@article{HermkesKuehnRiggelsen2014,
  author    = {Hermkes, Marcel and K{\"u}hn, Nicolas M. and Riggelsen, Carsten},
  title     = {Simultaneous quantification of epistemic and aleatory uncertainty in GMPEs using Gaussian process regression},
  series = {Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering},
  volume    = {12},
  journal   = {Bulletin of earthquake engineering : official publication of the European Association for Earthquake Engineering},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {1570-761X},
  doi       = {10.1007/s10518-013-9507-7},
  pages     = {449 -- 466},
  year      = {2014},
  abstract  = {This paper presents a Bayesian non-parametric method based on Gaussian Process (GP) regression to derive ground-motion models for peak-ground parameters and response spectral ordinates. Due to its non-parametric nature there is no need to specify any fixed functional form as in parametric regression models. A GP defines a distribution over functions, which implicitly expresses the uncertainty over the underlying data generating process. An advantage of GP regression is that it is possible to capture the whole uncertainty involved in ground-motion modeling, both in terms of aleatory variability as well as epistemic uncertainty associated with the underlying functional form and data coverage. The distribution over functions is updated in a Bayesian way by computing the posterior distribution of the GP after observing ground-motion data, which in turn can be used to make predictions. The proposed GP regression models is evaluated on a subset of the RESORCE data base for the SIGMA project. The experiments show that GP models have a better generalization error than a simple parametric regression model. A visual assessment of different scenarios demonstrates that the inferred GP models are physically plausible.},
  language  = {en}
}
@article{DerrasBardCotton2017,
  author    = {Derras, Boumediene and Bard, Pierre-Yves and Cotton, Fabrice Pierre},
  title     = {V-S30, slope, H-800 and f(0): performance of various site-condition proxies in reducing ground-motion aleatory variability and predicting nonlinear site response},
  series = {Earth, planets and space},
  volume    = {69},
  journal   = {Earth, planets and space},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1880-5981},
  doi       = {10.1186/s40623-017-0718-z},
  pages     = {1623 -- 1629},
  year      = {2017},
  abstract  = {The aim of this paper is to investigate the ability of various site-condition proxies (SCPs) to reduce ground-motion aleatory variability and evaluate how SCPs capture nonlinearity site effects. The SCPs used here are time-averaged shear-wave velocity in the top 30 m (V-S30), the topographical slope (slope), the fundamental resonance frequency (f(0)) and the depth beyond which V-s exceeds 800 m/s (H800). We considered first the performance of each SCP taken alone and then the combined performance of the 6 SCP pairs [V-S30-f(0)], [V-S30-H-800], [f(0)-slope], [H-800-slope], [V-S30-slope] and [f(0)-H-800]. This analysis is performed using a neural network approach including a random effect applied on a KiK-net subset for derivation of ground-motion prediction equations setting the relationship between various ground-motion parameters such as peak ground acceleration, peak ground velocity and pseudo-spectral acceleration PSA (T), and Mw, RJB, focal depth and SCPs. While the choice of SCP is found to have almost no impact on the median groundmotion prediction, it does impact the level of aleatory uncertainty. VS30 is found to perform the best of single proxies at short periods (T < 0.6 s), while f(0) and H-800 perform better at longer periods; considering SCP pairs leads to significant improvements, with particular emphasis on [V-S30-H-800] and [f(0)-slope] pairs. The results also indicate significant nonlinearity on the site terms for soft sites and that the most relevant loading parameter for characterising nonlinear site response is the "stiff" spectral ordinate at the considered period.},
  language  = {en}
}