A study of Guptkashi,Uttarakhand earthquake of 6 February 2017 (<Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript>5.3) in the Himalayan arc and implications for ground motion estimation

The 2017 Guptkashi earthquake occurred in a segment of the Himalayan arc with high potential for a strong earthquake in the near future. In this context, a careful analysis of the earthquake is important as it may shed light on source and ground motion characteristics during future earthquakes. Using the earthquake recording on a single broadband strong-motion seismograph installed at the epicenter, we estimate the earthquake’s location (30.546° N, 79.063° E), depth (H?=?19 km), the seismic moment (M₀?=?1.12×10¹⁷ Nm, M _w 5.3), the focal mechanism (φ?=?280°, δ?=?14°, λ?=?84°), the source radius (a?=?1.3 km), and the static stress drop (Δσ _s ~22 MPa). The event occurred just above the Main Himalayan Thrust. S-wave spectra of the earthquake at hard sites in the arc are well approximated (assuming ω^?2 source model) by attenuation parameters Q(f)?=?500f^0.9, κ?=?0.04 s, and f_max?=?infinite, and a stress drop of Δσ?=?70 MPa. Observed and computed peak ground motions, using stochastic method along with parameters inferred from spectral analysis, agree well with each other. These attenuation parameters are also reasonable for the observed spectra and/or peak ground motion parameters in the arc at distances ≤?200 km during five other earthquakes in the region (4.6?≤?M _w ?≤?6.9). The estimated stress drop of the six events ranges from 20 to 120 MPa. Our analysis suggests that attenuation parameters given above may be used for ground motion estimation at hard sites in the Himalayan arc via the stochastic method.     

Understanding single-station ground motion variability and uncertainty (sigma): lessons learnt from EUROSEISTEST

Accelerometric data from the well-studied valley EUROSEISTEST are used to investigate ground motion uncertainty and variability. We define a simple local ground motion prediction equation (GMPE) and investigate changes in standard deviation (σ) and its components, the between-event variability (τ) and within-event variability (φ). Improving seismological metadata significantly reduces τ (30–50%), which in turn reduces the total σ. Improving site information reduces the systematic site-to-site variability, φ _S2S (20–30%), in turn reducing φ, and ultimately, σ. Our values of standard deviations are lower than global values from literature, and closer to path-specific than site-specific values. However, our data have insufficient azimuthal coverage for single-path analysis. Certain stations have higher ground-motion variability, possibly due to topography, basin edge or downgoing wave effects. Sensitivity checks show that 3 recordings per event is a sufficient data selection criterion, however, one of the dataset’s advantages is the large number of recordings per station (9–90) that yields good site term estimates. We examine uncertainty components binning our data with magnitude from 0.01 to 2 s; at smaller magnitudes, τ decreases and φ _SS increases, possibly due to κ and source-site trade-offs Finally, we investigate the alternative approach of computing φ _SS using existing GMPEs instead of creating an ad hoc local GMPE. This is important where data are insufficient to create one, or when site-specific PSHA is performed. We show that global GMPEs may still capture φ _SS , provided that: (1) the magnitude scaling errors are accommodated by the event terms; (2) there are no distance scaling errors (use of a regionally applicable model). Site terms (φ _S2S ) computed by different global GMPEs (using different site-proxies) vary significantly, especially for hard-rock sites. This indicates that GMPEs may be poorly constrained where they are sometimes most needed, i.e., for hard rock.     

Atypical soil behavior during the 2011 Tohoku earthquake (<Emphasis Type="Italic">М</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> = 9)

To understand physical mechanisms of generation of abnormally high peak ground acceleration (PGA; >1g) during the Tohoku earthquake, models of nonlinear soil behavior in the strong motion were constructed for 27 KiK-net stations located in the near-fault zones to the south of FKSH17. The method of data processing used was developed by Pavlenko and Irikura, Pure Appl Geophys 160:2365–2379, 2003 and previously applied for studying soil behavior at vertical array sites during the 1995 Kobe (М _w ?=?6.8) and 2000 Tottori (М _w ?=?6.7) earthquakes. During the Tohoku earthquake, we did not observe a widespread nonlinearity of soft soils and reduction at the beginning of strong motion and recovery at the end of strong motion of shear moduli in soil layers, as usually observed during strong earthquakes. Manifestations of soil nonlinearity and reduction of shear moduli during strong motion were observed at sites located close to the source, in coastal areas. At remote sites, where abnormally high PGAs were recorded, shear moduli in soil layers increased and reached their maxima at the moments of the highest intensity of the strong motion, indicating soil hardening. Then, shear moduli reduced with decreasing the intensity of the strong motion. At soft-soil sites, the reduction of shear moduli was accompanied by a step-like decrease of the predominant frequencies of motion. Evidently, the observed soil hardening at the moments of the highest intensity of the strong motion contributed to the occurrence of abnormally high PGA, recorded during the Tohoku earthquake.     

Ground-motion models for average spectral acceleration in a period range: direct and indirect methods

Average spectral acceleration, AvgSA, is defined as the geometric mean of spectral acceleration values over a range of periods and it is a ground motion intensity measure used for structural response prediction. One of its advantages stands on the assumption that its distribution is computable from the available GMPEs for spectral acceleration, GMPE-SA, (called here indirect method) without the need for deriving new specific GMPEs for AvgSA, GMPE-AvgSA, (called here direct method). To what extent this assumption is valid, however, has never been verified. As such, we derived an empirical GMPE-AvgSA based on RESORCE ground motion dataset and we compared its predicted values with those from a GMPE-SA via the indirect approach. As expected, the results show that the indirect approach yields median AvgSA estimates that are identical to those of the direct approach. However, the estimates of AvgSA variance of the two methods are identical only if both the GMPE-SA and their empirical correlation coefficients among different SA ordinates are derived from the same record dataset.     

Seismic response of reduced micropolar elastic half-space

This paper explores reduced micropolar theory to simulate ground motion during an earthquake. In this theory, rotational motions are kinematically independent of translational motions. Analytical expressions for ground displacement and rotational motions due to a buried seismic source are presented in this paper. This theory requires two additional material constants which characterise the microstructure of the medium compared with linear elastic theory. Ground motions are simulated for an earthquake of magnitude (M _w) 5.0. The sensitivity of ground motion to these new material constants is reported. It is observed that rotations are sensitive to microstructure of the medium. A comparison with recorded rotations of the M _w 5.2 Izu peninsula, Japan event is also presented in this article.     

Activation of seismicity in Central and South Asia after the Makran earthquakes: Possible acceleration of preparation of large seismic events in the Tien Shan region

Two zones of seismicity (ten events with M _w = 7.0–7.7) stretching from Makran and the Eastern Himalaya to the Central and EasternTien Shan, respectively, formed over 11 years after the great Makran earthquake of 1945 (M _w = 8.1). Two large earthquakes (M _w = 7.7) hit theMakran area in 2013. In addition, two zones of seismicity (M ≥ 5.0) occurred 1–2 years after theMakran earthquake in September 24, 2013, stretching in the north-northeastern and north-northwestern directions. Two large Nepal earthquakes struck the southern extremity of the “eastern” zone (April 25, 2015, M _w = 7.8 and May 12, 2015, M _w = 7.3), and the Pamir earthquake (December 7, 2015, M _w = 7.2) occurred near Sarez Lake eastw of the “western” zone. The available data indicate an increase in subhorizontal stresses in the region under study, which should accelerate the possible preparation of a series of large earthquakes, primarily in the area of the Central Tien Shan, between 70° and 79° E, where no large earthquakes (M _w ≥ 7.0) have occurred since 1992.     

Seismic source zoning and maximum credible earthquake prognosis of the Greater Kashmir Territory,NW Himalaya

We present the seismic source zoning of the tectonically active Greater Kashmir territory of the Northwestern Himalaya and seismicity analysis (Gutenberg-Richter parameters) and maximum credible earthquake (m _max) estimation of each zone. The earthquake catalogue used in the analysis is an extensive one compiled from various sources which spans from 1907 to 2012. Five seismogenic zones were delineated, viz. Hazara-Kashmir Syntaxis, Karakorum Seismic Zone, Kohistan Seismic Zone, Nanga Parbat Syntaxis, and SE-Kashmir Seismic Zone. Then, the seismicity analysis and maximum credible earthquake estimation were carried out for each zone. The low b value (<1.0) indicates a higher stress regime in all the zones except Nanga Parbat Syntaxis Seismic Zone and SE-Kashmir Seismic Zone. The m _max was estimated following three different methodologies, the fault parameter approach, convergence rates using geodetic measurements, and the probabilistic approach using the earthquake catalogue and is estimated to be M _w 7.7, M _w 8.5, and M _w 8.1, respectively. The maximum credible earthquake (m _max) estimated for each zone shows that Hazara Kashmir Syntaxis Seismic Zone has the highest m _max of M _w 8.1 (±0.36), which is espoused by the historical 1555 Kashmir earthquake of M _w 7.6 as well as the recent 8 October 2005 Kashmir earthquake of M _w 7.6. The variation in the estimated m _max by the above discussed methodologies is obvious, as the definition and interpretation of the m _max change with the method. Interestingly, historical archives (～900 years) do not speak of a great earthquake in this region, which is attributed to the complex and unique tectonic and geologic setup of the Kashmir Himalaya. The convergence is this part of the Himalaya is distributed not only along the main boundary faults but also along the various active out-of-sequence faults as compared to the Central Himalaya, where it is mainly adjusted along the main boundary fault.     

On a possible origin of the anomalous effects that were observed during the May 24, 2013 earthquake in the Sea of Okhotsk

The deep-focus Sea of Okhotsk earthquake that occurred on May 24, 2013 (h = 630 km, M _w = 8.3) was accompanied by anomalous effects that were unknown previously. A combined analysis of published data concerning the source rupture evolution and some features of the deep structure provided an explanation of some anomalous effects, such as the large number of aftershocks and the low level of ground shaking in the epicentral area. However, GPS observations revealed high coseismic vertical displacements in the area. The seafloor uplift in the Sea of Okhotsk and the adjacent coasts was 3–12 mm, peaking at the approximate center of the sea, while Kamchatka and the North Kuril Islands subsided by 3–18 mm, peaking at the Apacha station 190 km east of the earthquake epicenter. These maximum estimates are 1.2–1.8 times the analogous values (10 mm) for the Chile mega-earthquake of May 20, 1960 (M _w ~ 9.5). It is known that the large distances at which ground shaking is felt during deep-focus earthquakes are due to the fact that the body waves travel through the high-Q lower mantle. However, this does not explain the paradox of the present earthquake in the Sea of Okhotsk, viz., a constant intensity of shaking (two grades) in the range of epicentral distances between 1300 and 9500 km. The explanation requires consideration of the earth’s free oscillations excited by the earthquake.     

Strong motion characteristics of the <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> 6.6 Lushan earthquake,Sichuan, China — an insight into the spatial difference of a typical thrust fault earthquake

Near-field strong ground motions are useful for engineering seismology studies and seismic design, but dense observation networks of damaging earthquakes are still rare. In this study, based on the strong-motion data from the M w 6.6 Lushan earthquake, the ground motion parameters in different spatial regions are systematically analyzed, and the contributions from different effects, like the hanging-wall effect, directivity effect, and attenuation effect are separated to the extent possible. Different engineering parameters from the observed ground motions are compared with the local design response spectra and a new attenuation relation of Western China. General results indicate that the high frequency ground motion, like the peak ground acceleration, on two sides of the fault plane is sensitive to the hanging-wall effect, whereas the low frequency ground motion, like the long period spectral acceleration, in the rupture propagation direction is affected by the directivity effect. Moreover, although the M w 6.6 Lushan earthquake is not a large magnitude event, the spatial difference of ground motion is still obvious; thus, for a thrust faulting earthquake, in addition to the hanging effect, the directivity effect should also be considered.     

Strong ground motion from the November 12, 2017, <Emphasis Type="Bold">M</Emphasis> 7.3 Kermanshah earthquake in western Iran

In this paper, we analyzed the strong ground motion from the November 12, 2017, Kermanshah earthquake in western Iran with moment magnitude (M) of 7.3. Nonlinear and linear amplification of ground motion amplitudes were observed at stations with soft soil condition at hypocentral distances below and above 100 km, respectively. Observation of large ground motion amplitudes dominated with long-period pulses on the strike-normal component of the velocity time series suggests a right-lateral component of movement and propagation of rupture towards southeast. Comparison of the horizontal peak ground acceleration (PGA) from the M 7.3 earthquake with global PGA values showed a similar decay in ground motion amplitudes, although it seems that PGA from the M 7.3 Kermanshah earthquake is higher than global values for NEHRP site class B. We also found that the bracketed duration (D_b) was higher in the velocity domain than in the acceleration domain for the same modified Mercalli intensity (MMI) threshold. For example, D_b reached ~?30 s at the maximum PGA while it was ~?50 s at the maximum peak ground velocity above the threshold of MMI?=?5. Although the standard design spectrum from Iranian Code of Practice for Seismic Resistant Design of Buildings (standard No. 2800) seems to include appropriate values for the design of structures with fundamental period of 1 s and higher, it is underestimated for near-field ground motions at lower periods.     

Seismic analysis of nailed vertical excavation using pseudo-dynamic approach

An attempt has been made to study the behavior of nailed vertical excavations in medium dense to dense cohesionless soil under seismic conditions using a pseudo-dynamic approach. The effect of several parameters such as angle of internal friction of soil(Φ), horizontal(k_h) and vertical(k_v) earthquake acceleration coefficients, amplification factor(f_a), length of nails(L), angle of nail inclination(α) and vertical spacing of nails(S_v) on the stability of nailed vertical excavations has been explored. The limit equilibrium method along with a planar failure surface is used to derive the formulation involved with the pseudo-dynamic approach, considering axial pullout of the installed nails. A comparison of the pseudo-static and pseudo-dynamic approaches has been established in order to explore the effectiveness of the pseudo-dynamic approach over pseudo-static analysis, since most of the seismic stability studies on nailed vertical excavations are based on the latter. The results are expressed in terms of the global factor of safety(FOS). Seismic stability, i.e., the FOS of nailed vertical excavations is found to decrease with increase in the horizontal and vertical earthquake forces. The present values of FOS are compared with those available in the literature.     

Stochastic finite-fault simulation of ground motion from the August 11, 2012, <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> 6.4 Ahar earthquake,northwestern Iran

In this study, the 11 August 2012 M _w 6.4 Ahar earthquake is investigated using the ground motion simulation based on the stochastic finite-fault model. The earthquake occurred in northwestern Iran and causing extensive damage in the city of Ahar and surrounding areas. A network consisting of 58 acceleration stations recorded the earthquake within 8–217 km of the epicenter. Strong ground motion records from six significant well-recorded stations close to the epicenter have been simulated. These stations are installed in areas which experienced significant structural damage and humanity loss during the earthquake. The simulation is carried out using the dynamic corner frequency model of rupture propagation by extended fault simulation program (EXSIM). For this purpose, the propagation features of shear-wave including \( {Q}_s \) value, kappa value \( {k}_0 \), and soil amplification coefficients at each site are required. The kappa values are obtained from the slope of smoothed amplitude of Fourier spectra of acceleration at higher frequencies. The determined kappa values for vertical and horizontal components are 0.02 and 0.05 s, respectively. Furthermore, an anelastic attenuation parameter is derived from energy decay of a seismic wave by using continuous wavelet transform (CWT) for each station. The average frequency-dependent relation estimated for the region is \( Q=\left(122\pm 38\right){f}^{\left(1.40\pm 0.16\right)}. \) Moreover, the horizontal to vertical spectral ratio \( H/V \) is applied to estimate the site effects at stations. Spectral analysis of the data indicates that the best match between the observed and simulated spectra occurs for an average stress drop of 70 bars. Finally, the simulated and observed results are compared with pseudo acceleration spectra and peak ground motions. The comparison of time series spectra shows good agreement between the observed and the simulated waveforms at frequencies of engineering interest.     

Estimation of maximum mass velocities in the focal zones of strong earthquakes based on measured displacements of rock blocks: A case study of Kyrgyzstan

An important task in seismic hazard assessment is estimation of the intensity and frequency of extremely strong earthquake effects, in particular, peak ground velocities (PGV). Earlier, a method was proposed to evaluate PGV values based on the magnitude of displacements of rock blocks (Rodkin et al., 2012). In this study, this method is used to analyze field data on the source zones of the August 19, 1992, M_S = 7.3 Susamyr earthquake and the January 3, 1911, M_w = 7.9 Kemin earthquake, and estimate maximum ground shaking at the upper construction site of the Upper Naryn series of hydropower plants, Kyrgyz Republic. It is shown that the resulting estimates are consistent with data obtained through other techniques. Therefore, the new approach can be recommended to estimate earthquake effects.     

Structural features and seismotectonic implications of coseismic surface ruptures produced by the 2016 <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> 7.1 Kumamoto earthquake

Field investigations and analyses of satellite images and aerial photographs reveal that the 2016 M _w 7.1 (Mj 7.3) Kumamoto earthquake produced a ～40-km surface rupture zone striking NE-SW on central Kyushu Island, Japan. Coseismic surface ruptures were characterized by shear faults, extensional cracks, and mole tracks, which mostly occurred along the pre-existing NE-SW-striking Hinagu–Futagawa fault zone in the southwest and central segments, and newly identified faults in the northeast segment. This study shows that (i) the Hinagu–Futagawa fault zone triggered the 2016 Kumamoto earthquake and controlled the spatial distribution of coseismic surface ruptures; (ii) the southwest and central segments were dominated by right-lateral strike-slip movement with a maximum in-site measured displacement of up to 2.5 m, accompanied by a minor vertical component. In contrast, the northeast segment was dominated by normal faulting with a maximum vertical offset of up to 1.75 m with a minor horizontal component that formed graben structures inside Aso caldera; (iii) coseismic rupturing initiated at the jog area between the Hinagu and Futagawa faults, then propagated northeastward into Aso caldera, where it terminated. The 2016 M _w 7.1 Kumamoto earthquake therefore offers a rare opportunity to study the relationships between coseismic rupture processes and pre-existing active faults, as well as the seismotectonics of Aso volcano.     

Engineering characteristics of near-fault vertical ground motions and their effect on the seismic response of bridges

A wide variety of near-fault strong ground motion records were collected from various tectonic environments worldwide and were used to study the peak value ratio and response spectrum ratio of the vertical to horizontal component of ground motion, focusing on the effect of earthquake magnitude, site conditions, pulse duration, and statistical component. The results show that both the peak value ratio and response spectrum ratio are larger than the 2/3 value prescribed in existing seismic codes, and the relationship between the vertical and horizontal ground motions is comparatively intricate. In addition, the effect of the near-fault ground motions on bridge performance is analyzed, considering both the material nonlinear characteristics and the P~? effect.     

New magnitude scaling relations for earthquake early warning in the Alborz region,Iran

Rapid magnitude estimation relations for earthquake early warning systems in the Alborz region have been developed based on the initial first seconds of the P-wave arrival. For this purpose, a total of 717 accelerograms recorded by the Building and Housing Research Center in the Alborz region with the magnitude (M_w) range of 4.8–6.5 in the period between 1995 and 2013 were employed. Average ground motion period (\( \tau_{\text{c}} \)) and peak displacement (\( P_{\text{d}} \)) in different time windows from the P-wave arrival were calculated, and their relation with magnitude was examined. Four earthquakes that were excluded from the analysis process were used to validate the results, and the estimated magnitudes were found to be in good agreement with the observed ones. The results show that using the proposed relations for the Alborz region, earthquake magnitude could be estimated with acceptable accuracy even after 1 s of the P-wave arrival.     

Determination of GMPE functional form for an active region with limited strong motion data: application to the Himalayan region

Advancement in the seismic networks results in formulation of different functional forms for developing any new ground motion prediction equation (GMPE) for a region. Till date, various guidelines and tools are available for selecting a suitable GMPE for any seismic study area. However, these methods are efficient in quantifying the GMPE but not for determining a proper functional form and capturing the epistemic uncertainty associated with selection of GMPE. In this study, the compatibility of the recent available functional forms for the active region is tested for distance and magnitude scaling. Analysis is carried out by determining the residuals using the recorded and the predicted spectral acceleration values at different periods. Mixed effect regressions are performed on the calculated residuals for determining the intra- and interevent residuals. Additionally, spatial correlation is used in mixed effect regression by changing its likelihood function. Distance scaling and magnitude scaling are respectively examined by studying the trends of intraevent residuals with distance and the trend of the event term with magnitude. Further, these trends are statistically studied for a respective functional form of a ground motion. Additionally, genetic algorithm and Monte Carlo method are used respectively for calculating the hinge point and standard error for magnitude and distance scaling for a newly determined functional form. The whole procedure is applied and tested for the available strong motion data for the Himalayan region. The functional form used for testing are five Himalayan GMPEs, five GMPEs developed under NGA-West 2 project, two from Pan-European, and one from Japan region. It is observed that bilinear functional form with magnitude and distance hinged at 6.5 M _w and 300 km respectively is suitable for the Himalayan region. Finally, a new regression coefficient for peak ground acceleration for a suitable functional form that governs the attenuation characteristic of the Himalayan region is derived.     

A new energy-based ground motion selection and modification method limiting the dynamic response dispersion and preserving the median demand

A novel ground motion selection and modifications method to perform response history analysis of structures is presented in this paper. Currently, the accessibility of ground motion information permits the analysis of structures using real ground motion data. Predicting the dynamic behavior of structures is a primary objective; therefore, the selection of a set of ground motions that shows a reduction in the variability of the structural response and accuracy in preserving the median demand is a challenging task. The new selection and scaling procedure emerges from comparing a set of horizontal ground motions at various ranges of frequency. In this study, the conditional mean spectrum and the design response spectrum are used as target spectra, and the records that give an applicable and compelling contribution to the hazard are considered. It is possible to obtain a set of ground motions with similar seismic severity by matching the target spectrum at the period of interest T _ref , where the scaled spectrum should have an equivalent Housner intensity in the period range 0.2T _ref –2T _ref . The horizontal components for every band of frequency is obtained using a specific index that depends on the energy-frequency trend’s shape as well as on its scattering degree around the mean value. This allows obtaining a set of spectrum-compatible records with almost identical severity and low dispersion of the structural response parameters. The methodology has been tested showing a significant effectiveness in terms of low variability of parameters and accuracy in preserving the median demand for a given hazard scenario.     

Temporal and spatial distributions of precursory seismicity rate changes in the Thailand-Laos-Myanmar border region: implication for upcoming hazardous earthquakes

To study the prospective areas of upcoming strong-to-major earthquakes, i.e., M _w  ≥ 6.0, a catalog of seismicity in the vicinity of the Thailand-Laos-Myanmar border region was generated and then investigated statistically. Based on the successful investigations of previous works, the seismicity rate change (Z value) technique was applied in this study. According to the completeness earthquake dataset, eight available case studies of strong-to-major earthquakes were investigated retrospectively. After iterative tests of the characteristic parameters concerning the number of earthquakes (N) and time window (T _w ), the values of 50 and 1.2 years, respectively, were found to reveal an anomalous high Z-value peak (seismic quiescence) prior to the occurrence of six out of the eight major earthquake events studied. In addition, the location of the Z-value anomalies conformed fairly well to the epicenters of those earthquakes. Based on the investigation of correlation coefficient and the stochastic test of the Z values, the parameters used here (N = 50 events and T _w  = 1.2 years) were suitable to determine the precursory Z value and not random phenomena. The Z values of this study and the frequency-magnitude distribution b values of a previous work both highlighted the same prospective areas that might generate an upcoming major earthquake: (i) some areas in the northern part of Laos and (ii) the eastern part of Myanmar.     

Magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> in metropolitan France

The recent seismicity catalogue of metropolitan France Sismicité Instrumentale de l’Hexagone (SI-Hex) covers the period 1962–2009. It is the outcome of a multipartner project conducted between 2010 and 2013. In this catalogue, moment magnitudes (M _w) are mainly determined from short-period velocimetric records, the same records as those used by the Laboratoire de Détection Géophysique (LDG) for issuing local magnitudes (M _L) since 1962. Two distinct procedures are used, whether M _L-LDG is larger or smaller than 4. For M _L-LDG >4, M _w is computed by fitting the coda-wave amplitude on the raw records. Station corrections and regional properties of coda-wave attenuation are taken into account in the computations. For M _L-LDG ≤4, M _w is converted from M _L-LDG through linear regression rules. In the smallest magnitude range M _L-LDG <3.1, special attention is paid to the non-unity slope of the relation between the local magnitudes and M _w. All M _w determined during the SI-Hex project is calibrated according to reference M _w of recent events. As for some small events, no M _L-LDG has been determined; local magnitudes issued by other French networks or LDG duration magnitude (M _D) are first converted into M _L-LDG before applying the conversion rules. This paper shows how the different sources of information and the different magnitude ranges are combined in order to determine an unbiased set of M _w for the whole 38,027 events of the catalogue.