Empirical ground-motion models for point- and extended-source crustal earthquake scenarios in Europe and the Middle East

This article presents equations for the estimation of vertical strong ground motions caused by shallow crustal earthquakes with magnitudes M w 5 and distance to the surface projection of the fault less than 100km. These equations were derived by weighted regression analysis, used to remove observed magnitude-dependent variance, on a set of 595 strong-motion records recorded in Europe and the Middle East. Coefficients are included to model the effect of local site effects and faulting mechanism on the observed ground motions. The equations include coefficients to model the observed magnitude-dependent decay rate. The main findings of this study are that: short-period ground motions from small and moderate magnitude earthquakes decay faster than the commonly assumed 1/r, the average effect of differing faulting mechanisms is similar to that observed for horizontal motions and is not large and corresponds to factors between 0.7 (normal and odd) and 1.4 (thrust) with respect to strike-slip motions and that the average long-period amplification caused by soft soil deposits is about 2.1 over those on rock sites.

This article presents equations for the estimation of horizontal strong ground motions caused by shallow crustal earthquakes with magnitudes Mw ≥ 5 and distance to the surface projection of the fault less than 100km. These equations were derived by weighted regression analysis, used to remove observed magnitude-dependent variance, on a set of 595 strong-motion records recorded in Europe and the Middle East. Coefficients are included to model the effect of local site effects and faulting mechanism on the observed ground motions. The equations include coefficients to model the observed magnitude-dependent decay rate. The main findings of this study are that: short-period ground motions from small and moderate magnitude earthquakes decay faster than the commonly assumed 1/r, the average effect of differing faulting mechanisms is not large and corresponds to factors between 0.8 (normal and odd) and 1.3 (thrust) with respect to strike-slip motions and that the average long-period amplification caused by soft soil deposits is about 2.6 over those on rock sites. Disappointingly the standard deviations associated with the derived equations are not significantly lower than those found in previous studies.

A revised Italian strong motion archive has become available since July 2007, including all the records of the strongest events occurred from 1972 to 2004. It contains the uncorrected and corrected accelerograms and the metadata relevant to seismic events, recording stations and instruments added after a careful revision. The availability of this archive allowed us to perform a first step towards an update of the reference ground motion prediction equations for Italy, which were evaluated by Sabetta and Pugliese in (Bull Seismol Soc Am 77:1491–1513, 1987), for peak ground acceleration and velocity, and subsequently extended to the 5% damped pseudovelocity response spectra in 1996. A subset with the 27 major earthquakes occurred in Italy from 1972 to 2002, in the magnitude range 4.6–6.9, was extracted and 235 good quality waveforms were selected, recorded at distances up to 183 km. The goodness of fit of the Sabetta and Pugliese (Bull Seismol Soc Am 86:337–352, 1996) model was explored using two independent statistical approaches (Spudich et al. Bull Seismol Soc Am 89:1156–1170, 1999 and Scherbaum et al. Bull Seismol Soc Am 94:2164–2185, 2004). The results obtained show that the Sabetta and Pugliese (Bull Seismol Soc Am 77:1491–1513, 1987) does not adequately fit the new strong-motion data set, for its small standard deviation and its non-zero bias. In particular, the most noteworthy result is that the Sabetta and Pugliese (Bull Seismol Soc Am 77:1491–1513, 1987) over-predicts peak ground acceleration and velocity at rock sites. New coefficients for the prediction of horizontal peak ground acceleration, peak ground velocity and acceleration response spectra, adopting the same functional form in Sabetta and Pugliese (Bull Seismol Soc Am 77:1491–1513, 1987), were then evaluated in order to fit the new data set. This paper illustrates the steps made to update the existing ground motion prediction equations for Italy, discusses their limitations and provides the basis for future developments.

SUMMARY We derived new, reversible relationships between macroseismic intensity (I), expressed in either the European Macroseismic (EMS-98) or the Mercalli–Cancani–Sieberg (MCS) scales and peak ground acceleration (PGA), peak ground velocity (PGV) and the spectral acceleration (SA) at 0.3, 1.0 and 3.0 s [SA(0.3), SA(1.0) and SA(3.0)] for Italy. We adopted the orthogonal distance regression technique to fit a quadratic function. This research aims to improve ground motion and intensity estimates for earthquake hazard applications, and for the calculation of shakemaps in Italy. To this end, the recently published INGe data set was used (https://doi.org/10.13127/inge.2). The new relations are: $$\begin{equation*} I = 3.01 \pm 0.12 + 0.86 \pm 0.04 \log ^2 \mathrm{ PGA},~\sigma = 0.30,~~\sigma _{\mathrm{ PGA}} = 0.25,~~\sigma _{I} = 0.16 \end{equation*}$$$$\begin{equation*} I = 4.31 \pm 0.15 + 1.99 \pm 0.18 \log \mathrm{ PGV} + 0.58 \pm 0.18 \log ^2 \mathrm{ PGV},~\sigma = 0.34,~~\sigma _{\mathrm{ PGV}} \\ = 0.31,~~\sigma _{I} = 0.15 \end{equation*}$$$$\begin{equation*} I = 2.77 \pm 0.15 + 0.68 \pm 0.03 \log ^2 \mathrm{ SA}(0.3),~\sigma = 0.31,~~\sigma _{\mathrm{ SA}(0.3)} = 0.28,~~\sigma _{I} = 0.14 \end{equation*}$$$$\begin{equation*} I = 3.00 \pm 0.28 + 0.91 \pm 0.55 \log \mathrm{ SA}(1.0) + 0.51 \pm 0.20 \log ^2 \mathrm{ SA}(1.0),~\sigma = 0.40,~~\sigma _{\mathrm{ SA}(1.0)} \\ = 0.38,~~\sigma _{I} = 0.14 \end{equation*}$$$$\begin{equation*} I = 4.04 \pm 0.20 + 1.63 \pm 0.19 \log \mathrm{ SA}(3.0) + 0.66 \pm 0.20 \log ^2 \mathrm{ SA}(3.0),~\sigma = 0.38,~~\sigma _{\mathrm{ SA}(3.0)} \\ = 0.35,~~\sigma _{I} = 0.14 \end{equation*}$$where PGA and SAs are expressed in cm s−2 and PGV is expressed in cm s−1. Tests performed to assess the robustness and the accuracy of the results demonstrate that adoption of quadratic relationships for this regression problem is a suitable choice within the range of values of the available data set. Comparison with similar published regressions for Italy evidences that the proposed relations provide statistically significant improved fits to the data. The new relations are also tested by inserting them in the ShakeMap system of the Italian configuration evidencing a significant improvement when compared to those implemented.

Ground motion models for shallow crustal and deep earthquakes in Hawaii and analyses of the 2018 M 6.9 Kalapana sequence

An expanded Pacific Earthquake Engineering Research (PEER) Center Next Generation Attenuation Phase 2 (NGA-West2) ground motion database, compiled using shallow crustal earthquakes in active crustal regions (ACRs), was used to develop the closed-form GS24b backbone ground motion model (GMM) for the RotD50 horizontal components of peak ground acceleration (PGA), peak ground velocity (PGV), and 5% damped elastic pseudo-absolute response spectral accelerations (SA). The GS24b model is applicable to earthquakes with moment magnitudes of 4.0 ≤ M ≤ 8.5, at rupture distances of 0 ≤ Rrup ≤ 400 km, with time-averaged S-wave velocity in the upper 30 m of the profile at 150 ≤ VS30 ≤ 1500 m/s, and for periods of 0.01 ≤ T ≤ 10 s. The new backbone model includes VS30 site correction developed based on multiple representative S-wave velocity profiles. For crustal wave attenuation, we used the apparent anelastic attenuation of SA—QSA (f, M). In contrast to the GK17, the GS24b backbone is a generic ACR model designed specifically to be adjusted to any ACRs. The GS24bc is an example of a partially non-ergodic model created by adjusting the backbone GS24b model for magnitude M, S-wave velocity VS30, and fault rupture distance residuals.

The critical intensity of earthquake ground motion which separates liquefiable to non-liquefiable conditions is investigated. The peak ground acceleration and velocity are calculated at about 130 liquefied and non-liquefied sites during 19 Japanese earthquakes. These sites are on natural levee, river channel, reclaimed land or drained land, and have high liquefaction susceptibility. In the calculation, the effects of fault rupture and local site condition are considered, to obtain more accurate results than those in previous studies. The results of the calculation indicate that (1) the occurrence of soil liquefaction is better correlated with the peak ground velocity than with the peak ground acceleration, (2) soil liquefaction is likely to occur for the ground with high liquefaction susceptibility, when the peak ground velocity exceeds 15 kines (cm/s), and (3) the degree of soil liquefaction shows no clear correlation with peak ground velocity or acceleration.

Correlations of spectral accelerations in the Chilean subduction zone

Relationships between Peak Ground Acceleration, Peak Ground Velocity, and Modified Mercalli Intensity in California

Values for peak ground acceleration and peak ground velocity using in seismic hazard assessment for Song Tranh 2 hydropower region

We have taken advantage of the great collection of ground-motion acceleration records from the Central Weather Bureau of Taiwan to derive new attenuation relations corresponding to different geological settings: the shallow crustal earthquakes in the active tectonic region and the subduction zone. The new equations use a shape of magnitude dependence modulated by depth effect. For shallow crustal earthquakes, the focal depth also plays an adjusting factor for the geometrical spreading. A two-step stratified regression is used to decouple the evaluations of the distance dependence of data from that of magnitude and focal depth. The resultant attenuation relations are as follows. Using the data from shallow crustal earthquakes, we obtained: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\begin{array}{l}\mathrm{ln}{ }A=2.8096+0.8993\mathbf{M}-0.4381{ }\mathrm{ln}{ }D\_{\mathrm{p}}-(1.0954-0.0079D\_{\mathrm{p}}){ }\mathrm{ln}{ }D_{\mathrm{e}},\\{\sigma}=0.60.\end{array}\] \end{document} Using the data from the subducting-plate earthquakes, we obtained: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathrm{ln}{ }A=4.7141+0.8468\mathbf{M}-0.1745{ }\mathrm{ln}{ }D\_{\mathrm{p}}-1.2972{ }\mathrm{ln}{ }D\_{\mathrm{h}},{\sigma}=0.56,\] \end{document} where A is the ground-motion acceleration in gal (cm/sec2), D e and D h are the epicentral and the hypocentral distances (km), respectively, D p is the focal depth (km), M is the moment magnitude, and σ the standard deviation. Several comparisons between our resulting attenuation relations and the others are presented in this study. Compared with other empirical attenuation models of Taiwan, our results show a better fit for the Chi-Chi earthquake. These new attenuation laws predict a stronger ground motion in the far distance for the shallow crustal earthquakes as compared with previous studies. Our results also show lower ground motions than the other countries for subduction zone events. The residual ground-motion maps show a high consistency with the local geology of Taiwan. Manuscript received 31 October 2000.

Response spectral attenuation relations for shallow crustal earthquakes in Taiwan

The true performance of ground-motion prediction equations is often not fully appreciated until they are used in practice for seismic hazard analyses and applied to a wide range of scenarios and exceedance levels. This has been the case for equations published recently for the prediction of peak ground velocity (PGV), peak ground acceleration (PGA), and response spectral ordinates in Europe, the Middle East, and the Mediterranean (Akkar and Bommer 2007a,b). This paper presents an update that corrects the shortcomings identified in those equations, which are primarily, but not exclusively, related to the model for the ground-motion variability. Strong-motion recording networks in Europe and the Middle East were first installed much later than in the United States and Japan but have grown considerably over the last four decades. The databanks of strong-motion data have grown in parallel with the accelerograph networks, and in addition to national collections there have been concerted efforts over more than two decades to develop and maintain a European database of associated metadata ( e.g. , Ambraseys et al. 2004). As the database of strong-motion records from Europe, the Mediterranean region, and the Middle East has expanded, there have been two distinct trends in terms of developing empirical ground-motion prediction equations (GMPEs): equations derived from a large dataset covering several countries, generally of moderate-to-high seismicity; and equations derived from local databanks for application within national borders. We refer to the former as pan-European models, noting that this is for expedience since the equations are really derived for southern Europe, the Maghreb (North Africa), and the active areas of the Middle East. The history of the development of both pan-European and national equations is discussed by Bommer et al. (2010), who also review studies that consider the arguments for and against the existence of consistent regional …

A set of new empirical relationships between modified Mercalli intensity (MMI) and synthetic peak ground acceleration (PGA) is developed for shallow crustal earthquakes in central and north-west Mexico. Few strong-motion recordings of shallow crustal earthquakes in these regions have led to uncertainties in estimating seismic risk even though they comprise some of the most densely populated urban sites in the country. We present relationships in which MMI is a function of PGA and its inverse form. No relationship for this type of events has been developed, although these earthquakes represent a high-risk potential for nearby highly populated urban regions. Ground motion data from 18 moderate-to-large earthquakes (4.5 < M W < 7.5) that took place in the Basin and Range, Sierra Madre Oriental Fold-thrust belt, and Trans-Mexican Volcanic Belt provinces and the corresponding 531 MMI information reports were employed. Synthetic PGA data were generated using the finite-fault stochastic method, assuming different rupture scenarios to extend the limitations of the dataset. Linear and bilinear regression techniques were used, considering a binning averaging procedure and the whole dataset, respectively. As the first approach, a set of MMI predictive equations independent of moment magnitude ( M W ) and hypocentral distance ( R ) was derived. Despite weak dependencies of the residuals on M W and R terms, we also developed complementary predictive relationships that include these parameters as independent variables. The conversion equations between PGA and MMI, including all terms, show slightly less variability than simple linear equations in predicting intensity values. The proposed predictive equations are consistent with similar relationships in other regions of the world. The discrepancies among the different relationships may reflect variations in input data, particularly concerning the macroseismic intensity assignments, which are inherently subjective, and the tectonic regime. The conversion relationships that we have developed can be used to generate maps of estimated shaking intensities based on ground motion observations for crustal earthquakes in Mexico.

In the current study, ground motion models (GMMs) are derived using the European Strong Motion (ESM) database for pseudo‐spectral acceleration (PSA), peak ground acceleration (PGA), peak ground velocity (PGV), peak ground displacement (PGD), cumulative absolute velocity (CAV), arias intensity (Ia), and significant duration. In addition to addressing random effects associated with ground motion regression, such as inter‐event, inter‐site, inter‐locality, and inter‐region variabilities, the current study also aims at reducing the standard deviations (STDs) of the GMMs through development of a hybrid non‐parametric GMM. The hybrid model is derived through an ensemble‐weighted method of five non‐parametric machine learning models: shallow neural network, deep neural network (DNN), gated recurrent unit (GRU), support vector, and random forest (RF) regression techniques; with weights based on model performances. The resulting hybrid model, which also accounts for epistemic uncertainty, is compared against other regional models and is found superior for all output variables. The inter‐event, inter‐site, inter‐locality, and inter‐region deviations, and total ergodic sigma of PSA for the ensemble model lies between 0.3164–0.4478, 0.4156–0.5339, 0.1449–0.3687, 0.0819–0.2421, and 0.668–0.8545, respectively. The coefficient of determination (R2) between predicted and recorded values lies between 0.8435–0.9114 for all the output variables.