Development of an offshore ground motion prediction equation considering path effects based on S-net data

Development of an offshore ground motion prediction equation considering path effects based on S-net data | 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 Development of an offshore ground motion prediction equation considering path effects based on S-net data Ryo Nakanishi, Shunsuke Takemura This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4348314/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Nov, 2024 Read the published version in Earth, Planets and Space → Version 1 posted 5 You are reading this latest preprint version Abstract Ground motion prediction equations (GMPEs) in offshore regions are important for not only earthquake early warning but also evaluating the durability of subsea structures and tsunami risk associated with seafloor slope failures. Since the ground conditions and propagation path effects differ between onshore and offshore areas, it is desirable to develop a GMPE specific to the seafloor. Previous models have some problems, such as the influence of buried observation equipment and path effects. In this study, to predict the distribution of seafloor seismic acceleration, a new GMPE was regressed on the peak ground acceleration (PGA) data of S-net using minimum necessary seismic parameters as explanatory variables. The path effects through the offshore area were emphasized from the residual analysis by the conventional GMPE and were corrected by the depth up to the plate boundary. The new model successfully predicted PGA with smaller errors compared to conventional onshore and offshore GMPEs. The residuals between the observed and predicted PGAs were used to examine the factors responsible for the effects of the S-net site conditions. The new GMPE can obtain PGAs within 300 km of the epicenter from the moment magnitude (Mw 5.4–7.4), focal depth, focal type, and source distance. In this model, the distance attenuation is smaller than in conventional models, and consequently, the PGAs along the trench axis amplified due to path effects are reproduced. This means that the PGA is unexpectedly large even at the point far from the hypocenter when considering slope failure and earthquake resistance assessments. Ground motion prediction equation S-net Peak ground acceleration Path effect Japan Trench Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Introduction The empirical distance attenuation formula for ground motion is useful for urgent disaster prevention information, such as earthquake early warning, because of its simplicity and promptness (e.g., Tajima and Hayashida 2018 ; Allen and Melgar 2019 ; Hoshiba et al. 2008 ). It is also crucial in assessing the durability of buildings under strong ground motions and in preventing slope failures (e.g., Canals et al. 2004 ). Ground motion prediction equations (GMPEs) for the onshore region have been proposed in the form of empirical equations owing to the abundance of observational data (e.g., Kanno et al. 2006 ), and complex models have also been proposed to account for site-specific amplification effects (e.g., Zhao et al. 2006 ; Morikawa and Fujiwara 2013 ). Some studies for an offshore turbidite have used onshore GMPEs to estimate the peak ground acceleration (PGA) at offshore sites by triggering earthquakes that occurred slope failures (Noda et al. 2008 ; Pouderoux et al. 2014 ; Lehu et al. 2016 ; Pope et al. 2017 ; Ikehara et al. 2023 ). On the other hand, it has been shown that offshore sites exhibit different distance attenuation than onshore sites (Gomberg 2018 ; Hu et al. 2020 ; Dhakal et al. 2021 ), and either corrections to an onshore model or a new empirical equation is needed (Scholz et al. 2016 ). In other words, GMPEs for evaluating offshore slope failures have not yet been sufficiently established. In Japan, offshore observation networks of DONET and S-net have been operated since 2011 and 2016, respectively (Aoi et al. 2020 ). Thus, continuous observations of seismic waves at the ocean bottom have been available. The stations of DONET are limited southeast off the Kii Peninsula and off Cape Muroto only; however, the S-net stations were widely deployed off Kanto to Hokkaido regions. However, only limited GMPEs exist due to the shorter observation period (Hu et al. 2020 , 2023 ). Because they are based on the onshore GMPE models, it is expected that there will be an under/overestimation in cases where there are amplification effects specific to offshore areas. The reference GMPEs include site effect terms with four levels of classification based on the mean S-wave velocity of 30-m thick surface ground (Vs30) or a horizontal-to-vertical spectral ratio (HVSR), which is the function for a horizontal ground motion of surface layers (Nakamura 1989 ). However, it is not discussed whether the site class and coefficients on offshore sites, which should reflect the actual site amplification and reduce the residuals. Even in the Japan Trench, where S-net was widely covered, it is difficult to clarify what causes site effects because of the lack of physical property data in the offshore region compared to the onshore region. In addition, the S-net stations below a water depth of ~ 1500 m were buried, resulting in differences in raw data with unburied stations (Tan and Hu 2023 ). Hu et al. ( 2023 ) model did not take into account differences between buried and unburied stations even using the S-net data. Therefore, it is important to verify the characteristics of distance attenuation or site effects in offshore areas and to clarify the robustness of the GMPEs through residual analysis. The purpose of this study is to develop a new simple GMPE for predicting PGAs on the seafloor. We examine the distance attenuation features peculiar to the offshore sites and the effect of the burial by residual analysis using conventional GMPE. We derive a regression equation with correction terms using S-net data and compare its performance with other models. The residuals from the PGA predicted by the regression equation will be used to discuss the factors that cause site effects. Dataset and Processing The seismic events used in this study are listed as earthquakes with moment magnitudes (Mw) > 5.4 and focal depths < 130 km (Fig. 1 and Table A1 ). Data for crustal earthquakes greater than Mw 5.0 are also used because of their small number and close source distance. The earthquake mechanism and Mw in formation is obtained from the F-net moment tensor catalog, which has been systematically monitored by the National Research Institute for Earth Science and Disaster Resilience (NIED) (Fukuyama et al. 1998 ; https://www.fnet.bosai.go.jp/top.php?LANG=en : last accessed on 2024.02.11). These events occurred within the area of the longitude of 138–147ºE and latitude of 33.5–44ºN from August 2016 to March 2024. The hypocenter locations and origin times of the selected events are referred from the unified hypocenter catalog of the Japan Meteorological Agency. Excluding events with no stations within distances ≤ 100 km from a source fault, the total number of events is 99 (numbers of crust and slab events are 21 and 20, respectively) (Figs. 1 and 2 , Table A1 ). Of these, the latest 2 events of each earthquake type are not used in the regression for validation purposes. Acceleration data are obtained for 10 min from 1 min before the earthquake origin time at 150 S-net stations (Kanazawa et al. 2016 ; Uehira et al. 2016 ; Mochizuki et al. 2016 ) (Table A2 ). For the source distances (R: km), a plane fault is assumed in three-dimensional space, and the shortest distance to each station is obtained (Fig. 2 ). The fault lengths and widths of plane faults are defined from a fault length and fault area according to the Mw by the Utsu ( 2001 ) formulas (Fig. 2 ). Table 1. Coefficients, AIC, and standard deviation for the horizontal offshore ground motion prediction equation. Base fomula b d e k Coefficient 0.6483 -0.00075 0.00196 0.6007 AIC 3678 The acceleration data are used from the stations within distances R ≤ 300 km and PGA > 5 cm/s 2 . The average amplitudes within the 60-s time window before P-wave arrival are subtracted at each time step for the S-net records as offset amplitudes. The acceleration data are applied to a fourth-order bandpass filter with a frequency band from 0.1 to 25 Hz and then horizontal and vertical acceleration seismograms are obtained by following Takagi et al. ( 2019 ). The Y component (horizontal and perpendicular to the cable) of the cylindrical S-net instruments, specifically unburied station due to poor coupling, can be contaminated by rotation and tilt effects caused by a strong motion (Sawazaki and Nakamura 2020 ; Dhakal et al. 2023 ; Dhakal and Kunugi 2023a ). The X component, which is along the cable, has a minor degree of those contaminations such a rotation and tilt; however, tends to have greater variation than vector synthesis of the X and Y components. Therefore, we check for rotation and tilt due to strong motion by comparing one-minute averages before and after the earthquake (Dhakal et al. 2023 ; Dhakal and Kunugi 2023a ). As a result, if the rotation is greater than 0.1 degree, the X component is only used, and if the tilt is greater than 0.2 degree, the station data is eliminated. The PGAs of the horizontal component are calculated by vector synthesis of the X and Y components ( \(\sqrt{{X}^{2}+{Y}^{2}}\) ). The horizontal site amplifications for 2–8 Hz at S-net stations are also larger than those in the vertical component (Yabe et al. 2021 ). Therefore, the horizontal component for a total of 4242 (354 of these are for validation) is focused on because of its greater impact on slope failure and artificial structures. Correction of Deviation between Shallow and Deep Stations The PGAs on a buried station are reported to be less amplified compared with those on an unburied station (Tan and Hu 2023 ; Dhakal et al. 2021 : the right-upper panel of Fig. 4 ), making the derivation of regression equations difficult. We discuss the factors that contribute to this deviation. Factors that cause such deviations include the following: suppression due to buried equipment or amplification due to unburied equipment, path effects depending on the hypocenter-station location regardless of burial (Dhakal and Kunugi 2023b ; Tonegawa et al. 2023 ), site amplification factors depending on the station location (Dhakal et al. 2023 ; Tan and Hu 2023 ). The location of the buried stations is biased toward the landward side (Fig. 1 ), making it difficult to distinguish whether it is the effects of the location (path) or the burial. We attempted residual analysis using an onshore GMPE. The GMPE model is Morikawa and Fujiwara ( 2013 : MF13), which includes a correction term for distance from the volcanic front (Xvf) as a path effect and the depth where S-wave velocity reaches 1400 m/s (D14) as a site effect ( Appendix ). We used Model 2 of MF13 because there are no events above Mw 8; the Vs30 term is not used. The residuals between observed and predicted PGA are calculated for all 99 events. The average residuals at each station are larger near the trench (Fig. 5 a). Stations off the coast of Hokkaido are not buried; however, the residuals are small even in shallow water areas. The PGA distribution from the epicenter shows concentric attenuation for the crustal earthquake (Fig. 5 b). The interplate and slab earthquakes do not much attenuation toward the trench side or spreading along the trench axis (Fig. 5 cd). The onshore GMPE mostly predicts the PGAs of the crustal earthquakes; however, it does not reproduce the spreading along the trench axis of interplate or slab earthquakes (Fig. 5 ). These results are also the same for the existing offshore model, which assumes simple distance-dependent attenuation (Hu et al. 2020 , 2023 ). Plotting the residuals against several factors on the stations (Fig. 6 ), we found that the Pearson correlation coefficients are, in descending order, the distance from the trench axis (Xtr), depth to the plate (Dpl), Xvf, and water depth. The correlation with Xvf is found even though the correction term had already been applied, indicating a significant amplification effect in the offshore sites near the trench. The importance of path effects in strong motion or high-frequency seismic wave has been noted (Tonegawa et al., 2023 ; Dhakal and Kunugi, 2023b ), and the results of the residual analysis support this. Figure 7 shows waveforms for the event where the largest deviation between the buried and unburied stations was observed. At the trench-side sites (N.S3N07 and N.S3N08), large amplitude wave trains including PGAs are consists of lower frequency (long-period) components. This is the result of seismic energy trapping due to multiple reflections between the seafloor and the oceanic Moho or plate interface, similar in other subduction zones (e.g., Furumura and Singh 2002 ). At shallower parts (near the trench), seismic energy can be mainly trapped within oceanic sediments just below the seafloor. The low-velocity/low-Q oceanic sediments can cause a dominant frequency shift of PGAs. To evaluate the degree of deviation between the buried and unburied stations, the intercepts (alpha) of the buried and unburied stations were obtained in each event by the least squares method, with beta as the same slope for both in the following equation. \({log}_{10}{preY}_{{i}_{k} j} ={ \alpha }_{jk}-{\beta }_{j} {l{og}_{10}R}_{{i}_{k} j}\) (1), where Subscript j denotes the event number and i denotes the record number from event j . k is the suffix of the buried or unburied stations. The events with < 5 buried stations are not included in this regression. A difference of alpha between the buried and unburied stations indicates the degree of deviation (Fig. 8 ). Path effects seem to be dominant for the reason of deviation, since crustal earthquakes or earthquakes with a focal depth shallower than 15 km show little deviation between the buried and unburied stations. Derivation of a regression equation The derivation of the GMPE in this study followed the flow in Fig. 9 . Since correct regression coefficients cannot be obtained when there is such a large deviation, the regression equation is obtained after correcting for path effects discussed above. In previous empirical equations, Xvf, Xtr, and Dpl have been used as path effect variables (Kanno et al. 2006 ; Morikawa et al. 2003 ; Morikawa and Fujiwara 2013 ; Matsu’ura et al. 2020 ). We employ Dpl because Xtr is uniquely determinable including the boundary between the Philippine Sea Plate and the Pacific Plate. In Fig. 6 , the residuals are generally constant when Dpl is > 40 km; therefore, the stations with Dpl > 40 km are corrected as constant at Dpl = 40 km. Prediction PGAs are calculated using the basic equation and coefficients of Morikawa and Fujiwara ( 2013 ), and the correction term of path effect ( Cp ) was obtained by the least squares method. $${log}_{10} \left({preY}_{ij}\right) = 0.5507 {Mw}_{j} + d {R}_{ij} -{log}_{10}({R}_{ij}+ 0.006875 {10}^{0.5 {Mw}_{j}})$$ 2 $${log}_{10} \left(\frac{{obsY}_{ij}}{{preY}_{ij}}\right)= Cp=pa + pb {Dpl}_{i}$$ 3 where obsY and preY are observed and predicted PGAs (in Gal, cm/s 2 ), d , pa and pb are regression coefficients. The distance coefficient ( d ) is also optimized to match the S-net data. In this process, the average of residuals is adjusted to zero for each earthquake. The correction terms are obtained for interplate and slab earthquakes with a focal depth of > 15 km. In other words, no correction is made for crustal earthquakes and earthquakes with focal depths of < 15 km. The obtained correction terms result in a smaller discrepancy between the buried and unburied stations (Figs. 4 and 8 ). However, the log PGA is as high as ~ 0.2 at the unburied stations. Equation (4) is used as the basic equation as a function of the source distance and Mw, and coefficients are obtained to minimize the residuals from the observed data. \({log}_{10} \left({preY1}_{ij}\right)= a + b {Mw}_{j} + d {R}_{ij} -{log}_{10}\left({R}_{ij}+ e {10}^{k {Mw}_{j}}\right) + Cp+ {\eta }_{j}+{\xi }_{ij}\) (4), where a, b, d, e, k are regression coefficients. The random variable η j denotes the between-event error (representing the event-to-event component of the total variability) with a zero mean and a standard deviation of τ⁠ , and the random variable ξ ij denotes the within-event error (representing the site-to-site component of variability) with a zero mean and a standard deviation of φ⁠ . To avoid underestimating the term representing the saturation of the amplification effect ( e, k ) due to the small number of stations close to the epicenter, the residual is weighted by the source distance. $$weight= \left\{\begin{array}{c}8.0 R \le 30 km\\ 4.0 30 km < R \le 60 km\\ 2.0 60 km < R \le 90 km\\ 1.0 90 km < R\end{array}\right\}$$ The source distances and Mw are known to be correlated (Fukushima and Tanaka 1990 ). To avoid that interdependency, a distance coefficient ( d ) was obtained with the Mw term ( a + b Mw) as dummy variables using a single regression. To obtain the coefficients of Eq. (4), which is nonlinear, the coefficients b , k , and e are optimized to minimize the total standard deviation σ ( \(\sqrt{{\phi }^{2}+{\tau }^{2}}\) ) by the differential evolution method to avoid convergence to a local solution based on the distance coefficients obtained in advance. The distance coefficient was again obtained using single regression based on the optimized coefficients b , k , and e . These iteration calculations lasted until the rate of change in the distance coefficient converged to 0.1%. The coefficients of Eq. (4) obtained from the regression analysis are listed in Table 1 . The total standard deviation of the regression equation with only the source distance and Mw as explanatory variables with the path effect term is 0.40. To examine additional correction terms, the residuals between the predicted and observed PGAs were illustrated in Fig. 10 . The focal depths have been incorporated into most GMPEs as a factor that amplifies acceleration (Morikawa and Fujiwara 2013 ; Kanno et al. 2006 ; Hu et al. 2020 ) and are also considered a variable with a large influence in offshore sites (Tan and Hu 2023 ). The Y1 residuals showed a correlation with focal depths was also confirmed (Fig. 10 a). Therefore, the coefficients of the correction term ( Ch ) were obtained from a single regression by a generalized linear mixed model that accounts for intra-event errors (Gilmour et al. 1985 ). \({log}_{10} \left(\frac{{obsY}_{ij}}{{preY1}_{ij}}\right)= Ch = c {H}_{j}+ha\) (5), where H is focal depth (km), c and ha are regression coefficients. Combining Equations 4 and 5, \({log}_{10}\left({preY2}_{ij}\right)= b {Mw}_{j} + d {R}_{ij} -{log}_{10}\left({R}_{ij}+ e {10}^{k {Mw}_{j}}\right)+Cp+Ch+ {\eta }_{j}+{\xi }_{ij}\) (6), and the residuals obtained by Eq. 6 no longer show a significant trend with the focal depths (Fig. 10 b); the total standard deviation was 0.36. The residuals for each earthquake type show a normal distribution with a peak at 0 when the focal depth term is taken into account, suggesting that the amplification of PGAs by earthquake types is mainly due to the focal depth. However, since other factors such as the propagation path of seismic waves depending on the earthquake types are also possible (left side of Fig. 10 b), a correction term ( Ct ) was obtained by regressing the distance coefficient with the earthquake types as a dummy variable. \({log}_{10} \left(\frac{{obsY}_{ij}}{{preY2}_{ij}}\right)= Ct = t {{log}_{10}R}_{ij}+ta\) (7), where t and ta are regression coefficients. As a result, the following equation is obtained. $${log}_{10}\left({preY3}_{ij}\right)= b {Mw}_{j} + d {R}_{ij} -{log}_{10}\left({R}_{ij}+ e {10}^{k {Mw}_{j}}\right)+Cp+Ch+Ct+ {\eta }_{j}+{\xi }_{ij}$$ 8 The residuals obtained from this equation show a uniform variation regardless of the change in each variable (Fig. 10 c), and its total standard deviation was 0.32. Eq. ( 8 ) is hereafter referred to as the NT24 model. Comparing with conventional models Morikawa and Fukushima (2013), widely used as the onshore GMPE, and Hu et al. ( 2020 ) and Hu et al. ( 2023 ), which are derived from the offshore stations, are compared with the NT24 model (Refer to Appendix for these GMPE equations). Hu et al. ( 2020 ) proposed an integrated empirical equation (H20 model) using six temporary ocean-bottom seismometers (OBSs) and nearby onshore K-NET stations around Sagami Bay. Hu et al. ( 2020 ) showed the difference in HVSR on each OBS and obtained regression coefficients for each station as the site conditions. Since the data for site term Sk in the H20 model are site-specific due to little information such as V S 30, we apply 2.7 as the average Sk for Sagami Bay to the S-net stations. The HZ23 model (Hu et al. 2023 ) is the onshore GPME of Zhao et al. ( 2006 ) applied to the S-net data with correction terms to reduce the residuals as a referenced empirical approach (Atkinson 2008 ). The model includes site effect terms ( Ck ), and we used the same site classes estimated from the HVSR by Hu et al. ( 2023 ). Data from six events not used in the regression are used to validate each model (Table A1 ). Due to the limited number of data to calculate errors between events, we used the standard deviation between sites ( φ ) as the reproducibility between models (Table 2 ). Table 2. Data used by offshore and onshore ground motion prediction equations and standard deviations obtained by these models using the PGA data in this study. The NT24 model reproduces the observations well for data not used in the regression and shows smaller standard deviations than the other models for the S-net data despite the small number of coefficients (Table 2 and Fig. 12 . To investigate which variables might be responsible for this difference, the residuals of the predicted and observed all PGA data are shown (Fig. 11 ). In the MF13 model, the predicted PGAs are underestimated as source distance increases, suggesting that the path effects in the offshore sites are larger and distance coefficients are smaller than the onshore sites. The results of the H20 model tended to overestimate overall. The amplification around Sagami Bay tends to be small compared to S-net stations, which may have caused the H20 model to overpredict northeastern Japan. The residuals can be improved by changing the site term Sk (2.1) treated as the constant term. The HZ23 model has biased residuals corresponding to focal depth, particularly for the slab and crustal types. The negative correlation between Mw and the residuals may be due to most of the data being from Mw 4–5 earthquakes. This result means that different regression equations can be obtained depending on the range of Mw, and the distance attenuation effect of Mw may be nonlinear. Residual analysis for site effects Dhakal et al. ( 2021 ) and Tan and Hu ( 2023 ) performed residual analysis on the onshore GMPEs to the S-net records and showed the relationship between site amplification and water column, Xvf, and D14. The sediment layers are known to amplify PGAs (Dobry et al. 2000 ; Morikawa and Fujiwara 2013 ). The site amplification effects in the onshore stations are demonstrated by D14 and Vs30 as deep sediment layer and shallow soft sediment, respectively (e.g., Morikawa and Fujiwara 2013 ). In the offshore region around Japan, D14 has been published (NIED 2019). Nishizawa et al. ( 2022 ) estimated the sediment thickness from seismic reflection surveys. We also examined the effects of the placement conditions of the observation stations in addition to the above factors because of the possible influence of cable azimuths or seafloor slopes. The azimuths of observation devices were referred to as the value by Takagi et al. ( 2019 ). The seafloor slope angles of the placement sites were calculated from the bathymetry map (J-EGG500: https://jdoss1.jodc.go.jp/vpage/depth500_file.html ). The geometric means of the residuals per station for the NT24 model are not constant (Fig. 13 a) and are expected to have site-specific amplification rates. The residuals show a slight correlation with D14 and the sediment thickness based on seismic reflection surveys (Fig. 13 b). The MF13 and HZ23 models using the variable D14 values or the site classes were tested to check if the residuals decreased in the offshore region when these were held constant or when they are variables. For the variable site classes ( Ck ) in the HZ23 model and the D14 correction term in the MF13 model, the smaller standard deviation than the results with the averaged constant Ck or D14 terms (Table 2 ). The NT24 model is also regressed using D14, which is more encompassing throughout Japan than the sediment thickness (Nishizawa et al., 2022 ), and additional correction term Cv is obtained. \({log}_{10} \left(\frac{{obsY}_{ij}}{{preY3}_{ij}}\right)= Cv = v {{log}_{10}D14}_{i}+va\) (9), where v and va are regression coefficients (Table 1 ). The availability is examined by the Akaike information criterion (AIC: Akaike 1973 ). The AIC is a statistic that expresses the goodness of fit of a model; the smaller the value, the better the fit, but it is used as a relative evaluation. There was a significant improvement from the basic equation to the focal type correction term, from 3678 to 980 (Table 1 ). When the D14 correction term was applied, the AIC was 921, and little changed from the model with the focal type correction term. The correction by these sediment thickness proxies as a site effect slightly improves offshore GMPEs, and the sediment thickness from seismic reflection surveys may be useful because it highly correlates with the residual (Fig. 13 b). The small effect of the correction by the sediment thickness may be due to the path effect has already been corrected, since the residual analysis by the onshore GMPE also shows a stronger correlation with Dpl and Xtr than with the thickness of the deposition layer (Fig. 6 ). To investigate a regional bias of the residuals on each station, the geographic distribution of the geometric mean residuals is shown in Fig. 14 , along with the seafloor geology (Inoue and Honza 1983 ). Dhakal et al. ( 2023 ) obtained the site amplification factor for the S-net stations from the spectral inversion technique. The amplification factors at 5 Hz are consistent with the sites where the positive residuals are large in this study (Fig. 14 ). On the other hand, the predicted values off Chiba exceed the observed values, indicating that the site amplifications are small. These sites are generally in the area where the semi-consolidated to consolidated pre-Quaternary sediments are exposed (Fig. 14 : Inoue and Honza 1983 ). The negative residuals were also observed at sites outside the trench where submarine volcanoes are distributed. Since these areas are supposed to have thick sediment layers from seismic reflection surveys (1–2 km from D14), the underestimated areas may be attenuated by the lack of very shallow unconsolidated sediment layers. No clear relationship was found between water depth or seafloor slope degrees and residuals in the observations (Fig. 13 b). This is consistent with previous studies that showed little effect of the water column on the horizontal amplitude (Tan and Hu 2023 ). Simulations of high-frequency seismic waves also demonstrated that seawater has little influence on the high-frequency maximum S-wave amplitude (Takemura et al. 2020 , 2023 ). There appears to be an offset between the buried and unburied stations based on the residual around 1500 m water depth (Fig. 12 b). All buried stations show negative residuals (Fig. 14 ), which means that the predicted values are intermediate between buried and unburied stations. The positive and negative residuals are always reversed at the unburied station and the adjacent buried station, suggesting a difference in PGAs due to burial rather than water depth or site conditions. The buried stations would provide high-quality data because of their small errors (Fig. 13 b: Sawazaki and Nakamura 2020 ; Dhakal et al. 2023 ). The unburied stations likely show actual large PGAs where the seafloor surface because the effects of rolling and tilting are eliminated. In addition to poor coupling due to exposure to the seafloor, it is also necessary to consider effects by not only strong motion but also slope failures or turbidity currents associated with earthquake events. Although the difference between both residuals is ~ 1–4 gal (Fig. 8 ), it is reasonable to take this offset into account when assessing safety. Additionally, the residuals seem to be biased positively and negatively depending on a cable azimuth (Fig. 13 a). When the stations are compared in the order in which they are connected, there is a continuity in the residuals, which may be related to the cable azimuth as pointed out by Dhakal et al. ( 2023 ). If there is an amplification factor due to cable azimuths, it is expected to be relative to the epicenter location; thus, these interrelationships would need to be individually examined for each event. Limitation The NT24 model should be used for earthquakes with Mw > 5.4 (crustal event is Mw > 5.0) because it shows a different trend from other models including Mw 4.0–5.4. The majority of earthquakes with Mw > 5.4 were interplate type events (thrust faulting), and the applicability of the other focal types needs to be evaluated additionally because there was no significant difference in the coefficients of the earthquake type terms (Table 1 ). The adoption of a correction term for the focal depths resulted in a normal distribution centered at 0. Given the paucity of data for Mw > 6.3, additional evaluation through data accumulation will be important to confirm these results. In areas where the basement is exposed, residuals of ~ 2.0 cm/s 2 are observed; therefore, the seafloor geology needs to be confirmed, and an attenuated PGA should be assumed in these sites. If a hypocenter and observation points are across other plates, the application of the distance attenuation equation requires caution. The observed wedge-shaped trapping above the subducting plate makes the application of a distance attenuation formula within the same plate challenging. In Fig. 14 , the overestimation at the stations in the Philippine Sea Plate indicates attenuation jumps during interplate transmission. Applicability and Summary In this study, the residual analysis based on the existing GMPE revealed that the path effects are more strongly affected than the onshore sites. Therefore, the NT24 model corrected for path effects based on the conventional GMPE, and the deviations between the buried and unburied stations were reduced by accounting for the depth to the plate boundary. The NT24 model, which takes into account the focal depth and type, can reproduce the observed PGAs with smaller residuals than previous offshore and onshore GMPEs. The unique points from previous GMPEs are that the NT24 model can account for the small distance attenuation rate of the offshore sites and the large PGA along the trench axis without distance attenuation in concentric circles that appear due to the trapping of seismic energies in an overriding plate wedge (Fig. 5 ). Residual analysis for site effects in the offshore sites, especially sediment thickness, show that the correction using site effect terms slightly improved prediction accuracy. These features of the offshore region mean that large PGAs can appear even in areas far from the epicenter, which is important for slope stability analysis and seismic structures. Abbreviations AIC: Akaike information criterion; F-net: Full-range seismograph network; GMPE: Ground Motion Prediction Equations; HVSR: Horizontal-to-Vertical Spectral Ratio; NIED: National Research Institute for Earth Science and Disaster Resilience; S-net: Seafoor observation network for earthquakes and tsunamis along the Japan Trench; OBS: Ocean-Bottom Seismometers; PGA: Peak Ground Acceleration. Declarations Acknowledgements We are thankful to Hajime Naruse (Kyoto University) for a useful discussion of regression analysis. We would like to thank the JMA for providing us with hypocenter information. Author contributions R.N. processed the ground motion recordings, performed the regression analysis, and drafted the manuscript. S.T. conceptualized the study, and reviewed and edited the manuscript. All authors approved the final version of this manuscript. Funding This work was supported by JSPS as a Grant-in-Aid for JSPS Fellows (KAKENHI Grant Number JP23KJ1152). Availability of data and materials The bathymetry data was downloaded from the Japan Oceanographic Data Center (Japan Coast Guard): https://jdoss1.jodc.go.jp/vpage/mgd77.html. The peak ground acceleration recordings at the S-net sites were retrieved from NIED S-net, National Research Institute for Earth Science and Disaster Resilience, https://doi.org/10.17598/nied.0007. https://hinetwww11.bosai.go.jp/auth/download/cont/?LANG=en. The Japan Seismic Hazard Information Station deep subsurface model was downloaded from the website: http://www.j-shis.bosai.go.jp/map/JSHIS2/download.html?lang=en. The moment magnitudes, focal depths, and coordinates of epicenter were taken from the website: http://www.fnet.bosai.go.jp/event/joho.php?LANG=en. All the websites were accessed on October 13, 2023. Competing interests The authors declare that they have no competing interests. References Akaike H (1973) Information theory and an extension of the maximum likelihood principle. 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Physics of the Earth and Planetary Interiors 152:144–162. https://doi.org/10.1016/j.pepi.2005.06.010 Supplementary Files GA.png Appendix.docx AppendixTables.docx Cite Share Download PDF Status: Published Journal Publication published 20 Nov, 2024 Read the published version in Earth, Planets and Space → Version 1 posted Editorial decision: Major Revision 01 Jul, 2024 Reviewers agreed at journal 10 May, 2024 Reviewers invited by journal 09 May, 2024 Editor assigned by journal 07 May, 2024 First submitted to journal 30 Apr, 2024 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. 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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-4348314","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":300809607,"identity":"55573d6c-d780-46ec-aeb0-a9e3c5308222","order_by":0,"name":"Ryo Nakanishi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVRIiWNgGAWjYFACNiA2YEhgA3MKbIAEY+MBErQYpIG0NBChhYEhAcIxOAym8GoxZz+W+LmgoC6Pj4H94oMPBuft1rYfBtpSYxONS4tlT9ph6RkGh4vZGHiKDWcY3E7ediYRqOVYWm4DDi0GB9IbpHkMDiS2MfCkARm3k80OALUwNhzGreX88+bfPAZ1IC3pQMa5ZLPzDwlouZF2DGg4M1AL+zFmoHV2ZjcI2XLjWZo1j8HhxDZmHmbJGQbJCWY3gLYk4PPL+TTj2zx/6hLnt7c//PChws7e7Hz6wwcfamxwakEAoKtAVCJYZQJB5WDA/gBE2hOneBSMglEwCkYSAADifF+pRmMc4gAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-8271-2583","institution":"Kyoto University: Kyoto Daigaku","correspondingAuthor":true,"prefix":"","firstName":"Ryo","middleName":"","lastName":"Nakanishi","suffix":""},{"id":300809608,"identity":"31d99d49-8287-47e6-9501-11a25533d5ba","order_by":1,"name":"Shunsuke Takemura","email":"","orcid":"","institution":"The University of Tokyo: Tokyo Daigaku","correspondingAuthor":false,"prefix":"","firstName":"Shunsuke","middleName":"","lastName":"Takemura","suffix":""}],"badges":[],"createdAt":"2024-04-30 10:27:51","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4348314/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4348314/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40623-024-02078-5","type":"published","date":"2024-11-20T15:57:59+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":56789491,"identity":"6a7a0ea0-eaf9-4f0c-bcf1-84755ff73829","added_by":"auto","created_at":"2024-05-20 13:22:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2137727,"visible":true,"origin":"","legend":"\u003cp\u003eIndex maps with bathymetry. Circles denote the location of the epicenters of earthquakes and their size indicates the magnitude. Shades of green indicate depth. The depth to the Pacific Plate is displayed with solid line contours at intervals of 10 km. Broken lines indicate the trench axis. Squares denote the recording stations on the ocean bottom (S-net). Triangles show the location of active volcanoes.\u003c/p\u003e","description":"","filename":"fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/9a1744fc982e4bd2fe63d8f6.png"},{"id":56789492,"identity":"25afaa3e-e8ac-4ae3-b855-e7e7f8c2cf34","added_by":"auto","created_at":"2024-05-20 13:22:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":520026,"visible":true,"origin":"","legend":"\u003cp\u003eGeneral distribution of data in terms of PGA, magnitude, source distance, magnitude, and focal depth by earthquake types.\u003c/p\u003e","description":"","filename":"fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/4363f527c826ddf6612f2982.png"},{"id":56789495,"identity":"9efcad5e-98df-4dfc-976d-35b2cad3e023","added_by":"auto","created_at":"2024-05-20 13:22:59","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":306747,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of source distance and plate subduction zone structure. (a) Conceptual diagram of calculation of source distance according to plane faults. Plane faults are assumed according to Mw following Utsu's (2002) formula, where R is the source distance. (b) Vertical cross-sections based on Zhi and Zhao (2005) along the trench-arc direction. The blue dotted line shows an example of a reflected wave.\u003c/p\u003e","description":"","filename":"fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/bcd9054975febb870a2b300e.png"},{"id":56789503,"identity":"338f407e-4e06-49e3-a038-b1348b140691","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":969313,"visible":true,"origin":"","legend":"\u003cp\u003eComparison PGAs between the buried and unburied stations depending on the source distance. Examples of the interplate and crustal earthquakes are shown.\u003c/p\u003e","description":"","filename":"fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/1a80f7b606f049a4b81d5e05.png"},{"id":56790521,"identity":"7b995362-92d1-4c96-be12-6652071feebe","added_by":"auto","created_at":"2024-05-20 13:30:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1824462,"visible":true,"origin":"","legend":"\u003cp\u003eDistributions of observed and GMPE-predicted PGAs at S-net stations. (a) Residuals of the PGAs observed and predicted by the MF13 model for all seismic events. The examples of observed PGAs and PGAs predicted by the MF13 model and the NT24 model for the crustal (b), slab (c), and interplate earthquakes (d), respectively.\u003c/p\u003e","description":"","filename":"fig5.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/953a3813a66643403fcaf454.png"},{"id":56789505,"identity":"a83060d6-23f4-4def-a4d6-838f521e9225","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":982979,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Xtr, Dpl, D14, water depth, sediment thickness, and slope angle, with residuals from the MF13 model prediction for all observed PGA data. The green dots indicate the mean value for each S-net station, and the solid green line and shading denote the results of the cubic function fitting and the error range, respectively. PCC indicates the Pearson correlation coefficient.\u003c/p\u003e","description":"","filename":"fig6.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/73c0ac2fce431d654160abac.png"},{"id":56789500,"identity":"2c169cfc-126c-4cb9-b182-4e2adaf566a5","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1225703,"visible":true,"origin":"","legend":"\u003cp\u003eWaveforms of the 2016-11-12 event. (a) Station locations used for waveform plots. Legends are the same as those in Fig. 1. Black star shows the epicenter. (b) Waveform plots. PGA waveforms are plotted at the corresponding distance from the epicenter.\u003c/p\u003e","description":"","filename":"fig7.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/943736aa86f6cf10279e307f.png"},{"id":56790522,"identity":"c7ccfbec-5e04-4fcb-8b61-b9a2c3c76e57","added_by":"auto","created_at":"2024-05-20 13:31:00","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":453373,"visible":true,"origin":"","legend":"\u003cp\u003eBiplots of α deviation between the buried and unburied stations and focal characteristics (Mw, focal depth, and distance from the trench axis). The α deviations (a) before and (b) after the correction of the path effect is used.\u003c/p\u003e","description":"","filename":"fig8.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/6f90d05f5eec84764657797d.png"},{"id":56789498,"identity":"34695ff4-b254-4c57-8221-35c833f7c357","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":498367,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart for deriving regression equation.\u003c/p\u003e","description":"","filename":"fig9.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/66fef29832fdc4bd81da24ec.png"},{"id":56789504,"identity":"067c2acf-7a28-42b0-ba22-d3cb589e34fb","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1253686,"visible":true,"origin":"","legend":"\u003cp\u003eResiduals between predicted and observed PGAs obtained from each regression equation. The basic equation and the residuals for each stage using the focal depth and focal type correction terms are shown. Different colors indicate the focal types. Histograms of the residuals are also provided.\u003c/p\u003e","description":"","filename":"fig10.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/916ac925f6f3ec6f9f912122.png"},{"id":56789499,"identity":"26c2e033-bd1c-480a-9ae3-ad5faae2a7d4","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":818041,"visible":true,"origin":"","legend":"\u003cp\u003eResiduals between the regression lines of the NT24 model and the conventional models and the observed values in the test cases. The right panels show the corresponding residuals.\u003c/p\u003e","description":"","filename":"fig11.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/9cb274e2748f669dc2c2a4f2.png"},{"id":56789502,"identity":"297a1285-93f6-49eb-8f47-2d11f9b19023","added_by":"auto","created_at":"2024-05-20 13:23:00","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":1208244,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of residuals with source distance, focal depth, and Mw from each model prediction for all observed PGA data.\u003c/p\u003e","description":"","filename":"fig12.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/403783707c40aa4a0906a2fb.png"},{"id":56790520,"identity":"fa4cfdfe-4097-48db-a414-bd89978d8963","added_by":"auto","created_at":"2024-05-20 13:30:59","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":1928810,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of cable azimuth of device, Xtr, Dpl, D14, water depth, sediment thickness, slope angle, with residuals from the NT24 model prediction for all observed PGA data. (a) Residual values showing S-net stations in the order in which they are connected by submarine cables. Gray dots indicate all residual values and green dots indicate mean values. Red diamonds indicate the cable azimuth of the station with 0 degrees east of the station (Takagi et al. 2019). (b) The green dots indicate the mean value for each S-net station, and the solid green line and shading denote the results of the cubic function fitting and the error range, respectively. PCC indicates the Pearson correlation coefficient.\u003c/p\u003e","description":"","filename":"fig13.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/d1ea7ac4b797ef01fffc1431.png"},{"id":56790523,"identity":"3065067c-9fae-4a42-83e5-0b53d4900561","added_by":"auto","created_at":"2024-05-20 13:31:00","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":1502459,"visible":true,"origin":"","legend":"\u003cp\u003eMean values of residuals per the S-net station. Bathymetry is shaded according to slope angle. Marine geology is shown for areas where the base rock is exposed based on Inoue and Honza (1983). Diamonds indicate the buried stations.\u003c/p\u003e","description":"","filename":"fig14.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/1efd22cda8ffe54081469843.png"},{"id":69835074,"identity":"304a9512-f47d-44bc-8f98-5a66a9462711","added_by":"auto","created_at":"2024-11-25 16:11:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":18991159,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/1d809ddb-b244-4b2a-95dd-7ea79eeafb96.pdf"},{"id":56789493,"identity":"223067bc-20fa-4e5b-9b5c-3ade58f15f7d","added_by":"auto","created_at":"2024-05-20 13:22:59","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":106930,"visible":true,"origin":"","legend":"","description":"","filename":"GA.png","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/bbdbc72fadda0173e017254e.png"},{"id":56789490,"identity":"dfd5d8c1-125c-4382-9558-98598da7f636","added_by":"auto","created_at":"2024-05-20 13:22:59","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":27804,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/bd9ec7752535f9421cc6f32a.docx"},{"id":56789497,"identity":"9bb985fc-928d-4cfa-9d44-adbbf13cb590","added_by":"auto","created_at":"2024-05-20 13:22:59","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":65504,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixTables.docx","url":"https://assets-eu.researchsquare.com/files/rs-4348314/v1/c81c2bf44f8e13b72fd9aac8.docx"}],"financialInterests":"","formattedTitle":"Development of an offshore ground motion prediction equation considering path effects based on S-net data","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe empirical distance attenuation formula for ground motion is useful for urgent disaster prevention information, such as earthquake early warning, because of its simplicity and promptness (e.g., Tajima and Hayashida \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Allen and Melgar \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Hoshiba et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). It is also crucial in assessing the durability of buildings under strong ground motions and in preventing slope failures (e.g., Canals et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Ground motion prediction equations (GMPEs) for the onshore region have been proposed in the form of empirical equations owing to the abundance of observational data (e.g., Kanno et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), and complex models have also been proposed to account for site-specific amplification effects (e.g., Zhao et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Morikawa and Fujiwara \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Some studies for an offshore turbidite have used onshore GMPEs to estimate the peak ground acceleration (PGA) at offshore sites by triggering earthquakes that occurred slope failures (Noda et al. \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Pouderoux et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Lehu et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Pope et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Ikehara et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). On the other hand, it has been shown that offshore sites exhibit different distance attenuation than onshore sites (Gomberg \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Hu et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Dhakal et al. \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and either corrections to an onshore model or a new empirical equation is needed (Scholz et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). In other words, GMPEs for evaluating offshore slope failures have not yet been sufficiently established.\u003c/p\u003e \u003cp\u003eIn Japan, offshore observation networks of DONET and S-net have been operated since 2011 and 2016, respectively (Aoi et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Thus, continuous observations of seismic waves at the ocean bottom have been available. The stations of DONET are limited southeast off the Kii Peninsula and off Cape Muroto only; however, the S-net stations were widely deployed off Kanto to Hokkaido regions. However, only limited GMPEs exist due to the shorter observation period (Hu et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Because they are based on the onshore GMPE models, it is expected that there will be an under/overestimation in cases where there are amplification effects specific to offshore areas. The reference GMPEs include site effect terms with four levels of classification based on the mean S-wave velocity of 30-m thick surface ground (Vs30) or a horizontal-to-vertical spectral ratio (HVSR), which is the function for a horizontal ground motion of surface layers (Nakamura \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1989\u003c/span\u003e). However, it is not discussed whether the site class and coefficients on offshore sites, which should reflect the actual site amplification and reduce the residuals. Even in the Japan Trench, where S-net was widely covered, it is difficult to clarify what causes site effects because of the lack of physical property data in the offshore region compared to the onshore region. In addition, the S-net stations below a water depth of ~\u0026thinsp;1500 m were buried, resulting in differences in raw data with unburied stations (Tan and Hu \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Hu et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) model did not take into account differences between buried and unburied stations even using the S-net data. Therefore, it is important to verify the characteristics of distance attenuation or site effects in offshore areas and to clarify the robustness of the GMPEs through residual analysis.\u003c/p\u003e \u003cp\u003eThe purpose of this study is to develop a new simple GMPE for predicting PGAs on the seafloor. We examine the distance attenuation features peculiar to the offshore sites and the effect of the burial by residual analysis using conventional GMPE. We derive a regression equation with correction terms using S-net data and compare its performance with other models. The residuals from the PGA predicted by the regression equation will be used to discuss the factors that cause site effects.\u003c/p\u003e"},{"header":"Dataset and Processing","content":"\u003cp\u003eThe seismic events used in this study are listed as earthquakes with moment magnitudes (Mw)\u0026thinsp;\u0026gt;\u0026thinsp;5.4 and focal depths\u0026thinsp;\u0026lt;\u0026thinsp;130 km (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and Table \u003cspan class=\"InternalRef\"\u003eA1\u003c/span\u003e). Data for crustal earthquakes greater than Mw 5.0 are also used because of their small number and close source distance. The earthquake mechanism and Mw in formation is obtained from the F-net moment tensor catalog, which has been systematically monitored by the National Research Institute for Earth Science and Disaster Resilience (NIED) (Fukuyama et al. \u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e; \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.fnet.bosai.go.jp/top.php?LANG=en\u003c/span\u003e\u003c/span\u003e: last accessed on 2024.02.11). These events occurred within the area of the longitude of 138\u0026ndash;147\u0026ordm;E and latitude of 33.5\u0026ndash;44\u0026ordm;N from August 2016 to March 2024. The hypocenter locations and origin times of the selected events are referred from the unified hypocenter catalog of the Japan Meteorological Agency. Excluding events with no stations within distances\u0026thinsp;\u0026le;\u0026thinsp;100 km from a source fault, the total number of events is 99 (numbers of crust and slab events are 21 and 20, respectively) (Figs. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, Table \u003cspan class=\"InternalRef\"\u003eA1\u003c/span\u003e). Of these, the latest 2 events of each earthquake type are not used in the regression for validation purposes. Acceleration data are obtained for 10 min from 1 min before the earthquake origin time at 150 S-net stations (Kanazawa et al. \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; Uehira et al. \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e; Mochizuki et al. \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e) (Table \u003cspan class=\"InternalRef\"\u003eA2\u003c/span\u003e). For the source distances (R: km), a plane fault is assumed in three-dimensional space, and the shortest distance to each station is obtained (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). The fault lengths and widths of plane faults are defined from a fault length and fault area according to the Mw by the Utsu (\u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e) formulas (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eTable 1. Coefficients, AIC, and standard deviation for the horizontal offshore ground motion prediction equation.\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"379\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"22.95514511873351%\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd width=\"77.04485488126649%\" colspan=\"4\"\u003e\n \u003cp\u003eBase fomula\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.015873015873016%\"\u003e\n \u003cp\u003e \u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.195767195767196%\"\u003e\n \u003cp\u003eb\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.486772486772487%\"\u003e\n \u003cp\u003ed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.105820105820104%\"\u003e\n \u003cp\u003ee\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.195767195767196%\"\u003e\n \u003cp\u003ek\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.015873015873016%\"\u003e\n \u003cp\u003eCoefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.195767195767196%\"\u003e\n \u003cp\u003e0.6483\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.486772486772487%\"\u003e\n \u003cp\u003e-0.00075\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.105820105820104%\"\u003e\n \u003cp\u003e0.00196\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.195767195767196%\"\u003e\n \u003cp\u003e0.6007\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.015873015873016%\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.195767195767196%\"\u003e\n \u003cp\u003e \u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"22.486772486772487%\"\u003e\n \u003cp\u003e \u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.105820105820104%\"\u003e\n \u003cp\u003e \u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.195767195767196%\"\u003e\n \u003cp\u003e3678\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1716210898.png\"\u003e\u003c/p\u003e\n\u003cp\u003eThe acceleration data are used from the stations within distances R\u0026thinsp;\u0026le;\u0026thinsp;300 km and PGA\u0026thinsp;\u0026gt;\u0026thinsp;5 cm/s\u003csup\u003e2\u003c/sup\u003e. The average amplitudes within the 60-s time window before P-wave arrival are subtracted at each time step for the S-net records as offset amplitudes. The acceleration data are applied to a fourth-order bandpass filter with a frequency band from 0.1 to 25 Hz and then horizontal and vertical acceleration seismograms are obtained by following Takagi et al. (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The Y component (horizontal and perpendicular to the cable) of the cylindrical S-net instruments, specifically unburied station due to poor coupling, can be contaminated by rotation and tilt effects caused by a strong motion (Sawazaki and Nakamura \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Dhakal et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dhakal and Kunugi \u003cspan class=\"CitationRef\"\u003e2023a\u003c/span\u003e). The X component, which is along the cable, has a minor degree of those contaminations such a rotation and tilt; however, tends to have greater variation than vector synthesis of the X and Y components. Therefore, we check for rotation and tilt due to strong motion by comparing one-minute averages before and after the earthquake (Dhakal et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dhakal and Kunugi \u003cspan class=\"CitationRef\"\u003e2023a\u003c/span\u003e). As a result, if the rotation is greater than 0.1 degree, the X component is only used, and if the tilt is greater than 0.2 degree, the station data is eliminated. The PGAs of the horizontal component are calculated by vector synthesis of the X and Y components (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sqrt{{X}^{2}+{Y}^{2}}\\)\u003c/span\u003e\u003c/span\u003e). The horizontal site amplifications for 2\u0026ndash;8 Hz at S-net stations are also larger than those in the vertical component (Yabe et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Therefore, the horizontal component for a total of 4242 (354 of these are for validation) is focused on because of its greater impact on slope failure and artificial structures.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eCorrection of Deviation between Shallow and Deep Stations\u003c/h2\u003e\n \u003cp\u003eThe PGAs on a buried station are reported to be less amplified compared with those on an unburied station (Tan and Hu \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dhakal et al. \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e: the right-upper panel of Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e), making the derivation of regression equations difficult. We discuss the factors that contribute to this deviation. Factors that cause such deviations include the following: suppression due to buried equipment or amplification due to unburied equipment, path effects depending on the hypocenter-station location regardless of burial (Dhakal and Kunugi \u003cspan class=\"CitationRef\"\u003e2023b\u003c/span\u003e; Tonegawa et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e), site amplification factors depending on the station location (Dhakal et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Tan and Hu \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eThe location of the buried stations is biased toward the landward side (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e), making it difficult to distinguish whether it is the effects of the location (path) or the burial.\u003c/p\u003e\n \u003cp\u003eWe attempted residual analysis using an onshore GMPE. The GMPE model is Morikawa and Fujiwara (\u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e: MF13), which includes a correction term for distance from the volcanic front (Xvf) as a path effect and the depth where S-wave velocity reaches 1400 m/s (D14) as a site effect (\u003cspan class=\"InternalRef\"\u003eAppendix\u003c/span\u003e). We used Model 2 of MF13 because there are no events above Mw 8; the Vs30 term is not used. The residuals between observed and predicted PGA are calculated for all 99 events.\u003c/p\u003e\n \u003cp\u003eThe average residuals at each station are larger near the trench (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea). Stations off the coast of Hokkaido are not buried; however, the residuals are small even in shallow water areas. The PGA distribution from the epicenter shows concentric attenuation for the crustal earthquake (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb). The interplate and slab earthquakes do not much attenuation toward the trench side or spreading along the trench axis (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ecd). The onshore GMPE mostly predicts the PGAs of the crustal earthquakes; however, it does not reproduce the spreading along the trench axis of interplate or slab earthquakes (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). These results are also the same for the existing offshore model, which assumes simple distance-dependent attenuation (Hu et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). Plotting the residuals against several factors on the stations (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e), we found that the Pearson correlation coefficients are, in descending order, the distance from the trench axis (Xtr), depth to the plate (Dpl), Xvf, and water depth. The correlation with Xvf is found even though the correction term had already been applied, indicating a significant amplification effect in the offshore sites near the trench. The importance of path effects in strong motion or high-frequency seismic wave has been noted (Tonegawa et al., \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e; Dhakal and Kunugi, \u003cspan class=\"CitationRef\"\u003e2023b\u003c/span\u003e), and the results of the residual analysis support this. Figure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e shows waveforms for the event where the largest deviation between the buried and unburied stations was observed. At the trench-side sites (N.S3N07 and N.S3N08), large amplitude wave trains including PGAs are consists of lower frequency (long-period) components. This is the result of seismic energy trapping due to multiple reflections between the seafloor and the oceanic Moho or plate interface, similar in other subduction zones (e.g., Furumura and Singh \u003cspan class=\"CitationRef\"\u003e2002\u003c/span\u003e). At shallower parts (near the trench), seismic energy can be mainly trapped within oceanic sediments just below the seafloor. The low-velocity/low-Q oceanic sediments can cause a dominant frequency shift of PGAs.\u003c/p\u003e\n \u003cp\u003eTo evaluate the degree of deviation between the buried and unburied stations, the intercepts (alpha) of the buried and unburied stations were obtained in each event by the least squares method, with beta as the same slope for both in the following equation.\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\({log}_{10}{preY}_{{i}_{k} j} ={ \\alpha }_{jk}-{\\beta }_{j} {l{og}_{10}R}_{{i}_{k} j}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (1),\u003c/p\u003e\u003cp\u003ewhere Subscript \u003cem\u003ej\u003c/em\u003e denotes the event number and \u003cem\u003ei\u003c/em\u003e denotes the record number from event \u003cem\u003ej\u003c/em\u003e. \u003cem\u003ek\u003c/em\u003e is the suffix of the buried or unburied stations. The events with \u0026lt;\u0026thinsp;5 buried stations are not included in this regression. A difference of alpha between the buried and unburied stations indicates the degree of deviation (Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e). Path effects seem to be dominant for the reason of deviation, since crustal earthquakes or earthquakes with a focal depth shallower than 15 km show little deviation between the buried and unburied stations.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003eDerivation of a regression equation\u003c/h2\u003e\u003cp\u003eThe derivation of the GMPE in this study followed the flow in Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. Since correct regression coefficients cannot be obtained when there is such a large deviation, the regression equation is obtained after correcting for path effects discussed above. In previous empirical equations, Xvf, Xtr, and Dpl have been used as path effect variables (Kanno et al. \u003cspan class=\"CitationRef\"\u003e2006\u003c/span\u003e; Morikawa et al. \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e; Morikawa and Fujiwara \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Matsu\u0026rsquo;ura et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). We employ Dpl because Xtr is uniquely determinable including the boundary between the Philippine Sea Plate and the Pacific Plate. In Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the residuals are generally constant when Dpl is \u0026gt;\u0026thinsp;40 km; therefore, the stations with Dpl\u0026thinsp;\u0026gt;\u0026thinsp;40 km are corrected as constant at Dpl\u0026thinsp;=\u0026thinsp;40 km. Prediction PGAs are calculated using the basic equation and coefficients of Morikawa and Fujiwara (\u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e), and the correction term of path effect (\u003cem\u003eCp\u003c/em\u003e) was obtained by the least squares method.\u003c/p\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${log}_{10} \\left({preY}_{ij}\\right) = 0.5507 {Mw}_{j} + d {R}_{ij} -{log}_{10}({R}_{ij}+ 0.006875 {10}^{0.5 {Mw}_{j}})$$\n\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$${log}_{10} \\left(\\frac{{obsY}_{ij}}{{preY}_{ij}}\\right)= Cp=pa + pb {Dpl}_{i}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eobsY\u003c/em\u003e and \u003cem\u003epreY\u003c/em\u003e are observed and predicted PGAs (in Gal, cm/s\u003csup\u003e2\u003c/sup\u003e), \u003cem\u003ed\u003c/em\u003e, \u003cem\u003epa\u003c/em\u003e and \u003cem\u003epb\u003c/em\u003e are regression coefficients. The distance coefficient (\u003cem\u003ed\u003c/em\u003e) is also optimized to match the S-net data. In this process, the average of residuals is adjusted to zero for each earthquake. The correction terms are obtained for interplate and slab earthquakes with a focal depth of \u0026gt;\u0026thinsp;15 km. In other words, no correction is made for crustal earthquakes and earthquakes with focal depths of \u0026lt;\u0026thinsp;15 km. The obtained correction terms result in a smaller discrepancy between the buried and unburied stations (Figs. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e). However, the log PGA is as high as ~\u0026thinsp;0.2 at the unburied stations.\u003c/p\u003e\n\u003cp\u003eEquation (4) is used as the basic equation as a function of the source distance and Mw, and coefficients are obtained to minimize the residuals from the observed data.\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\({log}_{10} \\left({preY1}_{ij}\\right)= a + b {Mw}_{j} + d {R}_{ij} -{log}_{10}\\left({R}_{ij}+ e {10}^{k {Mw}_{j}}\\right) + Cp+ {\\eta }_{j}+{\\xi }_{ij}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (4),\u003c/p\u003e\n\u003cp\u003ewhere \u003cem\u003ea, b, d, e, k\u003c/em\u003e are regression coefficients. The random variable \u003cem\u003e\u0026eta;\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e denotes the between-event error (representing the event-to-event component of the total variability) with a zero mean and a standard deviation of \u003cem\u003e\u0026tau;⁠\u003c/em\u003e, and the random variable \u003cem\u003e\u0026xi;\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e denotes the within-event error (representing the site-to-site component of variability) with a zero mean and a standard deviation of \u003cem\u003e\u0026phi;⁠\u003c/em\u003e. To avoid underestimating the term representing the saturation of the amplification effect (\u003cem\u003ee, k\u003c/em\u003e) due to the small number of stations close to the epicenter, the residual is weighted by the source distance.\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$weight= \\left\\{\\begin{array}{c}8.0 R \\le 30 km\\\\ 4.0 30 km \u0026lt; R \\le 60 km\\\\ 2.0 60 km \u0026lt; R \\le 90 km\\\\ 1.0 90 km \u0026lt; R\\end{array}\\right\\}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe source distances and Mw are known to be correlated (Fukushima and Tanaka \u003cspan class=\"CitationRef\"\u003e1990\u003c/span\u003e). To avoid that interdependency, a distance coefficient (\u003cem\u003ed\u003c/em\u003e) was obtained with the Mw term (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eb\u003c/em\u003e Mw) as dummy variables using a single regression. To obtain the coefficients of Eq. (4), which is nonlinear, the coefficients \u003cem\u003eb\u003c/em\u003e, \u003cem\u003ek\u003c/em\u003e, and \u003cem\u003ee\u003c/em\u003e are optimized to minimize the total standard deviation \u0026sigma; (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sqrt{{\\phi }^{2}+{\\tau }^{2}}\\)\u003c/span\u003e\u003c/span\u003e) by the differential evolution method to avoid convergence to a local solution based on the distance coefficients obtained in advance. The distance coefficient was again obtained using single regression based on the optimized coefficients \u003cem\u003eb\u003c/em\u003e, \u003cem\u003ek\u003c/em\u003e, and \u003cem\u003ee\u003c/em\u003e. These iteration calculations lasted until the rate of change in the distance coefficient converged to 0.1%.\u003c/p\u003e\n\u003cp\u003eThe coefficients of Eq. (4) obtained from the regression analysis are listed in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The total standard deviation of the regression equation with only the source distance and Mw as explanatory variables with the path effect term is 0.40. To examine additional correction terms, the residuals between the predicted and observed PGAs were illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e. The focal depths have been incorporated into most GMPEs as a factor that amplifies acceleration (Morikawa and Fujiwara \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Kanno et al. \u003cspan class=\"CitationRef\"\u003e2006\u003c/span\u003e; Hu et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) and are also considered a variable with a large influence in offshore sites (Tan and Hu \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). The Y1 residuals showed a correlation with focal depths was also confirmed (Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003ea). Therefore, the coefficients of the correction term (\u003cem\u003eCh\u003c/em\u003e) were obtained from a single regression by a generalized linear mixed model that accounts for intra-event errors (Gilmour et al. \u003cspan class=\"CitationRef\"\u003e1985\u003c/span\u003e).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\({log}_{10} \\left(\\frac{{obsY}_{ij}}{{preY1}_{ij}}\\right)= Ch = c {H}_{j}+ha\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (5),\u003c/p\u003e\n\u003cp\u003ewhere H is focal depth (km), \u003cem\u003ec\u003c/em\u003e and \u003cem\u003eha\u003c/em\u003e are regression coefficients. Combining Equations 4 and 5,\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\({log}_{10}\\left({preY2}_{ij}\\right)= b {Mw}_{j} + d {R}_{ij} -{log}_{10}\\left({R}_{ij}+ e {10}^{k {Mw}_{j}}\\right)+Cp+Ch+ {\\eta }_{j}+{\\xi }_{ij}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (6),\u003c/p\u003e\n\u003cp\u003eand the residuals obtained by Eq. 6 no longer show a significant trend with the focal depths (Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003eb); the total standard deviation was 0.36. The residuals for each earthquake type show a normal distribution with a peak at 0 when the focal depth term is taken into account, suggesting that the amplification of PGAs by earthquake types is mainly due to the focal depth. However, since other factors such as the propagation path of seismic waves depending on the earthquake types are also possible (left side of Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003eb), a correction term (\u003cem\u003eCt\u003c/em\u003e) was obtained by regressing the distance coefficient with the earthquake types as a dummy variable.\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\({log}_{10} \\left(\\frac{{obsY}_{ij}}{{preY2}_{ij}}\\right)= Ct = t {{log}_{10}R}_{ij}+ta\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (7),\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003et\u003c/em\u003e and \u003cem\u003eta\u003c/em\u003e are regression coefficients. As a result, the following equation is obtained.\u003c/p\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$${log}_{10}\\left({preY3}_{ij}\\right)= b {Mw}_{j} + d {R}_{ij} -{log}_{10}\\left({R}_{ij}+ e {10}^{k {Mw}_{j}}\\right)+Cp+Ch+Ct+ {\\eta }_{j}+{\\xi }_{ij}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe residuals obtained from this equation show a uniform variation regardless of the change in each variable (Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003ec), and its total standard deviation was 0.32. Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e) is hereafter referred to as the NT24 model.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003eComparing with conventional models\u003c/h2\u003e\n \u003cp\u003eMorikawa and Fukushima (2013), widely used as the onshore GMPE, and Hu et al. (\u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) and Hu et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e), which are derived from the offshore stations, are compared with the NT24 model (Refer to \u003cspan class=\"InternalRef\"\u003eAppendix\u003c/span\u003e for these GMPE equations). Hu et al. (\u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) proposed an integrated empirical equation (H20 model) using six temporary ocean-bottom seismometers (OBSs) and nearby onshore K-NET stations around Sagami Bay. Hu et al. (\u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) showed the difference in HVSR on each OBS and obtained regression coefficients for each station as the site conditions. Since the data for site term \u003cem\u003eSk\u003c/em\u003e in the H20 model are site-specific due to little information such as V\u003csub\u003eS\u003c/sub\u003e30, we apply 2.7 as the average \u003cem\u003eSk\u003c/em\u003e for Sagami Bay to the S-net stations. The HZ23 model (Hu et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) is the onshore GPME of Zhao et al. (\u003cspan class=\"CitationRef\"\u003e2006\u003c/span\u003e) applied to the S-net data with correction terms to reduce the residuals as a referenced empirical approach (Atkinson \u003cspan class=\"CitationRef\"\u003e2008\u003c/span\u003e). The model includes site effect terms (\u003cem\u003eCk\u003c/em\u003e), and we used the same site classes estimated from the HVSR by Hu et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). Data from six events not used in the regression are used to validate each model (Table \u003cspan class=\"InternalRef\"\u003eA1\u003c/span\u003e). Due to the limited number of data to calculate errors between events, we used the standard deviation between sites (\u003cem\u003e\u0026phi;\u003c/em\u003e) as the reproducibility between models (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eTable 2. Data used by offshore and onshore ground motion prediction equations and standard deviations obtained by these models using the PGA data in this study.\u003c/p\u003e\n \u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1716197875.png\"\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n \u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n \u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n \u003cdiv\u003e\u0026nbsp;\u003c/div\u003e\n \u003cp\u003eThe NT24 model reproduces the observations well for data not used in the regression and shows smaller standard deviations than the other models for the S-net data despite the small number of coefficients (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e. To investigate which variables might be responsible for this difference, the residuals of the predicted and observed all PGA data are shown (Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e). In the MF13 model, the predicted PGAs are underestimated as source distance increases, suggesting that the path effects in the offshore sites are larger and distance coefficients are smaller than the onshore sites. The results of the H20 model tended to overestimate overall. The amplification around Sagami Bay tends to be small compared to S-net stations, which may have caused the H20 model to overpredict northeastern Japan. The residuals can be improved by changing the site term \u003cem\u003eSk\u003c/em\u003e (2.1) treated as the constant term. The HZ23 model has biased residuals corresponding to focal depth, particularly for the slab and crustal types. The negative correlation between Mw and the residuals may be due to most of the data being from Mw 4\u0026ndash;5 earthquakes. This result means that different regression equations can be obtained depending on the range of Mw, and the distance attenuation effect of Mw may be nonlinear.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003eResidual analysis for site effects\u003c/h2\u003e\n \u003cp\u003eDhakal et al. (\u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) and Tan and Hu (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) performed residual analysis on the onshore GMPEs to the S-net records and showed the relationship between site amplification and water column, Xvf, and D14. The sediment layers are known to amplify PGAs (Dobry et al. \u003cspan class=\"CitationRef\"\u003e2000\u003c/span\u003e; Morikawa and Fujiwara \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). The site amplification effects in the onshore stations are demonstrated by D14 and Vs30 as deep sediment layer and shallow soft sediment, respectively (e.g., Morikawa and Fujiwara \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e). In the offshore region around Japan, D14 has been published (NIED 2019). Nishizawa et al. (\u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e) estimated the sediment thickness from seismic reflection surveys. We also examined the effects of the placement conditions of the observation stations in addition to the above factors because of the possible influence of cable azimuths or seafloor slopes. The azimuths of observation devices were referred to as the value by Takagi et al. (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The seafloor slope angles of the placement sites were calculated from the bathymetry map (J-EGG500: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://jdoss1.jodc.go.jp/vpage/depth500_file.html\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eThe geometric means of the residuals per station for the NT24 model are not constant (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003ea) and are expected to have site-specific amplification rates. The residuals show a slight correlation with D14 and the sediment thickness based on seismic reflection surveys (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003eb). The MF13 and HZ23 models using the variable D14 values or the site classes were tested to check if the residuals decreased in the offshore region when these were held constant or when they are variables. For the variable site classes (\u003cem\u003eCk\u003c/em\u003e) in the HZ23 model and the D14 correction term in the MF13 model, the smaller standard deviation than the results with the averaged constant \u003cem\u003eCk\u003c/em\u003e or D14 terms (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). The NT24 model is also regressed using D14, which is more encompassing throughout Japan than the sediment thickness (Nishizawa et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e), and additional correction term \u003cem\u003eCv\u003c/em\u003e is obtained.\u003c/p\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\({log}_{10} \\left(\\frac{{obsY}_{ij}}{{preY3}_{ij}}\\right)= Cv = v {{log}_{10}D14}_{i}+va\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e (9),\u003c/p\u003e\u003cp\u003ewhere \u003cem\u003ev\u003c/em\u003e and \u003cem\u003eva\u003c/em\u003e are regression coefficients (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The availability is examined by the Akaike information criterion (AIC: Akaike \u003cspan class=\"CitationRef\"\u003e1973\u003c/span\u003e). The AIC is a statistic that expresses the goodness of fit of a model; the smaller the value, the better the fit, but it is used as a relative evaluation. There was a significant improvement from the basic equation to the focal type correction term, from 3678 to 980 (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). When the D14 correction term was applied, the AIC was 921, and little changed from the model with the focal type correction term. The correction by these sediment thickness proxies as a site effect slightly improves offshore GMPEs, and the sediment thickness from seismic reflection surveys may be useful because it highly correlates with the residual (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003eb). The small effect of the correction by the sediment thickness may be due to the path effect has already been corrected, since the residual analysis by the onshore GMPE also shows a stronger correlation with Dpl and Xtr than with the thickness of the deposition layer (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo investigate a regional bias of the residuals on each station, the geographic distribution of the geometric mean residuals is shown in Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e, along with the seafloor geology (Inoue and Honza \u003cspan class=\"CitationRef\"\u003e1983\u003c/span\u003e). Dhakal et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e) obtained the site amplification factor for the S-net stations from the spectral inversion technique. The amplification factors at 5 Hz are consistent with the sites where the positive residuals are large in this study (Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e). On the other hand, the predicted values off Chiba exceed the observed values, indicating that the site amplifications are small. These sites are generally in the area where the semi-consolidated to consolidated pre-Quaternary sediments are exposed (Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e: Inoue and Honza \u003cspan class=\"CitationRef\"\u003e1983\u003c/span\u003e). The negative residuals were also observed at sites outside the trench where submarine volcanoes are distributed. Since these areas are supposed to have thick sediment layers from seismic reflection surveys (1\u0026ndash;2 km from D14), the underestimated areas may be attenuated by the lack of very shallow unconsolidated sediment layers.\u003c/p\u003e\u003cp\u003eNo clear relationship was found between water depth or seafloor slope degrees and residuals in the observations (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003eb). This is consistent with previous studies that showed little effect of the water column on the horizontal amplitude (Tan and Hu \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). Simulations of high-frequency seismic waves also demonstrated that seawater has little influence on the high-frequency maximum S-wave amplitude (Takemura et al. \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). There appears to be an offset between the buried and unburied stations based on the residual around 1500 m water depth (Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003eb). All buried stations show negative residuals (Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e), which means that the predicted values are intermediate between buried and unburied stations. The positive and negative residuals are always reversed at the unburied station and the adjacent buried station, suggesting a difference in PGAs due to burial rather than water depth or site conditions. The buried stations would provide high-quality data because of their small errors (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003eb: Sawazaki and Nakamura \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Dhakal et al. \u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). The unburied stations likely show actual large PGAs where the seafloor surface because the effects of rolling and tilting are eliminated. In addition to poor coupling due to exposure to the seafloor, it is also necessary to consider effects by not only strong motion but also slope failures or turbidity currents associated with earthquake events. Although the difference between both residuals is ~\u0026thinsp;1\u0026ndash;4 gal (Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e), it is reasonable to take this offset into account when assessing safety.\u003c/p\u003e\u003cp\u003eAdditionally, the residuals seem to be biased positively and negatively depending on a cable azimuth (Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003ea). When the stations are compared in the order in which they are connected, there is a continuity in the residuals, which may be related to the cable azimuth as pointed out by Dhakal et al. (\u003cspan class=\"CitationRef\"\u003e2023\u003c/span\u003e). If there is an amplification factor due to cable azimuths, it is expected to be relative to the epicenter location; thus, these interrelationships would need to be individually examined for each event.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003eLimitation\u003c/h2\u003e\u003cp\u003eThe NT24 model should be used for earthquakes with Mw\u0026thinsp;\u0026gt;\u0026thinsp;5.4 (crustal event is Mw\u0026thinsp;\u0026gt;\u0026thinsp;5.0) because it shows a different trend from other models including Mw 4.0\u0026ndash;5.4. The majority of earthquakes with Mw\u0026thinsp;\u0026gt;\u0026thinsp;5.4 were interplate type events (thrust faulting), and the applicability of the other focal types needs to be evaluated additionally because there was no significant difference in the coefficients of the earthquake type terms (Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The adoption of a correction term for the focal depths resulted in a normal distribution centered at 0. Given the paucity of data for Mw\u0026thinsp;\u0026gt;\u0026thinsp;6.3, additional evaluation through data accumulation will be important to confirm these results. In areas where the basement is exposed, residuals of ~\u0026thinsp;2.0 cm/s\u003csup\u003e2\u003c/sup\u003e are observed; therefore, the seafloor geology needs to be confirmed, and an attenuated PGA should be assumed in these sites. If a hypocenter and observation points are across other plates, the application of the distance attenuation equation requires caution. The observed wedge-shaped trapping above the subducting plate makes the application of a distance attenuation formula within the same plate challenging. In Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e, the overestimation at the stations in the Philippine Sea Plate indicates attenuation jumps during interplate transmission.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e\u003cbr\u003e\u003c/h2\u003e\u003c/div\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"Applicability and Summary","content":"\u003cp\u003eIn this study, the residual analysis based on the existing GMPE revealed that the path effects are more strongly affected than the onshore sites. Therefore, the NT24 model corrected for path effects based on the conventional GMPE, and the deviations between the buried and unburied stations were reduced by accounting for the depth to the plate boundary. The NT24 model, which takes into account the focal depth and type, can reproduce the observed PGAs with smaller residuals than previous offshore and onshore GMPEs. The unique points from previous GMPEs are that the NT24 model can account for the small distance attenuation rate of the offshore sites and the large PGA along the trench axis without distance attenuation in concentric circles that appear due to the trapping of seismic energies in an overriding plate wedge (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Residual analysis for site effects in the offshore sites, especially sediment thickness, show that the correction using site effect terms slightly improved prediction accuracy. These features of the offshore region mean that large PGAs can appear even in areas far from the epicenter, which is important for slope stability analysis and seismic structures.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eAIC: Akaike information criterion; F-net: Full-range seismograph network; GMPE: Ground Motion Prediction Equations; HVSR: Horizontal-to-Vertical Spectral Ratio; NIED: National Research Institute for Earth Science and Disaster Resilience; S-net: Seafoor observation network for earthquakes and tsunamis along the Japan Trench; OBS: Ocean-Bottom Seismometers; PGA: Peak Ground Acceleration.\u003c/p\u003e\n"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe are thankful to Hajime Naruse (Kyoto University) for a useful discussion of regression analysis. We would like to thank the JMA for providing us with hypocenter information.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eR.N. processed the ground motion recordings, performed the regression analysis, and drafted the manuscript. S.T. conceptualized the study, and reviewed and edited the manuscript. All authors approved the final version of this manuscript.\u0026nbsp;\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by JSPS as a Grant-in-Aid for JSPS Fellows (KAKENHI Grant Number JP23KJ1152).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe bathymetry data was downloaded from the Japan Oceanographic Data Center (Japan Coast Guard): https://jdoss1.jodc.go.jp/vpage/mgd77.html.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe peak ground acceleration recordings at the S-net sites were retrieved from NIED S-net, National Research Institute for Earth Science and Disaster Resilience, https://doi.org/10.17598/nied.0007. https://hinetwww11.bosai.go.jp/auth/download/cont/?LANG=en. The Japan Seismic Hazard Information Station deep subsurface model was downloaded from the website: http://www.j-shis.bosai.go.jp/map/JSHIS2/download.html?lang=en. The moment magnitudes, focal depths, and coordinates of epicenter were taken from the website: http://www.fnet.bosai.go.jp/event/joho.php?LANG=en. All the websites were accessed on October 13, 2023.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAkaike H (1973) Information theory and an extension of the maximum likelihood principle. In BN Petrov, BF Csaki (Eds.), Second International Symposium on Information Theory, (pp. 267-281). Academiai Kiado: Budapest.\u003c/li\u003e\n\u003cli\u003eAllen RM, Melgar D (2019) Earthquake Early Warning: Advances, Scientific Challenges, and Societal Needs. 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Bull Seismol Soc Am 96: 879\u0026ndash;897. https://doi.org/10.1785/0120050138\u003c/li\u003e\n\u003cli\u003eLehu R, Lallemand S, Ratzov G, Babonneau N, Hsu SK, Lin AT, Dezileau L (2016) An attempt to reconstruct 2700 years of seismicity using deep-sea turbidites offshore eastern Taiwan. Tectonophysics 692: 309\u0026ndash;324. https://doi.org/10.1016/j.tecto.2016.04.030\u003c/li\u003e\n\u003cli\u003eMatsu\u0026rsquo;ura RS, Tanaka H, Furumura M, Takahama T, Noda A (2020) A New Ground‐Motion Prediction Equation of Japanese Instrumental Seismic Intensities Reflecting Source Type Characteristics in Japan. Bulletin of the Seismological Society of America 110:2661\u0026ndash;2692. https://doi.org/10.1785/0120180337\u003c/li\u003e\n\u003cli\u003eMochizuki M, Kanazawa T, Uehira K, Shimbo T, Shiomi K, Kunugi T, Aoi S, Matsumoto T, Sekiguchi S, Yamamoto N, Takahashi N, Shinohara M, Yamada T (2016) S-net project: Construction of large scale seafloor observatory network for tsunamis and earthquakes in Japan, AGU Fall Meeting, NH43B-1840.\u003c/li\u003e\n\u003cli\u003eMorikawa N, Kanno T, Narita A, Fujiwara H, Fukushima Y (2003) Additional Correction Terms for Attenuation Relations Corresponding to the Anomalous Seismic Intensity in Northeast Japan. Journal of Japan Association for Earthquake Engineering 3; 14\u0026ndash;\u0026shy;26.\u003c/li\u003e\n\u003cli\u003eMorikawa N, Fujiwara H (2013) A New Ground Motion Prediction Equation for Japan Applicable up to M9 Mega-Earthquake. 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Technical Note of the National Research Institute for Earth Science and Disaster Resilience, No. 471 (in Japanese with English abstract)\u003c/li\u003e\n\u003cli\u003ePope EL, Talling PJ, Carter L (2017) Which earthquakes trigger damaging submarine mass movements: Insights from a global record of submarine cable breaks? Mar Geol 384: 131\u0026ndash;146. https://doi.org/10.1016/j.margeo.2016.01.009\u003c/li\u003e\n\u003cli\u003ePouderoux H, Proust JN, Lamarche G (2014) Submarine paleoseismology of the northern Hikurangi subduction margin of New Zealand as deduced from Turbidite record since 16 ka. Quat Sci Rev 84: 116\u0026ndash;131. https://doi.org/10.1016/j.quascirev.2013.11.015\u003c/li\u003e\n\u003cli\u003eSawazaki K, Nakamura T (2020) \u0026ldquo;N\u0026rdquo;-shaped Y/X coda spectral ratio observed for in-line-type OBS networks; S-net and ETMC: interpretation based on natural vibration of pressure vessel. 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Kyoritsu Shuppan Co Ltd, Tokyo (in Japanese).\u003c/li\u003e\n\u003cli\u003eYabe S, Baba S, Tonegawa T, Nakano M, Takemura S (2021) Seismic energy radiation and along-strike heterogeneities of shallow tectonic tremors at the Nankai Trough and Japan Trench. Tectonophysics 800: 228714. https://doi.org/10.1016/j.tecto.2020.228714\u003c/li\u003e\n\u003cli\u003eZhao J X, Zhang J, Asano A, Ohno Y, Oouchi T, Takahashi T, et al. (2006) Attenuation Relations of Strong Ground Motion in Japan Using Site Classification Based on Predominant Period. Bull Seismol Soc Am 96: 898\u0026ndash;913. https://doi.org/10.1785/0120050122\u003c/li\u003e\n\u003cli\u003eZhi W, Zhao D (2005) Seismic imaging of the entire arc of Tohoku and Hokkaido in Japan using P-wave, S-wave and sP depth-phase data. Physics of the Earth and Planetary Interiors 152:144\u0026ndash;162. https://doi.org/10.1016/j.pepi.2005.06.010\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"Ground motion prediction equation, S-net, Peak ground acceleration, Path effect, Japan Trench","lastPublishedDoi":"10.21203/rs.3.rs-4348314/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4348314/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGround motion prediction equations (GMPEs) in offshore regions are important for not only earthquake early warning but also evaluating the durability of subsea structures and tsunami risk associated with seafloor slope failures. Since the ground conditions and propagation path effects differ between onshore and offshore areas, it is desirable to develop a GMPE specific to the seafloor. Previous models have some problems, such as the influence of buried observation equipment and path effects. In this study, to predict the distribution of seafloor seismic acceleration, a new GMPE was regressed on the peak ground acceleration (PGA) data of S-net using minimum necessary seismic parameters as explanatory variables. The path effects through the offshore area were emphasized from the residual analysis by the conventional GMPE and were corrected by the depth up to the plate boundary. The new model successfully predicted PGA with smaller errors compared to conventional onshore and offshore GMPEs. The residuals between the observed and predicted PGAs were used to examine the factors responsible for the effects of the S-net site conditions. The new GMPE can obtain PGAs within 300 km of the epicenter from the moment magnitude (Mw 5.4\u0026ndash;7.4), focal depth, focal type, and source distance. In this model, the distance attenuation is smaller than in conventional models, and consequently, the PGAs along the trench axis amplified due to path effects are reproduced. This means that the PGA is unexpectedly large even at the point far from the hypocenter when considering slope failure and earthquake resistance assessments.\u003c/p\u003e","manuscriptTitle":"Development of an offshore ground motion prediction equation considering path effects based on S-net data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-20 13:22:54","doi":"10.21203/rs.3.rs-4348314/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revision","date":"2024-07-02T03:18:08+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-05-10T06:50:27+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-05-10T00:26:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-07T11:09:10+00:00","index":"","fulltext":""},{"type":"submitted","content":"Earth, Planets and Space","date":"2024-04-30T06:27:32+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":"f8c70612-1155-4a57-81b3-4a39dec3ce58","owner":[],"postedDate":"May 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-11-25T16:04:26+00:00","versionOfRecord":{"articleIdentity":"rs-4348314","link":"https://doi.org/10.1186/s40623-024-02078-5","journal":{"identity":"earth-planets-and-space","isVorOnly":false,"title":"Earth, Planets and Space"},"publishedOn":"2024-11-20 15:57:59","publishedOnDateReadable":"November 20th, 2024"},"versionCreatedAt":"2024-05-20 13:22:54","video":"","vorDoi":"10.1186/s40623-024-02078-5","vorDoiUrl":"https://doi.org/10.1186/s40623-024-02078-5","workflowStages":[]},"version":"v1","identity":"rs-4348314","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4348314","identity":"rs-4348314","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}