catalog quality evaluation ” section.

The CC -values of LFEs (Supplementary Fig. S1 ) ranged between 0.1 (poor correlation with a template LFE) and 1 (strong correlation with, and identical to, the corresponding template LFE). Setting the minimum CC to a low value implies the use of an incomplete catalog influenced by the nature of low signal-to-noise ratios of LFEs. The minimum threshold for CC ( CC th ), above which LFEs are used for our analysis, should be above the upper noise limit. We decided to use CC th  = 0.25, 0.3, 0.35, and 0.5 for the following reasons. Histograms of CC -values in Supplementary Fig. S1 show an asymmetric distribution with a tall peak at CC  ~ 0.2. We followed previous studies 27 , 28 , 29 , in which the distribution of lower CC -values was modeled by a normally distributed curve that would be expected for random correlations between signals and noise, while the upper tail was considered to represent the presence of well-correlated LFEs. Visual inspection shows that frequencies at and below CC  ~ 0.2 are in good agreement with the left-hand side of the normally distributed curve where the mean is 0.19 and its standard deviation is 0.03 (Supplementary Fig. S1 ). We selected CC th  = 0.25, which corresponds to the mean plus two standard deviations. Moreover, we selected CC th  = 0.3 and 0.35, which are higher than the mean plus three standard deviations, to examine the dependence of the result on CC th . Similar to Green and Neuberg 27 and Petersen 28 , we found an outliner peak at CC  ~ 0.3 (Supplementary Fig. S1 ). This peak was clearly observed in the histogram of CC -values for M  ≥ 0 (Supplementary Fig. S1 ). This histogram is displayed because our analysis basically did not include LFEs with M  < 0. Previous researchers, who studied Shishaldin volcanoes (Alaska), the Soufriere volcano (West Indies), and the Unzen volcano (Japan) 27 , 28 , 29 , selected CC th -values > 0.5, by showing normally distributed curves with larger means and standard deviations than those shown in this study. We also examined the case for CC th  = 0.5.

The scope of this study did not permit us to reveal repeating LFEs, nor cyclic activities and cluster characteristic, as were studied by Lamb et al. 29 . Rather, this study’s objective was to resolve the difficulty in detecting smaller LFEs. Our future research will be to conduct in-depth analyses of repeating LFEs for each cluster beneath Mount Fuji, referring to Lamb et al. 29 , and using a sophisticated MF method that can locate detected LFEs to appreciate if they occurred in the same cluster as the template LFE used to find them.

Catalog quality evaluation

As a basis of catalog completeness, understanding magnitude scales used in this study is critical. We examined whether large LFEs in our catalog were indeed large, as in the JMA catalog, and vice versa. An LFE in our catalog was paired with that in the JMA catalog if the time difference between them was within two seconds, while ignoring one-to-multiple cases. In this pairing, differences in the locations of LFEs were not considered because, as described in the “ MF method ” section in “ Methods ”, the locations of LFEs in our catalog were assigned to the hypocenter of the matched template LFE determined by JMA. A list of paired LFEs shows that magnitude in our catalog was positively correlated with that in the JMA catalog, and that the former was nearly equal to the latter (Supplementary Fig. S4 ), allowing us to assume a one-to-one transformation in magnitude between our catalog and the JMA catalog.

Analyses of the ETAS model (see the “ ETAS model ” section in “ Methods ”) are critically dependent on a robust estimate of completeness magnitude ( M c ) of the processed LFE data. Above M c , all events are considered to be detected. In particular, underestimates of M c lead to unreliable ETAS fitting. Attention always needs to be paid to M c when assessing M c in each time window. Details of how to compute M c are provided in the “ Computation of M c ” section in “ Methods ”.

M c was about 0.3 ~ 0.5 for the JMA catalog and about 0.2 ~ 0.3 for the MF catalogs (Supplementary Fig. S4 ). These estimates of M c were based on precut catalogs covering several time periods (Supplementary Fig. S4 ). Therefore, we did not consider a single M c over the entire catalog. To verify whether the results depended on the choice of minimum magnitude ( M th ), above which the ETAS model was fitted, we assumed M th  = 0.2, 0.3, and 0.4 ( M  ≥ 0.2, 0.3 and 0.4), suggesting that the feature generally appears to remain stable (see the “ ETAS model ” section in “ Methods ”, Figs. 2 , 3 and 4 , and Supplementary Figs. S5 – S7 and Tables S2 and S3 ). Visual inspection of Fig.  2 shows that the catalog for M  = 0 or less is affected by incompleteness. However, it was not necessary to account for such small LFEs because M th  = 0.2, 0.3, and 0.4 were assumed for the ETAS analyses. For the JMA catalog, M th  = 0.3, 0.4, and 0.5 were used (Fig.  2 and Supplementary Fig. S5 ).

Computation of M c

To compute M c , we used the Gutenberg-Richter (GR) relation 50 , given by log 10 N  =  a - bM , where N is the cumulative number of earthquakes with a magnitude larger than or equal to M , a characterizes seismic activity or earthquake productivity of a region, and constant b is used to describe the relative occurrence of large and small events (i.e., a high b -value indicates a larger proportion of small earthquakes, and vice versa). Changes in b -values of ordinary earthquakes are known to reflect structural heterogeneity, strength, and temperature in the Earth 51 , 52 , 53 , 54 , 55 , and the b -value is also known to be inversely dependent on differential stress 56 , 57 . We assumed that the GR relation was applicable to not only ordinary earthquakes 55 , 58 , 59 but also LFEs. In this section, the word “earthquake” includes LFEs.

We employed the Entire-Magnitude-Range (EMR) technique 60 , which simultaneously calculates the a - and b -values and the completeness magnitude M c , above which all events are considered to be detected. We always paid attention to a robust estimate of M c , because it is critical for analyses of the ETAS models (details of catalog quality evaluation in “ Methods ”). EMR applies the maximum-likelihood method when computing the b -value to events with magnitudes above M c . Uncertainty in b was according to Shi and Bolt 61 . Substitution of M c , N at M c , and the maximum-likelihood b -value into M , N , and b of a  = log 10 N  +  bM , respectively, gives the a -value. Supplementary Fig. S4 shows a good fit of the GR relation to observations in the present cases.

To compute M c , the EMR technique 60 combines the GR relation with a detection rate function. Details are provided next. Statistical modeling was performed separately for completely detected and incompletely detected parts of the frequency-magnitude distribution. The b - and a -values in the GR relation were computed based on earthquakes above a certain magnitude ( M cc ). For earthquakes whose magnitudes were smaller than M cc , it was hypothesized that the detection rate depended on their magnitudes in such a way that large earthquakes were almost entirely detected while smaller ones were detected at lower rates. Earthquakes with M  ≥  M cc were assumed to be detected with a detection rate of 1. To evaluate the fitness of the model to data, the log-likelihood was computed by changing the value of M cc . The best fitting model was that which maximized the log-likelihood value.

The software package ZMAP 62 was used to facilitate the computation of a , b , and M c based on the EMR method. Although the package, whose code is open, is written in Mathworks’ commercial software language Matlab®, no knowledge is needed since ZMAP is GUI-driven. ZMAP combines many standard seismological tools. A user can use ZMAP to create a graph of frequency-magnitude distribution with the GR relation with a , b , and M c values calculated by EMR (Supplementary Fig. S4 ).

The ETAS model 30 was originally introduced for ordinary earthquakes, but we assumed that the model can be extended and applied for LFEs beneath Mount Fuji. In this section, when the word “earthquake” is used, the reader should understand that it also includes LFEs.

The ETAS model is a point-process model that represents the activity of earthquakes of a minimum magnitude ( M th ) and above in a certain region during a specified time interval. Seismic activity includes the background activity at a constant occurrence rate μ (Poisson process). The model assumes that each earthquake (including the aftershock of another earthquake) is followed by aftershocks. Aftershock activity is represented by the Omori-Utsu formula 63 in the time domain. The rate of an aftershock occurrence at time t following the i -th earthquake (time t i and magnitude M i ) is given by ν i ( t ) =  K 0 exp{α( M i - M th )}( t - t i  +  c ) - p for t  >  t i , where K 0 , α, c , and p are constants, which are common to each target aftershock sequence in a region. The rate of occurrence of the whole earthquake series at t becomes \(\lambda \left(t|{H}_{t}\right)=\mu +{\sum }_{S<{t}_{i}<t}{\nu }_{i}\left(t\right)\) . The summation is performed for all i satisfying t i  <  t . Here, H t represents the history of occurrence times with associated magnitudes from the data {( t i , M i )} before time t . The parameter set θ = (μ, K 0 , α, c , p ) represents the characteristics of seismic activity. The units of the parameters are day −1 , day −1 , no unit, day, and no unit, respectively. For the case of K 0  = 0, the ETAS model reduces to the Poisson model (Supplementary Fig. S6 ). We estimated these parameters using the maximum likelihood method. Because K 0 depends on M in this model, it is necessary to assume a magnitude at which a value for K 0 needs to be known. Throughout this study, M  = 2 was assumed for estimating K 0 .

Using the maximum likelihood estimate, it is possible to visualize how well or poorly the model fits an earthquake sequence by comparing the cumulative number of earthquakes with the rate calculated by the model. If the model presents a good approximation of observed seismicity, an overlap with each other is expected. Ordinary time can be converted to transformed time in such a way that the transformed sequence follows the Poisson process (uniformly distributed occurrence times) with unit intensity (occurrence rate) so that visualization can be achieved in two ways 31 , 32 , 33 : one graph using ordinary time and the other using transformed time (Fig.  3 ). Included in the latter graph is the parabola of 95% significance. When the number of earthquakes is insufficiently large, significance actually depends on sample size due to the estimation accuracy of the parameters. The significance of deviation is defined in the case where the empirical curve deviates outside the parabola.

A FORTRAN program package (SASeis2006) associated with a manual for the ETAS analysis was used to calculate maximum likelihood estimates and also to visualize model performance 64 . This has been extended to the program package XETAS 31 using GUI.

When the stationary ETAS model does not fit a dataset well, the simplest alternative model is a “two-stage ETAS model” that considers different parameter values in subperiods before and after a particular time, referred to as change-point T c . AIC is used to test whether or not the changes in seismicity pattern at T c reduces model selection 34 . In this procedure, we separately fitted the ETAS models for each divided period and then compared their total goodness-of-fit values against the one-fit value over the whole period using the principle of minimum AIC. AIC was calculated from the maximum log-likelihood and number of adjusted parameters.

If T c is hypothetically prefixed based on some information other than the occurrence data themselves, such as a notable geophysical event or a notable outside large earthquake, AIC single (AIC for the model fitted over the whole period) can be compared with AIC 2stage (AIC for the 2-stage model fitted on divided periods) to select the model with the smaller value that performs a better fit to the data in the entire target period. If T c is searched from the target data, the 2-stage model becomes harder to accept. Namely, AIC 2stage is compared with AIC single plus the penalty term 2 q to select the model. Here q is the degree of freedom to search for the best candidate T c from the data. q depends on sample size (number of earthquakes in the target period) 33 , 65 : q increases with sample size and, for example, lies in the 4–5 range for q between 100 and 1000.

Although we adopted AIC for model selection, it cannot always be used for other cases such as the identification of possible earthquake precursors in ionospheric electric content (TEC) 66 .

Time-dependent μ and K 0

The standard stationary ETAS model can be temporally extended to the non-stationary ETAS model 33 , 67 , 68 , 69 in such a way that μ and K 0 are assigned as a function of t . The function μ( t ) and K 0 ( t ) are represented by a broken line connecting the respective sequences ( t i , μ( t i )) and ( t i , K 0 ( t i )) for the i -th earthquake, using a Bayesian function.

Although such a sophisticated model is available, a simpler approach was taken to capture essential aspects of the time-dependent background and aftershock activities (Fig.  4 and Supplementary Fig. S7 and Tables S1 – S3 ). This involves taking a time-window approach. In Fig.  4 , the time-windows 2003–2010 and 2012–2019 were considered where the time-window of 2011, which included the Tohoku and Shizuoka earthquakes, was not considered. When creating Fig.  4 (Supplementary Table S1 ), μ and K 0 were computed, given that other parameters (α, c , p ) were constants, where the values for (α, c , p ) were obtained as follows. The parameters θ = (μ, K 0 , α, c , p ) were first computed for each time-window, each M th , and each CC th . Typical values for α, c , p were α = 0.5, c  = 0.0015, and p  = 2.8. Using these typical values, parameters μ and K 0 were recomputed for each time-window, each M th , and each CC th . The error bars for μ and K 0 , which can be calculated by XETAS 31 , are based on error distribution depending on the sample size when the number of LFEs is not large enough 65 .

K 0 was forced to express time-dependent aftershock activity (Fig.  4 ), so the same analysis can be performed for other parameters to support the assumption that the μ- CC th pattern generally remains stable. Namely, p was considered as a time-variable parameter, given that other aftershock parameters ( K 0 , α, c ) were prefixed as constant, resulting in Supplementary Fig. S7 . The same analysis was performed by assuming time-variable α, given that K 0 , c , p were constant (Supplementary Fig. S7 ). The parameter values are summarized in Supplementary Tables S1 – S3 .

The slope ( g ) and intersection ( h ) of the least-square regression line and the square of the sample correlation coefficient ( R 2 ) for Fig.  4 a are μ =  gCC th  +  h with ( g , h , R 2 ) = (− 0.46, 0.25, 0.96) for M  ≥ 0.2 (blue solid line), (− 0.34, 0.19, 0.96) for M  ≥ 0.3 (red solid line), and (− 0.24, 0.14, 0.95) for M  ≥ 0.4 (green solid line) before 2011, and (− 0.54, 0.34, 0.99) for M  ≥ 0.2 (blue dashed line), (− 0.37, 0.25, 1.00) for M  ≥ 0.3 (red dashed line), and (− 0.24, 0.17, 1.00) for M  ≥ 0.4 (green dashed line) after 2011.

Similarly, for Fig.  4 b, K 0  =  gCC th  +  h with ( g , h , R 2 ) = (− 3.84 × 10 –5 , 2.58 × 10 –5 , 0.91) for M  ≥ 0.2 (blue solid line), (− 3.16 × 10 –5 , 2.19 × 10 –5 , 0.90) for M  ≥ 0.3 (red solid line), and (− 2.59 × 10 –5 , 1.85 × 10 –5 , 0.87) for M  ≥ 0.4 (green solid line) before 2011, and (− 3.93 × 10 –5 , 3.13 × 10 –5 , 0.97) for M  ≥ 0.2 (blue dashed line), (− 3.53 × 10 –5 , 2.85 × 10 –5 , 0.97) for M  ≥ 0.3 (red dashed line), and (− 3.03 × 10 –5 , 2.57 × 10 –5 , 0.97) for M  ≥ 0.4 (green dashed line) after 2011.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. The JMA catalog was obtained from https://www.data.jma.go.jp/eqev/data/bulletin/hypo.html . The waveform records were obtained from the permanent stations of the National Research Institute for Earth Science and Disaster Resilience, the Earthquake Research Institute at the University of Tokyo, JMA, and the Hot Springs Research Institute of Kanagawa Prefectural Government. Locations of active volcanoes used for Fig.  1 a were obtained from https://www.mri-jma.go.jp/Dep/sei/fhirose/plate/en.PlateData.html . The fault model of the 2011 Tohoku earthquake, used to create Fig.  1 a, was obtained from Asano et al. 70 . The fault model of the 2011 Shizuoka earthquake, used to create Fig.  1 b and Supplementary Fig. S1 , was obtained from Fujita et al. 19 . The seismicity analysis software ZMAP 62 , used for Supplementary Fig. S4 , was obtained from http://www.seismo.ethz.ch/en/research-and-teaching/products-software/software/ZMAP . The program XETAS 31 , used for Figs. 2 – 4 and Supplementary Figs. S5 – S7 and Tables S2 and S3 , was obtained from http://evrrss.eri.u-tokyo.ac.jp/software/xetas/index.html . Generic Mapping Tools (GMT) 71 , used for Fig.  1 a,b and Supplementary Fig. S1 , is an open-source collection ( https://www.generic-mapping-tools.org ).

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Acknowledgements

This study was partially supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, under The Second Earthquake and Volcano Hazards Observation and Research Program (Earthquake and Volcano Hazard Reduction Research) (K.Z.N., Y.Y.) and under STAR-E (Seismology TowArd Research innovation with data of Earthquake) Program Grant Number JPJ010217 (K.Z.N., T.K.), JSPS KAKENHI Grant Number JP 20K05050 (K.Z.N.), 21K04613 (K.Z.N.), 22K03752 (Y.Y.), 20K11704 (T.K.), the Chubu Electric Power's research based on selected proposals (K.Z.N.), the Consortium of Universities & Local Communities in Shizuoka (K.Z.N., Y.Y.), the Certified Nonprofit Organization Mount Fuji Research Station (K.Z.N.), the Japan Tobacco SDGs Contribution Project (K.Z.N.), and the WNI W-Bunka Foundation (K.Z.N.). The authors thank Y. Noda for help with implementing the MF method.

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K.Z.N. and Y.Y. designed the study. K.Z.N. conceived the analysis method, created figures, and wrote the paper. Preparation of waveform records used in this study were carried out by Y.Y. The MF method was modified by Y.Y. and K.Z.N. to be applicable to Mount Fuji. ETAS analyses were carried out by T.K. and K.Z.N. All authors developed the manuscript and approved the final manuscript.

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Correspondence to K. Z. Nanjo .

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Nanjo, K.Z., Yukutake, Y. & Kumazawa, T. Activated volcanism of Mount Fuji by the 2011 Japanese large earthquakes. Sci Rep 13 , 10562 (2023). https://doi.org/10.1038/s41598-023-37735-4

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Received : 27 January 2023

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DOI : https://doi.org/10.1038/s41598-023-37735-4

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