TY - JOUR A1 - Mayor, Jessie A1 - Bora, Sanjay Singh A1 - Cotton, Fabrice Pierre T1 - Capturing regional variations of hard‐rock κ0 from coda analysis JF - The bulletin of the Seismological Society of America : BSSA N2 - We propose an alternative procedure for the capture of the hard‐rock regional kappa (⁠κ0ref⁠). In our approach, we make use of a potential link between the well‐known κ parameter and the properties of coda waves. In our analysis, we consider near‐distance records of four crustal earthquakes of local magnitude 3.7–4.9 that occurred in four regions of France in different geological contexts: the crystalline axial chain of Pyrenees to the southwest, the large sedimentary basin to the southeast, the Alpine range to the east, and the extensional Rhine graben to the northeast. Each earthquake has been recorded at a pair of nearby soft‐ and hard‐rock station sites. The high‐frequency (16–32 Hz) spectral amplitudes of the coda window (carefully selected on the time series of the accelerograms) confirm an exponential decrease, which we quantify by κAHcoda and call “kappa of coda.” It is found that κAHcoda is independent of the soil type but shows significant regional variations. κ measurements (Anderson and Hough, 1984) over the coda window (⁠κAHcoda⁠) and full time series (⁠κAH⁠) show strong correlation at hard‐rock sites. This suggests that κAHcoda can provide a new proxy to estimate the regional hard rock κ0ref (Ktenidou et al., 2015). Theoretical analysis is also presented to relate the regional κAHcoda and coda quality factor Qc⁠, which quantifies the average attenuation properties of the crust (both scattering and absorption). It allows interpreting κAHcoda as the time spent by the waves in the medium, weighted by its attenuation properties. This theoretical analysis also shows that the classical κ measurement should be frequency dependent; this was confirmed by the spectra of the observed records. Y1 - 2018 U6 - https://doi.org/10.1785/0120170153 SN - 0037-1106 SN - 1943-3573 VL - 108 IS - 1 SP - 399 EP - 408 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Cotton, Fabrice Pierre A1 - Scherbaum, Frank T1 - NGA-West2 Empirical Fourier and Duration Models to Generate Adjustable Response Spectra JF - Earthquake spectra : the professional journal of the Earthquake Engineering Research Institute N2 - Adjustment of median ground motion prediction equations (GMPEs) from one region to another region is one of the major challenges within the current practice of seismic hazard analysis. In our approach of generating response spectra, we derive two separate empirical models for a) Fourier amplitude spectrum (FAS) and b) duration of ground motion. To calculate response spectra, the two models are combined within the random vibration theory (RVT) framework. The models are calibrated on recordings obtained from shallow crustal earthquakes in active tectonic regions. We use a subset of NGA-West2 database with M3.2-7.9 earthquakes at distances 0-300 km. The NGA-West2 database expanded over a wide magnitude and distance range facilitates a better constraint over derived models. A frequency-dependent duration model is derived to obtain adjustable response spectral ordinates. Excellent comparison of our approach with other NGA-West2 models implies that it can also be used as a stand-alone model. Y1 - 2019 U6 - https://doi.org/10.1193/110317EQS228M SN - 8755-2930 SN - 1944-8201 VL - 35 IS - 1 SP - 61 EP - 93 PB - Sage Publ. CY - Thousand Oaks ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Cotton, Fabrice Pierre A1 - Scherbaum, Frank A1 - Edwards, Benjamin A1 - Traversa, Paola T1 - Stochastic source, path and site attenuation parameters and associated variabilities for shallow crustal European earthquakes JF - Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering N2 - We have analyzed the recently developed pan-European strong motion database, RESORCE-2012: spectral parameters, such as stress drop (stress parameter, Delta sigma), anelastic attenuation (Q), near surface attenuation (kappa(0)) and site amplification have been estimated from observed strong motion recordings. The selected dataset exhibits a bilinear distance-dependent Q model with average kappa(0) value 0.0308 s. Strong regional variations in inelastic attenuation were also observed: frequency-independent Q(0) of 1462 and 601 were estimated for Turkish and Italian data respectively. Due to the strong coupling between Q and kappa(0), the regional variations in Q have strong impact on the estimation of near surface attenuation kappa(0). kappa(0) was estimated as 0.0457 and 0.0261 s for Turkey and Italy respectively. Furthermore, a detailed analysis of the variability in estimated kappa(0) revealed significant within-station variability. The linear site amplification factors were constrained from residual analysis at each station and site-class type. Using the regional Q(0) model and a site-class specific kappa(0), seismic moments (M-0) and source corner frequencies f (c) were estimated from the site corrected empirical Fourier spectra. Delta sigma did not exhibit magnitude dependence. The median Delta sigma value was obtained as 5.75 and 5.65 MPa from inverted and database magnitudes respectively. A comparison of response spectra from the stochastic model (derived herein) with that from (regional) ground motion prediction equations (GMPEs) suggests that the presented seismological parameters can be used to represent the corresponding seismological attributes of the regional GMPEs in a host-to-target adjustment framework. The analysis presented herein can be considered as an update of that undertaken for the previous Euro-Mediterranean strong motion database presented by Edwards and Fah (Geophys J Int 194(2):1190-1202, 2013a). KW - Stochastic model KW - Attenuation KW - Stress parameter KW - Kappa KW - Crustal earthquakes Y1 - 2017 U6 - https://doi.org/10.1007/s10518-017-0167-x SN - 1570-761X SN - 1573-1456 VL - 15 SP - 4531 EP - 4561 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Gianniotis, Nikolaos A1 - Schnoerr, Christoph A1 - Molkenthin, Christian A1 - Bora, Sanjay Singh T1 - Approximate variational inference based on a finite sample of Gaussian latent variables JF - Pattern Analysis & Applications N2 - Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lower bound is then optimised with respect to its free parameters, the so-called variational parameters. However, this is not always possible as for certain integrals it is very challenging (or tedious) to come up with a suitable lower bound. Here, we propose a simple scheme that overcomes some of the awkward cases where the usual variational treatment becomes difficult. The scheme relies on a rewriting of the lower bound on the model log-likelihood. We demonstrate the proposed scheme on a number of synthetic and real examples, as well as on a real geophysical model for which the standard variational approaches are inapplicable. KW - Bayesian inference KW - Posterior estimation KW - Expectation maximisation Y1 - 2016 U6 - https://doi.org/10.1007/s10044-015-0496-9 SN - 1433-7541 SN - 1433-755X VL - 19 SP - 475 EP - 485 PB - Springer CY - New York ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Scherbaum, Frank A1 - Kuehn, Nicolas A1 - Stafford, Peter T1 - On the Relationship between Fourier and Response Spectra: Implications for the Adjustment of Empirical Ground-Motion Prediction Equations (GMPEs) JF - Bulletin of the Seismological Society of America N2 - The functional form of empirical response spectral ground-motion prediction equations (GMPEs) is often derived using concepts borrowed from Fourier spectral modeling of ground motion. As these GMPEs are subsequently calibrated with empirical observations, this may not appear to pose any major problems in the prediction of ground motion for a particular earthquake scenario. However, the assumption that Fourier spectral concepts persist for response spectra can lead to undesirable consequences when it comes to the adjustment of response spectral GMPEs to represent conditions not covered in the original empirical data set. In this context, a couple of important questions arise, for example, what are the distinctions and/or similarities between Fourier and response spectra of ground motions? And, if they are different, then what is the mechanism responsible for such differences and how do adjustments that are made to Fourier amplitude spectrum (FAS) manifest in response spectra? The present article explores the relationship between the Fourier and response spectrum of ground motion by using random vibration theory (RVT). With a simple Brune (1970, 1971) source model, RVT-generated acceleration spectra for a fixed magnitude and distance scenario are used. The RVT analyses reveal that the scaling of low oscillator-frequency response spectral ordinates can be treated as being equivalent to the scaling of the corresponding Fourier spectral ordinates. However, the high oscillator-frequency response spectral ordinates are controlled by a rather wide band of Fourier spectral ordinates. In fact, the peak ground acceleration, counter to the popular perception that it is a reflection of the high-frequency characteristics of ground motion, is controlled by the entire Fourier spectrum of ground motion. Additionally, this article demonstrates how an adjustment made to FAS is similar or different to the same adjustment made to response spectral ordinates. For this purpose, two cases: adjustments to the stress parameter (Delta sigma) (source term), and adjustments to the attributes reflecting site response (V-S - kappa(0)) are considered. Y1 - 2016 U6 - https://doi.org/10.1785/0120150129 SN - 0037-1106 SN - 1943-3573 VL - 106 SP - 1235 EP - 1253 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Scherbaum, Frank A1 - Kühn, Nicolas A1 - Stafford, Peter A1 - Edwards, Benjamin T1 - Development of a Response Spectral Ground-Motion Prediction Equation (GMPE) for Seismic-Hazard Analysis from Empirical Fourier Spectral and Duration Models JF - Bulletin of the Seismological Society of America N2 - Empirical ground-motion prediction equations (GMPEs) require adjustment to make them appropriate for site-specific scenarios. However, the process of making such adjustments remains a challenge. This article presents a holistic framework for the development of a response spectral GMPE that is easily adjustable to different seismological conditions and does not suffer from the practical problems associated with adjustments in the response spectral domain. The approach for developing a response spectral GMPE is unique, because it combines the predictions of empirical models for the two model components that characterize the spectral and temporal behavior of the ground motion. Essentially, as described in its initial form by Bora et al. (2014), the approach consists of an empirical model for the Fourier amplitude spectrum (FAS) and a model for the ground-motion duration. These two components are combined within the random vibration theory framework to obtain predictions of response spectral ordinates. In addition, FAS corresponding to individual acceleration records are extrapolated beyond the useable frequencies using the stochastic FAS model, obtained by inversion as described in Edwards and Fah (2013a). To that end, a (oscillator) frequency-dependent duration model, consistent with the empirical FAS model, is also derived. This makes it possible to generate a response spectral model that is easily adjustable to different sets of seismological parameters, such as the stress parameter Delta sigma, quality factor Q, and kappa kappa(0). The dataset used in Bora et al. (2014), a subset of the RESORCE-2012 database, is considered for the present analysis. Based upon the range of the predictor variables in the selected dataset, the present response spectral GMPE should be considered applicable over the magnitude range of 4 <= M-w <= 7.6 at distances <= 200 km. Y1 - 2015 U6 - https://doi.org/10.1785/0120140297 SN - 0037-1106 SN - 1943-3573 VL - 105 IS - 4 SP - 2192 EP - 2218 PB - Seismological Society of America CY - Albany ER - TY - JOUR A1 - Bora, Sanjay Singh A1 - Scherbaum, Frank A1 - Kühn, Nicolas A1 - Stafford, Peter T1 - Fourier spectral- and duration models for the generation of response spectra adjustable to different source-, propagation-, and site conditions JF - Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering N2 - One of the major challenges related with the current practice in seismic hazard studies is the adjustment of empirical ground motion prediction equations (GMPEs) to different seismological environments. We believe that the key to accommodating differences in regional seismological attributes of a ground motion model lies in the Fourier spectrum. In the present study, we attempt to explore a new approach for the development of response spectral GMPEs, which is fully consistent with linear system theory when it comes to adjustment issues. This approach consists of developing empirical prediction equations for Fourier spectra and for a particular duration estimate of ground motion which is tuned to optimize the fit between response spectra obtained through the random vibration theory framework and the classical way. The presented analysis for the development of GMPEs is performed on the recently compiled reference database for seismic ground motion in Europe (RESORCE-2012). Although, the main motivation for the presented approach is the adjustability and the use of the corresponding model to generate data driven host-to-target conversions, even as a standalone response spectral model it compares reasonably well with the GMPEs of Ambraseys et al. (Bull Earthq Eng 3:1-53, 2005), Akkar and Bommer (Seismol Res Lett 81(2):195-206, 2010) and Akkar and Cagnan (Bull Seismol Soc Am 100(6):2978-2995, 2010). KW - Ground motion prediction equation KW - Fourier amplitude spectrum KW - Duration KW - Random vibration theory KW - Response Spectrum Y1 - 2014 U6 - https://doi.org/10.1007/s10518-013-9482-z SN - 1570-761X SN - 1573-1456 VL - 12 IS - 1 SP - 467 EP - 493 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Douglas, John A1 - Akkar, Sinan A1 - Ameri, Gabriele A1 - Bard, Pierre-Yves A1 - Bindi, Dino A1 - Bommer, Julian J. A1 - Bora, Sanjay Singh A1 - Cotton, Fabrice Pierre A1 - Derras, Boumediene A1 - Hermkes, Marcel A1 - Kuehn, Nicolas Martin A1 - Luzi, Lucia A1 - Massa, Marco A1 - Pacor, Francesca A1 - Riggelsen, Carsten A1 - Sandikkaya, M. Abdullah A1 - Scherbaum, Frank A1 - Stafford, Peter J. A1 - Traversa, Paola T1 - Comparisons among the five ground-motion models developed using RESORCE for the prediction of response spectral accelerations due to earthquakes in Europe and the Middle East JF - Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering N2 - This article presents comparisons among the five ground-motion models described in other articles within this special issue, in terms of data selection criteria, characteristics of the models and predicted peak ground and response spectral accelerations. Comparisons are also made with predictions from the Next Generation Attenuation (NGA) models to which the models presented here have similarities (e.g. a common master database has been used) but also differences (e.g. some models in this issue are nonparametric). As a result of the differing data selection criteria and derivation techniques the predicted median ground motions show considerable differences (up to a factor of two for certain scenarios), particularly for magnitudes and distances close to or beyond the range of the available observations. The predicted influence of style-of-faulting shows much variation among models whereas site amplification factors are more similar, with peak amplification at around 1s. These differences are greater than those among predictions from the NGA models. The models for aleatory variability (sigma), however, are similar and suggest that ground-motion variability from this region is slightly higher than that predicted by the NGA models, based primarily on data from California and Taiwan. KW - Strong-motion data KW - Ground-motion models KW - Ground-motion prediction equations KW - Style of faulting KW - Site amplification KW - Aleatory variability KW - Epistemic uncertainty KW - Europe KW - Middle East Y1 - 2014 U6 - https://doi.org/10.1007/s10518-013-9522-8 SN - 1570-761X SN - 1573-1456 VL - 12 IS - 1 SP - 341 EP - 358 PB - Springer CY - Dordrecht ER - TY - THES A1 - Bora, Sanjay Singh T1 - Regionally adaptable ground-motion Prediction Equations (GMPEs) for seismic hazard analysis T1 - Regional anpassungsfähige Bodenbewegungsmodelle (engl. ground motion prediction equations, GMPEs) für Erdbebengefährdungsabschätzungen N2 - Adjustment of empirically derived ground motion prediction equations (GMPEs), from a data- rich region/site where they have been derived to a data-poor region/site, is one of the major challenges associated with the current practice of seismic hazard analysis. Due to the fre- quent use in engineering design practices the GMPEs are often derived for response spectral ordinates (e.g., spectral acceleration) of a single degree of freedom (SDOF) oscillator. The functional forms of such GMPEs are based upon the concepts borrowed from the Fourier spectral representation of ground motion. This assumption regarding the validity of Fourier spectral concepts in the response spectral domain can lead to consequences which cannot be explained physically. In this thesis, firstly results from an investigation that explores the relationship between Fourier and response spectra, and implications of this relationship on the adjustment issues of GMPEs, are presented. The relationship between the Fourier and response spectra is explored by using random vibration theory (RVT), a framework that has been extensively used in earthquake engineering, for instance within the stochastic simulation framework and in the site response analysis. For a 5% damped SDOF oscillator the RVT perspective of response spectra reveals that no one-to-one correspondence exists between Fourier and response spectral ordinates except in a limited range (i.e., below the peak of the response spectra) of oscillator frequencies. The high oscillator frequency response spectral ordinates are dominated by the contributions from the Fourier spectral ordinates that correspond to the frequencies well below a selected oscillator frequency. The peak ground acceleration (PGA) is found to be related with the integral over the entire Fourier spectrum of ground motion which is in contrast to the popularly held perception that PGA is a high-frequency phenomenon of ground motion. This thesis presents a new perspective for developing a response spectral GMPE that takes the relationship between Fourier and response spectra into account. Essentially, this frame- work involves a two-step method for deriving a response spectral GMPE: in the first step two empirical models for the FAS and for a predetermined estimate of duration of ground motion are derived, in the next step, predictions from the two models are combined within the same RVT framework to obtain the response spectral ordinates. In addition to that, a stochastic model based scheme for extrapolating the individual acceleration spectra beyond the useable frequency limits is also presented. To that end, recorded acceleration traces were inverted to obtain the stochastic model parameters that allow making consistent extrapola- tion in individual (acceleration) Fourier spectra. Moreover an empirical model, for a dura- tion measure that is consistent within the RVT framework, is derived. As a next step, an oscillator-frequency-dependent empirical duration model is derived that allows obtaining the most reliable estimates of response spectral ordinates. The framework of deriving the response spectral GMPE presented herein becomes a self-adjusting model with the inclusion of stress parameter (∆σ) and kappa (κ0) as the predictor variables in the two empirical models. The entire analysis of developing the response spectral GMPE is performed on recently compiled RESORCE-2012 database that contains recordings made from Europe, the Mediterranean and the Middle East. The presented GMPE for response spectral ordinates should be considered valid in the magnitude range of 4 ≤ MW ≤ 7.6 at distances ≤ 200 km. N2 - Die Anpassung von empirisch gewonnenen Bodenbewegungsmodellen (engl. ground motion prediction equations, GMPEs) einer Region an andere Zielregionen bzw. -standorte, für die es nur eine schlechte oder ungenügende Datengrundlage gibt, ist eine der großen Herausforderungen in der seismischen Gefährdungsanalyse. Die abgeleiteten GMPEs werden oft zur Vorhersage von sogenannten Antwortspektren (AS) erstellt. Diese Zielgröße ist von besonderem Interesse für ingenieurtechnische Berechnungen zur erdbebensicheren Auslegung von Gebäuden. Die gewählten funktionalen Formen von GMPEs sind oft der physikalisch basierten Darstellung von seismischer Bodenbewegung als Fourier-Amplituden-Spektren (FAS) entlehnt. Die Annahme der Gültigkeit dieser Konzepte für die Modellierung von Antwortspektren kann jedoch zu Phänomenen führen, die physikalisch nicht erklärbar sind. Im ersten Teil der vorliegenden Doktorarbeit wird deshalb die Beziehung zwischen FAS und AS unter dem Aspekt möglicher Implikationen für die Anpassung von GMPEs an Zielstand-orte näher erforscht und die gefundenen Ergebnisse präsentiert. Die Beziehung zwischen FAS und AS wurde mit Hilfe der `random-vibration-theory' (RVT) untersucht. RVT ist ein Modellierungansatz, der extensiv im Erbebeningenieurwesen benutzt wird, wie zum Beispiel bei der Stochastischen Methode zur Simulation von Bodenbewegungen oder bei standortspezifischen Analysen zur Reaktion von Gebäuden auf seismische Bodenerschütterungen. Die RVT basierten Analysen für das Antwortverhalten eines 5 % gedämpften Einmassenschwingers auf Bodenunruhe zeigen, dass es keine eins zu eins Übertragbarkeit zwischen FAS und AS gibt, abgesehen von einem eingeschränkten Bereich von Eigenfrequenzen des Massenschwingers, deren Antwortspektralwerte unterhalb des charakteristischen Maximums des AS liegen. Für hohe Eigenfrequenzen werden die Werte des AS von Beiträgen des FAS dominiert, deren Frequenzbereich weit tiefer liegt als die betrachtete Eigenfrequenz im AS. Es konnte beobachtet werden, dass die maximale Bodenbeschleunigung (engl. Peak Ground Acceleration, PGA) mit dem Integral über das gesamte, die Bodenunruhe beschreibende FAS in Verbindung steht. Dies steht im Kontrast zur weit verbreiteten Auffassung, PGA sei ein Hochfrequenzphänomen. In dieser Doktorarbeit wird eine neue Perspektive für die Erstellung von GMPEs für die Vorhersage von Antwortspektren (AS-GMPEs) vorgestellt, die die Beziehung zwischen FAS und AS mit einbezieht. Dieser Ansatz beinhaltet eine Zweischrittmethode, um ein AS-GMPE zu erstellen: Im ersten Schritt werden zwei empirische Modelle abgeleitet, welche der Vorhersage des FAS und der Dauer der seismischen Bodenbewegung dienen; im zweiten Schritt werden diese Vorhersagen der beiden empirischen Modelle (FAS, Dauer der Bodenbewegung) unter Benutzung der RVT miteinander kombiniert, um Antwortspektralwerte abzuleiten. Darüber hinaus wird ein Verfahren vorgestellt, das es ermöglicht, erhobene FAS Daten (individuelle Beschleunigungsspektren) über den nutzbaren Frequenzbereich der Daten hinaus zu extrapolieren. Das Verfahren basiert auf der Stochasitischen Methode zur Simulation von Bodenbewegungen. Zu diesem Zweck wurden gemessene Zeitreihen von Erdbeben induzierter Bodenbeschleunigung invertiert, um die Modellparameter der Stochastischen Methode zu bestimmen, was eine konsistente Extrapolation des jeweiligen individuellen (Beschleunigungs-) FAS erlaubt. Ferner wurde ein empirisches Modell für ein Maß der Dauer von seismischer Bodenbewegung entwickelt, das konsistent innerhalb des Ansatzes der RVT ist. In einem nächsten Schritt wurde ein empirisches Modell für die Dauer von seismischer Bodenunruhe entwickelt, das von der Eigenfrequenz des Einmassenschwingers abhängig ist. Dies erlaubt eine möglichst zuverlässige Vorhersage von Antwortspektralwerten. Das hier präsentierte Verfahren zur Ableitung von AS-GMPEs ermöglicht eine einfache Anpassung des AS-GMPE an einen Zielstandort, da es den Stressparameter (∆σ) und den Parameter Kappa (κ0) als Prädiktoren in den beiden empirischen Modellen mit einschließt. Die gesamte Analyse und Ableitung des AS-GMPE basiert auf erhobenen Daten der RESORCE-2012 Datenbank, die Messungen aus Europa, dem Mittelmeerraum und dem Mittleren Osten enthält. Das präsentierte AS-GMPE ist für den Magnituenbereich 4 ≤ MW ≤ 7.6 und für Distanzen ≤ 200 km gültig. KW - seismic hazard KW - response spectra KW - Ground Motion Prediction Equation (GMPE) KW - Fourier spectra KW - duration KW - Erdbebengefährdungsabschätzungen KW - Bodenbewegungsmodelle KW - Antwortspektren KW - Fourier-Spektren KW - Dauer der Bodenbewegung Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-88806 ER -