Slip distribution of the 2024 Noto Peninsula earthquake (M JMA 7.6) estimated from tsunami waveforms and GNSS data

The 1 January 2024 Noto-Hanto (Noto Peninsula) earthquake (M JMA 7.6) generated strong ground motion, large crustal deformation and tsunamis that caused significant damage in the region. Around Noto Peninsula, both off-shore submarine and partially inland active faults have been identified by previous projects: Ministry of Land, Infrastructure, Transport and Tourism (MLIT) and Japan Sea Earthquake and Tsunami Research Project (JSPJ). We inverted the tsunami waveforms recorded on 6 wave gauges and 12 tide gauges around Sea of Japan and the GNSS data recorded at 53 stations in Noto Peninsula to estimate the slip amount and seismic moment on each of active faults. The results show that the 2024 coseismic slips were 3.5 m, 3.2 m, and 3.2 m on subfaults NT4, NT5 and NT6 of the JSPJ model, located on the northern coast of Noto Peninsula and dipping toward southeast. A smaller slip, 1.0 m, estimated on NT8 on the southwestern end of the 2024 rupture, may be attributed to its previous rupture during the 2007 Noto earthquake. The total length of these four faults is ~ 100 km, and the seismic moment is 1.90 × 10 20 Nm (Mw = 7.5). Almost no slip was estimated on the northeastern subfaults NT2 and NT3, which dip northwestward, opposite to NT4–NT5–NT6, and western subfault NT8. Aftershocks including the M JMA 6.1 event occurred in the NT2– NT3 region, but they are smaller than the potential magnitude (Mw 7.1) those faults can release in a tsunamigenic earthquake. Similar features are also found for the MLIT model; the 2024 slip was only on F43 along the northern coast of Noto Peninsula, and northeastern F42 did not rupture, leaving potential for future event

In the Noto Peninsula region, a swarm of earthquakes started around December 2020, with the largest size of M JMA 5.4 (June 19, 2022).The swarm activity was confined in a small region (~ 20 km × ~ 10 km) at the tip of the peninsula, and has been considered to be related to upwelling fluid (Nishimura et al. 2023).On May 5, 2023, a larger earthquake (M JMA 6.5) occurred (Kato 2024), and the area of swarm activity became larger (30 km × 30 km, according to Earthquake Research Committee, https:// www.static.jishin.go.jp/ resou rce/ month ly/ 2024/ 20240 101_ noto_3.pdf ).However, the seismic swarm was still limited beneath the tip of the peninsula and did not extend to offshore active faults.
Around Noto Peninsula, large earthquakes occurred on February 7, 1993 (M JMA 6.6) to the north of the 2024 event, and on March 25, 2007 (M JMA 6.9) to the west (Fig. 1b).The 1993 earthquake produced small tsunamis that were recorded at Wajima and Naoetsu with maximum double amplitude of ~ 0.5 m (Abe and Okada 1995).The crustal deformation and tsunami from the 2007 earthquake were recorded on GPS network and tide gauges, respectively, from which the fault models have

Graphical Abstract
Fig. 1 a Map of Sea of Japan.Blue and red stars indicate the epicenters of the 2024 Noto Peninsula earthquake and past major earthquakes, respectively.The focal mechanisms for the 1940 and the 1964 earthquakes are from Satake (1986) and Abe (1975), respectively, and the ones for the 1983 and the 1993 earthquakes are from the Global CMT.The thin gray rectangles and line segments indicate the 60 fault models by MLIT.Location of NOWPHAS wave gauges (WG, blue squares) and tide gauges (TG, triangles) at which tsunami records from the 2024 Noto Peninsula earthquake were collected.Yellow corresponds to UNESCO/IOC, purple to GSI, and light blue to KHOA tide stations.Colorless triangles indicate tide stations for which no data were obtained.Regular font corresponds to the station name used in the inversions, and narrow italic corresponds to the station name not used in the inversions.The black rectangle shows the extent of the magnified area in b enlarged area around Noto Peninsula.The black rectangles show 7 fault models by JSPJ (NT6 was slightly modified in this study), and the gray rectangles show 4 fault models by MLIT.Blue pentagons indicate the aftershocks between January 1 and 31 with M JMA > 6. Dark yellow, light blue, and green stars indicate the epicenters of the past earthquakes that occurred near Noto Peninsula.Aftershocks of M JMA 3 or higher (period: 2024/1/1-1/17) by JMA are indicated by red circles.The focal mechanism of the 1993 earthquake is from the Global CMT, and the other earthquakes, including the 2024 mainshock, are from the USGS W-phase solutions been proposed (Namegaya and Satake 2008).The tsunami was recorded on Toyama tide gauge with an early arrival, which was considered to be generated by a secondary tsunami source other than the earthquake (Abe et al. 2008).
Along the eastern margin of Sea of Japan, series of active faults have been identified.In 2014, a government committee jointly supported by the Ministry of Land, Infrastructure, Transport and Tourism (MLIT), the Ministry of Education, Culture, Sports, Science and Technology (MEXT), and the Cabinet Office of Japan compiled previous studies and proposed 60 rupture scenarios for submarine active faults (hereafter referred to as MLIT fault models) (Fig. 1a, b).MLIT (2014) conducted tsunami simulations using heterogeneous slip models, which included large slip patches surrounded by smaller background patches.Mulia et al. (2020) conducted a probabilistic tsunami hazard analysis for the coast of Sea of Japan assuming the 60 MLIT fault models as the potential tsunami sources.The fault parameters as well as the tsunami hazard curves for each municipality were provided in Mulia et al. (2020).
More recently, the Japan Sea earthquake and tsunami project, hereafter called JSPJ, was conducted (from 2013 to 2020) with support from the MEXT, and the submarine and coastal fault models along Sea of Japan were developed through seismic and geological surveys (Sato et al. 2020).Satake et al. (2022) selected 172 offshore and coastal faults with length of 20 km or greater, as well as 177 combinations of segments including 28 shorter faults, estimated the slip amounts using multiple scaling relations, and computed coastal tsunami heights (their Tables S1, S2).
Several large (M ~ 7 or larger) earthquakes have occurred along the eastern margin of Sea of Japan in the twentieth century (Fig. 1a), and they generated disastrous tsunamis.The 1940 off Shakotan Peninsula earthquake (M JMA 7.5) generated tsunami and caused damage including 10 casualties in northern Hokkaido.The tsunami was also recorded in Sakhalin and North Korea.Based on these tsunami waveform data, fault models have been proposed by Satake (1986) and Okamura et al. (2005).
The 1993 off the southwest coast of Hokkaido earthquake (M JMA 7.8), officially named as the 1993 Hokkaido Nansei-oki earthquake, caused significant damage with more than 200 casualties, mostly on Okushiri Island where the tsunami heights exceeded 20 m.Tanioka et al. (1995) analyzed seismic and tsunami waveforms and geodetic data to estimate the slip distribution on the earthquake fault.
The 1983 off Akita earthquake (M JMA 7.7) (officially named Central Sea of Japan, or the Nihonkai-Chubu earthquake) also caused tsunami waves as high as 14 m and resulted in 100 casualties.This tsunami also caused three casualties in Korea.Satake (1985) used the tsunami waveforms to estimate the fault model.Murotani et al. (2022) re-examined the tsunami waveforms and runup data from the above three earthquakes and estimated the causative faults among the active faults proposed by the JSPJ.
The 1964 Niigata earthquake (M JMA 7.5) caused damage due to ground shaking, liquefaction, and tsunamis.Abe (1978) used the recorded tsunami waveforms to estimate the fault model.The crustal deformation data recorded along the coast, seafloor and offshore island (Awashima) were used to estimate the fault model (Satake and Abe 1983).
In this paper, we use the tsunami waveforms recorded around Sea of Japan and GNSS data recorded in and around Noto Peninsula from the 2024 Noto Peninsula earthquake to estimate the coseismic slip on the active faults identified by the MLIT and JSPJ.

Tsunami and GNSS data
The tsunami generated by the 2024 Noto Peninsula earthquake propagated through Sea of Japan and was recorded on wave gauges (WG) and tide gauges (TG) located on the west coast of Japan (Fig. 1a, b), and on TGs of Primorye, Sakhalin, and Korea (Fig. 1a).The WGs are located several kilometers offshore from ports around Japan with water depths of 20 to 50 m.The raw data for the WGs with a high sampling interval of 0.5 s were provided by Port and Harbor Bureau of MLIT.We applied a 1 min moving average to the raw data to obtain the waveforms showing tsunami signals, as displayed in real time as offshore mean water surface by every min on the Nationwide Ocean Wave information network for Ports and HArbourS (NOWPHAS) website.Unfortunately, the TGs at Wajima and Noto on the northern coast of Noto Peninsula, which are located within the source area, and the TG at Ogi on Sado Island, which is near the source, stopped recording data immediately after the earthquake.The TG data at other stations were available from the UNESCO/Intergovernmental Oceanographic Commission (IOC), Geospatial Information Authority of Japan (GSI) and Korea Hydrographic and Oceanographic Agency (KHOA) websites, as the digital data with sampling rates of 1, 0.5 and 1 min, respectively.
To remove ocean tide signals from the WG and TG data, a polynomial function was fitted to each data using the GMT command "trend1d".The residuals obtained by this fitting were used as the observed tsunami waveforms for inversions by resampling the waveform data with an interval of 1 min.The observed tsunami waveforms (Fig. 2) show maximum amplitudes of about 0.2 to 0.4 m at most WG stations and 0.1 to 0.4 m at TG stations, respectively.The maximum amplitude of 1.4 m was observed on Naoetsu WG.The waveform on Wajima WG shows a baseline shift of water level to the positive side by about 0.2 m immediately after the earthquake (time zero), suggesting that the WG itself moved downward due to subsidence.On Toyama TG, the leading depression wave started immediately after the earthquake and reached a trough of −0.5 m, followed by a peak of 0.8 m at 25 min after the earthquake.
As geodetic (crustal deformation) data, we used 153 displacement data (3 components at 51 locations) digitized from the GNSS data reported by GSI https:// www.gsi.go.jp/ chiba nkansi/ chika kukan si_ 20240 101no to_5.html (Fig. 3a).The coseismic displacements are the differences between the final daily solutions (called F5 solutions) on December 25-31, 2023 and January 2, 2024 at each observation point.Additional data at two more points, 6 displacement data of 3 components at 2 locations, in the northwestern part of the Noto peninsula, which were obtained by GSI's emergency survey https:// www.gsi.go.jp/ sokuc hikij un/ R6-notop enins ula-earth quake-Emerg encyO bserv ation.html, were also digitized and added to the GNSS data (159 displacement data of 3 components at 53 locations in total).Horizontal displacements were more than 0.8 m in a west to westsouthwest direction in the northern part of Noto Peninsula, with a maximum of 2 m recorded at Wajima.In the central Noto Peninsula and Toyama Prefecture, located farther south from the source area, the horizontal displacement is oriented to the northwest, and ~ 0.14 m or more at Himi and Nyuzen.Vertical uplifts of more than 1 m, including the largest uplift of 4.1 m, are recorded from Wajima to Suzu on the northern coast of Noto Peninsula, while subsidence ranging from a few to several tens of centimeters are recorded at stations southern and central parts of Noto Peninsula.

Inversion methods
To estimate the slip distribution on the faults, we assumed the fault geometries proposed by JSPJ and MLIT as the tsunami sources (Fig. 1b).The JSPJ model consists of seven subfaults: NT2-NT6, NT8, and NT9 (Table 1).The MLIT model consists of four subfaults: F43 and F42, each consisting of two segments (Additional file 1: Table S1).The northeastern subfaults, i.e., NT2 and NT3 in the JSPJ model and F42 in the MLIT model, are northwest-dipping reverse faults, while the other subfaults are southeast-dipping reverse faults.In both MLIT and JSPJ models, the rake angles were estimated from the three-dimensional tectonic stress fields by Terakawa and Matsu'ura (2010).The position and length of subfault NT6 in the JSPJ model were slightly modified, so that the Wajima WG was located in the subsidence area just north of the top edge of the fault, and it is connected with neighboring subfaults (NT5 and NT8) (Fig. 1b).
The rupture propagation on the faults was not considered, and it was assumed that all subfaults ruptured simultaneously.The total length of the above subfaults is approximately 150 km, and the mainshock epicenter is located almost at the center of the fault area (Fig. 1b).The rupture delay time from the epicenter to the nearest edge of each subfault is less than a few tens of seconds, while the sampling interval of the tsunami waveform is 60 s, hence the effect of slip delay due to the fault rupture can be ignored.The rise time of all subfaults was assumed to be 10 s.
Horizontal and vertical displacements at the GNSS stations and seafloor due to each subfault were calculated from a rectangular fault model using the equations of Okada (1985).As initial conditions for the tsunami, we first calculated the displacement on a coarse grid data of 12 arc-sec.The sea surface displacement was then calculated by considering the effect of horizontal displacement on steep bathymetric slopes (Tanioka and Satake 1996), then resampled to 6 arc-sec grid data.
Tsunami propagation calculations were performed from each subfault to the WG and TG stations.The computation area (127°E-143°E, 33°N-48°N) for the tsunami propagation is shown in Fig. 1a.The 15 arcsec bathymetry grid data from GEBCO 2023 (GEBCO Compilation Group 2023) were resampled at 6 arc-sec  grid intervals, so the numbers of grid points were 9600 and 9000 in the longitude and latitude direction, respectively.While finer bathymetry data are available around the Japanese TG stations, for the offshore WG stations and Korean and Russian TG stations, the GEBCO data provides the best resolution.The linear shallow-water equations (Satake 1995) were solved numerically in spherical coordinates for the 6-h tsunami propagation, and the time step interval was set to 0.3 s to satisfy the CFL (Courant-Friedrichs-Lewy) stability condition.Computational time was about 17 min for one case using the GPGPU (NVIDIA Quadro RTX A6000 48 GB, CUDA 12.3) as used in Satake et al. (2017).
The tsunami waveforms simulated at given observation points from a subfault with unit amount of slip (1 m in this study) are called the Green's function and can be used for inversion and synthesis of tsunami waveforms.For the Green's functions on Wajima WG (Fig. 1b) close the fault, offsets due to crustal deformations (e.g., −0.14 m from a unit slip on subfault NT6 of the JSPJ model) were removed so that the Green's function starts from zero sea level and the mean sea level of Green's function corresponds to the relative mean sea level at the station after the crustal movement.The Wajima WG record indicates that the sea level became higher by about 0.2 m after the earthquake occurrence.The offset of Green's function in the tsunami waveform inversion corresponds to calculated crustal displacement from a unit amount of slip in a GNSS inversion, and the change in mean sea level (about 0.2 m in the case of Wajima WG) corresponds to an observed GNSS displacement.Similar corrections were systematically applied to the Green's functions at all the stations, although the effects of the deformation are negligible at stations farther from the source.
We performed a joint inversion of tsunami waveform and GNSS data, as well as inversions using only tsunami waveform data and only GNSS data.For the tsunami waveform inversions, we applied the same method of Fujii and Satake (2007) using the non-negative least squares method (Lawson and Hanson 1974) to estimate the slip on each subfault.In the tsunami waveform inversions, the same weights were used for both WG and TG data, since there are no significant differences in amplitudes between them.In the joint inversions, we set the weights of the tsunami waveform and GNSS data according to the method of Satake (1993).First, the norm of each data set was calculated, and then the weights were set so that the amplitude scales of the two data sets were comparable.The ratio of the norm of GNSS data and tsunami waveform (WG and TG) data was 1.95, so the larger weights of 1.95 were assigned to tsunami waveform data set than the GNSS data weights of 1.0.

Results
The slip distributions estimated from inversions of different data sets, i.e., the joint inversion of tsunami waveform and GNSS data, tsunami waveform data only, and GNSS data only are shown in Fig. 4 and Table 1.In the joint inversion result (Fig. 4a), large slips more than 3 m was estimated at NT5 near the epicenter and NT4 and NT6 on both sides.A significant slip of about 1 m was obtained at NT8 northwest of Noto Peninsula.On the other hand, NT9 on the west, NT2 and NT3 on the east side within the aftershock area showed almost no slip.Therefore, the length of the fault-slip zone during the 2024 earthquake was about 100 km.The inversion results of tsunami waveform data only (Fig. 4b) and GNSS data only (Fig. 4c) also show similar slip distributions and vertical displacements, but the tsunami waveform inversion shows a larger slip on NT5, while the GNSS inversion shows a larger slip on NT6.The extremely large slip on NT9 by the GNSS inversion is considered to be unreliable due to the lack of controlling data from nearby stations and the fixed fault geometries.
The displacements calculated at GNSS stations using the fault slips estimated by the different inversions (Fig. 3b, c, d) generally reproduce the observed uplift on the northern coast of Noto Peninsula (Fig. 3a), but the calculated displacements at the stations where subsidence was observed at southern area of central Noto Peninsula are almost zero.For the horizontal displacements, the calculated directions from the various inversions are almost consistent with the observation, but the amounts of displacements are significantly underestimated.This may be due to the fact that the fault sizes, the dip and rake angles of the fault models are fixed at the model values.
The joint inversion and the tsunami waveform inversion reproduce the observed tsunami waveforms on most of the WGs and TGs used in the inversions (Fig. 2 and Additional file 1: Fig. S1), although the amplitudes are slightly underestimated.The calculated amplitude is much smaller than the observed maximum amplitude of 1.4 m on Naoetsu WG, but they are similar on nearby Kashiwazaki TG.We confirmed that it is difficult to reproduce the amplitudes of these two stations from a single tsunami source model.The negative wave of Toyama TG that started immediately after the earthquake was not reproduced, but the positive amplitude of the second wave seems to be generally reproduced.Similarly, the receding wave of Toyama WG at about 5 min after the earthquake is also not reproduced.However, since this observation record shows a pulse-like waveform with a duration of about 1.5 min, we need to be careful to determine if it is an actual tsunami waveform or not.
The inversion analyses were also performed adopting the MLIT fault model geometries using the same data sets and data weights, and the results were similar to those for the JSPJ model (Additional file 1: Table S1, Figs.S2, S3, S4).Fault slips due to joint inversion is limited to the F43 segment, with the maximum slip of 3.5 m east of the epicenter, and the 2.1 m slip west of the epicenter.The F42 segment offshore to the east, far from the epicenter, hardly slips at all.The calculated seismic moments were 1.85 × 10 20 Nm (Mw = 7.4) for the joint inversion, 1.79 × 10 20 Nm (Mw = 7.4) for the tsunami waveform inversion, and 2.65 × 10 20 Nm (Mw = 7.5) for the GNSS inversion.

Discussion
The joint inversion of tsunami waveform and GNSS data indicates that the coseismic slip occurred on subfaults NT4, NT5, NT6 and NT8.The slip amounts are ~ 3.5 m, 3.2 m, 3.2 m, and 1.0 m on these subfaults.In the JSPJ, slip amounts on these subfaults were forecasted for single and multi-fault ruptures, using different scaling relations (Satake et al. 2022).The forecasted slip amounts for the multi-fault rupture of NT4, NT5, NT6 were 1.82 m, 1.93 m, and 2.69 m (Mw 7.3) from Recipe A, based on the relation between fault area and seismic moment by Irikura and Miyake (2001).The slips were 2.02 m, 2.11 m, and 2.96 m (Mw 7.4) from Recipe I, based on the scaling relation by Matsuda (1975).The slips were estimated to be 4.04 m, 4.25 m, and 8.55 m (Mw 7.6) using the scaling relation proposed by Takemura (1998) (see Table S2 of Satake et al. (2022)).The 2024 slip amounts estimated by the joint inversion are similar to the forecasted values using Recipes A and I.The Takemura (1998) relation seems to overestimate the slip amount, as suggested by Satake et al. (2022).
Subfault NT8 located at the western edge of Noto Peninsula seems to have ruptured in the 2007 earthquake (M JMA 6.9) (Namegaya and Satake 2008).The models based on GPS and coastal movements indicate that the slip on faults (15 to 20 km long), similar to NT8, were 1.2-1.7 m.The smaller slip amount on NT8 in the 2024 earthquake (1.0 m), compared to other ruptured subfaults, may be because this subfault slipped in 2007.The small slip on this fault during the 2024 earthquake may have prevented further rupture on neighboring subfault NT9.
The northern neighboring subfaults, NT2 and NT3, are dipping toward northwest, opposite direction to the NT4-NT5-NT6.This may be the reason why the 2024 rupture did not extend to these subfaults.A large (M JMA 6.1) aftershock occurred around NT2 on January 9, 2024.However, this magnitude is much smaller than the forecasted earthquake size on these faults.The forecasted slip in JSPJ is 1.2-1.9m (Mw 7.1) by Recipes A and I (Table S2 of Satake et al. (2022)).Therefore, these subfaults still have the potential to slip as a larger earthquake.If such an earthquake were to occur, it could generate tsunamis that would impact the coasts of Niigata prefecture and Sado Island.
MLIT (2014) also estimated the slip amounts on faults F42 and F43, and forecasted the tsunami heights along the Sea of Japa coast.They basically adopted the Irikura and Miyake (2001) relation, but increased the slip amount by 1.5 m considering the uncertainty.Their average slips are 3.1 m and 4.5 m, and the corresponding moment magnitudes Mw are 7.3 and 7.6 on F42 and F43, respectively.The estimated slip on F43 fault by the joint inversion (2.1 m and 3.5 m on two segments), as well as the 2024 moment magnitude, was slightly smaller than the MLIT forecast.Their forecasted magnitude of potential earthquake on F42 is similar to that on NT2-NT3 forecasted by JSPJ.

Conclusion
We inverted tsunami waveform and GNSS data from the 2024 Noto Peninsula earthquake to estimate the slip amounts on previously proposed active faults.The tsunami waveform data are sea levels recorded at 6 wave gauges on Niigata, Toyama, Ishikawa and Fukui coasts, and 12 tide gauges on the coasts of Honshu as well as on Korean and Russian coasts around Sea of Japan.The GNSS data consist of horizontal and vertical displacements recorded at 53 stations operated by GSI.Two sets of active fault geometries, proposed by MLIT and JSPJ were adopted for the inversions.
The results show that 2024 coseismic slips were 3.5 m, 3.2 m, and 3.2 m on NT4, NT5 and NT6 of the JSPJ model, located on the northern coast of Noto Peninsula.A smaller slip, 1.0 m, estimated on NT8 on the southwestern edge, may be due to the fact that it also ruptured during the 2007 Noto earthquake.Almost no slip was estimated on the northeastern subfaults NT2 and NT3, which dip northwestward, opposite to NT4-NT5-NT6, and western subfault NT8.Aftershocks, including the M JMA 6.1 event, occurred on NT2-NT3 region.This magnitude is smaller than the forecasted magnitude on these faults in Satake et al. (2022).This suggests that these two faults may still have the potential to produce larger earthquakes and associated tsunamis.Similar features are also found for the MLIT model; the 2024 slip occurred only on F43 along the northern coast of Noto Peninsula, and northeastern F42 did not rupture, indicating future potential.

Fig. 2
Fig. 2 Comparison of the observed and calculated tsunami waveforms from the joint inversion of tsunami waveform and GNSS data for the JSPJ fault models.The thick black and gray lines are the observed waveforms used and not used in the inversions, respectively.The red lines show the synthetic waveforms from the joint inversion result, with thick part used for the inversion.The gray bars below the waveforms indicate the time windows used in the inversions

Fig. 3
Fig. 3 Comparison of the observed GNSS data and calculated displacements from different inversions.Horizontal displacements are indicated by blue arrows and vertical displacements by red (uplift) to light-blue (subsidence) triangles.Displacements from a observed data from GNSS positioning analysis by GSI, and the calculated ones from b joint inversion, c inversion of tsunami waveform data only, and d inversion of GNSS data only.Solid black squares show fault models by JSPJ

Fig. 4
Fig. 4 Inversion results for the JSPJ fault model.(Top) Slip distribution of the 2024 Noto Peninsula earthquake.a Joint inversion, b inversion of tsunami waveform data only, c inversion of GNSS data only.The stars of the epicenters, the red circles of the aftershocks, and the symbols for the WGs and TGs are the same as in Fig. 1b.(Bottom) Vertical displacement calculated from the fault slips estimated from the inversions.d Joint inversion, e tsunami waveform inversion, and f GNSS inversion.Red lines and blue dotted lines indicate uplift and subsidence with the contour intervals of 0.2 m and 0.1 m, respectively

Table 1
Fault parameters of the JSPJ models and the inversion results# Subfault number.Lat., Lon., and depth: location and the top depth of the eastmost corners (with *), and the westmost corners (without *) † Modified from the original parameters by JSPJ model.Rigidity of 34.3 GPa is assumed