Validation and Uncertainties of Strong Ground Motion Prediction Methods for Seismic Hazard Assessment: A case study of the 2024 Noto Peninsula Earthquake (Mw7.5), Japan

Validation and Uncertainties of Strong Ground Motion Prediction Methods for Seismic Hazard Assessment: A case study of the 2024 Noto Peninsula Earthquake (Mw7.5), Japan | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Validation and Uncertainties of Strong Ground Motion Prediction Methods for Seismic Hazard Assessment: A case study of the 2024 Noto Peninsula Earthquake (Mw7.5), Japan Kimie Norimatsu, Hiroyuki Fujiwara, Shinji Toda This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8837779/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 5 You are reading this latest preprint version Abstract The major active fault earthquakes in Japan in recent years include the 2016 Kumamoto Earthquake and the 2024 Noto Peninsula earthquake. These earthquakes occurred along predicted fault models, however, uncertainties and variations in fault geometry and rupture propagation led to actual earthquake magnitudes exceeding prior expectations. The objective of this study is to verify if the Noto Peninsula earthquake could have been predicted, considering significant uncertainties in general strong motion prediction models, and to obtain feedback leading to improvements. Therefore, this study set a fault model using data from before the earthquake and performed a retrospective prediction analysis. This was compared with observed data to confirm predictability. Considering uncertainties in fault parameters and rupture propagation patterns, strong motion was generally predictable, except for the west coast and south coast of the Noto Peninsula. Subsequently, the uncertainties encompassed by this study was examined through the Tornado Plots for each calculation point, with a particular emphasis on the factors exerting the most substantial influence. The “Rupture Propagation Patterns” were the primary factor, with the “Concept of Fault Width” being the second most influential factor in many locations. However, at some locations near the fault top, the “Rake Angle” was shown to have a significant impact. This suggests that the effects of fault parameter uncertainties may exhibit regional characteristics. In the standard seismic hazard assessment methodology in Japan, the asperity model is utilized among characteristic source models. The asperity model effectively reproduces the pulsed waves near the source fault that can be represented by a simple model with a few asperities on a single fault plane. However, it is difficult to reproduce waveforms involving multiple fault ruptures and complex source processes, such as those seen in the Noto Peninsula earthquake. This study considers the limitations of applying characteristic source models. It proposes that, rather than aiming for exact waveform matching, evaluations should be permitted under loose criteria. Furthermore, by allowing for a certain degree of variability not only in fault parameter uncertainties but also in the calculation results themselves, such models can be considered suitable for use in assessments. Active fault earthquake Noto Peninsula earthquake Fault model Strong motion prediction Seismic hazard assessment Characteristic source model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1 Introduction In earthquake hazard assessment, a fault model is generally constructed based on data on active faults, seismic activity, and subsurface structure surveys, and simulations of strong motion and tsunamis are performed. From the results of these simulations, seismic hazard assessments are conduced to provide predict strong motion and tsunami damage. The Southern California Earthquake Center (SCEC) is developing CyberShake (e.g., Fayaz et al. 2021 ), a probabilistic seismic hazard analysis (PSHA) platform that uses 3D physical models to simulate specific fault ruptures and predict the seismic motions caused by those fault ruptures. SCEC also employs a community fault model (e.g., Plesch et al. 2007 ) based on various observational data to perform strong motion predictions and probabilistic hazard assessments. Concurrently, in Japan, following the proposal of the asperity model (Kanamori 1981 ), a “Strong ground motion prediction method for earthquakes with identified source faults (“Recipe”)” (Headquarters for Earthquake Research Promotion [ERP] 2017) has been developed and revised based on the method proposed in response to the 1995 Southern Hyogo prefecture earthquake and the 2000 Western Tottori prefecture earthquake (Irikura 2002 ). Setting up the fault models is an important part of hazard assessment, as it is a factor that determines the scale of the hazard. However, numerous challenges arise during the establishment of the fault models employed for strong motion prediction, with the underestimation of predictions being a subject of frequent discourse. In Japan, there are few examples of major earthquakes that occurred on predicted fault models, however the 2016 Kumamoto earthquake and the 2024 Noto Peninsula earthquake (Noto earthquake) are examples that demonstrate the need to consider parameter uncertainty and the diversity of fault propagation patterns in fault models when predicting damage. The 2016 Kumamoto earthquake (Mw 7.0: U.S. Geological survey [USGS] Earthquake Hazards Program 2017) was an earthquake for which active fault was evaluated and strong motion prediction results was published (ERP 2014). The previous evaluated fault length was 19 km, and the established fault model (ERP 2014) was 24km in length, 14km in width, and Mw6.5. During the earthquake, about 30 km of surface ruptures (e.g., Kumahara et al. 2022 ; Shirahama et al. 2016 ; Toda et al. 2016 ) appeared mostly along previously mapped active faults, as the Futagawa-Hinagu fault zone. The length of the fault estimated by source inversion analysis is even longer (for example, 47 km in Irikura et al. 2017 ). Furthermore, while the depth of the bottom of the fault was previously estimated to be 10 to 13 km (ERP 2013), subsequent aftershock distribution indicated it extended to approximately 18 km (e.g., Yano and Matsubara 2017 ). These are suggesting that these differences in fault posture and dimension resulted in underestimation of the prediction. Furthermore, the Kumamoto earthquake generated strong and long-period ground motions in the vicinity of the fault, as well as permanent displacement (e.g., Irikura et al. 2020 ; Tanaka et al. 2018 ). The observed strong motions exceeded those previously predicted for this region, indicating that this phenomenon cannot be adequately explained without considering not only the strong motions due to slip within the seismogenic layer, which is the target of the “Recipe,” however also the strong motions occurring in areas shallower than the seismogenic layer (Irikura et al. 2020 ; Tanaka et al. 2018 ). On January 1, 2024, the Noto earthquake occurred with a magnitude of 7.5 (USGS Earthquake Hazard program 2017). Hypocenter position is indicating red star in Fig. 1 . Various fault models have been analyzed for the Noto earthquake. These models indicate that the earthquake occurred along the north coast and the offshore area northeast of the Noto Peninsula. Guo et al. ( 2024 ) constructed a detailed fault model based on hypocenter relocation and estimated a north-dipping fault at the northern end of the rupture zone, with a dip direction opposite to that of the main source fault of the Noto earthquake. The rupture propagation is considered to be bilateral, with a small initial rupture occurring around the hypocenter, subsequently leading to rupture propagation in the west and subsequently in the east (e.g., Okuwaki et al. 2024 ; Xu et al. 2024 ; Ma et al. 2024 ). Prior to the Noto earthquake, several projects in the Japan Sea had compiled acoustic stratigraphic profiles, mapped fault traces, and established fault models (e.g., The Ministry of Education, Culture, Sports, Science and Technology [MEXT] and Japan Agency for Marine-Earth Science and Technology [JAMSTEC] 2015; Ministry of Load, Infrastructure, Transport and Tourism [MLIT ] 2014). These models were primarily used for the purpose of tsunami prediction, with limited ability to predict strong motions due to offshore faults. The Noto earthquake occurred on modelled faults based on the fault traces, with some exceptions. However, the propagation through long and multiple faults caused by the Noto earthquake was not included in prior hazard assessments, especially in the northeastern end of the aftershock area (fault planes A and B in Fig. 1 ). In order to mitigate the underestimation of earthquake hazard, it is important to consider uncertainty when setting the fault models. The expression of fault models is characterized by fault geometry and rupture characteristics. However, while there is a certain degree of regularity in fault rupture, earthquake magnitude, and hypocenter location, the occurrence of these events is subject to significant uncertainty. The observation data contained “epistemic uncertainty” due to insufficient data and expert interpretations. These uncertainties can be resolved through technological advances and the accumulation of knowledge. Conversely, “aleatoric variability” refers to the heterogeneity inherent in natural phenomena, exemplified by the non-linearity of seismic activity and the intricacy of fault geometries. It is widely accepted that prediction models must incorporate epistemic uncertainty and aleatoric variability to ensure their credibility and relevance. Despite the discourse surrounding the necessity of incorporating epistemic uncertainty into the analysis of fault models for strong motion prediction, this approach has yet to be formally recognized as a standard methodology. This study aims to examine the extent to which general strong motion prediction models, primarily those based on the “Recipe”, could predict the strong motion of the Noto earthquake if considerable uncertainty is taken into consideration, and seeks to obtain feedback that could lead to improvements. It is hypothesized that incorporating uncertainty and diversity into the model will reduce the underestimation of earthquake predictions and provide appropriate information to anticipate various seismic events in the region, facilitating the development of countermeasures. The ERP has validated the strong motion prediction method based on the “Recipe” using the observation record of the Kumamoto earthquake (ERP 2022). For the purposes of this validation, a fundamental fault model was obtained. This model was based on the distribution of surface ruptures (Shirahama et al. 2016 ), aftershock distribution, and source inversions (e.g., Irikura et al. 2017 ). Subsequently, adjustments were made to seismic moment and slip distribution. The identification of a fault model capable of reproducing the Kumamoto earthquake provided the necessary feedback needed to improve the method. In contrast, in this study, we utilize exclusively information published prior to the Noto earthquake to set the fault models. The extent to which the Noto earthquake could be predicted within the hazard level estimated from the fault models comprehensively set around the Noto Peninsula was verified. The fault modeling method used in this study is a general method such as “Recipe”, yet it incorporates uncertainty and diversity, including multiple parameterization patterns and multiple patterns of rupture propagation. 2 Setting of Fault Models 2.1 General Fault Modeling Methods in Japan The “J-SHIS model (Japan Seismic Hazard Information Station ("J-SHIS") by the National Research Institute for Earth Science and Disaster Resilience (NIED: NIED 2019))”, a national fault model of Japan, has been published, presenting the fault models of major active fault zones. The “J-SHIS model” is typically employed to evaluate strong motion, with the methods of the “Recipe” based on the method proposed by Irikura et al. (2002) and ERP (2017). The “Recipe” method is also generally used in other strong motion predictions and seismic hazard assessments. Here, we summarize the “Recipe” method (Irikura et al. 2002; ERP 2017). The “Recipe” includes “macroscopic fault characteristics” and “microscopic fault characteristics” as parameters that represent the characteristics of fault geometry and slip on fault plane. The “macroscopic fault characteristics” are parameters that describe the location, geometry, and scale of the source model, and include fault position, strike, size (length and width), depth, dip angle, magnitude, and average slip. The location is set by referring to the location of the active fault in the prior evaluation. The length of the fault model is a linear approximation of active fault. The fault width is set based on the relationship between the thickness of the seismogenic layer and the dip angle of the fault surface. The top and bottom depths of the seismogenic layer are estimated from the distribution of microearthquakes (Ito 1999 ). If there are detailed data available, such as reflection survey, the dip angle is referenced. If there are no data, a general value for the fault type is used: 45° for reverse faults, 60° for normal faults, and 90° for strike-slip faults. The moment magnitude (Mw) is calculated from following empirical relationship between the seismic moment (Mo) and the source fault area (S). 1st stage from Somerville et al. (1999): Mo=(S/2.23×10 15 ) 3/2 ×10 -7 , Mo < 7.5×10 18 (Mw < 6.5) (1) 2nd stage from Irikura and Miyake (2001): Mo=(S/4.24×10 11 ) 2 ×10 -7 , 7.5×10 18 <= Mo <= 1.8×10 20 (6.5 <= Mw 1.8×10 20 (7.4 <= Mw) (3) The average slip (D) is estimated from the equation D = Mo/(μS). Here, μ is stiffness factor. The “microscopic fault characteristics” are represent the characteristics of the slip on the fault that the location, number, and area of asperities, average slip of asperities (D asp ) and background areas (D back ), the rake angle, and the slip velocity time function. In the “Recipe”, asperities are considered to be strong motion generating area and indicate areas within the seismogenic layer where the amount of slip is larger than the surrounding area. The location of the asperities is based on the pre-evaluation and active fault map. However, this information is very uncertain, and multiple cases are conservatively recommended from the viewpoint of disaster prevention. The area of asperities is set based on the relationship between the short-period level of the source fault model and the total area of asperities (e.g., Dan et al. 2001). The D asp is twice the D (e.g., Somerville et al. 1999). The D back was recalculated by subtracting the Mo of the asperity from the Mo of the entire fault model and divide by the background area and μ. The rake angle is set based on the active fault evaluations, however if none is available, it is based on the standard slip direction of the fault type: reverse fault 90°, normal fault -90°, left lateral fault 0°, and right lateral fault 180°. The slip velocity time function that determines the shape of the synthetic waveform is approximated by Nakamura and Miyatake (2000). The rupture initiation point (hypocenter) is generally assumed to be located either the left or right end of the lower edge of the asperity for the case of a strike-slip fault, or the center of the lower end of the asperity for the case of a dip-slip fault. 2.2 Setting up a strong motion prediction model for the Noto Peninsula area using only prior information In this study, fault model was set using data obtained exclusively prior to the 2024 Noto earthquake, with the objective of conducting a retrospective prediction. Here, the fault traces are approximated by rectangles, and “consecutive rupturing models” set up based on the combination pattern of these rectangles. This approach is employed to investigate the diversity of rupture propagation. Six fault planes were chosen from the offshore fault traces around the north and eastern coast of the Noto Peninsula (Figure 1). Strong motions were computed by the10 cases of single and combined rupture models (“consecutive rupturing models”) with these 6 faults (Figure 2a). Subsequently, 4 additional uncertainties, “Concept of Fault Width”, “Shallow Fault Inclusion”, “Hypocenter Position” and “Rake Angle” were considered (Figure 2b). The fault position, length, and strike are set based on the fault traces that were mapped prior to the Noto earthquake. The width of the fault model (relation of the bottom depth and dip angle of the fault) is set based on the two concepts considering uncertainties. The “Average Model” uses the average value of the observed data, whereas the “Expansion Model” considers uncertainties and sets the moment to be larger than that of the “Average Model”. In the “Average Model”, the depth at the bottom of the fault is set to 16 km. The C-horizon in the acoustic stratigraphic profile is regarded as a Conrad discontinuity (MEXT and JAMSTEC 2015). The dip angle of 60° is derived from the apparent dip angle in the acoustic stratigraphic profile (MEXT and JAMSTEC 2015). Inversion tectonics has been observed in the Japan Sea region, where normal faults that formed during the opening of the Japan Sea reactivate as reverse faults within the current compressive stress field (Okamura 2000). The model is designed to align with these tectonic processes. In the “Expansion Model,” the depth at the bottom of the fault is set to 20 km. This value is derived from the distribution of hypocenters before the Noto earthquake, and refers to the slightly deeper hypocenters around earthquake swarm on the fault D in Figure 1 (e.g., Wang et al. 2024). The dip angle has been set to 45°, which is a standard setting for reverse faults as shown in the “Recipe”. The top depth of the fault was divided into two cases: one including and the other not including shallower than the seismogenic layer (shallow-zone). In the case of including the shallow-zone, depth of fault top is set to the seafloor (0 km). The depth of the top of the seismogenic layer is assumed to be around 3 km based on basically inland fault models. All parameters for length and width are rounded to the nearest 100 m to apply to a 1000 m mesh fault plane. As with the “Recipe”, the Mo was calculated using the three-stage scaling relation. The range of the Mw of the fault models is 7.0 to 7.6 for the “Average Model” and from7.2 to 7.7 for the “Expansion Model”. The average slip (D) was similarly set from the formula of D=Mo/μS (μ=3.12×10 10 N/m 2 ). In this study, we call the region with large slip in the seismogenic layer is the “strong motion generating area (SMGA)”, whereas the other area is defined as the “background area (BG)”. In the shallow-zone, the large slip area is called the “large slip area (LS)”, while the other area is referred to as the “small slip area (SS)”. The LS is an extension of the shallow side of the SMGA and has the same amount of slip as the SMGA. The SS has the same amount of slip as the BG. The SMGA was set in the middle of the strike direction of the fault plane, at the upper end of the seismogenic layer. With reference to previous study (Somerville et al. 1999; Miyakoshi et al. 2001), the area of the SMGA was set as 25% of the area of the seismogenic fault. The length of SMGA is about 50% of the fault length. The rupture initiation point was set at the center of the lower end of the SMGA. The amount of slip for SMGA and LS was set as twice that of average slip of the fault. The rake angle was set at 90° as the standard setting for reverse faults, and uncertainty of +45° was considered. All fault parameters are shown in additional file (see Additional File 1). Two different slip velocity functions that for seismogenic layer (Nakamura and Miyatake 2000) and long period waveform in shallow-zone (the regularized Yoffe function: Tinti et al. 2005) were used. The parameters of the regularized Yoffe function were derived from the empirical relation of previous study (Tanaka et al. 2018). 3 Strong motion calculation for Noto earthquake 3.1 Methods In this study the wavenumber integral (WI) method (e.g., Hisada 1997 ) is used for ground motion calculations. These seismic motions are evaluated under the assumption of parallel stratified ground. This method enables us to consider the directivity effects and fling step of the source fault. In addition to the parameters set in the previous chapter, the WI method requires 1D velocity structure at each calculation point (Fig. 1 ). The velocity structures are derived from the 250 m mesh subsurface structure published in “J-SHIS” a database of the NIED (NIED 2019). The coordinates of all calculation points are shown in additional file (see Additional File 2). The acceleration waveforms were calculated using the WI method, and the velocity waveforms were obtained by integrating the acceleration waveforms in the frequency domain. To focus on relatively long-period strong motions that may affect building damage, 1 second low-pass filter was applied to the calculated waveforms, and periods shorter than 1 second are truncated. The 1 second low-pass filter was also applied to the observed waveforms at the strong motion observation points, and the calculated results were compared with these observed waveforms and maximum horizontal velocities. As an example, Fig. 3 shows the time history waveforms of three components calculated from the fault models and the observed waveforms. Waveforms were calculated for 80 seconds, a time scale that fully encompasses the peak of strong motion in the study area, however here they are shown cut off at the time when the large waveform at the observation points had converged. The waveforms from the total 64 pattern models shown in Fig. 3 are plotted in gray, and the observed waveforms in red. Here, we summarize the characteristics at each observation point. At ISK001 (P50, Otani), the long duration in the observed waveform could not be reproduced. While the observed waveform exhibits two peaks around 5 seconds and 15 seconds, the calculated waveforms show either a peak around 5 seconds or around 12–13 seconds, with the peak position being one or the other. However, the predicted maximum velocity is generally well-captured except for the EW component. The UD component tends to be overestimated, however when the rake angle is set to 135°, the amplitude is suppressed, bringing it closer to the observed value. ISK003 (P52, Wajima) does not reproduce the long duration in the observed waveform. The waveform calculated from some patterns of the set fault model can express the peak around 10 seconds. There are models that are relatively well reproduced around 5 to 10 seconds. The amplitude covers the maximum velocity of all components, however for the UD component, the calculated waveform shows almost no down component. This includes the down wave observed around 15 seconds in the measured waveform. ISK006 (P54, Togi) shows that part of the set fault model well reproduces the peaks and troughs of the observed waveform up to around 27 seconds. However, the second peak, particularly prominent in the UD component around 30 seconds, does not appear in the calculated waveform. The amplitude generally covers the maximum values of the observed waveform for all components. For ISKH01 (P60, Suzu), setting the slip angle to 135° resulted in a larger horizontal component, bringing the waveform characteristics closer to the observed waveform, while the amplitude also approached that of the observed waveform. When the rake angle was set to 135°, the waveform captured the characteristics of the observed waveform for the very initial portion of the shaking up to around 10 seconds. The amplitude generally encompassed the maximum values of the observed waveform for all components. ISKH02 (P61, Yanagida) does not reproduce the long duration in the observed waveform. It reproduces the waveform up to around 15 seconds reasonably well for some of the configured models. Amplitudes tend to be underestimated for the NS component. This failure to reproduce the long duration prevents the capture of the large amplitude arriving around the 30-second mark in the observed waveform. 3.2 Results Figure 4 shows the predicted and observed strong motions. The calculation of strong motions was conducted at 26 observation stations (squares in Fig. 4 a) and 35 additional points near the coast to ensure coverage of the area between the stations (circles in Fig. 4 a). Figure 4 a plots the maximum horizontal velocity (upper left) and median values calculated by the “consecutive rupturing models”, Model 01 and Model 10, for the rake angles of 90° and 135°. Model 01 is an example of a rupture propagation pattern that closely resembles the rupture area of the Noto earthquake, while Model 10 is an example of rupture with a more limited area. The rupture propagation pattern demonstrates a strong correlation with the locations of significant amplitudes. The distribution of modeled strong motions along the northern coast of the Noto Peninsula and Sado Island is in good agreement with the observed strong motion pattern. Around Monzen, where peak motion is pronounced, there is a slight discrepancy between the observed and calculated peak locations. When the rake angle was set to 135°, the amplitude was found to be larger than when the rake angle was set to 90°, and was more pronounced around Monzen. Figure 4 b shows the results of all the “consecutive rupturing models”. The red crosses represent the observed values, which correspond to the values indicated by squares on the map in Fig. 4 a. The maximum values observed and calculated from Wajima to Suzu and Sado on the northern coast of the Noto Peninsula are comparable, considering variations in fault parameters, and are predicted with a reasonable. Conversely, the maximum values on the west coast tend to be similar or slightly smaller. The maximum value was observed in the Monzen area, with an amplitude of approximately 170 cm/s, which is comparable to the observed amplitude, including uncertainties. However, this location was not the Monzen observation point, but calculation point 22, which was situated slightly to the east. The maximum value on the southern coast of the Noto Peninsula also tends to be slightly smaller and is often underestimated, particularly in the Anamizu area. When the rake angle was set to 135°, the strong motion amplitude was comparable to or exceeded the observed amplitude at most points. However, it was slightly smaller on the west coast. In the southern coast, the results tend to be smaller than the observed amplitudes. 4 Range of uncertainties and regionality 4.1 Consideration by Tornado Plots for the Epistemic Uncertainty There are few examples discussing epistemic uncertainty in fault parameter settings. However, the “Ikata SSHAC Project (Fujiwara et al. 2024 )” is one such example. The project employed a Tornado Plot (TP) to evaluate the effect of epistemic uncertainty on strong motion prediction results. Additionally, the utilization of TP serves to illustrate the extent of uncertainty surrounding the given values. However, while examples discussing uncertainty are mainly related to the evaluation of nuclear power plant sites, no examples showing a wide-area distribution like this study have been identified to date. The TP plots the average velocity for all the branches in Fig. 2 b when only one branch is considered. By doing this approach for all 61 calculation points (Fig. 1 ) for the 5 branches, the most influential parameters for each region are identified. The examples of TP are shown in Fig. 5 a. The examples of calculation point affected by the fault planes D, E, F are shown. The influence of the “Concept of Fault Width” is significant at point 34 on the east side of the northern coast, while at point 27 on the west side of the northern coast, the “Rake Angle” is significant. At point 16 west of point 27, the “Concept of Fault Width” and the “Rake Angle” are nearly equivalent. Consequently, the parameters that have a significant influence differ depending on the position of calculation point. The standard deviations of each branch in the TP for the 61 calculation points are that ranked from largest to smallest, and plotted on the maps (Fig. 5 b). The predominant uncertainty at numerous locations is the “Propagation Pattern”. However, near the boundary between faults D and E, other factors such as “Rake Angle” and “Concept of Fault Width” emerged as significant contributors. In many locations, the second influential factor was the “Concept of Fault Width” which is associated with the amount of seismic moment. The third and fourth factors are relatively scattered. In the vicinity of the Monzen, the “Rake Angle” emerges as the second most influential factor, with the “Concept of fault width” ranking third in terms of influence. The “Shallow Fault Inclusion” does not have a substantial impact the third factor at on strong motion at the most sites, however it is the third factor at some sites. 4.2 Uncertainty of SMGA position The location of the SMGA is a parameter that is difficult to predict. Even in the “Recipe”, it is recommended that multiple patterns for the SMGA location should be considered. In this study, the “Expansion Model” of Model 01, the model most likely to the Noto earthquake, was used to illustrate the range of uncertainty regarding the SMGA location. The rupture initiation point was set to fault plane D, and with a rake angle was of 135°set within a configuration that considered the shallow segment of fault. The SMGA was set to a total of three locations: the center of the shallow side of the fault plane, as set in the previous chapter, along the strike direction, as well as on the right and left sides of the shallow side. By comprehensively combining these for six fault planes, a total of 729 combinations were formulated (Fig. 6 ). The calculation results are shown in Fig. 7 . Figure 7 a shows the distribution of maximum velocity is depicted each calculation point when the position of SMGA is set at all in the center, right, and left. Directly above the SMGA on the northern coast of the Noto Peninsula, differences in the location of SMGA affect the calculation results, particularly around Monzen. Figure 7 b shows the range of uncertainty due to the position of the SMGA. The median value among the 729 calculated patterns is indicated by a blue circle, with the error bars showing the range of variation. The calculation results for the three cases shown in Fig. 7 a are represented by gray symbols for reference. The observed values are indicated by red crosses. The range of variation is very small in locations distant from the SMGA, such as the west and south coasts of the Noto Peninsula and Sado Island. However, along the northern coast of the Noto Peninsula, this factor contributes to a substantial range in the predicted strong motion. Along the northern coast of the Noto Peninsula, the variation is about 1.5 times the median value (Fig. 7 b). 5 Discussions First, we discuss the reproducibility of observed waveforms and the challenges of characteristic source models in this study. The observed waveforms and calculated waveforms shown in Section 3.1 (Fig. 3 ) were evaluated based on the following three criteria and summarized in Table 1 : 1. Duration (reproducibility of waveform duration), 2. Waveform (reproducibility of waveforms around peak amplitude), and 3. Amplitude (whether the observed maximum velocity was covered). Based on this evaluation, we discuss the reasons why reproduction was difficult. Furthermore, among the characteristic source models commonly used for strong motion prediction in Japan, the asperity model (Kanamori 1981 ) is a source fault model designed to represent characteristics of strong motion linked to seismic hazards, such as the pulsed seismic waves observed near the source fault, without losing them. We consider what is necessary to ensure the minimum functionality required for setting up such characteristic source models. Table 1 Comparison of waveforms between observation and calculations. 〇=Relatively good fitting or no underestimation, △=Partially fit or slightly underestimated, ×=Doesn’t fit or underestimated. Station Rake 1. Duration 2. Waveform (around peak amplitudes) 3. Amplitude (coverage for maximum velocity) NS EW UD ISK001 (Otani, P50) 90 deg. × × 〇 × 〇 135 deg. × × 〇 △ 〇 ISK003 (Wajima, P52) 90 deg. × △ 〇 〇 〇 135 deg. × 〇 〇 〇 〇 ISK006 (Togi, P54) 90 deg. 〇 〇 △ 〇 〇 135 deg. 〇 〇 △ 〇 〇 ISKH01 (Suzu, P60) 90 deg. 〇 × 〇 〇 〇 135 deg. 〇 △ 〇 〇 〇 ISKH02(Yanagida, P61) 90 deg. × 〇 × 〇 〇 135 deg. × 〇 × 〇 〇 For “1. Duration,” while the duration of shaking characteristic of typical earthquakes was captured, the waveforms in Otani (ISK001), Wajima (ISK003), and Yanagida (ISKH02) did not reproduce the long duration waveforms with multiple wave groups characteristic of the Noto earthquake. Such waveforms are suggested to result from multiple sources rupturing with time delays and propagating over a wide area (e.g., Okuwaki et al. 2024 ; Xu et al. 2024 ; Ma et al. 2024 ). Characteristic source models can relatively well reproduce observed waveforms from previous earthquakes when the event can be approximated by a simple model, such as a single fault plane with a few asperities. However, in earthquakes like the Noto earthquake, where multiple fault segments ruptured simultaneously, or in earthquakes involving complex rupture processes, it is difficult to reproduce the observed waveforms using simple models. For “2. Waveform,” while some observed waveforms around the peak amplitude relatively captured characteristics predicted by calculated waveforms derived from parts of the set fault model patterns, results for locations such as Otani (ISK001) and Suzu (ISKH01) did not capture characteristics well. As mentioned in “1. Duration,” observed waveforms exhibiting multiple wave groups due to multiple rupture in the wide area or complex source processes that cannot be represented by a single fault plane are difficult to reproduce using simple characteristic source models. For “3. Amplitude,” while some components show tendencies toward underestimation or overestimation, the maximum velocity of each waveform component is covered equivalently or relatively well. The amplitude results presented here were obtained by setting the SMGA on the shallow side of the fault plane's strike direction center. Furthermore, the same setting was applied to all fault planes. Comprehensive examination by combining the right and left sides of the fault plane may offer potential for improvement. Based on these results, the characteristic source model examined in this study can to some extent capture the characteristics around the peak of seismic waveforms with a period of approximately one second near the source fault, which significantly influence building damage. Furthermore, by assuming the interaction of multiple segments rather than a single fault plane and employing parameter settings that account for multiple pattern combinations and uncertainties, it is generally possible to cover the maximum amplitude of observed waveforms. On the other hand, capturing the characteristics of multiple wave groups and long duration caused by complex rupture processes and multiple rupture propagation is difficult using simple methods for setting characteristic source models. To address this challenge, we propose an evaluation based on more lenient criteria that do not require waveform matching. This is because, particularly near faults, the influence of fault motion directly beneath the observation point is dominant, and the impact of seismic waves from distant faults on damage is small. Therefore, even if waveform shapes do not match, capturing minimal waveform characteristics is considered sufficient for hazard assessment. The proposal and rationale for this approach are summarized below. 1. Coverage of maximum amplitudes in the frequency band around 1 second related to building damage Amplitude, directly related to shaking intensity, is a critical characteristic of seismic waveforms related to building damage. Given that distance attenuation formulas are sometimes used in seismic hazard assessments, covering the maximum amplitudes from past earthquakes is considered the most important criterion. 2. The duration of main shaking is reproduced. The Noto earthquake suggested that long shaking may have exacerbated damage. The duration of shaking is a critical characteristic of seismic waveforms related to damage for disaster prevention. 3. The period response spectrum is appropriate Structures exhibit different response periods. Resonance occurs when the period of the seismic wave matches the building's period, leading to increased damage. Since the period of predicted seismic motion relates to seismic design and planning, it is necessary that the predominant period generally matches that of past major earthquakes. For point 1, while considering uncertainties in individual fault parameters as done in this study largely covered the maximum amplitude of the waveform, to address factors not covered by assuming a simple fault model, incorporating a range of several times the variation in the calculated waveform can reduce underestimation. For point 3, rather than focusing solely the fundamental period reaches maximum velocity, examining the range around the maximum velocity allows us to identify the critical period band that requires attention. Point 2 is a criterion that is currently not being well reproduced. As detailed later in this chapter, resolving this issue requires elucidating the relationship between shaking duration and damage effects, as well as understanding the mechanism of rupture propagation and the source triggering. The Noto earthquake was a large earthquake occurring within an earthquake swarm zone; the environment conducive to earthquake swarm likely led to complex rupture propagation. The environment around the source may also be relevant to predictability. Therefore, it is necessary to elucidate earthquake characteristics and propose modeling methods to simplify, standardize, and generalize these phenomena for incorporation into models. However, this is a challenge for the near future. Until it is resolved, it is important to conduct evaluations with flexibility for criteria like 1 and 3, indicating possible phenomena within a certain range. At this point, it is critically important to clearly distinguish and present the uncertainty of parameters for which scientific evidence can be provided, from the randomness or “variability” inherent in simulations and natural phenomena. Next, we describe the verification of the Noto earthquake based on the comparison of maximum velocities conducted in this study. Especially we will discuss for the underestimation on the southern and west coasts of the Noto Peninsula. A possible reason for the underestimation in the southern Noto Peninsula, particularly around Anamizu, is the amplification of effects resulting from irregular and heterogeneous subsurface conditions. The results of the reflection survey as Hayashi et al. ( 2008 ), indicate that in the vicinity of Anamizu, seismic waveforms are amplified by an edge effect caused by sudden changes in subsurface structure. It is important to the detailed characteristics of subsurface structural effects in highly accurate strong motion predictions. However, as the main focus of this study is on methods for constructing fault models, this is considered a separate issue and will not be discussed further here. However, point 51, located east of the southern coast of the Noto Peninsula, falls within the projection of the Fault plane D and is close to the hypocenter of the Noto earthquake. It is also close to the earthquake swarm that occurred before the Noto earthquake occurred, and there is a possibility that the slip on the fault plane is more complex and heterogeneous, which requires further consideration in the fault model. The tendency to underestimate the maximum velocity distribution along the west coast of the Noto Peninsula may be attributed to a discrepancy in strike between Fault F and the actual ruptured fault during the Noto earthquake. Figure 8 shows the Japan Meteorological Agency (JMA) hypocenter distribution and cross-section for one month after the Noto earthquake. Although the data are preliminary, the hypocenters on the A-A' cross section do not appear to align with the fault trace of the modeled fault plane F. Instead, they are located along an east-dipping structure with a generally north-south strike near the coastline, where no mapped fault trace currently exists. Information regarding active faults is essential for the development of fault models. It should be based on mapped fault traces and primary survey data. A fault model including this fault plane could not be predicted, however calculations were conducted to see how much the predicted results would have changed if this fault had been able to be estimated. The new fault model is Model 11, which represents a change in the strike of fault along the west coast compared to the previously mentioned Model 01, shifting to a north-south orientation. The modeling method and calculation techniques are the same as previous sections. Figure 9 a shows the median maximum values at each calculation point for the six calculation patterns included in Model 11. Figure 9 b compares them with Model 01 and observed data. Compared to Fig. 3 a, the predicted strong motions on the west coast of the Noto Peninsula are slightly larger than those of Model 01. This is particularly noticeable in the example where the rake angle is set to 135°. Figure 9 b presents the median value for each model as red or blue symbols, with error bars denoting the range of uncertainty. In the Hakui-Shika area on the west coast of the Noto Peninsula, Model 11 predicted larger strong motions than Model 01, where the fault on the west coast strikes east-west, and is closer to the observed values. Moreover, around Monzen, where particularly large shaking was observed, Model 11 predicted larger strong motions than Model 01. In contrast, the difference is not significant in the Wajima-Suzu and Sado areas on the north coast of the Noto Peninsula. Next, Fig. 10 shows the results of modifying the SMGA position for the “Expansion Model” of the Model 11, with the rupture initiation point at D and a rake angle of 135°. As with Model 01, SMGA is set in three patterns on the shallow side of the fault plane, and by comprehensively combining these a total of 729 calculation patterns are obtained. Figure 10 a shows the median of the maximum values at each calculation point is depicted when SMGA are all set to the center, right, or left on the six fault planes. The case in which SMGA are situated to the right of the fault plane shows significantly larger strong motions from the west coast of the Noto Peninsula to Monzen. Conversely, the case in which SMGA are all set to the left shows generally smaller ground motions compared to the other cases, although some areas of Shika show significantly larger strong motions. Figure 10 b shows the median values are represented by blue circles, with error bars denoting the range of variation. Gray symbols also show the results for the center, right, and left cases shown in Fig. 10 a. The observed values indicated by red crosses generally fall within the error bar range in most areas, with the exception of the southern coast of the Noto Peninsula. A comparison of Fig. 10 with Fig. 7 , the prediction results for the west coast of the Noto Peninsula have slightly improved, and the prediction for the Monzen area is significantly larger. The fault model on the west coast of the Noto Peninsula, when considered in relation to the source fault of the Noto earthquake, slightly improved prediction. However, even with the east-west strike models, there are no underestimation of the north coast and the Sado. Furthermore, there is no particular large underestimation on the west coast. Consequently, it can be deduced that, to some extent of prediction was possible with prior information alone. However, with the improvement of fault information, there is a possible for further enhancement in the accuracy of predictions. The treatment of faults not included on active fault maps necessitates discussion incorporating the distribution of active faults in surrounding areas and original survey data. Another characteristic of the strong motion from the Noto earthquake was its long duration. This study was used as a simple prediction model, so it was not possible to capture the characteristic waveforms that continued for long periods of time, as shown in Fig. 3 . Therefore, the model could not capture the waveform characteristic of long durations. As mentioned above, covering the maximum value is important in predictions. However, the long duration of the Noto earthquake may have amplified its damage. Therefore, predicting only the maximum value is insufficient. The characteristics of the ground motion from the Noto earthquake suggest that it was caused by the rupture of two hypocenters that occurred with a time lag (e.g., Okuwaki et al. 2024 ; Xu et al. 2024 ; Ma et al. 2024 ). In other words, the M5.9 earthquake occurred 13 seconds before the M7.5 earthquake, and the two earthquakes thought to be the result of a single source process (Peng et al. 2025 ). These two nearby earthquakes are thought to have propagated bilaterally, westward and eastward, respectively. Additionally, the area near the hypocenters experienced an increase in earthquake swarm activity since 2020. This swarm activity is thought to be related to water and to have a low-velocity structure (e.g., Xu et al. 2024 ; Peng et al. 2024; Liu et al. 2024 ). A future challenge will be determining how much of the environment’s complexity at and near the source can be reflected in predictive models. Furthermore, in this study we postulated an exhaustive array of rupture propagation patterns. For a hazard assessment, we need a measure of the “likelihood of occurrence” for these patterns. However, the activity of faults is not always clear. In such cases, Biasi and Wesnousky ( 2021 ) proposed a method for estimating the probability of rupture propagation based on the distance and geometry between faults. Although issues arise when applying this method to dip-slip faults or considering stress changes associated with earthquake occurrence, active fault information is the most readily available data prior to an earthquake. Thus, determining the rupture propagation rate using this method is considered beneficial for the modeling approach in this study, as it constructs fault models based on this information. As shown in Fig. 4 b, the uncertainty of parameters affects the results of strong motion prediction, with the “Rupture Propagation Patterns” being the main factor. The “Concept of Fault Width” is the second most influential parameter for most calculation points. However, on the western side of the northern coast, the “Rake Angle” is the influential parameter. This area is close to the upper end of the fault plane and is susceptible to the effect of slip generated in the shallow part of the fault. The reason the “Concept of Fault Width” had a significant influence was that setting the dip angle to 45° brought the calculation point closer to the fault plane than setting it to 60°. There is limited research on how to consider for epistemic uncertainty in fault parameters when setting up prediction models. More detailed examinations and discussions are needed. The position of the SMGA is one of the parameters that should be treated as aleatoric uncertainty. In this study, three locations were set along the strike direction of the shallow side of the fault plane: the center, right side, and left side, and their combined influence was confirmed. The influence was particularly large in areas where the shaking was large, with a range of approximately twice the median value. Conversely, in areas where the predicted shaking was small, the range of variation was also small. Finally, Fig. 11 shows a comparison of the prediction results from Model01 and the observed values from the Noto earthquake when considering all the uncertainties examined in this study. The uncertainty range was obtained by multiplying the maximum and minimum values derived from considering the “Concept of Fault Width”, “Shallow Fault Inclusion”, “Hypocenter Position” and “Rake Angle” (as shown in Fig. 2 b) by the multiplier relative to the medium value of the SMGA uncertainty range. Along the west coast of the Noto Peninsula, the predictions are slightly lower than the observed values, however then almost entirely cover them. Along the northern coast of the Noto Peninsula and on Sado Island, the observed values are within the predicted range. Along the southern coast of the Noto Peninsula, there is a clear underestimation around Anamizu; elsewhere, however predictions are quite close to observed values. Although the uncertainties considered in this study are limited, incorporating various uncertainties and diversities suggests that predictions using only information available prior to the Noto earthquake are generally feasible. However, as shown in Fig. 11 , there is significant uncertainty, particularly along the northern coast of the Noto Peninsula. This substantial uncertainty is largely influenced by the rake angle and the position of the SMGA. The rake angle can be constrained by tectonics, geology, and geodetic data to some extent. The position of the SMGA might also be constrained by its proximity to features like mountains and hills, where accumulated displacement from past seismic activity is thought to exist. Incorporating information not considered in this study, such as geology and topography, could potentially reduce this significant uncertainty in the future. 6 Conclusions To verify the predictability of strong motion from the Noto earthquake, we conducted a retrospective prediction analysis. By incorporating geological information as prior information into basic fault model setting methods (such as “Recipe”) and accounting for uncertainty, strong motion was generally predictable except for the west and south coasts of the Noto Peninsula. The tendency toward underestimation was attributed to the fact that the fault mapped prior to the Noto earthquake differed from the fault that actually ruptured on the west coast, and to significant ground amplification on the south coast. Regarding the uncertainties considered in this study, an examination of the factors exerting the most significant influence on each calculation site revealed that the “Rupture Propagation Patterns” is the primary factor at many sites. While the second most influential parameter at many sites is the “Concept to Fault Width,” the “Rake Angle” exerts a greater influence at calculation sites closer to the fault top. Since this study sets the fault models based on active fault distribution data, factors contributing significantly to uncertainty may exhibit regional characteristics. A key challenge in this study is the application limits of the characteristic source model. By incorporating fault parameter uncertainties and variation of rupture propagation patterns into the characteristic source model, it can relatively well reproduce observed waveforms within the range approximatable by a simple model. However, it difficult to reproduce observed waveforms associated with complex source processes, such as those possessing multiple wave groups. Rather than aiming for exact waveform matching, it is necessary to allow evaluation based on more lenient criteria such as “coverage of maximum amplitude,” “duration of shaking,” and “reasonableness of the periodic response spectrum.” Furthermore, by applying evaluations with a certain degree of flexibility not only to the uncertainty of fault model parameters but also to computed waveforms and periodic response spectra, it is considered possible to apply this approach to hazard prediction. However, regarding “duration of shaking,” it is necessary to elucidate the relationship between duration and damage, as well as the relationship between rupture propagation, triggering, and the environment around the source. It is also necessary to consider how to simplify such complex phenomena and incorporate them into the prediction model. Declarations Ethics approval and consent to participate Not applicable Consent for publication Not applicable Availability of data and materials The strong motion data from K-net and KiK-net set up by the National Research Institute for Earth Science and Disaster Resilience (NIED), and also used data by the Japan Meteorological Agency (JMA), for the comparison of calculated and observed strong motion. The JMA Unified Earthquake Catalog were used to plot the aftershock distribution for the 2024 Noto Peninsula earthquake. Competing interests The authors declare no conflicts of interest regarding this manuscript. Funding Not applicable Authors' contributions N K: Conceptualization, methodology, analysis and original draft F H: Supervision for Seismic Hazard Assessment and review T S: Supervision for Geology and review Acknowledgements This study used data from the strong motion observation network operated by the National Research Institute for Earth Science and Disaster Resilience and the Japan Meteorological Agency. This study was conducted within the Endowed Research Laboratory of OYO Corporation (October 2019 - October, 2025). We would like to express our gratitude to them here. Authors' information N K: Research fellow of International Research Institute of Disaster Science (IRIDeS), Tohoku University. Member of the Seismological Society of Japan and Japanese Society for Active Fault Studies. The Professional Engineer, Japan (Applied Science). F H: Project Director of National Research Institute for Earth Science and Disaster Resilience. Ph.D. in Science. 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GraphicalAbstractImage.png Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Major Revision 09 May, 2026 Reviewers agreed at journal 15 Mar, 2026 Reviewers invited by journal 13 Mar, 2026 Editor assigned by journal 19 Feb, 2026 First submitted to journal 09 Feb, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8837779","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":605630069,"identity":"e8a7b9e6-abd9-46ab-bf22-fac428b570e6","order_by":0,"name":"Kimie Norimatsu","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0009-2374-8218","institution":"Tohoku University - Aobayama New Campus: Tohoku Daigaku - Aobayama Shin Campus","correspondingAuthor":true,"prefix":"","firstName":"Kimie","middleName":"","lastName":"Norimatsu","suffix":""},{"id":605630070,"identity":"b8234006-9433-4f68-bf6e-ca43f1eeff4a","order_by":1,"name":"Hiroyuki Fujiwara","email":"","orcid":"","institution":"National Research Institute for Earth Science and Disaster Resilience: Bosai Kagaku Gijutsu Kenkyujo","correspondingAuthor":false,"prefix":"","firstName":"Hiroyuki","middleName":"","lastName":"Fujiwara","suffix":""},{"id":605630071,"identity":"d9f5c104-cec5-41f2-9ef6-c7a83c51f1dd","order_by":2,"name":"Shinji Toda","email":"","orcid":"","institution":"Tohoku University - Aobayama New Campus: Tohoku Daigaku - Aobayama Shin Campus","correspondingAuthor":false,"prefix":"","firstName":"Shinji","middleName":"","lastName":"Toda","suffix":""}],"badges":[],"createdAt":"2026-02-10 07:28:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8837779/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8837779/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104702555,"identity":"8f8531dd-df11-4395-8ad9-ee1b4c1b7978","added_by":"auto","created_at":"2026-03-16 08:43:49","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":456280,"visible":true,"origin":"","legend":"\u003cp\u003eMap of the Noto Peninsula study area. The epicenter locations of the Noto Peninsula earthquake and the mechanism solution by the USGS W-Phase inversion are shown. The locations of the fault models, rupture initiation points, and calculation points are also shown. The points indicated by squares are the calculation points on the strong motion observation points, and the points indicated by circles are the calculation points around the coastline to cover the space between the observation points.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/e9c28ddb883e5d0b13be4a1b.png"},{"id":104782243,"identity":"72c08731-1c2d-4e2f-8098-73f4647c5d2d","added_by":"auto","created_at":"2026-03-17 07:57:02","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":356918,"visible":true,"origin":"","legend":"\u003cp\u003eConcept of fault model setting. (a) Distribution and combination patterns of rectangular faults around the Noto Peninsula. A total of 10 “consecutive rupturing models” were set up. (b) The concept of uncertainty assumed for each “consecutive rupturing models”. Each model is divided into an “Average model” and an “Expansion model.” In addition, cases that include or exclude the shallower than the seismogenic layer and cases that have different Hypocenter position (nucleation points) are considered, resulting in 8 or 4 patterns. And also considered 2 patterns of rake angle uncertainties.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/f8b62b0fd4b238864871f7c8.png"},{"id":104702397,"identity":"7dbcf27d-d771-46da-b437-bc541b26d2dd","added_by":"auto","created_at":"2026-03-16 08:43:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":564787,"visible":true,"origin":"","legend":"\u003cp\u003eCalculated waveforms and observed waveforms. Calculated waveforms for all patterns set considering uncertainty (show in black) and observed waveforms at major strong motion observation points (show in red).\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/8b5d0243fb869d56f28a3983.png"},{"id":104702399,"identity":"9bb59574-fd0e-4216-b5c5-98d0a02e4612","added_by":"auto","created_at":"2026-03-16 08:43:11","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":599278,"visible":true,"origin":"","legend":"\u003cp\u003eComparison between the maximum velocity distribution calculated from the fault model and the observed. (a) Distribution of the maximum velocity observed during the Noto earthquake and the median values calculated using Models 01 and 10, rake angle setting on 90° and 135°. The median values correspond to the values of the colored circles in (b). The points indicated by squares are the calculation points on the strong motion observation points, and the points indicated by circles are the calculation points around the coastline to cover the space between the observation points. (b) Calculated velocity from all models, where the horizontal axis is the calculation point number, corresponding to Figure 1. The median of the velocity for each consecutive rupturing model is indicated by a colored circle, and the range of uncertainty is indicated by an error bar. The red crosses are observed values.\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/da3e25b877f75aa5a6a6bdec.png"},{"id":104702527,"identity":"96bc4c6c-0bec-4b06-ae89-3b8dfb7e89cf","added_by":"auto","created_at":"2026-03-16 08:43:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":540679,"visible":true,"origin":"","legend":"\u003cp\u003eEvaluation of the range of uncertainty and regional distribution of uncertainty. (a) Example of tornado plot make for each calculation point showing the range of uncertainty for the branches in Figure 2b. The horizontal axis shows the level of the hazard, and the vertical axis shows the branch items. (b) The standard deviation for each branch of the tornado plot at each calculation point was determined, ranked and plotted on the map to show the regional distribution of the uncertainty.\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/182c18ea779f569e65ebbbe1.png"},{"id":104702503,"identity":"dc3f90b0-0a0d-4aa3-95e1-93f5d23aadd1","added_by":"auto","created_at":"2026-03-16 08:43:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":206116,"visible":true,"origin":"","legend":"\u003cp\u003eSMGA settings for considering the positional uncertainty. a) SMGA positions were set in three patterns: center, right, and left of strike directions on the shallow side of the fault plane. b) By comprehensively combining the three patterns from a) across six faults, a total of 729 patterns.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/c966e292be189eb249575bb4.png"},{"id":104702558,"identity":"43a44145-bb21-42c6-809f-cb7b65013f22","added_by":"auto","created_at":"2026-03-16 08:43:50","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":318471,"visible":true,"origin":"","legend":"\u003cp\u003eCalculation results considering the positional uncertainty of the SMGA. a) Maximum velocity distribution when all SMGA are center, right, or left. b) The median value for all 729 patterns at each calculation point is shown as blue circle, with the range of variation indicated by error bars. Calculation results when all SMGA are center, right, or left are shown as gray symbols and observation data shown as red crosses.\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/7faf71eb9f5e4d6dc0d57c18.png"},{"id":104702564,"identity":"713b50f0-75b0-4aa7-af94-babd06b88c57","added_by":"auto","created_at":"2026-03-16 08:43:56","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":676358,"visible":true,"origin":"","legend":"\u003cp\u003eHypocenter distribution and cross sections. Hypocenter distribution by the JMA data during a month after the Noto Peninsula earthquake (January 1 to 31, 2024). Fault traces of the offshore area are also shown. In addition, cross sections plotted along three lines on the map are shown. The red dotted line indicates the assumed fault dip orientation.\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/974bb4c0d5c660233a282e4a.png"},{"id":104702487,"identity":"c6fbf555-8011-4dee-b84f-bf6093623dd2","added_by":"auto","created_at":"2026-03-16 08:43:32","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":324381,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of strong motion calculated from post-seismic data and pre-seismic data. Compared the strong motion distributions considering the north-south trending fault identified in the aftershock distribution following the Noto Earthquake and results from a fault model set using only the prior information. a) Distribution of median peak velocity. b) Comparison of results using a fault model based only on prior information (blue symbols) and a fault model using the aftershock distribution of the Noto Earthquake (red symbols). Error bars indicate the uncertainty range for both. Observed values are shown with black crosses.\u003c/p\u003e","description":"","filename":"Figure9.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/eef9ef96b9fbbafb27b6907d.png"},{"id":104702401,"identity":"a9df6d8c-ab73-48aa-be07-cc4323cddb83","added_by":"auto","created_at":"2026-03-16 08:43:12","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":321322,"visible":true,"origin":"","legend":"\u003cp\u003eResults considering SMGA uncertainty for the fault model set considering the aftershock distribution. a) Maximum velocity distribution when the SMGA location is set at the center, right, and left of the strike direction on the shallow side of the fault planes. b) Median values and range of variation for all 729 patterns with varying SMGA locations. The results for the three patterns shown in a) are referenced and indicated by gray symbols. Observed values are indicated by red crosses.\u003c/p\u003e","description":"","filename":"Figure10.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/91233be2fd4b5a710fe05b77.png"},{"id":104702364,"identity":"16979045-2c13-45e0-9213-abbaa047ee60","added_by":"auto","created_at":"2026-03-16 08:43:04","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":80920,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of calculation results applying all uncertainties and observed data. Compared the results obtained by applying all uncertainties considered in this study (Concept of Fault Width, Shallow Fault inclusion, Hypocenter Position, Rake Angle, SMGA position) to Model01, the model set from only the pre-seismic data and closest to the Noto earthquake, with observed data.\u003c/p\u003e","description":"","filename":"Figure11.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/47ab26fd44f0c0f5174ac2f0.png"},{"id":104808497,"identity":"a3e059d0-8aa2-431e-ad1b-9a0a08a98d6a","added_by":"auto","created_at":"2026-03-17 12:38:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4260845,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/eabe5566-c7f7-4eef-83f7-c165e696dff2.pdf"},{"id":104702428,"identity":"d9acde4c-bc62-4277-95c4-22ea939ac876","added_by":"auto","created_at":"2026-03-16 08:43:16","extension":"xlsx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":19382,"visible":true,"origin":"","legend":"\u003cp\u003eFile name: Additional File 1.xlsx (.xlsx)\u003c/p\u003e\n\u003cp\u003eTitle of data: Fault parameter list\u003c/p\u003e\n\u003cp\u003eAll fault parameters set in this study. In the strong motion calculation, fault models were set using a combination of these values. This file will be referred as “Additional File 1”.\u003c/p\u003e","description":"","filename":"AdditionalFile1.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/00be832ba6996742ce8b2c97.xlsx"},{"id":104702543,"identity":"39143113-281d-4481-9d2c-a6d52f515a09","added_by":"auto","created_at":"2026-03-16 08:43:45","extension":"xlsx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":11889,"visible":true,"origin":"","legend":"\u003cp\u003eFile name: Additional File 2.xlsx (.xlsx)\u003c/p\u003e\n\u003cp\u003eTitle of data: Calculation point list\u003c/p\u003e\n\u003cp\u003eThe coordinate information of all calculation points used in this study. This file will be referred as “Additional File 2”.\u003c/p\u003e","description":"","filename":"AdditionalFile2.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/34772814db4c9ffcea4a2414.xlsx"},{"id":104702383,"identity":"1cb53d66-9887-4c11-a0c1-8f6ebc0bb869","added_by":"auto","created_at":"2026-03-16 08:43:06","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":124557,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstractImage.png","url":"https://assets-eu.researchsquare.com/files/rs-8837779/v1/c7ef9ba4a46c5efe087e6732.png"}],"financialInterests":"","formattedTitle":"Validation and Uncertainties of Strong Ground Motion Prediction Methods for Seismic Hazard Assessment: A case study of the 2024 Noto Peninsula Earthquake (Mw7.5), Japan","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eIn earthquake hazard assessment, a fault model is generally constructed based on data on active faults, seismic activity, and subsurface structure surveys, and simulations of strong motion and tsunamis are performed. From the results of these simulations, seismic hazard assessments are conduced to provide predict strong motion and tsunami damage. The Southern California Earthquake Center (SCEC) is developing CyberShake (e.g., Fayaz et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), a probabilistic seismic hazard analysis (PSHA) platform that uses 3D physical models to simulate specific fault ruptures and predict the seismic motions caused by those fault ruptures. SCEC also employs a community fault model (e.g., Plesch et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) based on various observational data to perform strong motion predictions and probabilistic hazard assessments. Concurrently, in Japan, following the proposal of the asperity model (Kanamori \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1981\u003c/span\u003e), a \u0026ldquo;Strong ground motion prediction method for earthquakes with identified source faults (\u0026ldquo;Recipe\u0026rdquo;)\u0026rdquo; (Headquarters for Earthquake Research Promotion [ERP] 2017) has been developed and revised based on the method proposed in response to the 1995 Southern Hyogo prefecture earthquake and the 2000 Western Tottori prefecture earthquake (Irikura \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Setting up the fault models is an important part of hazard assessment, as it is a factor that determines the scale of the hazard. However, numerous challenges arise during the establishment of the fault models employed for strong motion prediction, with the underestimation of predictions being a subject of frequent discourse. In Japan, there are few examples of major earthquakes that occurred on predicted fault models, however the 2016 Kumamoto earthquake and the 2024 Noto Peninsula earthquake (Noto earthquake) are examples that demonstrate the need to consider parameter uncertainty and the diversity of fault propagation patterns in fault models when predicting damage.\u003c/p\u003e \u003cp\u003eThe 2016 Kumamoto earthquake (Mw 7.0: U.S. Geological survey [USGS] Earthquake Hazards Program 2017) was an earthquake for which active fault was evaluated and strong motion prediction results was published (ERP 2014). The previous evaluated fault length was 19 km, and the established fault model (ERP 2014) was 24km in length, 14km in width, and Mw6.5. During the earthquake, about 30 km of surface ruptures (e.g., Kumahara et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Shirahama et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Toda et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) appeared mostly along previously mapped active faults, as the Futagawa-Hinagu fault zone. The length of the fault estimated by source inversion analysis is even longer (for example, 47 km in Irikura et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Furthermore, while the depth of the bottom of the fault was previously estimated to be 10 to 13 km (ERP 2013), subsequent aftershock distribution indicated it extended to approximately 18 km (e.g., Yano and Matsubara \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). These are suggesting that these differences in fault posture and dimension resulted in underestimation of the prediction. Furthermore, the Kumamoto earthquake generated strong and long-period ground motions in the vicinity of the fault, as well as permanent displacement (e.g., Irikura et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Tanaka et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The observed strong motions exceeded those previously predicted for this region, indicating that this phenomenon cannot be adequately explained without considering not only the strong motions due to slip within the seismogenic layer, which is the target of the \u0026ldquo;Recipe,\u0026rdquo; however also the strong motions occurring in areas shallower than the seismogenic layer (Irikura et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Tanaka et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOn January 1, 2024, the Noto earthquake occurred with a magnitude of 7.5 (USGS Earthquake Hazard program 2017). Hypocenter position is indicating red star in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eVarious fault models have been analyzed for the Noto earthquake. These models indicate that the earthquake occurred along the north coast and the offshore area northeast of the Noto Peninsula. Guo et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) constructed a detailed fault model based on hypocenter relocation and estimated a north-dipping fault at the northern end of the rupture zone, with a dip direction opposite to that of the main source fault of the Noto earthquake. The rupture propagation is considered to be bilateral, with a small initial rupture occurring around the hypocenter, subsequently leading to rupture propagation in the west and subsequently in the east (e.g., Okuwaki et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xu et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Ma et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003ePrior to the Noto earthquake, several projects in the Japan Sea had compiled acoustic stratigraphic profiles, mapped fault traces, and established fault models (e.g., The Ministry of Education, Culture, Sports, Science and Technology [MEXT] and Japan Agency for Marine-Earth Science and Technology [JAMSTEC] 2015; Ministry of Load, Infrastructure, Transport and Tourism [MLIT ] 2014). These models were primarily used for the purpose of tsunami prediction, with limited ability to predict strong motions due to offshore faults. The Noto earthquake occurred on modelled faults based on the fault traces, with some exceptions. However, the propagation through long and multiple faults caused by the Noto earthquake was not included in prior hazard assessments, especially in the northeastern end of the aftershock area (fault planes A and B in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn order to mitigate the underestimation of earthquake hazard, it is important to consider uncertainty when setting the fault models. The expression of fault models is characterized by fault geometry and rupture characteristics. However, while there is a certain degree of regularity in fault rupture, earthquake magnitude, and hypocenter location, the occurrence of these events is subject to significant uncertainty. The observation data contained \u0026ldquo;epistemic uncertainty\u0026rdquo; due to insufficient data and expert interpretations. These uncertainties can be resolved through technological advances and the accumulation of knowledge. Conversely, \u0026ldquo;aleatoric variability\u0026rdquo; refers to the heterogeneity inherent in natural phenomena, exemplified by the non-linearity of seismic activity and the intricacy of fault geometries. It is widely accepted that prediction models must incorporate epistemic uncertainty and aleatoric variability to ensure their credibility and relevance. Despite the discourse surrounding the necessity of incorporating epistemic uncertainty into the analysis of fault models for strong motion prediction, this approach has yet to be formally recognized as a standard methodology.\u003c/p\u003e \u003cp\u003eThis study aims to examine the extent to which general strong motion prediction models, primarily those based on the \u0026ldquo;Recipe\u0026rdquo;, could predict the strong motion of the Noto earthquake if considerable uncertainty is taken into consideration, and seeks to obtain feedback that could lead to improvements. It is hypothesized that incorporating uncertainty and diversity into the model will reduce the underestimation of earthquake predictions and provide appropriate information to anticipate various seismic events in the region, facilitating the development of countermeasures.\u003c/p\u003e \u003cp\u003eThe ERP has validated the strong motion prediction method based on the \u0026ldquo;Recipe\u0026rdquo; using the observation record of the Kumamoto earthquake (ERP 2022). For the purposes of this validation, a fundamental fault model was obtained. This model was based on the distribution of surface ruptures (Shirahama et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), aftershock distribution, and source inversions (e.g., Irikura et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Subsequently, adjustments were made to seismic moment and slip distribution. The identification of a fault model capable of reproducing the Kumamoto earthquake provided the necessary feedback needed to improve the method.\u003c/p\u003e \u003cp\u003eIn contrast, in this study, we utilize exclusively information published prior to the Noto earthquake to set the fault models. The extent to which the Noto earthquake could be predicted within the hazard level estimated from the fault models comprehensively set around the Noto Peninsula was verified. The fault modeling method used in this study is a general method such as \u0026ldquo;Recipe\u0026rdquo;, yet it incorporates uncertainty and diversity, including multiple parameterization patterns and multiple patterns of rupture propagation.\u003c/p\u003e"},{"header":"2 Setting of Fault Models","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 General Fault Modeling Methods in Japan\u003c/h2\u003e \u003cp\u003eThe \u0026ldquo;J-SHIS model (Japan Seismic Hazard Information Station (\"J-SHIS\") by the National Research Institute for Earth Science and Disaster Resilience (NIED: NIED 2019))\u0026rdquo;, a national fault model of Japan, has been published, presenting the fault models of major active fault zones. The \u0026ldquo;J-SHIS model\u0026rdquo; is typically employed to evaluate strong motion, with the methods of the \u0026ldquo;Recipe\u0026rdquo; based on the method proposed by Irikura et al. (2002) and ERP (2017). The \u0026ldquo;Recipe\u0026rdquo; method is also generally used in other strong motion predictions and seismic hazard assessments.\u003c/p\u003e \u003cp\u003eHere, we summarize the \u0026ldquo;Recipe\u0026rdquo; method (Irikura et al. 2002; ERP 2017).\u003c/p\u003e \u003cp\u003eThe \u0026ldquo;Recipe\u0026rdquo; includes \u0026ldquo;macroscopic fault characteristics\u0026rdquo; and \u0026ldquo;microscopic fault characteristics\u0026rdquo; as parameters that represent the characteristics of fault geometry and slip on fault plane.\u003c/p\u003e \u003cp\u003eThe \u0026ldquo;macroscopic fault characteristics\u0026rdquo; are parameters that describe the location, geometry, and scale of the source model, and include fault position, strike, size (length and width), depth, dip angle, magnitude, and average slip. The location is set by referring to the location of the active fault in the prior evaluation. The length of the fault model is a linear approximation of active fault. The fault width is set based on the relationship between the thickness of the seismogenic layer and the dip angle of the fault surface. The top and bottom depths of the seismogenic layer are estimated from the distribution of microearthquakes (Ito \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). If there are detailed data available, such as reflection survey, the dip angle is referenced. If there are no data, a general value for the fault type is used: 45\u0026deg; for reverse faults, 60\u0026deg; for normal faults, and 90\u0026deg; for strike-slip faults.\u003c/p\u003e\u003c/div\u003e\n\u003cp\u003eThe moment magnitude (Mw) is calculated from following empirical relationship between the seismic moment (Mo) and the source fault area (S).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e1st stage from Somerville et al. (1999):\u003c/p\u003e\n\u003cp\u003eMo=(S/2.23\u0026times;10\u003csup\u003e15\u003c/sup\u003e)\u003csup\u003e3/2\u003c/sup\u003e\u0026times;10\u003csup\u003e-7\u003c/sup\u003e, Mo \u0026lt; 7.5\u0026times;10\u003csup\u003e18\u003c/sup\u003e (Mw \u0026lt; 6.5) (1)\u003c/p\u003e\n\u003cp\u003e2nd stage from Irikura and Miyake (2001):\u003c/p\u003e\n\u003cp\u003eMo=(S/4.24\u0026times;10\u003csup\u003e11\u003c/sup\u003e)\u003csup\u003e2\u003c/sup\u003e\u0026times;10\u003csup\u003e-7\u003c/sup\u003e, 7.5\u0026times;10\u003csup\u003e18\u003c/sup\u003e \u0026lt;= Mo \u0026lt;= 1.8\u0026times;10\u003csup\u003e20\u003c/sup\u003e (6.5 \u0026lt;= Mw \u0026lt; 7.4) (2)\u003c/p\u003e\n\u003cp\u003e3rd stage from Murotani et al. (2015):\u003c/p\u003e\n\u003cp\u003eMo=S\u0026times;10\u003csup\u003e17\u003c/sup\u003e, Mo \u0026gt; 1.8\u0026times;10\u003csup\u003e20\u003c/sup\u003e (7.4 \u0026lt;= Mw) (3)\u003c/p\u003e\n\u003cp\u003eThe average slip (D) is estimated from the equation D = Mo/(\u0026mu;S). Here, \u0026mu; is stiffness factor.\u003c/p\u003e\n\u003cp\u003eThe \u0026ldquo;microscopic fault characteristics\u0026rdquo; are represent the characteristics of the slip on the fault that the location, number, and area of asperities, average slip of asperities (D\u003csub\u003easp\u003c/sub\u003e) and background areas (D\u003csub\u003eback\u003c/sub\u003e), the rake angle, and the slip velocity time function. In the \u0026ldquo;Recipe\u0026rdquo;, asperities are considered to be strong motion generating area and indicate areas within the seismogenic layer where the amount of slip is larger than the surrounding area.\u003c/p\u003e\n\u003cp\u003eThe location of the asperities is based on the pre-evaluation and active fault map. However, this information is very uncertain, and multiple cases are conservatively recommended from the viewpoint of disaster prevention. The area of asperities is set based on the relationship between the short-period level of the source fault model and the total area of asperities (e.g., Dan et al. 2001).\u003c/p\u003e\n\u003cp\u003eThe D\u003csub\u003easp\u003c/sub\u003e is twice the D (e.g., Somerville et al. 1999). The D\u003csub\u003eback\u003c/sub\u003e was recalculated by subtracting the Mo of the asperity from the Mo of the entire fault model and divide by the background area and \u0026mu;. The rake angle is set based on the active fault evaluations, however if none is available, it is based on the standard slip direction of the fault type: reverse fault 90\u0026deg;, normal fault -90\u0026deg;, left lateral fault 0\u0026deg;, and right lateral fault 180\u0026deg;. The slip velocity time function that determines the shape of the synthetic waveform is approximated by Nakamura and Miyatake (2000).\u003c/p\u003e\n\u003cp\u003eThe rupture initiation point (hypocenter) is generally assumed to be located either the left or right end of the lower edge of the asperity for the case of a strike-slip fault, or the center of the lower end of the asperity for the case of a dip-slip fault.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2 \u0026nbsp;Setting up a strong motion prediction model for the Noto Peninsula area using only prior information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn this study, fault model was set using data obtained exclusively prior to the 2024 Noto earthquake, with the objective of conducting a retrospective prediction. Here, the fault traces are approximated by rectangles, and \u0026ldquo;consecutive rupturing models\u0026rdquo; set up based on the combination pattern of these rectangles. This approach is employed to investigate the diversity of rupture propagation. Six fault planes were chosen from the offshore fault traces around the north and eastern coast of the Noto Peninsula (Figure 1). Strong motions were computed by the10 cases of single and combined rupture models (\u0026ldquo;consecutive rupturing models\u0026rdquo;) with these 6 faults (Figure 2a). Subsequently, 4 additional uncertainties, \u0026ldquo;Concept of Fault Width\u0026rdquo;, \u0026ldquo;Shallow Fault Inclusion\u0026rdquo;, \u0026ldquo;Hypocenter Position\u0026rdquo; and \u0026ldquo;Rake Angle\u0026rdquo; were considered (Figure 2b).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe fault position, length, and strike are set based on the fault traces that were mapped prior to the Noto earthquake. The width of the fault model (relation of the bottom depth and dip angle of the fault) is set based on the two concepts considering uncertainties.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe \u0026ldquo;Average Model\u0026rdquo; uses the average value of the observed data, whereas the \u0026ldquo;Expansion Model\u0026rdquo; considers uncertainties and sets the moment to be larger than that of the \u0026ldquo;Average Model\u0026rdquo;. In the \u0026ldquo;Average Model\u0026rdquo;, the depth at the bottom of the fault is set to 16 km. The C-horizon in the acoustic stratigraphic profile is regarded as a Conrad discontinuity (MEXT and JAMSTEC 2015). The dip angle of 60\u0026deg; is derived from the apparent dip angle in the acoustic stratigraphic profile (MEXT and JAMSTEC 2015). Inversion tectonics has been observed in the Japan Sea region, where normal faults that formed during the opening of the Japan Sea reactivate as reverse faults within the current compressive stress field (Okamura 2000). The model is designed to align with these tectonic processes. In the \u0026ldquo;Expansion Model,\u0026rdquo; the depth at the bottom of the fault is set to 20 km. This value is derived from the distribution of hypocenters before the Noto earthquake, and refers to the slightly deeper hypocenters around earthquake swarm on the fault D in Figure 1 (e.g., Wang et al. 2024). The dip angle has been set to 45\u0026deg;, which is a standard setting for reverse faults as shown in the \u0026ldquo;Recipe\u0026rdquo;. The top depth of the fault was divided into two cases: one including and the other not including shallower than the seismogenic layer (shallow-zone). In the case of including the shallow-zone, depth of fault top is set to the seafloor (0 km). The depth of the top of the seismogenic layer is assumed to be around 3 km based on basically inland fault models. All parameters for length and width are rounded to the nearest 100 m to apply to a 1000 m mesh fault plane. As with the \u0026ldquo;Recipe\u0026rdquo;, the Mo was calculated using the three-stage scaling relation. The range of the Mw of the fault models is 7.0 to 7.6 for the \u0026ldquo;Average Model\u0026rdquo; and from7.2 to 7.7 for the \u0026ldquo;Expansion Model\u0026rdquo;. The average slip (D) was similarly set from the formula of D=Mo/\u0026mu;S (\u0026mu;=3.12\u0026times;10\u003csup\u003e10\u003c/sup\u003e N/m\u003csup\u003e2\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003eIn this study, we call the region with large slip in the seismogenic layer is the \u0026ldquo;strong motion generating area (SMGA)\u0026rdquo;, whereas the other area is defined as the \u0026ldquo;background area (BG)\u0026rdquo;. In the shallow-zone, the large slip area is called the \u0026ldquo;large slip area (LS)\u0026rdquo;, while the other area is referred to as the \u0026ldquo;small slip area (SS)\u0026rdquo;. The LS is an extension of the shallow side of the SMGA and has the same amount of slip as the SMGA. The SS has the same amount of slip as the BG. The SMGA was set in the middle of the strike direction of the fault plane, at the upper end of the seismogenic layer. With reference to previous study (Somerville et al. 1999; Miyakoshi et al. 2001), the area of the SMGA was set as 25% of the area of the seismogenic fault. The length of SMGA is about 50% of the fault length. The rupture initiation point was set at the center of the lower end of the SMGA.\u003c/p\u003e\n\u003cp\u003eThe amount of slip for SMGA and LS was set as twice that of average slip of the fault. The rake angle was set at 90\u0026deg; as the standard setting for reverse faults, and uncertainty of +45\u0026deg; was considered.\u003c/p\u003e\n\u003cp\u003eAll fault parameters are shown in additional file (see Additional File 1).\u003c/p\u003e\n\u003cp\u003eTwo different slip velocity functions that for seismogenic layer (Nakamura and Miyatake 2000) and long period waveform in shallow-zone (the regularized Yoffe function: Tinti et al. 2005) were used. The parameters of the regularized Yoffe function were derived from the empirical relation of previous study (Tanaka et al. 2018).\u003c/p\u003e"},{"header":"3 Strong motion calculation for Noto earthquake","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Methods\u003c/h2\u003e \u003cp\u003eIn this study the wavenumber integral (WI) method (e.g., Hisada \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) is used for ground motion calculations. These seismic motions are evaluated under the assumption of parallel stratified ground. This method enables us to consider the directivity effects and fling step of the source fault. In addition to the parameters set in the previous chapter, the WI method requires 1D velocity structure at each calculation point (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The velocity structures are derived from the 250 m mesh subsurface structure published in \u0026ldquo;J-SHIS\u0026rdquo; a database of the NIED (NIED 2019).\u003c/p\u003e \u003cp\u003eThe coordinates of all calculation points are shown in additional file (see Additional File 2).\u003c/p\u003e \u003cp\u003eThe acceleration waveforms were calculated using the WI method, and the velocity waveforms were obtained by integrating the acceleration waveforms in the frequency domain.\u003c/p\u003e \u003cp\u003eTo focus on relatively long-period strong motions that may affect building damage, 1 second low-pass filter was applied to the calculated waveforms, and periods shorter than 1 second are truncated.\u003c/p\u003e \u003cp\u003eThe 1 second low-pass filter was also applied to the observed waveforms at the strong motion observation points, and the calculated results were compared with these observed waveforms and maximum horizontal velocities. As an example, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the time history waveforms of three components calculated from the fault models and the observed waveforms. Waveforms were calculated for 80 seconds, a time scale that fully encompasses the peak of strong motion in the study area, however here they are shown cut off at the time when the large waveform at the observation points had converged. The waveforms from the total 64 pattern models shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e are plotted in gray, and the observed waveforms in red.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eHere, we summarize the characteristics at each observation point.\u003c/p\u003e \u003cp\u003eAt ISK001 (P50, Otani), the long duration in the observed waveform could not be reproduced. While the observed waveform exhibits two peaks around 5 seconds and 15 seconds, the calculated waveforms show either a peak around 5 seconds or around 12\u0026ndash;13 seconds, with the peak position being one or the other. However, the predicted maximum velocity is generally well-captured except for the EW component. The UD component tends to be overestimated, however when the rake angle is set to 135\u0026deg;, the amplitude is suppressed, bringing it closer to the observed value.\u003c/p\u003e \u003cp\u003eISK003 (P52, Wajima) does not reproduce the long duration in the observed waveform. The waveform calculated from some patterns of the set fault model can express the peak around 10 seconds. There are models that are relatively well reproduced around 5 to 10 seconds. The amplitude covers the maximum velocity of all components, however for the UD component, the calculated waveform shows almost no down component. This includes the down wave observed around 15 seconds in the measured waveform. ISK006 (P54, Togi) shows that part of the set fault model well reproduces the peaks and troughs of the observed waveform up to around 27 seconds. However, the second peak, particularly prominent in the UD component around 30 seconds, does not appear in the calculated waveform. The amplitude generally covers the maximum values of the observed waveform for all components.\u003c/p\u003e \u003cp\u003eFor ISKH01 (P60, Suzu), setting the slip angle to 135\u0026deg; resulted in a larger horizontal component, bringing the waveform characteristics closer to the observed waveform, while the amplitude also approached that of the observed waveform. When the rake angle was set to 135\u0026deg;, the waveform captured the characteristics of the observed waveform for the very initial portion of the shaking up to around 10 seconds. The amplitude generally encompassed the maximum values of the observed waveform for all components.\u003c/p\u003e \u003cp\u003eISKH02 (P61, Yanagida) does not reproduce the long duration in the observed waveform. It reproduces the waveform up to around 15 seconds reasonably well for some of the configured models. Amplitudes tend to be underestimated for the NS component. This failure to reproduce the long duration prevents the capture of the large amplitude arriving around the 30-second mark in the observed waveform.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Results\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the predicted and observed strong motions. The calculation of strong motions was conducted at 26 observation stations (squares in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) and 35 additional points near the coast to ensure coverage of the area between the stations (circles in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea plots the maximum horizontal velocity (upper left) and median values calculated by the \u0026ldquo;consecutive rupturing models\u0026rdquo;, Model 01 and Model 10, for the rake angles of 90\u0026deg; and 135\u0026deg;. Model 01 is an example of a rupture propagation pattern that closely resembles the rupture area of the Noto earthquake, while Model 10 is an example of rupture with a more limited area. The rupture propagation pattern demonstrates a strong correlation with the locations of significant amplitudes. The distribution of modeled strong motions along the northern coast of the Noto Peninsula and Sado Island is in good agreement with the observed strong motion pattern. Around Monzen, where peak motion is pronounced, there is a slight discrepancy between the observed and calculated peak locations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen the rake angle was set to 135\u0026deg;, the amplitude was found to be larger than when the rake angle was set to 90\u0026deg;, and was more pronounced around Monzen. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb shows the results of all the \u0026ldquo;consecutive rupturing models\u0026rdquo;. The red crosses represent the observed values, which correspond to the values indicated by squares on the map in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. The maximum values observed and calculated from Wajima to Suzu and Sado on the northern coast of the Noto Peninsula are comparable, considering variations in fault parameters, and are predicted with a reasonable. Conversely, the maximum values on the west coast tend to be similar or slightly smaller. The maximum value was observed in the Monzen area, with an amplitude of approximately 170 cm/s, which is comparable to the observed amplitude, including uncertainties. However, this location was not the Monzen observation point, but calculation point 22, which was situated slightly to the east. The maximum value on the southern coast of the Noto Peninsula also tends to be slightly smaller and is often underestimated, particularly in the Anamizu area. When the rake angle was set to 135\u0026deg;, the strong motion amplitude was comparable to or exceeded the observed amplitude at most points. However, it was slightly smaller on the west coast. In the southern coast, the results tend to be smaller than the observed amplitudes.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 Range of uncertainties and regionality","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Consideration by Tornado Plots for the Epistemic Uncertainty\u003c/h2\u003e \u003cp\u003eThere are few examples discussing epistemic uncertainty in fault parameter settings.\u003c/p\u003e \u003cp\u003eHowever, the \u0026ldquo;Ikata SSHAC Project (Fujiwara et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e)\u0026rdquo; is one such example. The project employed a Tornado Plot (TP) to evaluate the effect of epistemic uncertainty on strong motion prediction results. Additionally, the utilization of TP serves to illustrate the extent of uncertainty surrounding the given values. However, while examples discussing uncertainty are mainly related to the evaluation of nuclear power plant sites, no examples showing a wide-area distribution like this study have been identified to date.\u003c/p\u003e \u003cp\u003eThe TP plots the average velocity for all the branches in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb when only one branch is considered. By doing this approach for all 61 calculation points (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) for the 5 branches, the most influential parameters for each region are identified. The examples of TP are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea. The examples of calculation point affected by the fault planes D, E, F are shown. The influence of the \u0026ldquo;Concept of Fault Width\u0026rdquo; is significant at point 34 on the east side of the northern coast, while at point 27 on the west side of the northern coast, the \u0026ldquo;Rake Angle\u0026rdquo; is significant. At point 16 west of point 27, the \u0026ldquo;Concept of Fault Width\u0026rdquo; and the \u0026ldquo;Rake Angle\u0026rdquo; are nearly equivalent. Consequently, the parameters that have a significant influence differ depending on the position of calculation point. The standard deviations of each branch in the TP for the 61 calculation points are that ranked from largest to smallest, and plotted on the maps (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb). The predominant uncertainty at numerous locations is the \u0026ldquo;Propagation Pattern\u0026rdquo;. However, near the boundary between faults D and E, other factors such as \u0026ldquo;Rake Angle\u0026rdquo; and \u0026ldquo;Concept of Fault Width\u0026rdquo; emerged as significant contributors. In many locations, the second influential factor was the \u0026ldquo;Concept of Fault Width\u0026rdquo; which is associated with the amount of seismic moment. The third and fourth factors are relatively scattered. In the vicinity of the Monzen, the \u0026ldquo;Rake Angle\u0026rdquo; emerges as the second most influential factor, with the \u0026ldquo;Concept of fault width\u0026rdquo; ranking third in terms of influence. The \u0026ldquo;Shallow Fault Inclusion\u0026rdquo; does not have a substantial impact the third factor at on strong motion at the most sites, however it is the third factor at some sites.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Uncertainty of SMGA position\u003c/h2\u003e \u003cp\u003eThe location of the SMGA is a parameter that is difficult to predict. Even in the \u0026ldquo;Recipe\u0026rdquo;, it is recommended that multiple patterns for the SMGA location should be considered. In this study, the \u0026ldquo;Expansion Model\u0026rdquo; of Model 01, the model most likely to the Noto earthquake, was used to illustrate the range of uncertainty regarding the SMGA location. The rupture initiation point was set to fault plane D, and with a rake angle was of 135\u0026deg;set within a configuration that considered the shallow segment of fault. The SMGA was set to a total of three locations: the center of the shallow side of the fault plane, as set in the previous chapter, along the strike direction, as well as on the right and left sides of the shallow side. By comprehensively combining these for six fault planes, a total of 729 combinations were formulated (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe calculation results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea shows the distribution of maximum velocity is depicted each calculation point when the position of SMGA is set at all in the center, right, and left. Directly above the SMGA on the northern coast of the Noto Peninsula, differences in the location of SMGA affect the calculation results, particularly around Monzen. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb shows the range of uncertainty due to the position of the SMGA. The median value among the 729 calculated patterns is indicated by a blue circle, with the error bars showing the range of variation. The calculation results for the three cases shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea are represented by gray symbols for reference. The observed values are indicated by red crosses. The range of variation is very small in locations distant from the SMGA, such as the west and south coasts of the Noto Peninsula and Sado Island. However, along the northern coast of the Noto Peninsula, this factor contributes to a substantial range in the predicted strong motion. Along the northern coast of the Noto Peninsula, the variation is about 1.5 times the median value (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5 Discussions","content":"\u003cp\u003eFirst, we discuss the reproducibility of observed waveforms and the challenges of characteristic source models in this study.\u003c/p\u003e \u003cp\u003eThe observed waveforms and calculated waveforms shown in Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) were evaluated based on the following three criteria and summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e : 1. Duration (reproducibility of waveform duration), 2. Waveform (reproducibility of waveforms around peak amplitude), and 3. Amplitude (whether the observed maximum velocity was covered). Based on this evaluation, we discuss the reasons why reproduction was difficult. Furthermore, among the characteristic source models commonly used for strong motion prediction in Japan, the asperity model (Kanamori \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1981\u003c/span\u003e) is a source fault model designed to represent characteristics of strong motion linked to seismic hazards, such as the pulsed seismic waves observed near the source fault, without losing them. We consider what is necessary to ensure the minimum functionality required for setting up such characteristic source models.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of waveforms between observation and calculations. 〇=Relatively good fitting or no underestimation, △=Partially fit or slightly underestimated, \u0026times;=Doesn\u0026rsquo;t fit or underestimated.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eStation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eRake\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e1. Duration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e2. Waveform (around peak amplitudes)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c7\" namest=\"c5\"\u003e \u003cp\u003e3. Amplitude (coverage for maximum velocity)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eUD\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eISK001 (Otani, P50)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e135 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e△\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eISK003 (Wajima, P52)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e△\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e135 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eISK006 (Togi, P54)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e△\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e135 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e△\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eISKH01 (Suzu, P60)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e135 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e△\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eISKH02(Yanagida, P61)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e90 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e135 deg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026times;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e〇\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor \u0026ldquo;1. Duration,\u0026rdquo; while the duration of shaking characteristic of typical earthquakes was captured, the waveforms in Otani (ISK001), Wajima (ISK003), and Yanagida (ISKH02) did not reproduce the long duration waveforms with multiple wave groups characteristic of the Noto earthquake. Such waveforms are suggested to result from multiple sources rupturing with time delays and propagating over a wide area (e.g., Okuwaki et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xu et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Ma et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Characteristic source models can relatively well reproduce observed waveforms from previous earthquakes when the event can be approximated by a simple model, such as a single fault plane with a few asperities. However, in earthquakes like the Noto earthquake, where multiple fault segments ruptured simultaneously, or in earthquakes involving complex rupture processes, it is difficult to reproduce the observed waveforms using simple models. For \u0026ldquo;2. Waveform,\u0026rdquo; while some observed waveforms around the peak amplitude relatively captured characteristics predicted by calculated waveforms derived from parts of the set fault model patterns, results for locations such as Otani (ISK001) and Suzu (ISKH01) did not capture characteristics well. As mentioned in \u0026ldquo;1. Duration,\u0026rdquo; observed waveforms exhibiting multiple wave groups due to multiple rupture in the wide area or complex source processes that cannot be represented by a single fault plane are difficult to reproduce using simple characteristic source models.\u003c/p\u003e \u003cp\u003eFor \u0026ldquo;3. Amplitude,\u0026rdquo; while some components show tendencies toward underestimation or overestimation, the maximum velocity of each waveform component is covered equivalently or relatively well. The amplitude results presented here were obtained by setting the SMGA on the shallow side of the fault plane's strike direction center. Furthermore, the same setting was applied to all fault planes. Comprehensive examination by combining the right and left sides of the fault plane may offer potential for improvement.\u003c/p\u003e \u003cp\u003eBased on these results, the characteristic source model examined in this study can to some extent capture the characteristics around the peak of seismic waveforms with a period of approximately one second near the source fault, which significantly influence building damage. Furthermore, by assuming the interaction of multiple segments rather than a single fault plane and employing parameter settings that account for multiple pattern combinations and uncertainties, it is generally possible to cover the maximum amplitude of observed waveforms. On the other hand, capturing the characteristics of multiple wave groups and long duration caused by complex rupture processes and multiple rupture propagation is difficult using simple methods for setting characteristic source models. To address this challenge, we propose an evaluation based on more lenient criteria that do not require waveform matching. This is because, particularly near faults, the influence of fault motion directly beneath the observation point is dominant, and the impact of seismic waves from distant faults on damage is small. Therefore, even if waveform shapes do not match, capturing minimal waveform characteristics is considered sufficient for hazard assessment. The proposal and rationale for this approach are summarized below.\u003c/p\u003e\n\u003ch3\u003e1. Coverage of maximum amplitudes in the frequency band around 1 second related to building damage\u003c/h3\u003e\n\u003cp\u003eAmplitude, directly related to shaking intensity, is a critical characteristic of seismic waveforms related to building damage. Given that distance attenuation formulas are sometimes used in seismic hazard assessments, covering the maximum amplitudes from past earthquakes is considered the most important criterion.\u003c/p\u003e\n\u003ch3\u003e2. The duration of main shaking is reproduced.\u003c/h3\u003e\n\u003cp\u003eThe Noto earthquake suggested that long shaking may have exacerbated damage. The duration of shaking is a critical characteristic of seismic waveforms related to damage for disaster prevention.\u003c/p\u003e\n\u003ch3\u003e3. The period response spectrum is appropriate\u003c/h3\u003e\n\u003cp\u003eStructures exhibit different response periods. Resonance occurs when the period of the seismic wave matches the building's period, leading to increased damage. Since the period of predicted seismic motion relates to seismic design and planning, it is necessary that the predominant period generally matches that of past major earthquakes.\u003c/p\u003e \u003cp\u003eFor point 1, while considering uncertainties in individual fault parameters as done in this study largely covered the maximum amplitude of the waveform, to address factors not covered by assuming a simple fault model, incorporating a range of several times the variation in the calculated waveform can reduce underestimation.\u003c/p\u003e \u003cp\u003eFor point 3, rather than focusing solely the fundamental period reaches maximum velocity, examining the range around the maximum velocity allows us to identify the critical period band that requires attention.\u003c/p\u003e \u003cp\u003ePoint 2 is a criterion that is currently not being well reproduced. As detailed later in this chapter, resolving this issue requires elucidating the relationship between shaking duration and damage effects, as well as understanding the mechanism of rupture propagation and the source triggering. The Noto earthquake was a large earthquake occurring within an earthquake swarm zone; the environment conducive to earthquake swarm likely led to complex rupture propagation. The environment around the source may also be relevant to predictability. Therefore, it is necessary to elucidate earthquake characteristics and propose modeling methods to simplify, standardize, and generalize these phenomena for incorporation into models. However, this is a challenge for the near future. Until it is resolved, it is important to conduct evaluations with flexibility for criteria like 1 and 3, indicating possible phenomena within a certain range. At this point, it is critically important to clearly distinguish and present the uncertainty of parameters for which scientific evidence can be provided, from the randomness or \u0026ldquo;variability\u0026rdquo; inherent in simulations and natural phenomena. Next, we describe the verification of the Noto earthquake based on the comparison of maximum velocities conducted in this study. Especially we will discuss for the underestimation on the southern and west coasts of the Noto Peninsula.\u003c/p\u003e \u003cp\u003eA possible reason for the underestimation in the southern Noto Peninsula, particularly around Anamizu, is the amplification of effects resulting from irregular and heterogeneous subsurface conditions. The results of the reflection survey as Hayashi et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), indicate that in the vicinity of Anamizu, seismic waveforms are amplified by an edge effect caused by sudden changes in subsurface structure. It is important to the detailed characteristics of subsurface structural effects in highly accurate strong motion predictions. However, as the main focus of this study is on methods for constructing fault models, this is considered a separate issue and will not be discussed further here. However, point 51, located east of the southern coast of the Noto Peninsula, falls within the projection of the Fault plane D and is close to the hypocenter of the Noto earthquake. It is also close to the earthquake swarm that occurred before the Noto earthquake occurred, and there is a possibility that the slip on the fault plane is more complex and heterogeneous, which requires further consideration in the fault model.\u003c/p\u003e \u003cp\u003eThe tendency to underestimate the maximum velocity distribution along the west coast of the Noto Peninsula may be attributed to a discrepancy in strike between Fault F and the actual ruptured fault during the Noto earthquake. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the Japan Meteorological Agency (JMA) hypocenter distribution and cross-section for one month after the Noto earthquake. Although the data are preliminary, the hypocenters on the A-A' cross section do not appear to align with the fault trace of the modeled fault plane F. Instead, they are located along an east-dipping structure with a generally north-south strike near the coastline, where no mapped fault trace currently exists. Information regarding active faults is essential for the development of fault models. It should be based on mapped fault traces and primary survey data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA fault model including this fault plane could not be predicted, however calculations were conducted to see how much the predicted results would have changed if this fault had been able to be estimated. The new fault model is Model 11, which represents a change in the strike of fault along the west coast compared to the previously mentioned Model 01, shifting to a north-south orientation. The modeling method and calculation techniques are the same as previous sections.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003ea shows the median maximum values at each calculation point for the six calculation patterns included in Model 11. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb compares them with Model 01 and observed data. Compared to Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, the predicted strong motions on the west coast of the Noto Peninsula are slightly larger than those of Model 01. This is particularly noticeable in the example where the rake angle is set to 135\u0026deg;. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003eb presents the median value for each model as red or blue symbols, with error bars denoting the range of uncertainty. In the Hakui-Shika area on the west coast of the Noto Peninsula, Model 11 predicted larger strong motions than Model 01, where the fault on the west coast strikes east-west, and is closer to the observed values. Moreover, around Monzen, where particularly large shaking was observed, Model 11 predicted larger strong motions than Model 01. In contrast, the difference is not significant in the Wajima-Suzu and Sado areas on the north coast of the Noto Peninsula.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNext, Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the results of modifying the SMGA position for the \u0026ldquo;Expansion Model\u0026rdquo; of the Model 11, with the rupture initiation point at D and a rake angle of 135\u0026deg;. As with Model 01, SMGA is set in three patterns on the shallow side of the fault plane, and by comprehensively combining these a total of 729 calculation patterns are obtained. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea shows the median of the maximum values at each calculation point is depicted when SMGA are all set to the center, right, or left on the six fault planes. The case in which SMGA are situated to the right of the fault plane shows significantly larger strong motions from the west coast of the Noto Peninsula to Monzen. Conversely, the case in which SMGA are all set to the left shows generally smaller ground motions compared to the other cases, although some areas of Shika show significantly larger strong motions. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb shows the median values are represented by blue circles, with error bars denoting the range of variation. Gray symbols also show the results for the center, right, and left cases shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea. The observed values indicated by red crosses generally fall within the error bar range in most areas, with the exception of the southern coast of the Noto Peninsula.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA comparison of Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e with Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the prediction results for the west coast of the Noto Peninsula have slightly improved, and the prediction for the Monzen area is significantly larger. The fault model on the west coast of the Noto Peninsula, when considered in relation to the source fault of the Noto earthquake, slightly improved prediction. However, even with the east-west strike models, there are no underestimation of the north coast and the Sado. Furthermore, there is no particular large underestimation on the west coast. Consequently, it can be deduced that, to some extent of prediction was possible with prior information alone. However, with the improvement of fault information, there is a possible for further enhancement in the accuracy of predictions. The treatment of faults not included on active fault maps necessitates discussion incorporating the distribution of active faults in surrounding areas and original survey data.\u003c/p\u003e \u003cp\u003eAnother characteristic of the strong motion from the Noto earthquake was its long duration. This study was used as a simple prediction model, so it was not possible to capture the characteristic waveforms that continued for long periods of time, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Therefore, the model could not capture the waveform characteristic of long durations. As mentioned above, covering the maximum value is important in predictions. However, the long duration of the Noto earthquake may have amplified its damage. Therefore, predicting only the maximum value is insufficient. The characteristics of the ground motion from the Noto earthquake suggest that it was caused by the rupture of two hypocenters that occurred with a time lag (e.g., Okuwaki et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Xu et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Ma et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In other words, the M5.9 earthquake occurred 13 seconds before the M7.5 earthquake, and the two earthquakes thought to be the result of a single source process (Peng et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). These two nearby earthquakes are thought to have propagated bilaterally, westward and eastward, respectively. Additionally, the area near the hypocenters experienced an increase in earthquake swarm activity since 2020. This swarm activity is thought to be related to water and to have a low-velocity structure (e.g., Xu et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Peng et al. 2024; Liu et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). A future challenge will be determining how much of the environment\u0026rsquo;s complexity at and near the source can be reflected in predictive models.\u003c/p\u003e \u003cp\u003eFurthermore, in this study we postulated an exhaustive array of rupture propagation patterns. For a hazard assessment, we need a measure of the \u0026ldquo;likelihood of occurrence\u0026rdquo; for these patterns. However, the activity of faults is not always clear. In such cases, Biasi and Wesnousky (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) proposed a method for estimating the probability of rupture propagation based on the distance and geometry between faults. Although issues arise when applying this method to dip-slip faults or considering stress changes associated with earthquake occurrence, active fault information is the most readily available data prior to an earthquake. Thus, determining the rupture propagation rate using this method is considered beneficial for the modeling approach in this study, as it constructs fault models based on this information.\u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb, the uncertainty of parameters affects the results of strong motion prediction, with the \u0026ldquo;Rupture Propagation Patterns\u0026rdquo; being the main factor. The \u0026ldquo;Concept of Fault Width\u0026rdquo; is the second most influential parameter for most calculation points. However, on the western side of the northern coast, the \u0026ldquo;Rake Angle\u0026rdquo; is the influential parameter. This area is close to the upper end of the fault plane and is susceptible to the effect of slip generated in the shallow part of the fault. The reason the \u0026ldquo;Concept of Fault Width\u0026rdquo; had a significant influence was that setting the dip angle to 45\u0026deg; brought the calculation point closer to the fault plane than setting it to 60\u0026deg;. There is limited research on how to consider for epistemic uncertainty in fault parameters when setting up prediction models. More detailed examinations and discussions are needed.\u003c/p\u003e \u003cp\u003eThe position of the SMGA is one of the parameters that should be treated as aleatoric uncertainty. In this study, three locations were set along the strike direction of the shallow side of the fault plane: the center, right side, and left side, and their combined influence was confirmed. The influence was particularly large in areas where the shaking was large, with a range of approximately twice the median value. Conversely, in areas where the predicted shaking was small, the range of variation was also small.\u003c/p\u003e \u003cp\u003eFinally, Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows a comparison of the prediction results from Model01 and the observed values from the Noto earthquake when considering all the uncertainties examined in this study. The uncertainty range was obtained by multiplying the maximum and minimum values derived from considering the \u0026ldquo;Concept of Fault Width\u0026rdquo;, \u0026ldquo;Shallow Fault Inclusion\u0026rdquo;, \u0026ldquo;Hypocenter Position\u0026rdquo; and \u0026ldquo;Rake Angle\u0026rdquo; (as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb) by the multiplier relative to the medium value of the SMGA uncertainty range. Along the west coast of the Noto Peninsula, the predictions are slightly lower than the observed values, however then almost entirely cover them. Along the northern coast of the Noto Peninsula and on Sado Island, the observed values are within the predicted range. Along the southern coast of the Noto Peninsula, there is a clear underestimation around Anamizu; elsewhere, however predictions are quite close to observed values. Although the uncertainties considered in this study are limited, incorporating various uncertainties and diversities suggests that predictions using only information available prior to the Noto earthquake are generally feasible. However, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, there is significant uncertainty, particularly along the northern coast of the Noto Peninsula. This substantial uncertainty is largely influenced by the rake angle and the position of the SMGA. The rake angle can be constrained by tectonics, geology, and geodetic data to some extent. The position of the SMGA might also be constrained by its proximity to features like mountains and hills, where accumulated displacement from past seismic activity is thought to exist. Incorporating information not considered in this study, such as geology and topography, could potentially reduce this significant uncertainty in the future.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"6 Conclusions","content":"\u003cp\u003eTo verify the predictability of strong motion from the Noto earthquake, we conducted a retrospective prediction analysis. By incorporating geological information as prior information into basic fault model setting methods (such as \u0026ldquo;Recipe\u0026rdquo;) and accounting for uncertainty, strong motion was generally predictable except for the west and south coasts of the Noto Peninsula. The tendency toward underestimation was attributed to the fact that the fault mapped prior to the Noto earthquake differed from the fault that actually ruptured on the west coast, and to significant ground amplification on the south coast.\u003c/p\u003e \u003cp\u003eRegarding the uncertainties considered in this study, an examination of the factors exerting the most significant influence on each calculation site revealed that the \u0026ldquo;Rupture Propagation Patterns\u0026rdquo; is the primary factor at many sites. While the second most influential parameter at many sites is the \u0026ldquo;Concept to Fault Width,\u0026rdquo; the \u0026ldquo;Rake Angle\u0026rdquo; exerts a greater influence at calculation sites closer to the fault top. Since this study sets the fault models based on active fault distribution data, factors contributing significantly to uncertainty may exhibit regional characteristics.\u003c/p\u003e \u003cp\u003eA key challenge in this study is the application limits of the characteristic source model. By incorporating fault parameter uncertainties and variation of rupture propagation patterns into the characteristic source model, it can relatively well reproduce observed waveforms within the range approximatable by a simple model. However, it difficult to reproduce observed waveforms associated with complex source processes, such as those possessing multiple wave groups. Rather than aiming for exact waveform matching, it is necessary to allow evaluation based on more lenient criteria such as \u0026ldquo;coverage of maximum amplitude,\u0026rdquo; \u0026ldquo;duration of shaking,\u0026rdquo; and \u0026ldquo;reasonableness of the periodic response spectrum.\u0026rdquo; Furthermore, by applying evaluations with a certain degree of flexibility not only to the uncertainty of fault model parameters but also to computed waveforms and periodic response spectra, it is considered possible to apply this approach to hazard prediction. However, regarding \u0026ldquo;duration of shaking,\u0026rdquo; it is necessary to elucidate the relationship between duration and damage, as well as the relationship between rupture propagation, triggering, and the environment around the source. It is also necessary to consider how to simplify such complex phenomena and incorporate them into the prediction model.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe strong motion data from K-net and KiK-net set up by the National Research Institute for Earth Science and Disaster Resilience (NIED), and also used data by the Japan Meteorological Agency (JMA), for the comparison of calculated and observed strong motion. The JMA Unified Earthquake Catalog were used to plot the aftershock distribution for the 2024 Noto Peninsula earthquake.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest regarding this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eN K: Conceptualization, methodology, analysis and original draft\u003c/p\u003e\n\u003cp\u003eF H: Supervision for Seismic Hazard Assessment and review\u003c/p\u003e\n\u003cp\u003eT S: Supervision for Geology and review\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study used data from the strong motion observation network operated by the National Research Institute for Earth Science and Disaster Resilience and the Japan Meteorological Agency. This study was conducted within the Endowed Research Laboratory of OYO Corporation (October 2019 - October, 2025). We would like to express our gratitude to them here.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eN K: Research fellow of International Research Institute of Disaster Science (IRIDeS), Tohoku University. Member of the Seismological Society of Japan and Japanese Society for Active Fault Studies. The Professional Engineer, Japan (Applied Science).\u003c/p\u003e\n\u003cp\u003eF H: Project Director of National Research Institute for Earth Science and Disaster Resilience. Ph.D. in Science.\u003c/p\u003e\n\u003cp\u003eT S: Professor of International Research Institute of Disaster Science (IRIDeS), Tohoku University. Ph. D. in Science.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBiasi GP, Wesnousky SG (2021) S. G. 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Earth Planet Space 69:74. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1186/s40623-017-0656-9\u003c/span\u003e\u003cspan address=\"10.1186/s40623-017-0656-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Active fault earthquake, Noto Peninsula earthquake, Fault model, Strong motion prediction, Seismic hazard assessment, Characteristic source model","lastPublishedDoi":"10.21203/rs.3.rs-8837779/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8837779/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe major active fault earthquakes in Japan in recent years include the 2016 Kumamoto Earthquake and the 2024 Noto Peninsula earthquake. These earthquakes occurred along predicted fault models, however, uncertainties and variations in fault geometry and rupture propagation led to actual earthquake magnitudes exceeding prior expectations.\u003c/p\u003e \u003cp\u003eThe objective of this study is to verify if the Noto Peninsula earthquake could have been predicted, considering significant uncertainties in general strong motion prediction models, and to obtain feedback leading to improvements. Therefore, this study set a fault model using data from before the earthquake and performed a retrospective prediction analysis. This was compared with observed data to confirm predictability. Considering uncertainties in fault parameters and rupture propagation patterns, strong motion was generally predictable, except for the west coast and south coast of the Noto Peninsula.\u003c/p\u003e \u003cp\u003eSubsequently, the uncertainties encompassed by this study was examined through the Tornado Plots for each calculation point, with a particular emphasis on the factors exerting the most substantial influence. The \u0026ldquo;Rupture Propagation Patterns\u0026rdquo; were the primary factor, with the \u0026ldquo;Concept of Fault Width\u0026rdquo; being the second most influential factor in many locations. However, at some locations near the fault top, the \u0026ldquo;Rake Angle\u0026rdquo; was shown to have a significant impact. This suggests that the effects of fault parameter uncertainties may exhibit regional characteristics.\u003c/p\u003e \u003cp\u003eIn the standard seismic hazard assessment methodology in Japan, the asperity model is utilized among characteristic source models. The asperity model effectively reproduces the pulsed waves near the source fault that can be represented by a simple model with a few asperities on a single fault plane. However, it is difficult to reproduce waveforms involving multiple fault ruptures and complex source processes, such as those seen in the Noto Peninsula earthquake. This study considers the limitations of applying characteristic source models. It proposes that, rather than aiming for exact waveform matching, evaluations should be permitted under loose criteria. Furthermore, by allowing for a certain degree of variability not only in fault parameter uncertainties but also in the calculation results themselves, such models can be considered suitable for use in assessments.\u003c/p\u003e","manuscriptTitle":"Validation and Uncertainties of Strong Ground Motion Prediction Methods for Seismic Hazard Assessment: A case study of the 2024 Noto Peninsula Earthquake (Mw7.5), Japan","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-16 08:40:43","doi":"10.21203/rs.3.rs-8837779/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revision","date":"2026-05-09T08:53:58+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2026-03-16T00:04:27+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-13T11:40:22+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-19T14:04:21+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth, Planets and Space","date":"2026-02-10T02:27:48+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c084c618-b378-4c02-a8f8-a9677a99e86b","owner":[],"postedDate":"March 16th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Major Revision","date":"2026-05-09T08:53:58+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[],"tags":[],"updatedAt":"2026-05-09T12:56:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-16 08:40:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8837779","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8837779","identity":"rs-8837779","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}