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The Geldingadalir and Meradalir eruptions at Mt. Fagradalsfjall in the Reykjanes Peninsula on 19 March 2021 and 3 August 2022, respectively, were preceded by intense volcano-tectonic swarms. Eight earthquakes with M ≥ 5 were recorded by the Icelandic Strong Motion Network. We present an overview of the seismicity in Fagradalsfjall, and salient features of the strong ground motion caused by the swarms in the epicentral area. The largest recorded horizontal Peak Ground Acceleration (PGA) was ~ 0.45g at Grindavík, which is the strongest PGA recorded in Iceland since the MW6.3 2008 Ölfus Earthquake. Recorded waveforms show a rich long-period energy content, with a burst of higher frequencies at the beginning of shaking. This leads to larger response spectral accelerations at long periods that those from typical shallow crustal earthquakes. Moreover, an empirical mixed-effects ground motion model for PGA was calibrated based on the available recordings. The attenuation rate of PGA from this model is similar to that introduced by Lanzano and Luzi (2020) which is based on data from volcanic events in Italy, but the magnitude scaling of our model is much lower. The overall results indicate that scaling and attenuation of ground motion from volcanic events and purely tectonic earthquakes in Iceland are likely very different. This is an important observation because seismic hazard in parts of the Reykjavik area and of the central highlands, where important hydroelectric power plants are located, could potentially be dominated by events of volcanic origin. Therefore, it is important to take these observations into account for seismic hazard and risk assessment in Iceland.

Ground motion selection is one of the most important phases in the derivation of fragility curves through non-linear dynamic analyses. In this context, an easy-to-use software, namely S&M—Select & Match, has been adopted for the selection and spectral matching of recorded ground motions approaching a target response spectrum in a broad period range. In this paper, after a brief description of the key features of the S&M tool, two sets of 125 accelerograms, separately for stiff (i.e. site classes A and B according to the Italian code) and soft soil (i.e. site classes C and D) conditions, have been selected on the basis of the elastic design spectra of the Italian seismic code defined for different return periods. The selected ground motions have been analysed and used for non-linear dynamic analysis of a case study representative of a common Italian RC building type designed only to gravity loads. Results have been analysed in order to check the capability of the considered signals to adequately cover all the damage levels generally adopted in seismic risk analyses, as well as the effects on seismic response due to the selection criteria permitted by the proposed tool.

This article introduces a strong-motion dataset of near-source broadband earthquake ground motions from 3D physics-based numerical simulations—named BB-SPEEDset—obtained by the code SPEED (SPectral Elements in Elastodynamics with Discontinuous Galerkin)—developed at Politecnico di Milano, Italy. Taking advantage of the earthquake ground-motion scenarios produced so far by SPEED, in most cases validated against earthquake recordings, the main objective of this work is to construct and validate a dataset of simulated broadband waveforms to be used as a support for characterization and modeling of near-source earthquake ground motions. To pursue this objective, the following steps were necessary, namely: (1) the implementation of an effective workflow suitable to process in an homogeneous format various SPEED simulations; (2) the generation of broadband time histories using a technique based on artificial neural networks, trained on strong-motion records; (3) the creation of a flat file collecting, for each simulated scenario, the most relevant metadata (fault rupture scenario, site response proxies, source-to-site distances) as well as a comprehensive set of ground-motion intensity measures of the processed broadband waveforms (peak ground acceleration, velocity and displacement, spectral ordinates, duration, pulse period, etc.). Finally, a comprehensive set of consistency checks is made to verify the absence of any systematic bias in the trend of the BB-SPEEDset results with respect to the NEar-Source Strong-motion (NESS) version 2.0 near-source recorded ground-motion dataset. Indeed, the main features of near-source ground motion in BB-SPEEDset, ranging from the statistical distributions of peak and integral measures both at short and long periods, the ground-motion attenuation with distance, to the features of impulsive ground motions and directionality effects, are in substantial agreement with those from NESS.

In this paper, a comprehensive validation exercise of 3D physics-based numerical simulations (PBS) of seismic wave propagation is presented for a low-to-moderate seismicity area in the south east of France, within the Rhône River Valley, that hosts several operating nuclear installations. This area was hit on Nov 11, 2019, by an unusually damaging Mw 4.9 earthquake (Le Teil event). The numerical code SPEED (http://speed.mox.polimi.it/), developed at Politecnico di Milano, Italy, was used to validate the simulations against the available recordings. When comparing simulations with records, a good to excellent agreement was found up to 8–10 Hz, showing that, even without a very detailed 3D numerical model of the medium, the PBS may provide realistic broadband predictions of earthquake ground motion. This also demonstrates that PBS, if suitably calibrated and validated, may be either an alternative or a useful complement to empirical ground motion models. Referring to the seismic risk evaluation of strategic and critical structures, infrastructures and industrial plants, such as nuclear power plants, the failure of which during an earthquake may endanger safety of population and cause environmental disasters, the 3D PBS may throw light on region- and site-specific features of ground shaking, especially in near-source conditions, that are typically poorly constrained in empirical models.

This paper explores and validates the use of ground shaking scenarios generated via 3D physics-based numerical simulations (PBS) for seismic fragility studies. The 2009 L’Aquila seismic event is selected as case-study application, given the availability of a robust and exhaustive post-earthquake database, gathering observed seismic damages detected on several building typologies representative of the Italian built environment, and of a validated numerical model for PBS ground shaking scenarios. Empirical fragility curves are derived as a function of different seismic intensity measures, by taking advantage of an improved statistical technique, overcoming possible uncertainties in the resulting estimates entailed by data aggregation. PBS-based fragility functions are compared to the corresponding sets of curves relying on updated ShakeMaps. The predictive capability of the adopted simulation strategies is then verified in terms of seismic damage scenarios, by respectively coupling PBS- and ShakeMap-based fragility models with the corresponding ground shaking scenarios. Comparison of observed and predicted damage distributions highlights the suitability of PBS for region-specific seismic vulnerability and risk applications.

In this paper we describe a mathematical and numerical approach that combines physics-based simulated ground motion caused by earthquakes with fragility functions to model the structural damages induced to buildings. To simulate earthquake ground motion we use the discontinuous Galerkin spectral element method to solve a three-dimensional differential model at regional scale describing the propagation of seismic waves through the earth layers up to the surface. Selected intensity measures, retrieved from the synthetic time histories, are then employed as input for a vulnerability model based on fragility functions, in order to predict building damage scenarios at urban scale. The main features and effectiveness of the proposed numerical approach are tested on the Beijing metropolitan area.

With the aim of evaluating the effect of spatial variability of recorded ground motions on spatially extended structures, we present a numerical study on the linear and nonlinear response of an ide...

We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the exibility of discontinuous Galerkin meth-ods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the compu-tational costs. The theoretical properties of the semidiscrete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. Here space dis-cretization is obtained based on employing the leap-frog time marching scheme. The capabilities of the present approach are demonstrated through a set of computations of realistic earthquake scenar-ios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering.

The main aim of this work is to present a prototype of seismic risk assessment study at urban scale which incorporates next generation tools for hazard assessment, with application to the city of Thessaloniki, Northern Greece. The key ingredient of the proposed approach is the characterization of earthquake ground motion by means of three-dimensional broadband physics-based numerical simulations, which explicitly account for the fault rupture, the propagation path in heterogeneous media and complex geological conditions. The seismic damage of contemporary reinforced concrete building stock of the city of Thessaloniki has been evaluated using the capacity spectrum method, for a scenario corresponding to the destructive historical earthquake of June 20th 1978 (MW 6.5). Although the vulnerability model considered in these analyses reflects the contemporary building stock and, hence, differs from the situation at the time of the earthquake, the soundness of our damage estimates has been successfully verified through the comparison with the post-1978 earthquake damage observations. Results of this study demonstrate that 3D physics-based simulations can provide a more accurate and detailed characterization of earthquake ground motion and of its spatial variability, as compared to standard empirical approaches, and can be effectively used to improve seismic risk studies for strategic urban areas.

In this article the seismic site response of the Norcia basin, Central Italy, has been analyzed using both 1D and 2D ground response numerical models. Period-dependent aggravation factors (PDAFs) quantifying the difference between 2D and 1D site response are provided for two representative cross-sections of the basin. Time-domain linear visco-elastic and non-linear analyses were carried out by the finite difference commercial program FLAC2D. For the former, the PDAFs were computed using a suite of representative ground motion records. Although the basin sediments are constituted by rather stiff soils, the Norcia basin is found to produce a consistent modification and enhancement of ground motion. It is found that the most important source of ground motion aggravation was the generation of Rayleigh waves at the basin edges. The variability of the PDAFs was explored by considering the effects of frequency content of input motion, damping ratio, irregularity of the alluvial-bedrock interface. The effect of the non-linear response of the sediments on the PDAFs was also addressed with reference to the Mw 5 October 30, 2016 event.

Summary In the framework of the revision of Part 1 of Eurocode 8, this study aims at developing new empirical correlations to compute peak values of ground velocity (PGV) and displacement (PGD) as a function of elastic spectral ordinates for design. At variance with the expressions for PGV and PGD currently adopted in the Eurocode 8, based solely on the peak ground acceleration (PGA), in this paper reference is made to spectral ordinates of the short and intermediate period range, namely Ss, which is the constant acceleration spectral ordinate, and S1, which is the spectral ordinate at 1 s. On the one hand, a relationship between PGV and the product (Ss⋅S1) was found based on the regression analysis on a high-quality strong-motion dataset. On the other hand, the PGD was estimated by extrapolating to long periods the constant displacement branch of the elastic response spectrum, introducing a correlation between the corner period TD and S1. For this purpose, results of a long period probabilistic seismic hazard assessment study for Italy, encompassing low to high seismicity areas, were considered. Furthermore, verification of the proposed relationship against strong-motion records was carried out, and differences justified in terms of the concept of uniform hazard spectrum.

The Gubbio basin in Central Italy is a intermountain basin of extensional tectonic origin, typical of Central and Southern Apennines, characterized by moderate seismicity. The strongest recorded event within the area is a magnitude 5.7 earthquake which occurred on 29 April 1984 along the Gubbio fault, bordering the eastern side of the basin. The main objective of this study is to analyze the features of earthquake ground motion as related to basin-edge effects, by performing physics-based numerical simulations of the 1984 earthquake through a high-performance spectral element code. The simulated ground motions are found in reasonable agreement with the recorded motions when using the kinematic source model developed by Ameri et al. (Bull Seismol Soc Am 99:647–663, 2009), with a rise-time equal to 1 s and a nucleation point located in the middle of the fault. Pronounced differences were noted between records from the basin and adjacent sites at outcropping bedrock, owing to both the strong impedance contrast between soft alluvial sites and bedrock formations (lithostratigraphic amplification), as well as lateral discontinuities related to the 2D/3D geometry of the basin (generation of surface waves). Since the fault was located beneath the basin, 1D amplification effects were found to be more relevant than those associated with the generation of surface waves from the basin edge. Finally, an envelope delay spectrum was computed for the simulated ground motions, showing that surface waves are excited in the frequency band of 0.2–0.8 Hz with a significant increase of ground motion duration within the basin.

In this article, a novel strategy to generate broadband earthquake ground motions from the results of 3D physics-based numerical simulations (PBSs) is presented. Physics-based simulated ground motions embody a rigorous seismic-wave propagation model (i.e., including source, path, and site effects), which is however reliable only in the long-period range (typically above 0.75–1 s), owing to the limitations posed both by computational constraints and by insufficient knowledge of the medium at short wavelengths. To cope with these limitations, the proposed approach makes use of Artificial Neural Networks (ANNs), trained on a set of strong-motion records, to predict the response spectral ordinates at short periods. The essence of the procedure is, first, to use the trained ANN to estimate the short-period response spectral ordinates using as input the long-period ones obtained by the PBS, and, then, to enrich the PBS time histories at short periods by scaling iteratively their Fourier spectrum, with no phase change, until their response spectrum matches the ANN target spectrum. After several validation checks of the accuracy of the ANN predictions, the case study of the 29 May 2012 Mw 6.0 Po Plain earthquake is illustrated as a comprehensive example of application of the proposed procedure. The capability of the proposed approach to reproduce in a realistic way the engineering features of earthquake ground motion, including the peak values and their spatial correlation structure, is successfully proven.

In this paper, an overview is presented to motivate the use of 3D physics-based numerical simulations of seismic wave propagation to support enhanced Probabilistic Seismic Hazard Assessment. With reference to the case study of Istanbul, we introduce the activities required to construct a numerical model of the surface geology and topography and to determine the input conditions to trigger future earthquakes in a physically sound way. Owing to the intrinsic frequency limitations of the numerical simulations, a post-processing technique to produce realistic broadband waveforms is introduced, allowing to correlate short-period to long-period spectral ordinates from an Artificial Neural Network. Finally, the results obtained in Istanbul from numerous physics-based ground motion scenarios of M7+ earthquakes allow us to throw light on the potential added value to PSHA of the 3D numerical simulations. Namely, to provide locally constrained probabilistic distributions of ground motion intensity measures, matching the actual footprint of a large earthquake in the specific area under study.

In this study earthquake ground motion in the Thessaloniki urban area is evaluated using a 3D spectral element numerical approach. The availability of detailed geotechnical/geophysical data from past microzonation studies together with the seismological information regarding the relevant fault sources allowed for the creation of a large-scale 3D numerical model. The latter is suitable for generating finite-fault physics-based ground shaking scenarios within the city of Thessaloniki up to maximum frequencies of about 1.5 Hz. As a representative case study, the simulation of the historical MW 6.5 June 20th 1978 Volvi earthquake is addressed. The results show that reasonable estimates can be obtained in terms both of ground motion time histories at the only available strong motion station and of spatial distribution of peak ground motion parameters, as compared to the regional map of macroseismic intensity and to the predictions of attenuation laws. The numerical model is, then, used to provide insights into 3D site effects occurring in the city of Thessaloniki, by showing the comparison between synthetic and experimental Standard Spectral Ratios (SSR) as well as the effect of non-linear visco-elastic soil behavior and the spatial variability of amplification factors with respect to outcrop bedrock basement. The results of this study demonstrate the potentialities of 3D physics-based numerical modeling for deterministic-based seismic hazard assessment studies in large urban areas characterized by complex geological configurations, such as the Thessaloniki area.

SUMMARY This work presents a new high performance open-source numerical code, namely SPectral Elements in Elastodynamics with Discontinuous Galerkin, to approach seismic wave propagation analysis in visco-elastic heterogeneous three-dimensional media on both local and regional scale. Based on non-conforming high-order techniques, such as the discontinuous Galerkin spectral approximation, along with efficient and scalable algorithms, the code allows one to deal with a non-uniform polynomial degree distribution as well as a locally varying mesh size. Validation benchmarks are illustrated to check the accuracy, stability, and performance features of the parallel kernel, whereas illustrative examples are discussed to highlight the engineering applications of the method. The proposed method turns out to be particularly useful for a variety of earthquake engineering problems, such as modeling of dynamic soil structure and site-city interaction effects, where accounting for multiscale wave propagation phenomena as well as sharp discontinuities in mechanical properties of the media is crucial. Copyright © 2013 John Wiley & Sons, Ltd.

A numerical study on the 2009 M w 6.3 L’Aquila earthquake is here presented using a high‐performance spectral element (SE) code to clarify the issues regarding the generation of physics‐based deterministic ground‐motion scenarios in near‐fault conditions and over a broad range of frequencies. Numerical simulations provide reliable ground‐motion scenarios up to about 2.5 Hz in the epicentral region of the L’Aquila earthquake, as confirmed by the good agreement between the simulated peak ground velocity (PGV) wave field and the observed distribution of damage. Moreover, the synthetic waveforms fit reasonably well the strong‐motion recordings within the town of L’Aquila and the surrounding areas. Nevertheless, some discrepancies are found in the upper Aterno Valley, associated to a considerable extent with the details of the rupture process. Improvements on the source modeling are obtained through the definition of stochastically (but realistically) varying kinematic source parameters that may play a relevant role in propagating high‐frequency (HF) components of ground motion, poorly controlled by numerical approaches. Finally, the proposed hybrid scheme to generate broadband (BB) synthetic waveforms, by combining the low‐frequency (LF) synthetics from SE simulations ( f

Αντικείμενο της παρούσας μελέτης είναι η αριθμητική προσομοίωση της σεισμικής εδαφικής κίνησης στην αστική περιοχή της Θεσσαλονίκης με τη χρήση της μεθόδου των φασματικών στοιχείων. Η διαθεσιμότητα λεπτομερών γεωτεχνικών γεωφυσικών δεδομένων, καθώς και σεισμολογικών πληροφοριών για τα ρήγματα που επηρεάζουν την περιοχή, μας επέτρεψε την κατασκευή ενός τρισδιάστατου αριθμητικού προσομοιώματος μεγάλης κλίμακας, κατάλληλου για την παραγωγή σεναρίων εδαφικής κίνησης για την πόλη της Θεσσαλονίκης και για μέγιστη συχνότητα 2 Hz. Στη μελέτη αυτή παρουσιάζονται αποτελέσματα της αριθμητικής προσομοίωσης του καταστροφικού σεισμού της Βόλβης του 1978, μεγέθους Mw6.5, καταδεικνύοντας τη δυνατότητα επίτευξης ρεαλιστικών εκτιμήσεων. Τέλος, χρησιμοποιούνται χάρτες εδαφικής ταλάντωσης σε όρους παραμέτρων εδαφικής κίνησης όπως PGV για τη μελέτη των κύριων φαινομένων διάδοσης σεισμικών κυμάτων σε μεγάλη κλίμακα., This study aims at showing the numerical modelling of earthquake ground motion in the Thessaloniki urban area, using a 3D spectral element approach. The availability of detailed geotechnical/geophysical data together with the seismological information regarding the relevant fault sources allowed us to construct a large-scale 3D numerical model suitable for generating physics based ground shaking scenarios within the city of Thessaloniki up to maximum frequencies of about 2 Hz. Results of the numerical simulation of the destructive MW6.5 1978 Volvi earthquake are addressed, showing that realistic estimates can be obtained. Shaking maps in terms of ground motion parameters such as PGV are used to discuss the main seismic wave propagation effects at a wide scale.

The vertical spectral shape suggested by the main offshore codes does not reflect actual earthquake behavior. The problem is exacerbated in time history analysis, as the incorrect spectral shape leads to unrealistic scaling of records. Vertical spectra from codes are compared to published measurements from offshore sites and the results of numerical modeling. The effects of the water column and the mismatch between code spectra and real time histories are illustrated. Results of the spectral matching show that the vertical spectral shape defined by offshore codes leads to over conservative vertical time histories at short periods.Often vertical response is expressed as a fraction of the horizontal spectral acceleration at the same frequency (V/H ratio). Current practice regarding V/H is reviewed, considering design codes and recent research. Conventional V/H ratios are compared to sea bottom measurements by Boore and Smith (1999) which highlight the peculiarities of offshore sites. A relatively simple numerical analysis of vertically propagating compressive waves is used to evaluate vertical amplification and the effect of the water column for a case history.Current practice shows a certain degree of variability among the codes/papers. For onshore sites, there is consensus that V/H>1 at low periods but that vertical is less than horizontal at long periods. Boore and Smith's seafloor recordings suggest that offshore motions have very low vertical motion compared to onshore conditions, especially at low periods. The numerical modeling shows that the vertical response is mainly controlled by the water layer, which induces a strong deamplification at the resonance period of P waves within the water layer. Such an effect is in agreement with the findings of Boore and Smith (1999).The paper highlights the poor definition of the vertical seismic spectra for offshore sites in seismic codes and makes a first step towards the development of more reliable vertical spectra. The overconservatism induced by the code vertical spectra on definition of time histories is presented to stimulate future developments.

On 6 April 2009, 01:32:40 UTC, an Mw 6.3 earthquake occurred in the Abruzzo region (central Italy), close to L'Aquila, a town of 68,500 inhabitants. About 300 people died because of the collapse of many residential and public buildings, and damage was widespread in L'Aquila and its neighboring municipalities. The earthquake occurred at 9.5 km depth along a NW-SW normal fault with SW dip, located below the city of L'Aquila (Istituto Nazionale di Geofisica e Vulcanologia [INGV] 2009a). The maximum observed intensity is IX–X in the MCS scale and the most relevant damages are distributed in the NW-SE direction, with evident predominance toward the southeast (Istituto Nazionale di Geofisica e Vulcanologia 2009b). This event represents the third largest earthquake recorded by strong-motion instruments in Italy, after the 1980 Mw 6.9 Irpinia and the 1976 Mw 6.4 Friuli earthquakes (Luzi et al. 2008). The mainshock was followed by seven aftershocks of moment magnitude larger than or equal to 5, the two strongest of which occurred on April 7 ( Mw = 5.6) and April 9 ( Mw = 5.4). The mainshock and its aftershocks have been recorded by several digital stations of the Italian strong-motion network (Rete Accelerometrica Nazionale, RAN), operated by the Italian Department of Civil Protection (DPC); by the Italian seismometric network (Rete Sismometrica Nazionale, operated by INGV-Centro Nazionale Terremoti (CNT); http://cnt.rm.ingv.it); and by a temporary strong-motion array installed by the INGV Sezione di Milano-Pavia (MI-PV; http://www.mi.ingv.it). A total of 56 three-component strong-motion recordings were obtained within 280 km for the mainshock, with 23 being within 100 km of the epicenter. Horizontal peak ground motions in the near-fault region range from 327 to 646 cm/sec2, the latter representing one of the highest values recorded in Italy. This strong-motion data set, consisting of …

The increasing interest in performance-based earthquake engineering has promoted research on the improvement of hazard-consistent seismic input definition and on advanced criteria for strong motion record selection to perform nonlinear time history analyses. Within the ongoing research activities to improve the representation of seismic actions and to develop tools as a support for engineering practice, this study addresses the selection of displacement-spectrum-compatible real ground motions, with special reference to Italy. This involved (1) the definition of specific target displacement spectra for Italian sites, constrained—both at long and short periods—by results of probabilistic seismic hazard analyses; (2) the compilation of a high-quality strong ground motion database; and (3) the development of a software tool for computer-aided displacement-based record selection. Application examples show that sets of unscaled, or lightly scaled, accelerograms with limited record-to-record spectral variability can also easily be obtained when a broadband spectral compatibility is required.

With the ongoing progress of computing power made available not only by large supercomputer facilities but also by relatively common workstations and desktops, physics-based source-to-site 3D numerical simulations of seismic ground motion will likely become the leading and most reliable tool to construct ground shaking scenarios from future earthquakes. This paper aims at providing an overview of recent progress on this subject, by taking advantage of the experience gained during a recent research contract between Politecnico di Milano, Italy, and Munich RE, Germany, with the objective to construct ground shaking scenarios from hypothetical earthquakes in large urban areas worldwide. Within this contract, the SPEED computer code was developed, based on a spectral element formulation enhanced by the Discontinuous Galerkin approach to treat non-conforming meshes. After illustrating the SPEED code, different case studies are overviewed, while the construction of shaking scenarios in the Po river Plain, Italy, is considered in more detail. Referring, in fact, to this case study, the comparison with strong motion records allows one to derive some interesting considerations on the pros and on the present limitations of such approach.

Almost six months after the MW 7.1 Darfield (Canterbury) earthquake, on 22 February 2011 at 12:51 p.m. (local time), an MW 6.2 earthquake struck the city and suburbs of Christchurch—the largest city on the South Island of New Zealand, with about 400,000 inhabitants. The Christchurch earthquake can be considered one of the greatest natural disasters recorded in New Zealand. The death toll was more than 180, with around 2,000 people injured, and structures already weakened by the Darfield event and its aftershocks were badly affected (Cubrinovski and Green 2010; Tonkin and Taylor Ltd. 2010; Kam et al. 2011). The earthquake was generated by an oblique thrust fault located between the Australian and Pacific plates, within about 6 km of the city center. It is worth recalling that prior to the Darfield event there was no surface evidence of the fault that generated the Christchurch earthquake on February 2011, nor of the Greendale fault, recognized as responsible for the September 2010 earthquake (Quigley et al. 2010). During the last decade a set of seismic surveys across the Canterbury Plains had been carried out (Green et al. 2010), but they did not reveal any convincing evidence of the Greendale fault and there was no clear indication that a major earthquake was imminent in this particular region. Beyond the effects and the consequences of the seismic event, the attention of the scientific community was drawn to two aspects that had a primary role in the Christchurch earthquake: 1) the extremely severe, strong ground shaking observed, especially on the vertical component; and 2) the widespread liquefaction phenomena across the city (Cubrinovski and Green 2010; Green et al. 2011, page 927 of this issue). Between September 2010 and June 2011 the Canterbury area experienced three major earthquakes with M …

During the nineteenth and twentieth centuries observational seismologists recorded primarily the earthquake-induced translational wave field, while the rotational motion still remains poorly observed and investigated. We aim to further understand the rotational ground motion and its relation to the translational wave field, with a special emphasis on the near field, a few wavelengths away from the hypocenter, where damage related to rotational motion might need to be considered. A broad picture of the available values of rotational amplitudes and their variability is obtained by gathering most of the published data on strong rotational motion. To obtain a more detailed picture we perform a large scale 3D numerical study of a strike-slip event in the Grenoble valley where a combination of topographic, source, and site effects produces a realistic wave field. We analyzed the synthetic dataset in terms of the rotational and translational peak amplitudes and their dependence on two effects: nonlinear soil behavior and source directivity. On a soft soil deposit, we observe peak ground rotation of 1 mrad and the peak ground rotation rate of 10 mrad/sec, for an Mw 6.0 event. Those values show a strong dependence on the hypocenter location, the local site conditions, and the topographical features, inducing a variability of almost one order of magnitude in a range of distances of 20 km. Finally, we compare our numerical results in terms of peak ground velocity (PGV) versus peak ground rotation (PGω) with field data obtained at similar scenarios (e.g., Parkfield) by array techniques to investigate the relation between translational and rotational amplitudes expected in the near field for shallow, medium-sized earthquakes. Results of our numerical simulation fit reasonably well with those observed in past studies. Furthermore, the spatial variations of the PGV/PGω ratio show a trend, which is correlated with the velocity structure of the model under study

Stimulated by the lack of direct measurements of earthquake-induced ground rotations, a set of experimental and numerical results on rotational ground motion is illustrated. The results cover a relatively broad range of magnitude (4–6.5), and regard both far field and near source conditions. Experimentally, results are derived through a suitable spatial interpolation procedure of displacement records collected from two dense arrays, Parkway Valley (New Zealand) and UPSAR (California). Validation checks both with other array-derived methods and with numerical simulations are carried out, to verify the reliability of our estimations and the capability of numerical wave propagation analysis codes to provide realistic estimates of rotational ground motions over a reasonable frequency band. Peak Ground Velocity (PGV) and Peak Ground Rotation (PGR) values obtained via the spatial interpolation procedure over dense seismic arrays are then put in comparison with the numerical results computed along two representa...

A theoretical approach is presented to study the antiplane seismic response of underground structures, subjected to the incidence of both plane and cylindrical waves. The structure is assumed to be a circular inclusion embedded in a homogenous, isotropic and linear visco-elastic halfspace. The inclusion may consist either of a cavity, with or without a ring-shaped boundary, or it may be filled in with a linear-elastic material, without loss of generality. The analytical solution is obtained using expansions of wave functions in terms of Bessel and Hankel functions, relying on the technique of images and the use of Graf's addition theorem to enforce the boundary conditions. The effects of underground cavities on surface earthquake ground motion are studied as a function of the size of the cavity, its embedment depth, the frequency content of the excitation, the incidence angle and the distance from the axis of symmetry of the cavity itself. A simple application of Rayleigh's method allows us to verify that the ground surface response is dominated by the fundamental vibration mode of the portion of soil between the cavity and ground surface itself, in the frequency range of interest for engineering purposes. A simple relationship to estimate the fundamental natural frequency as a function of the embedment depth of the cavity is given. Finally, amplification factors on response spectra are obtained, to provide a practical insight into the effect of an underground cavity on surface ground motion during real earthquakes. Copyright © 2009 John Wiley & Sons, Ltd.

The surface displacement field along a topographical profile of an elastic half-space subjected to the incidence of elastic waves can be computed using different numerical methods. The method of fundamental solutions (MFS) is one of such tech- niques in which the diffracted field is constructed by means of a representation in terms of the Green's functions for discrete forces located outside the domain of inter- est. From the enforcement of boundary conditions, such forces can be computed; thus, the ground motion can be calculated. One important advantage of MFS over boundary integral techniques is that singularities are avoided. The computation of ground- motion rotations implies the application of the rotational operator to the displacement field. This can be done using either numerical derivatives or analytical expressions to compute the rotational Green's tensor. We validate the method using exact analytical solutions in terms of both displacement and rotation, which are known for simple geometries. To demonstrate the accuracy for generic geometries, we compare results against those obtained using the spectral-element method. We compute surface rota- tions for incoming plane waves (P, SV, and Rayleigh) near a topographical profile. We point out the effects of topography on rotational ground motion in both frequency and time domains. Online Material: Analysis of the dependence of rotational motion on incident plane-wave frequency.