dataesr/scientific-paragraphs-categorization huggingface dataset:
The second procedure involves comparisons with the EGM-DIR-R5 model. To reduce the effect of the omission error in the GGM, we have used EGM-DIR-R5 augmented with high-resolution RTM effects beyond its selected resolution (degree 260). The RTM effects were computed using the GRAVSOFT TC program. The reference height grid was estimated in order to represent the topographic signal above degree 260 of EGM-DIR-R5. The 3" resolution of DTM is equivalent to spherical harmonic d/o 216000, so the reduction in gravity data has been evaluated in the following way:  The results are given in Table  3. The differences in VIGAC data show a STD of 9. 1 mGal and average bias of -0. 6 mGal, whereas IGP data show a STD of 19. 1 mGal and average bias of 4. 5 mGal. This again indicates that the IGP gravity dataset contains gross errors.
Aiming for IGP data with the same precision as the VIGAC gravity data (i. e. 9. 1 mGal in STD), and assuming a normal distribution, we have eliminated those IGP data for which differences are greater than three STD of the VIGAC data (i. e. 27. 3 mGal). There are 1960 points greater than this threshold, which we rejected. Table  2  indicates that the differences in elevation of these points (compared to SRTM) have a STD of 171. 68 m and average bias of -57. 97 m, while the 17,307 accepted points have a STD of 49. 42 m. There is still a big difference in the IGP cleaned data due to horizontal errors as indicated above. To confirm that these gross errors in IGP gravity anomaly are due to elevation errors, we have done tests using different subsets of the gravity points according to an elevation threshold (100 m).
The results of these tests are also given in Table  3. The higher elevation points in the IGP data increase by 12 mGal in average bias and 9 (5) g res = g FA -g DIR5 | 260 2 -g RTM | 216000 261 mGal in STD while VIGAC results change by < 2 mGal. For the lower altitude points, the accuracy of VIGAC and IGP data is 8. 4 and 9. 5 mGal, respectively. This proves that there is a small effect of elevation in VIGAC data, whereas it is large in IGP data. After editing the IGP dataset, they are at the same level as the VIGAC data (about 9 mGal in STD when comparing with EGM-DIR-R5 together with RTM effect). As with the IGP data, we found 21 gravity points of VIGAC data with large differences that were excluded from the computation. Thus, a total of 1981 points was eliminated. After cleaning, the difference between the observed gravity anomalies with EGM-DIR-R5 (d/o = 260) together with RTM effects is -0.
3 mGal on average and 9. 0 mGal STD, whereas with only EGM-DIR-R5 (d/o = 260) it is -12. 0 mGal and 21. 7 mGal, respectively. This result clearly shows that the terrain effect is the most important parameter to consider in order to enhance the consistency of available terrestrial gravimetric data and GGMs and to produce a unified database. The RTM data succeed in filling the spectral gap between land gravity measurements and GGMs. Figure  4a   data, but this bias in residual anomaly is significantly reduced by taking RTM effects into account (Fig. 4b ). The mixed DIR/EGM model up to d/o 2159 together with topographic effects was used to fill-in data on land. The fill-in data have been evaluated following a spectral enhancement approach as: The use of the mixed DIR/EGM model instead of EGM-DIR-R5 only in combination with RTM effect is because of EGM2008, which performs better than RTM effect within the spectral window 260-2159 in Vietnam.
This issue will be further clarified in the next section. The DTU15 gravity field model (Andersen and Knudsen 2016) was used for marine areas. Altimetric gravity is of good quality over the open seas. However, coastal zones remain problematic because most altimeters cannot measure up to the coast  (Hirt 2013). Airborne  (Forsberg and Olesen 2010)  or shipborne  (Featherstone 2010)  gravimetry is used preferentially to close the gap between gravity data on land and marine altimetric gravity fields if it is available. These observations are (6) �g fill-in = �g DIR/EGM | 2159 2 + �g RTM | 216000 2160 not available for Vietnam's coastal zones, so the accuracy of the quasigeoid in coastal zones is a difficult problem. DTM and DBM provide information on the short wavelengths of the gravity field in coastal zones and can be used to augment and improve global gravity fields  (Hirt 2013).
In this study, we used RTM effects together with GGM in coastal zones instead of using the altimetric gravity field. Finally, these heterogeneous gravity data were merged in a complex procedure described below: (1) For the Stokes FFT program, a 5′ × 5′ grid is interpolated with the GRAVSOFT GEOGRID program using the LSC method on the gravity measurements. Then, only grid nodes lying within 5′ radius circles centred on each of the terrestrial gravity points were kept; (2) The grid nodes lying 50 km and more beyond the 5′ radius circles were filled in with the mixed DIR/ EGM model together with RTM effect over land (green points in Fig. 5a ) and with DTU15 over sea (blue points in Fig. 5a ). The full-resolution GMT (3) The transition areas between observations and fillin models (land transitions starting at the 5′ radius circles to 50 km beyond, coastal transitions starting at the coastline to 50 km on sea) were filled using a combination of data and models.
From measurement points, the differences between observations and fill-in data were calculated in the following way: whereas the differences in the fill-in grids (beyond 50 km from the 5′ radius circles) were set to zero. The LSC method in GEOGRID program was then used to interpolate these differences to the transition points ( g grid dif ). Gravity anomalies of transition points were then constructed by adding g grid dif to the fill-in data of transition points as follows: (4) For collocation, the actual measurements were used; however, the same fill-in and transition data as in (  2 ) and (3), respectively, were used. The combination of the heterogeneous gravity data is shown in Fig. 5a. Statistics of the merged gravity anomalies are given in Table  4  and shown in Fig. 5b. These gravity anomalies were reduced using the GGM and RTM effects according to Eq.
GNSS/levelling points From 2009 to 2010, Vietnam Department of Surveying and Cartography carried out GNSS observations on the levelling points. The GNSS baselines were observed using dual-frequency instruments in static mode with a minimum measurement time of 6 h per session. The GNSS data were processed with Bernese software to obtain ellipsoidal heights referred to the WGS84 ellipsoid. The total number of GNSS/levelling stations used in this study is 812, and these are shown in Fig. 6. GNSS/ levelling data include horizontal coordinates (latitude, longitude) and the computed height anomaly. Of the 812   6  shows that gravity measurements of VIGAC have been made alongside the first-and second-order levelling. The GNSS/levelling geometric height anomalies were compared with those derived from the EGM-DIR-R5 or the mixed DIR/EGM model together with RTM effects.
Quasigeoid model estimation and validation The residual height anomalies have been determined using the regular grid of residual gravity anomalies employing the Stokes' integral in the 1D-FFT approach  (Haagmans et al. 1993 ) implemented in the GRAVS-OFT SPFOUR program with the Wong-Gore modification (WG) of the Stokes' kernel function  (Wong and Gore 1969). WG removes low harmonics up to degree N 1 , so the influence of the local data at long wavelengths is eliminated and then linearly tapered to N 2  (Forsberg and Tscherning 2008). N 1 and N 2 are selected according to data and the GGM used in the remove step, but they should be less than or equal to degree n max of the GGM. To find out the optimum N 1 and N 2 degree, the quasigeoid was computed by the Stokes FFT using WG with N 1 and N 2 being tested from 100 to 260 (maximum degree of the EGM-DIR-R5 model used in combination with EGM2008) in steps of 10°.
Degree 719 agrees best with the empirical data for fitting the model covariance function. The empirical covariance function of the data has been computed using the GRAVSOFT EMP-COV program and was fitted to the Tscherning and Rapp model using the GRAVSOFT COVFIT program. We have determined the following optimum parameters for inputs of GEOCOL: the depth to the Bjerhammar sphere R -R B = -0. 028 km and the variance of the gravity anomalies at zero height VARG = 131. 06 mGal 2. Figure  7  shows the plot of the empirical covariance (blue line) and fitted covariance functions for the residual gravity anomalies Δg res (red line). The residual height anomalies �ζ FFT res computed with the SPFOUR program vary from -0. 701 to 0. 402 m. The height anomalies, obtained by restoration of ζ GGM and ζ RTM , vary from -35.
3 ) where there is sufficient terrestrial gravity as well as GNSS/levelling data (136 GNSS/levelling points in a northern area defined by 20° ≤ φ ≤ 22° in latitude and 105° ≤ λ ≤ 108° in longitude and 120 GNSS/levelling points in a southern area defined by 8° ≤ φ ≤ 11° in latitude and 104° ≤ λ ≤ 108° in longitude). For the northern area, the STD of the LSC and 1D FFT methods is 7. 4 cm and 8. 2 cm, respectively;  for the southern area, the STDs are 9. 2 cm and 10. 0 cm, respectively. The results of the comparison indicated that the LSC method is more precise than the 1D FFT method, 0. 8 cm of STD for each area. However, quality of the available gravity data in Vietnam is not homogeneous (bias, precision between IGP, VIGAC, and fillin data) and not enough information on the accuracy is available, which is challenging with the LSC method while with the Stokes FFT method a good data density is required.
Acknowledgements We are very grateful to the  VIGAC, IGP-VAST , and  BGI  (http://bgi. obs-mip. fr/)that supplied data for this study. This study was also supported by  CNES. The authors would like to thank the authors of  GRAVSOFT (DTU)  for providing their software. The SRTM3arc_v4. 1 is available via http://srtm. csi. cgiar. org/SELECTION/input Coord. asp. The SRTM15arc_plus model is available via https ://topex. ucsd. edu/pub/srtm1 5_plus/. All used GGMs in this paper are available via http://icgem. gfz-potsdam. de/tom_longt ime. The DTU15 gravity is available via https ://ftp. space. dtu. dk/pub/. In this paper, we used the Generic Mapping.
Shear-waves are the most energetic body-waves radiated from an earthquake, and are responsible for the destruction of engineered structures. In both short-term emergency response and long-term risk forecasting of disaster-resilient built environment, it is critical to predict spatially accurate distribution of shear-wave amplitudes. Although decades' old theory proposes a deterministic, highly anisotropic, four-lobed shear-wave radiation pattern, from lack of convincing evidence, most empirical groundshaking prediction models settled for an oversimplified stochastic radiation pattern that is isotropic on average. Today, using the large datasets of uniformly processed seismograms from several strike, normal, reverse, and oblique-slip earthquakes across the globe, compiled specifically for engineering applications, we could reveal, quantify, and calibrate the frequency-, distance-, and style-of-faulting dependent transition of shear-wave radiation between a stochastic-isotropic and a deterministicanisotropic phenomenon.
Most empirical ground-shaking models are derived to predict the scaling of S-wave amplitudes with earthquake moment magnitude (M), and its distance from the affected site (R). Coupling the largest datasets 2,3 and numerical simulations, recent ground-shaking prediction models 4,5 have achieved considerable explanatory and predictive power. Despite being intuitive and computationally efficient, empirical ground-shaking models have one major limitation; these models assume and predict the radiation pattern of S-wave energy to be isotropic. This is far from reality, because a double-couple shear dislocation (e. g. , an earthquake) radiates energy very differently from an explosive/implosive dislocation (e. g. , a bomb).
In most studies related to S-wave radiation pattern, despite differences in underlying methodologies, the equally essential distance-dependence of radiation pattern is often ignored. Studies  20, 21  based on observed energy partitioning of S-waves revealed a very weak distance dependency for frequencies 2-5 Hz, and distance independent isotropic pattern beyond 6 Hz -but the dataset consisted of only three earthquakes recorded in the distance range 13-27 km. A more recent study  13  based on observed spatial distribution of maximum amplitudes, used a larger dataset consisting of 13 strike-slip earthquakes (in Chugoku region, Japan) recorded in 0-150 km distance range. The resulting empirical model  13  captures both frequency-and distance-dependence, wherein the cross-correlation coefficient between observed and theoretical low frequency S-wave (0.
5-1 Hz) amplitudes decreases linearly (from 0. 75) beyond a normalized hypocentral distance log(kL) ∼ 1. 64, which is approximately 30 km when wave number k = 1. 33 km -1. While a few earlier studies  12, 22  suggested that four-lobbed pattern remains intact up to 40 km, even for high frequencies (>4 Hz). Essentially, a good understanding, and robust empirical models of the frequency-and distance-dependent S-wave radiation pattern are sought. Although there is a reasonable agreement across all these studies, we observe that most are based on rather small datasets consisting of few (predominantly) strike-slip events. In addition, we identify that: (1) the frequency range (e. g. 1-3 Hz) wherein the transition appears to occur, needs to evaluated, (2) the datasets were rather limited in terms of magnitude and distance ranges, and diversity of style-of-faulting (i.
e. strike, reverse, normal, and oblique-slip events), and (3) most analyses were performed in the Fourier domain, which limits their adoption in engineering applications relying heavily on PSA (Pseudo-Spectral Acceleration) predictions  23, 24. In this study, we tackle these limitations using the recently published large datasets compiled of several thousand seismograms, from a variety of earthquake focal-mechanisms, occurring across the globe, and uniformly processed specifically for engineering applications i. e. , code  23, 24  based design of earthquake resistant structures. Even with such large datasets derived from spatially dense strong-motion networks in Japan  25  and southern California, USA  26  , the imprint of S-wave radiation pattern remained untraceable and unquantifiable within the mixed-effects regression based empirical ground-shaking models  11.
empirical evidence of s-Wave Radiation patterns In our recent studies  29, 30  , we tackled the various assumptions and limitations in development of mixed-effects regression based empirical ground-shaking models. Taking advantage of recently published large datasets  2, 3, 31  and mixed-effects regression analyses  32  , we systematically quantified and isolated the dominant physical processes that control the spatial variability of ground-shaking. In the present study, we have gone a step further to analyze the left-over regression residuals, those quantifying the record-to-record variability of observed ground-shaking, from two empirical ground-shaking models  33, 34  (equation 1) developed from two recently compiled datasets  2, 3  of active shallow crustal earthquake recordings: one 3 from the Japanese KiK-net  25  strong-motion network; and another as a global NGA-West2 dataset 2 compiled mostly of events from southern California 26 (USA), plus a few large events from Italy, Taiwan, Turkey, China, Alaska, Georgia, Montenegro, New Zealand, and other active seismic regions.
δ δ δ = + + + + PSA f M R f M B S S WS ln( ) ( , ) ( ) 2 (1) R M e s e s , The most common expression of S-wave amplitudes used in engineering seismology and earthquake engineering is an average 35 of two-component (i. e. , NS, EW) horizontal PSAs, for a range of spectral periods (e. g. T = 0. 01-10. 0 s). All of the ground-shaking datasets 2,3 disseminate the observed ground-shaking intensity data only in terms of PSAs. The two ground-shaking models  33, 34  we considered were also developed to predict PSAs, because most seismic design codes  23, 24  rely on predicted PSAs. PSAs are essentially the peak acceleration responses to seismic excitation (i. e. , a seismogram) of a suite of viscous damped (5% or other) single-degree-offreedom oscillators with fundamental frequencies = f osc T 1.
It is true that conversion of 'as recorded' Fourier amplitudes to 'engineering purposed' PSAs is nonlinear  36  , which often makes the physical interpretations made in either of the domains non-interchangeable. However, within the earthquake moment magnitude (M3. 4-M6. 9) and period range of interest in this study (T = 0. 1-1. 0 s), responses of a single-degree-of-freedom (i. e. , the PSAs) are dominated by the Fourier amplitudes of S-wave frequencies around f osc  36. Hence, we can interpret the radiation pattern effects in PSA residuals as Fourier spectral features of the seismic input. Typically, empirical ground-shaking prediction models (e. g. , equation 1) are regressed from datasets of observed PSAs at several surface sites from multiple past earthquakes in a region. In equation (1), the fixed-effect f R (M, R) captures the geometric spreading and apparent anelastic attenuation of PSAs with rupture moment magnitude (M) and distance to site (R), and f M (M) captures the scaling of PSAs with M.
δB e and δS2S s are the random-effects quantifying event-to-event (event index e) and site-to-site (surface site index s) variabilities, respectively. The left-over record-specific residuals δWS e,s (of event e recorded at surface site s) contain all of the phenomena that evade the fixed-and random-effects, including the four-lobed S-wave radiation pattern. For brevity, we refer interested readers to the articles  33, 34  elaborating on the ground-shaking model development. Figure  1  presents the empirical evidence of S-wave radiation patterns in ground-shaking data (i. e. , residuals δWS e,s ). While the most recent studies  13, 22  considered 13 events, we select 1615 and 3193 δWS e,s residuals (records) at R ≤ 100 km of 91 and 78 strike-slip events from the KiK-net 3 and NGA-West2 2 datasets, respectively.
Instead of an actual crustal velocity model, we used a take-off angle table  38  provided by the Japanese Meteorological Agency. Although AS (as with + F F SH SV 2 2 ) are all positive values, these were zero-centered and standardized for visualization in Fig. 1. Clearly, the theoretical and empirical amplitudes show identical azimuthal dependence. While Fig. 1  shows the evidence of S-wave radiation patterns for strike-slip events from both the KiK-net and NGA-West2 datasets, Fig. 2  presents similar plots for normal (1468 records from 64 events in M3. 5-M6. 0), reverse (2747 records from 198 events in M3. 5-M6. 0), and oblique (1864 records from 102 events of M3. 5-M5. 5) faulting events in the KiK-net dataset (including six events larger than M6. 0). Since the global NGA-West2 dataset contains only large magnitude normal and reverse faults from diverse tectonic regions across the world, the coherency between theoretical and observed radiation patterns is not as clear as with the numerous smaller events of the Japanese KiK-net dataset (see Fig.
transition from stochastic to Deterministic phenomenon Following the non-parametric analyses, we derived parametric models aiming to extract the S-wave radiation anisotropy from the ground-shaking residuals, and reintroduce anisotropic adjustments into the isotropic prediction models. For each dataset 2,3 independently, using a linear mixed-effects regression algorithm (lmer)  32  , we fit a simple, linear relation between the theoretical far-field S-wave radiation amplitudes and the residuals from isotropic ground-shaking models  33, 34. In equation (  2 ), s 0 is the intercept and s 1 is the slope. Both s 0 and s 1 are set to vary with style-of-faulting (i. e. , oblique, normal, reverse, strike-slip) in the mixed-effects regressions. δ = +. WS s s AS (2) e s e s , 0 1 , The top panels of Fig.
3  show the number of residuals/record used in deriving the s 1 (and s 0 ) values for the range T = 0. 01 s to 1. 0 s for each style-of-faulting and dataset. Most of the NGA-West2 data is constituted by strike-slip and oblique-slip events, while the distribution is more even in KiK-net dataset -the style-of-faulting dependent values of s 1 (and s 0 ), estimated as random-effects in an lmer  32  of equation (  2 ), is to account for such dataset imbalances. There is a reason we limit our analyses to the period range T = 0. 01-1 s. The KiK-net strong-motion dataset 3 we used is the product of an automatic processing of ~150,000 seismograms from the NIED KiK-net database  25  , and is specifically built for engineering ground-shaking (PSA) studies such as ours  33. Only through such automatic processing algorithms, it is possible to compile large datasets with thousands of records.
However, the limitation of automatic processing is that we are required to apply a strict high-pass frequency filtering  39  criterion to discard records with limited usable low-frequency content. Consequently, the number of usable KiK-net  3  records drops rapidly for periods longer than T = 1 s. The NGA-West2 dataset 2 on the other hand, is a product of manual processing of seismograms from active shallow crustal earthquakes, and therefore allows a wider usable period   e, s  ). Top panels: the (decreasing) number of records with increasing T at R ≤ 100 km of oblique, normal, reverse, and strike-slip events in the KiK-net (blue) and NGA-West2 (red) datasets. Middle panels: the estimated period-dependent s 1 (with 95% confidence interval) of equation (  2 ), which quantifies the presence of S-wave radiation patterns in ground-shaking residuals.
Bottom panels: the reduction in the ground-shaking variability (φ 0 ) with the removal of the S-wave radiation pattern through the linear relationship. range of T = 0. 01-10 s. However, to maintain consistency across datasets, we limited our investigation only in the period range T = 0. 01-1 s. Further details on data selection are available in the relevant articles elaborating on the development of Ground-Motion Prediction Equations  33, 34  that we used in this study.
Frequency Dependence of Radiation Pattern. The agreement between theoretical and empirical radi- ation patterns is period (T) dependent. In the middle panels of Fig. 3 , considering s 1 as a measure of correlation between empirical and theoretical patterns, and approximating f osc (1/T) as S-wave frequencies, the monotonically increasing trend of s 1 from T = 0. 1 s to 1. 0 s (f osc = 1-10 Hz) can be interpreted as the transition of the S-wave radiation pattern from a stochastic to a deterministic process, which supports earlier findings  17. Strike-slip events (Fig. 3 , middle-right panel) from both datasets exhibit best the transition regime of the S-wave radiation patterns in their residuals -with statistically significant (as shown by its 95% confidence interval) estimates of s 1. Normal, oblique, and reverse-slip events of the KiK-net show a clear trend as well, while there is very little data from normal-slip events in NGA-West2.
The efficiency of equation (  2 ) in capturing and removing S-wave radiation anisotropy from the δWS e,s is measured in terms of the reduction in prediction variance (φ 0 , the standard deviation of δWS e,s ) of the parent ground-shaking models  33, 34. In the bottom panels of Fig. 3 , we see up to 8% reduction in φ 0 for normal, oblique, and strike-slip events of the KiK-net dataset. Such reductions in the ground-shaking prediction variance are highly sought in Probabilistic Seismic Hazard Assessment  40. Reverse-slip events do not show as much reduction -we discuss this in the following section.