dataesr/scientific-paragraphs-categorization huggingface dataset:
Regional variability of anelastic attenuation may in fact be a combination of regional variability of crustal shear-wave velocity, crustal thermal gradient influencing the rigidity modulus of the crust, Moho depth, and other parameters that, at the time of this study, were not uniformly mappable across the pan-European region. Activity Index (AIx) is a unique composite parameter that we preferred in this study. Activity Index is a data-driven continuous parameter inferred from a fuzzy combination of shear-wave velocity, seismic moment rate density, and crustal quality factors across the globe. A 0. 5 0 gridded map of AIx was generated by Chen et al. (  2018 ) for the sole purpose of regionalising GMMs or selecting suitable GMMs for a region with no region-specific ground-motion data. In this study, we extracted the AIx for every site location in the ESM dataset.
7), and to that of shear-wave velocity and 1Hz code Q in relatively stable regions ( < 0. 7). ESM dataset contains sites located in regions with 0. 4 ≤  as seen in Fig. 9. The smooth transition of δc 3,r between stable cratonic (0. 4 ≤  < 0. 7) to the more seismically active regions (0. 7 ≤  ≤  1 ) is an indication that it is a physically meaningful random-effect. However, these regionalisation models are different in nature: Activity Index is fully data-driven and gridded, while the regionalisation used in this GMM regression is based on expert elicitation and polygonised. In that sense, although there is a decent agreement, neither of the models may sufficiently replace the other.
EVENT LOCALITY VARIABILITY Source variability is divided into two components in this GMM-FA: variability across tectonic localities producing the earthquakes 2 ≈ Ɲ(0,  2 ) , and the locality corrected between-event variability  , 0 ≈ Ɲ(0,  0 ). Since events are exclusively nested in their respective tectonic localities, 2  quantifies the average of the nested events' ground-motion characteristics as  , 0 ≈   -2  ; with notations from Al  Atik et al. (2010). Fig. 6  illustrates the frequency dependence of  2 and  0. It appears that the two random-variances capture disjoint frequency dependent earthquake characteristics; where  0 >  2 at low-moderate frequencies, and vice versa at high frequencies. Fig. 11  shows the 2  ( = 0. 15 -20) of the 55 tectonic localities in ESM dataset. Resembling Fig.
6 , the scatter of 2  significantly increases at  ≥ 5 in Fig. 11. The epistemic uncertainty of 2  , i. e. the standard-error (2  ), are generally smaller than  2. In this regard, dropping  2 from the aleatoric variability () and using instead the 2  ± (2  ) adjustments to regionalise the GMM predictions is recommended. A database of 2  , (2  ), and their rlmm weights indicating outliers can be provided on request for analyses and applications. For instance, Fig. 11  suggests that the number of detected outliers increases towards higher frequencies, along with  2. A few of these outliers are also well-sampled localities with a low (2  ); implying a more source specific study could be worthwhile. It is important to note that the color scale ranges in Fig. 12  are not frequency dependent. Despite, an interesting feature in Fig.
12  Tectonic localities and the 2  for these locality polygons. Rred colored localities produced events capable of higher ( = 0. 3,1,3,10) than the GMM median predictions, blue colored localities produced earthquakes weaker than dataset average, and grey colored localities are close to the dataset average. Localities with fewer ground-motion observations, thereby larger epistemic error on 2  , are more transparent and appear fainter. Note that the color scale is the same in all the maps in order to emphasize the frequency dependence of spatial variability of event characteristics of several 0. 5 0 grid cells with similar AIx values are unlikely to resolve event-specific differences. On the other hand, the size of tectonic localities is comparable to the size of regions with distinguishable AIx values (Fig.
g. Bommer et al. (2015). In this case, stable continental regions are those with lower AIx and appear to coincide with tectonic localities with higher 2  values in Fig. 13. Alternatively, the large  2 value at high frequencies could be from regional variability of a high frequency source parameter, e. g. the   ; which is the high frequency decay parameter of Brune's  2 source model  (Bindi et al. 2019b ). Bindi and Kotha (2020) estimated the   of several events in the ESM dataset, but the large variability of, and uncertainty in, deter us from associating these estimates with the already uncertain Through an exploratory analysis, we deduced a third hypothesis by comparing the three bestsampled localities in: central Appenines of Italy ("PTTC007" -2  ( = 10ℎ) = -0. 6), north-west segment ("SETC003" -2  ( = 10ℎ) = 0.
Chounet et al. (  2018 ) followed up with a global database showing an anticorrelation between stress-drop and rupture speed. An earlier study by  Radiguet et al. (2009)  connected the lower near-field ground-motions (e. g. peak ground acceleration) to structural maturity of fault systems. Based on these studies, we infere that the structurally immature fault segments produced earthquakes capable of stronger high frequency groundmotions. In this study, we concur with the hypothesis that the younger, westward growing north-west Anatolian fault system produced stronger earthquakes than the older, north-east Anatolian and central Appenine fault systems. In summary, 2  is introduced to capture partially, in a predictable way, the spatial variability of event dependent ground-motion variability.
Magnitude-dependent heteroskedasticity of   makes physical sense because larger ruptures tend to occur more-or-less on the same area of the fault plane, and periodically release a similar amount of accumulated elastic energy or stress. However, if the large events of similar magnitude originate in fault systems (or tectonic localities) with very different stress accumulation and release rates, the variability of stress-drop (and the δ  ) could be as large as that of smaller events. This means that, heteroskedasticity of   in a global dataset consisting of events from Italy, Turkey, Japan, China, etc. , (e. g. NGA-West2) may not be as significant as that of events within a tectonic locality within any of these geopolitical boundaries. In our case, we remove the locality-to-locality variability of event characteristics through the random-effect 2  = Ɲ(0,  2 ), leaving us a large sample of  , 0 = Ɲ(0,  0 ) that can be examined for a generic heteroskedasticity with   , independent of events' localities.
SITE-RESPONSE VARIABILITY The next, and by far the largest, random variability is the site-response component 2  = Ɲ(0,  2 ). Fig. 6  shows that  2 is consistently the largest random-variance at all frequencies, when measured as site-to-site ground-motion variability across the 1622 sites in ESM dataset. Site-specific ground-motion predictions are more accurate and precise (smaller aleatory variability) than ergodic or region-specific predictions, but are only possible when site-specific ground-motion data are available. In absence of site-specific observations, site-response proxies are necessary to extrapolate spatially the site-specific terms 2   (Kotha et al. 2018; Weatherill et al. 2020b ). For such studies, we disseminate a database of 2  ( = 0. 15 -20) derived from the ESM dataset. suggests that class C and D sites exhibit high frequency amplifications lower than that a linear  30 scaling function would predict.
Although this is likely from nonlinear behavior of soft soils when subjected to strong input ground-motion, a further record-to-record investigation is necessary. Alternatively the left-over residuals at these sites can be examined for nonlinear soil response, as in  Loviknes et al. (2021). For now, we only provide the site-response (  30 ,   ) as quadratic functions of  30 and slope, along with a database of site-response terms, as in equations (  6 ) and (  7 ). Here, the measured  30 Slope is a poorer explanatory parameter of site-response than measured  30 , but is relatively easier to obtain at any site location. The left panel of Fig. 16  shows the reduction in  2 from using when using  30 , and to ( 2  ,   ) when using  as site-response proxies  30 and slope as site-response proxies in the GMM-FA.
2019) , SmS reflections at intermediate-and farsource distances  (Bindi and Kotha 2020; Bindi et al. 2006) , nonlinear soil response  (Loviknes et al. 2021) , etc. However, each of these phenomena require information that are not currently available in the ESM dataset (e. g. centroid-moment-tensor solutions and crustal shear-wave velocity profiles). For sake of brevity of the manuscript, we anticipate in-depth residual analyses to follow-up studies.
The direction (  2 ) is already on course using the recently published groundmotion dataset for France  (Traversa et al. 2020 ) and a weak motion dataset for central and north Europe  (Zaccarelli et al. 2019). We strongly encourage the various ground-motion seismology communities to collaborate in testing our inferences and in adapting our model to their datasets; especially those not integrated into ESM. Despite our efforts however, the very high site-response variability at high frequencies remains a glaring challenge. Site-specific ground-motion prediction using the site-specific random-effects seems to be the most reasonable approach yetif we were to avoid the very large ergodic aleatory variability in seismic hazard and risk assessments. It is however quite encouraging to see several research groups attempting to investigate and parametrize site-specific characteristics (e.
g. anisotropic) predictions. Of course, to quantify these effects would require much more information (e. g. centroid moment tensor solutions and incidence angles) in ground-motion datasets. Currently, we are attempting to populate the ESM dataset with as much of relevant information as possible, in order to faciliate further realism of ground-motion models. Based on the experience from and utility of this Fourier amplitude groundmotion model, we plan to pursue such improvements preferably in Fourier domain rather than in response spectra domain.
DATA AND RESOURCES The European Strong Motion flatfile is available at https://esm. mi. ingv. it//flatfile-2018/ with persistent identifier PID: 11099/ESM_flatfile_2018. The analyses in this study have been performed in R software  (Team 2013). In particular, we used the libraries rlmm  (Koller 2016) , dplyr  (Wickham et al. 2019b) Figure 3 Distribution of records from shallow crustal events in each of the 55 event localisation polygons (tectonic zones) Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.
Please see the Manuscript PDF le for the complete gure caption. and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. Tectonic localities and the 2 for these locality polygons. Rred colored localities produced events capable of higher (= 0. 3,1,3,10) than the GMM median predictions, blue colored localities produced earthquakes weaker than dataset average, and grey colored localities are close to the dataset average. Localities with fewer ground-motion observations, thereby larger epistemic error on 2, are more transparent and appear fainter.
g. ,  Horvath et al. 2018; Kusche et al. 2009) , they ensure replicable results from one study to another, as long as the same versions of the same products are used. In this study, we used the CSR and JPL Level 3 Release 6 mascon solutions, consisting of monthly mass grids spanning from April 2002 to July 2020 at the time of the download (September 2020). All mass changes are assumed to occur within a thin layer at the Earth's ellipsoid surface (WGS84) and are expressed in equivalent water heights. The JPL and the CSR provide global mascon solutions, using 3° spherical caps  (Watkins et al. 2015)  and 1° equal area elements  (Save et al. 2016). Because the CSR and JPL solutions are developed, processed and archived in a shared Science Data System (SDS), they harmonize several necessary processing steps.
The PDO consists in a decadal SST oscillation, characterized by a basin-wide dipole dividing the North Pacific along a typical northeast-southwest chevron pattern  (Mantua et al. 1997). It is defined as the leading EOF of SST anomalies north of 20° N in the Pacific region  (Newman et al. 2016 ) and estimated with the ERSSTV5 dataset  (Huang et al. 2017 ). The PDO is closely related to the ENSO and is sometimes referred to as a "long-lived ENSO", to characterize the longer periods of the climate index. The NPGO expresses as a double gyre in the North Pacific  (Di Lorenzo et al. 2008). It is defined as the second mode of sea surface height variability in the Northeast Pacific (180° W-110° W; 25° N-62° N). Connected with ENSO and PDO, it contributes to global climate variability, which is evidenced by global sea level trends and sea surface temperature  (Di Lorenzo et al.
2010). The AMO consists in a multidecadal SST oscillation across the whole Atlantic basin, with cool and warm phases that may last for 20-40 years  (Enfield et al. 2001). We use the unsmoothed index, provided by the NOAA/OAR/ESRL PSL, Boulder, Colorado, USA, from their Web site at https:// psl. noaa. gov and calculated from 1948 to present as the area weighted average of the Kaplan SST V2 dataset  (Kaplan et al. 1998 ) over the North Atlantic (0-70° N). The NAO index reflects the difference in surface sea level pressure between the Subtropical Azores High and the Subpolar Low  (Lamb and Peppler 1987). The NAO impacts the intensity and location of the North Atlantic jet streams and storm tracks  (Woollings and Blackburn 2012). It modulates heat and moisture transport, resulting in temperature and precipitation changes that can extend from North America to central Europe  (Hurrell et al.
1 SST dataset with the 1981-2000 climatology removed. To be consistent with the processing of satellite gravity solutions, all climate indices have been detrended and deseasoned. Decadal trends and seasonal signals have been removed using the outputs of an ordinary least squares regression of a linear trend, annual sinusoid, semi-annual sinusoid and a constant carried out for the GRACE/GRACE-FO time period  (April 2002 -September 2020). Besides, to facilitate the comparison of climate modes, all indices have been normalized, so that their time average equals zero and their standard deviation equals one. The MEI, PDO, AMO and DMI (IOD index) are distributed by the NOAA (National Oceanic and Atmospheric Administration) PSL (Physical Science Laboratory) climate data repository (https:// psl. noaa.
The degree of shrinkage of the coefficients β i depends on the value of the penalty λ (Fig. 2b ). If λ = 0, the regression becomes an ordinary least squares regression. On the other hand, if λ is too high, all explanatory variables will be eliminated from the regression model, as all β i coefficients will be set to zero (Fig. 2b ). The penalty λ is therefore calculated to minimize the standard error of a fivefold cross validation (called CV below, see Fig. 2c. ) (e. g. , Arlot and Celisse 2010), i. e. , each time series is randomly divided in five parts, successively used as testing (one part) and training (four parts) datasets. Detailed information about the search of optimal LASSO penalty through cross-validation procedures can be found in the Sects. 3 and 7 of  Hastie et al. (2009). The minimization of the standard error of a K-fold cross-validation has been shown to work well in the presence of correlated variables  (Hebiri and Lederer 2013).
OR9 ). The standard error, defined as the average CV error plus one standard deviation (see for example Fig. 2. 3 in  Hastie et al. 2019) , takes into account the dispersion due to the random division of the dataset during the CV procedure. The penalty minimizing the standard error is therefore higher, and is able to select the relevant predictors of the regression model (MEI, NAO and IOD) and set all other parameters to exactly zero. The final OLS regression carried out on the selected predictors succeeds in recovering the full amplitude of ENSO, NAO and IOD signals (Table  1 ).
This gives us a dataset of 36 global earthquakes (6:0 ≤ M ≤ 7:3) between 2014 and 2020. We find that the resulting FinDer line-source models are generally consistent with the spatially dependent intensity patterns described by the felt reports, and in many earthquakes achieve a good agreement with the finite-source models published in the literature: for 50% of events the difference in strike is less than 30°, and for 75% less than 55°. FinDer line-source models could be calculated automatically for global earthquakes (M ≥ 6) within 10-30 min after their occurrence, provided a sufficient number of felt reports were available. However, our proposed method not only provides faster results, but also helps to fill a general information gap for many earthquakes around the world, for which rupture geometry information is currently unavailable.
Felt Reports The EMSC has been collecting citizen intensity felt reports at global scale for many years. The felt reports used in this study are collected through a set of 12 cartoons representing the different levels of the European Macroseismic Scale  (Grünthal, 1998)  via its websites and its LastQuake smartphone application  (Bossu, Roussel, et al. , 2018). User reported intensities are considered only for intensity values of up to 10, because higher values are unrealistic. They were shown to be well correlated with the USGS "Did You Feel It?" (DYFI, e. g. ,  Wald et al. , 2011)  responses and with manually derived macroseismic datasets  (Bossu et al. , 2017). Additional work is being carried out to systematize their inclusion in ShakeMap  (Quitoriano and Wald, 2020). LastQuake app is an efficient tool to rapidly crowd-source felt reports with, on average, half of them being collected within around 10 min of the earthquake  (Bossu et al.
Data and Processing In this feasibility study, we use earthquake catalog information and intensity felt reports collected by the EMSC for a set of global earthquakes that occurred between August 2014 and March 2020. The catalog parameters we are using here include the earthquake location, (moment) magnitude, and origin time (see Data and Resources). The felt reports dataset includes the reported intensities I felt , the location of observation, and the report time. Because the current FinDer code is optimized for shallow crustal earthquakes  (Böse et al. , 2018) , we restrain this feasibility study to events with source depths of less than 50 km. We select only events with (moment) magnitudes larger than M 6. 0 to ensure a significant rupture length (>10 km). Our goal in this study is to compute FinDer line-source models whose strike is a measure of the strike of the earthquake fault rupture.
We then run FinDer on each of the 5000 datasets and plot the resulting errors as a function of azimuthal gap (Fig. S1 , available in the supplemental material to this article). We bin the error data in overlapping intervals of 10°for the azimuthal gap and in three magnitude ranges: 6:0 < M ≤ 6:5, 6:5 < M ≤ 7:0, and 7:0 < M ≤ 7:5. Finally, we compute the 75th percentile of each distribution and run a linear regression through these data. The resulting relations are shown in Figure  S1  and Table  S2. For the 100 km distance range, we obtain the following relations for the strike error as a function of azimuthal gap: EΘ 0:17 × azimuthal gap 28 for 6:0 < M ≤ 6:5, EΘ 0:17 × azimuthal gap 11 for 6:5 < M ≤ 7:0, and EΘ 0:11 × azimuthal gap 2 for 7:0 < M ≤ 7:5. These for 25%, 50%, and 75% of felt reports (t 25% , t 50% , and t 75% , respectively) becoming available as a function of intensity.
Two groups can be distinguished: 1 ≤ I felt ≤ 5 and I felt ≥ 6. The collection times in the second group are higher with great disparities (which corroborates the study on the "doughnut" effect). The median collection time taken over all intensities is 681 s (∼12 min). (b) Epicenters of the 36 earthquakes. The events cover various source regions and focal mechanisms and provide a representative dataset for this feasibility study. For EΘ < 60°, we require at least five felt reports within 100 km from the epicenter, distributed at a maximum azimuthal gap of 190°for 6:0 < M ≤ 6:5, and of 290°f or 6:5 < M ≤ 7:0. Gaps for very large earthquakes (M ≥ 7:0) are less critical, probably because of their large source dimensions and large areas affected by strong motions with a strong quasielliptic shape as is taken advantage of in FinDer's binary template matching (see the FinDer Algorithm section).
This selection gives us a total of 36 earthquakes with magnitudes ranging from 6. 0 to 7. 3, and up to N felt 1571 felt reports. The median collection time taken over all intensities for this dataset is ∼12 min (Fig. 1a ). Figure  1b  shows the distribution of these events and Table  1  summarizes the respective source parameters. We take the following steps to prepare the data: first, because FinDer is largely insensitive to data points far from the epicenter and it helps speeding up its computation, we remove felt reports at epicentral distances larger than Δ max , in which Δ max corresponds to the magnitudedependent distance at which the expected intensity computed from  Allen et al. (2012)  has dropped down to 3. 0 (e. g. , Δ max 330 km for M 6. 0; Δ max 970 km for M 7. 3). Furthermore, we remove felt reports with intensities that are more than three units larger or smaller than what is predicted by  Allen et al.
Although Θ FinDer might not agree well with Θ ref in these events, the line-source models cross the surface projected rupture plane and generally provide a good approximation of the finite-source characteristics. This implies that the FinDer strike estimate actually agrees better with the major rupture extension direction rather than with the real strike of the event. section), we model an additional artificial data point at the epicenter using the EMSC reported point-source parameters and relations of  Fourth, we simulate the temporal evolution of feltreport collection by splitting the dataset for each earthquake into several subsets, each including the reports that were becoming available at a certain time after event origin. We start at 10 min after origin, (d) (a) (c) (b) (f) (d) Figure  5.
We constrain the FinDer search in rupture length to L min ≤ L FinDer ≤ L max , with L min and L max determined from empirical rupture-length-magnitude relations after  Wells and Coppersmith (1994)  using the (preliminary) catalog magnitude, M 0:3. This value (0. 3) reflects the expected uncertainties when estimating magnitudes from empirical rupture-length-magnitude relations (e. g. ,  Wells and Coppersmith, 1994; Blaser et al. , 2010; Leonard, 2014). We neglect that magnitude uncertainties are likely time and magnitude dependent. In addition, we constrain the search for rupture strike to 0°≤ FinDer ≤ 175°with increments of 5°. We use the following four metrics to characterize the distributions of felt reports and the reliability of each FinDer line-source model for each dataset (Table  1)  E Q -T A R G E T ; t e m p : i n t a l i n k -; d f 2 ; 4 1 ; 2 4 9 C P x ′ ;y ′ Tx ′ ; y ′ × Ix x ′ ; y y ′ P x ′ ;y ′ Tx ′ ; y ′ 2 × P x ′ ;y ′ Ix x ′ ; y y ′ 2 r : 2 See  Böse et al.