### Refine

#### Keywords

#### Institute

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.

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).

Ground-motion prediction equations (GMPE) are essential in probabilistic seismic hazard studies for estimating the ground motions generated by the seismic sources. In low-seismicity regions, only weak motions are available during the lifetime of accelerometric networks, and the equations selected for the probabilistic studies are usually models established from foreign data. Although most GMPEs have been developed for magnitudes 5 and above, the minimum magnitude often used in probabilistic studies in low-seismicity regions is smaller. Disaggregations have shown that, at return periods of engineering interest, magnitudes less than 5 may be contributing to the hazard. This paper presents the testing of several GMPEs selected in current international and national probabilistic projects against weak motions recorded in France (191 recordings with source-site distances up to 300 km, 3:8 <= M-w <= 4:5). The method is based on the log-likelihood value proposed by Scherbaum et al. (2009). The best-fitting models (approximately 2:5 <= LLH <= 3:5) over the whole frequency range are the Cauzzi and Faccioli (2008), Akkar and Bommer (2010), and Abrahamson and Silva (2008) models. No significant regional variation of ground motions is highlighted, and the magnitude scaling could be the predominant factor in the control of ground-motion amplitudes. Furthermore, we take advantage of a rich Japanese dataset to run tests on randomly selected low-magnitude subsets, and confirm that a dataset of similar to 190 observations, the same size as the French dataset, is large enough to obtain stable LLH estimates. Additionally we perform the tests against larger magnitudes (5-7) from the Japanese dataset. The ranking of models is partially modified, indicating a magnitude scaling effect for some of the models, and showing that extrapolating testing results obtained from low-magnitude ranges to higher magnitude ranges is not straightforward.

Probabilistic seismic-hazard analysis (PSHA) is the current tool of the trade used to estimate the future seismic demands at a site of interest. A modern PSHA represents a complex framework that combines different models with numerous inputs. It is important to understand and assess the impact of these inputs on the model output in a quantitative way. Sensitivity analysis is a valuable tool for quantifying changes of a model output as inputs are perturbed, identifying critical input parameters, and obtaining insight about the model behavior. Differential sensitivity analysis relies on calculating first-order partial derivatives of the model output with respect to its inputs; however, obtaining the derivatives of complex models can be challenging.
In this study, we show how differential sensitivity analysis of a complex framework such as PSHA can be carried out using algorithmic/automatic differentiation (AD). AD has already been successfully applied for sensitivity analyses in various domains such as oceanography and aerodynamics. First, we demonstrate the feasibility of the AD methodology by comparing AD-derived sensitivities with analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. Second, we derive sensitivities via AD for a more complex PSHA study using a stochastic simulation approach for the prediction of ground motions. The presented approach is general enough to accommodate more advanced PSHA studies of greater complexity.

Large research initiatives such as the Global Earthquake Model (GEM) or the Seismic HAzard haRmonization in Europe (SHARE) projects concentrate a great collaborative effort on defining a global standard for seismic hazard estimations. In this context, there is an increasing need for identifying ground-motion prediction equations (GMPEs) that can be applied at both global and regional scale. With increasing amounts of strong-motion records that are now available worldwide, observational data can provide a valuable resource to tackle this question. Using the global dataset of Allen and Wald (2009), we evaluate the ability of 11 GMPEs to predict ground-motion in different active shallow crustal regions worldwide. Adopting the approach of Scherbaum et al. (2009), we rank these GMPEs according to their likelihood of having generated the data. In particular, we estimate how strongly data support or reject the models with respect to the state of noninformativeness defined by a uniform weighting. Such rankings derived from this particular global dataset enable us to explore the potential of GMPEs to predict ground motions in their host region and also in other regions depending on the magnitude and distance considered. In the ranking process, we particularly focus on the influence of the distribution of the testing dataset compared with the GMPE's native dataset. One of the results of this study is that some nonindigenous models present a high degree of consistency with the data from a target region. Two models in particular demonstrated a strong power of geographically wide applicability in different geographic regions with respect to the testing dataset: the models of Akkar and Bommer (2010) and Chiou et al. (2010).