«EMPIRICAL GROUND-MOTION MODELS FOR PROBABILISTIC SEISMIC HAZARD ANALYSIS: A GRAPHICAL MODEL PERSPECTIVE Kumulative Dissertation zur Erlangung des ...»
McGuire, R. K. and T. C. Hanks (1980). RMS Accelerations and Spectral Amplitudes of Strong Ground Motion During the San Fernando, California Earthquake, Bull. Seism. Soc. Am. 70, 1907-1919.
Mitchell, T. (1997). Machine Learning, McGraw-Hill.
Mosteller, F. and J. Tukey (1977). Data Analysis and Regression, Addison-Wesley, Redding, MA.
Musson, R. M. W. (2009). Ground motion and probabilistic hazard, Bull. Earthq. Eng. 7, 575-589.
Newmark, N. M. and W. J. Hall (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, El Cerrito, California.
Nikovski, D. (2000). Constructing Bayesian networks for medical diagnosis from incomplete and partially correct statistics. IEEE Transactions on Knowledge and Data Engineering 12(4), 509-516.
Ordaz, M., A. Arciniega, and S. K. Singh (1994). Bayesian Attenuation Regressions: an Application to Mexico City, Geophy. J. Int. 117, 335-344.
Panza, G.F., R. Cazzaro and F. Vaccari (1997). Correlation between macroseismic intensities and seismic ground motion parameters, Ann. Geoﬁs. 40, 1371-1382.
Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems, Morgan Kaufman Publishers, San Mateo, California.
Pearl, J. and S. Russell (2000). Bayesian Networks. UCLA Cognitive Systems Laboratory, Technical Report (R-277).
Power, M., B. Chiou, N. Abrahamson, Y. Bozorgnia, T. Shantz, and C. Roblee (2008). An Overview of the NGA Project, Earthquake Spectra, 24 3-21.
Reiter, L. (1990). Earthquake Hazard Analysis: Issues and Insight, Columbia University Press, New York.
Rhoades, D. A. (1997). Estimation of attenuation relations for strong motion data allowing for individual earthquake magnitude uncertainties, Bull. Seism. Soc. Am. 87, 1674-1678.
Riggelsen, C. (2006). Learning bayesian networks from incomplete data: An efﬁcient method for generating approximate predictive distributions. In: Jonker, W., Petkovi´, M. (eds.) SDM c
2006. LNCS, vol. 4165, Springer, Heidelberg (2006).
Riggelsen, C. (2008). Learning Bayesian Networks: A MAP Criterion for Joint Selection of Model Structure and Parameter, ICDM, pp.522-529, 2008 Eighth IEEE International Conference on Data Mining, 2008.
Rubin, D. (1976). Inference and Missing Data, Biometrika 63, 591-592.
Sabetta, F., A. Lucantoni, H. Bungum and J.J. Bommer (2005). Sensitivity of PSHA results to ground motion prediction relations and logic-tree weights. Soil Dyn. and Earthq. Eng. 25, 317-329.
Sammon, J. W. (1969). A nonlinear mapping for data structure analysis, IEEE Trans. Comput.
Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data, Chapman & Hall, London.
Scherbaum, F., E. Delavaud, and C. Riggelsen (2009). Model Selection in Seismic Hazard Analysis: an Information-Theoretic Perspective, Bull. Seism. Soc. Am. 99, 3234-3247.
Scherbaum, F., F. Cotton and H. Staedtke (2006). The Estimation of Minimum-Misﬁt Stochastic Models from Empirical Ground-Motion Prediction Equations, Bull. Seismol. Soc. Am. 96, 427-445.
Scherbaum, F., F. Cotton, and P. Smit (2004a). On the use of response spectral-reference data for the selection of ground-motion models for seismic hazard analysis: the case of rock motion, Bull. Seism. Soc. Am. 94, 2164-2185.
Scherbaum, F., J. Schmedes and F. Cotton (2004b). On the Conversion of Source-to-Site distance measures for extended earthquake source models, Bull. Seismol. Soc. Am. 94, 1053-1069.
Scherbaum, F., N. M. Kuehn, M. Ohrnberger, and A. Koehler (2010). Exploring the Proximity of Ground-Motion Models Using High-Dimensional Visualization Techniques, Earthquake Spectra, in press.
Schwarz (1978). Estimating the Dimension of a Model, Annals of Statistics 6, 461-464.
Sieberg, A. (1930). Geologie der Erdbeben, Handbuch der Geophysik, 2,4, 552-555.
Somerville, P. G. and Yoshimura, J. (1990). The Inﬂuence of Critical Moho Reﬂections on Strong Ground Motions Recorded in San Francisco and Oakland during the 1989 Loma Prieta Earthquake, Geophys. Res. Lett. 17, 1203-1206.
Souriau, A. (2006). Quantifying felt events: A joint analysis of intensities, accelerations and dominant frequencies, J. Seism. 10, 23-38.
Spiegelhalter, D. J (1998). Bayesian graphical modelling: a case-study in monitoring health outcomes. Applied Statistics 47, 115-133.
Spiegelhalter, D. and K. Rice (2009), Scholarpedia, 4(8):5230.
Spudich, P. and B. S.-J. Chiou (2008). Directivity in NGA Earthquake Ground Motions: Analysis using Isochrone Theory, Earthquake Spectra 24, 279-298.
Stafford, P. J., F. O. Strasser and J. J. Bommer (2008). An Evaluation of the Applicability of the NGA models to Ground-Motion Prediction in the Euro-Mediterranean Region, Bull. Earthq.
Eng. 6, 149-177.
Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions, J. Roy. Statist.
Soc. B 36, 111-147.
Strasser, F. O., N. A. Abrahamson and J. J. Bommer (2009). Sigma: Issues, Insights and Challenges, Seismol. Res. Lett 80, 41-56.
Straub, D. (2005). Natural hazards risk assessment using Bayesian networks, in Safety and Reliability of Engineering Systems and Structures (Proc. ICOSSAR 05, Rome), Augusti et al. (eds), Millpress.
Tavakoli, B. and S. Pezeshk (2007). A New Approach to Estimate a Mixed Model-Based Ground Motion Prediction Equation, Earthquake Spectra 22, 665-684.
Theodulidis, N.P., and B.C. Papazachos (1992). Dependence of strong ground motion on magnitudedistance, site geology and macroseismic intensity for shallow earthquakes in Greece: I, peak horizontal acceleration, velocity and displacement, Soil Dyn. Earthq. Eng. 11, 387-402.
Toro. G. R. (2006). The Effects of Ground-Motion Uncertainty on Seismic Hazard Results: Examples and Approximate Results, Annual Meeting of the Seismological Society of America, San Francisco.
Tselentis, G-A. and L. Danciu (2008). Empirical Relationships between Modiﬁed Mercalli Intensity and Engineering Ground-Motion Parameters in Greece, Bull. Seism. Soc. Am. 98, 1863-1875.
Wald D. J. and T. I. Allen (2007). Topographic slope as a proxy for seismic site conditions and ampliﬁcation, Bull. Seism. Soc. Am. 97(5),1379-1395.
Wald, D.J., V. Quitoriano, T.H. Heaton, H. Kanamori, C.W. Scrivner, and B.C. Worden (1999a).
TriNet “ShakeMaps”: Rapid generation of peak ground-motion and intensity maps for earthquakes in southern California: Earthquake Spectra 15, 537-556.
Wald, D., V. Quitoriano, T.H. Heaton, and H. Kanamori (1999b). Relationships between peak ground acceleration, peak ground velocity and Modiﬁed Mercalli Intensity in California, Earthquake Spectra 15, 557-564.
Walling, M. (2009). Non-ergodic probabilistic seismic hazard analysis and spatial simulation of variation in ground motion, PhD Thesis, University of California, Berkeley.
Wang, M. and T. Takada (2009). A Bayesian Framework for Prediction of Seismic Ground Motion, Bull. Seism. Soc. Am. 99, 2348-2364.
Weisstein, E. W. (cited 01/2010). “Cholesky Decomposition.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/CholeskyDecomposition.html Zhao, J. X., J. Zhang, A. Asano, Y. Ohno, T. Oouchi, H. Ogawa, K. Irikura, H. K. Thio, P. G.
Somerville, Y. Fukushima (2006). Attenuation Relations of Strong Ground Motion in Japan Using Site Classiﬁcation Based on Predominant Period, Bull. Seism. Soc. Am. 96, 898-913.
SUMMARYThe goal of a probabilistic seismic hazard analysis (PSHA) is the estimation of the expected rate of exceedance of a particular ground motion level A, (Y A), where Y is a ground motion intensity parameter such as peak ground acceleration or the response spectrum. This is achieved by combining probabilistic assumptions about earthquake occurrences (spatial and temporal), magnitudes and generated ground motions, which yields a so-called hazard curve that relates a ground motion level with its expected rate of exceedance. Any such analysis is accompanied by large uncertainties, both aleatory and epistemic in nature. It has been noted (Toro, 2006) that uncertainties in the estimation of ground motions, i.e. so-called ground motion models (GMMs), have the largest effect on the results of PSHA, in particular for very low rates of exceedance, which are important for critical facilities such as nuclear power plants.
In this work, several investigations are carried out with respect to GMMs. These investigations address different issues in the development and estimation of GMMs.
First, a polynomial GMM is developed, where the order of the polynomials is determined based on generalization capability. The model is rather complex and non-physical, but is optimized for predictive power. Partial dependence plots reveal the characteristical scaling of the ground motion parameter with the predictor variables. They also show ranges which are not well sampled by data. The polynomial model is converted into a physical stochastic model to make it physically interpretable. The results are in good agreement with other published models.
Going a step further, a Bayesian network is learned on roughly the same dataset as the polynomial model. The Bayesian network provides a multivariate model for the ground motion domain, where direct (in)dependencies between quantities are estimated. It can both be used as a powerful tool for reasoning under uncertainty, as well as to investigate which parameters are directly relevant for QH predicting ground motions. In particular, VS is not directly connected to PGA in the Bayesian network, but is mediated through the depth to the 2.5 km/s shear wave horizon. This is an indiQH cation that VS might not be the parameter characterizing site effects with the highest predictive power for ground motions. The Bayesian network is in reasonable agreement with regression models in regions of good data coverage.
Two Bayesian GMMs are developed to investigate parameter uncertainty. Prior distributions of the coefﬁcients are determined by setting prior distributions on physical parameters, simulating a synthetic ground motion dataset and determining the coefﬁcients by regression on the synthetic dataset. This provides a way to combine both physical knowledge (simulations) and data-driven models in a principled way. The parameters related to source scaling (magnitude and style-offaulting dependence) are generally associated with higher uncertainty than the ones related to path and site scaling. This is not surprising, since the latter ones are based on much more data – there are generally more records than earthquakes in a strong motion dataset.
The two Bayesian GMMs are similar in that they both comprise the same base model, which is expanded in different ways: The ﬁrst model estimates directly the covariance (both between-event and within-event) between different ground motion intensity values during learning, which are usually considered independently. Strong correlations are found, the strength depending on the difference in period of the response spectrum. The between-event correlation is larger than the within-event correlation.
The second model takes into account possible regional differences in ground motion scaling.
Therefore, the global dataset is split into 10 regions, each of which is represented by an individual GMM. These regional GMMs are assumed to be sampled from a global distribution of GMMs, which are parameterized by global hyperparameters. Data from all regions is used to estimate the parameters of the regional GMMs, though autochthonous data is assigned more weight. This procedure makes it possible to estimate an individual GMM in regions with a sparse amount of data.
The analysis is not supposed to prove or disprove regional differences in ground motion scaling, but merely to present a methodology to take them into account in the light of large uncertainties.
Consequently, results regarding regional differences are inconclusive. It seems to be that regional differences in magnitude scaling of PGA are small – the model is developed for magnitudes between 5 and 7.9 – while differences regarding anelastic attenuation appear to be genuine. However, results may be obfuscated due to large differences in the amount of data between different regions.
Finally, a naive Bayes classiﬁer to predict seismic intensities from peak ground acceleration or peak ground velocity is learned, based on an Italian dataset. Such a model is useful for the rapid generation of so-called ShakeMaps or for the selection of GMMs in regions where instrumental ground motion data is sparse. The naive Bayes classiﬁer performs better than commonly employed regression models, judged by generalization error under 0-1 loss. It also provides a better representation of the uncertainty by estimating a (discrete) conditional distribution of intensity given r(I P GA; P GV ), which makes a fully probabilistic the instrumental ground motion variables, treatment of the conversion possible.