Effective Sampling of Spatially Correlated Intensity Maps Using Hazard Quantization: Application to Seismic Events
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4, Issue 1
Abstract
The paper presents a methodology for the selection of an optimal set of stochastic intensity measure (IM) maps representing the regional hazard over a geographic area, which can subsequently be used for the analysis of spatially distributed infrastructure systems. A key characteristic of the proposed approach, named Hazard Quantization (HQ), is that it embraces the nature of regional IM maps as two-dimensional (2D) random fields, and therefore uses a methodology for the optimal representation of non-Gaussian and nonhomogeneous random fields with a limited number of samples. In HQ, the representation of the regional hazard is supported by proofs of optimality. In particular, HQ ensures mean-square convergence of the ensemble of representative IM maps to the complete portfolio of possible hazard events, which is a particularly important property for risk analysis. HQ does not require the use of specialized simulation techniques, such as importance sampling or hierarchical sampling of the involved parameters, making the method simple to use. Other desirable characteristics make the method robust and applicable to a variety of hazard sources. In this paper, HQ is demonstrated for the regional seismic hazard analysis of the Charleston, South Carolina, region. A small set of IM maps and their associated probabilities resulting from the application of HQ are evaluated at all points and all pairs of points, on their ability to correctly represent the hazard curve and autocorrelation. Finally, a detailed comparison of the proposed technique with other popular methodologies in the same field is presented.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The support from Lehigh University, through the Department of Civil and Environmental Engineering and the P.C. Rossin College of Engineering; and Hofstra University, through the Department of Engineering and the Fred DeMatteis School of Engineering and Applied Science, is greatly appreciated. The first author acknowledges Professor Daniel Conus and Dr. Graziano Fiorillo for the constructive conversations, and Carla Prieto for her help in editing the drafts. The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.
References
Apivatanagul, P., Davidson, R., Blanton, B., and Nozick, L. (2011). “Long-term regional hurricane hazard analysis for wind and storm surge.” Coastal Eng., 58(6), 499–509.
Baker, J. W., and Jayaram, N. (2008). “Effects of spatial correlation of ground motion parameters for multi-site seismic risk assessment: Collaborative research with Stanford University and AIR.”, U.S. Geological Survey National Earthquake Hazards Reduction Program External Research Program Award 07HQGR0031, 69.
Bocchini, P., Christou, V., and Miranda, M. J. (2016). “Correlated maps for regional multi-hazard analysis: Ideas for a novel approach.” Multi-hazard approaches to civil infrastructure engineering, Springer, New York, 15–39.
Bocchini, P., and Frangopol, D. M. (2011). “A stochastic computational framework for the joint transportation network fragility analysis and traffic flow distribution under extreme events.” Probab. Eng. Mech., 26(2), 182–193.
Bommer, J. J., and Crowley, H. (2006). “The influence of ground-motion variability in earthquake loss modelling.” Bull. Earthquake Eng., 4(3), 231–248.
Bommer, J. J., Douglas, J., and Strasser, F. O. (2003). “Style-of-faulting in ground-motion prediction equations.” Bull. Earthquake Eng., 1(2), 171–203.
Boore, M. D., and Atkison, M. G. (2008). “Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5 and 10.00s.” Earthquake Spectra, 24(1), 99–138.
Campbell, K. W., and Seligson, H. A. (2003). “Quantitative method for developing hazard-consistent earthquake scenarios.” Proc., 6th U.S. Conf. and Workshop on Lifeline Earthquake Engineering (TCLEE), Advancing Mitigation Technologies and Disaster Response for Lifeline Systems, ASCE, Reston, VA, 829–838.
CEUS-SSCn (Central and Eastern United States-Seismic Source Characterization). (2012). “Central and eastern United States seismic source characterization for nuclear facilities.”, EPRI, U.S. DOE., and U.S. NRC, Palo Alto, CA.
Chang, E. S., Shinozuka, M., and Moore, E. J. (2000). “Probabilistic earthquake scenarios: Extending risk analysis methodologies to spatially distributed systems.” Earthquake Spectra, 16(3), 557–572.
Christou, V., Bocchini, P., and Miranda, J. M. (2016). “Optimal representation of multi-dimensional random fields with a moderate number of samples: Application to stochastic mechanics.” Probab. Eng. Mech., 44, 53–65.
Cornell, C. A. (1968). “Engineering seismic risk analysis.” Bull. Seismol. Soc. Am., 58(5), 1583–1606.
Crowley, H., and Bommer, J. J. (2006). “Modelling seismic hazard in earthquake loss models with spatially distributed exposure.” Bull. Earthquake Eng., 4(3), 249–273.
Department of Homeland Security. (2003). HAZUS-MH 2.1 earthquake model technical manual, Federal Emergency Management Agency, Washington, DC.
Dueñas-Osorio, L., and Vemuru, S. M. (2009). “Cascading failures in complex infrastructure systems.” Struct. Saf., 31(2), 157–167.
Ebel, J. E., and Kafka, A. L. (1999). “A Monte Carlo approach to seismic hazard analysis.” Bull. Seismol. Soc. Am., 89(4), 854–866.
FEMA. (2008). “Estimated annualized earthquake losses for the United States.” FEMA 366, Washington, DC.
Gardoni, P., Mosalam, K. M., and Der Kiureghian, A. (2003). “Probabilistic seismic demand models and fragility estimates for RC bridges.” J. Earthquake Eng., 7(S1), 79–106.
Gersho, A., and Gray, R. M. (1991). Vector quantization and signal compression, Kluwer Academic, Norwell, MA.
Goda, K., and Atkinson, G. M. (2009). “Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan.” Bull. Seismol. Soc. Am., 99(5), 3003–3020.
Goda, K., and Hong, H. (2008a). “Estimation of seismic loss for spatially distributed buildings.” Earthquake Spectra, 24(4), 889–910.
Goda, K., and Hong, H. (2008b). “Spatial correlation of peak ground motions and response spectra.” Bull. Seismol. Soc. Am., 98(1), 354–365.
Goda, K., and Hong, H. (2009). “Deaggregation of seismic loss of spatially distributed buildings.” Bull. Earthquake Eng., 7(1), 255–272.
Han, Y., and Davidson, R. A. (2012). “Probabilistic seismic hazard analysis for spatially distributed infrastructure.” Earthquake Eng. Struct. Dyn., 41(15), 2141–2158.
HAZUS-MH [Computer software]. FEMA, Washington, DC.
Jayaram, N., and Baker, J. W. (2009). “Correlation model for spatially distributed ground-motion intensities.” Earthquake Eng. Struct. Dyn., 38(15), 1687–1708.
Jayaram, N., and Baker, J. W. (2010). “Efficient sampling and data reduction techniques for probabilistic seismic lifeline risk assessment.” Earthquake Eng. Struct. Dyn., 39(10), 1109–1131.
Karamlou, A., and Bocchini, P. (2016). “Sequencing algorithm with multiple-input genetic operators: application to disaster resilience.” Eng. Struct., 117, 591–602.
Karamlou, A., Bocchini, P., and Christou, V. (2016). “Metrics and algorithm for optimal retrofit strategy of resilient transportation networks.” Maintenance, monitoring, safety, risk and resilience of bridges and bridge networks, Taylor & Francis, Foz do Iguaçu, Brazil, 1121–1128.
Kiremidjian, S. A., Stergiou, E., and Lee, R. (2007). “Issues in seismic risk assessment of transportation networks.” Earthquake geotechnical engineering, K. D. Pitilakis, ed., Springer, Dordrecht, Netherlands, 461–480.
Kramer, S. L. (1996). Geotechnical earthquake engineering, Vol. 80, Prentice Hall, Upper Saddle River, NJ.
Kunz, M., et al. (2013). “Investigation of superstorm sandy 2012 in a multi-disciplinary approach.” Nat. Hazards Earth Syst. Sci., 13(10), 2579–2598.
Lee, R., and Kiremidjian, S. A. (2007). “Uncertainty and correlation for loss assessment of spatially distributed systems.” Earthquake Spectra, 23(4), 753–770.
Legg, R. M., Nozick, K. L., and Davidson, A. R. (2010). “Optimizing the selection of hazard-consistent probabilistic scenarios for long-term regional hurricane loss estimation.” Struct. Saf., 32(1), 90–100.
Lloyd, S. (1982). “Least squares quantization in PCM.” IEEE Trans. Inf. Theory, 28(2), 129–137.
Luschgy, H., and Pagès, G. (2002). “Functional quantization of Gaussian processes.” J. Funct. Anal., 196(2), 486–531.
MacQueen, J. (1967). “Some methods for classification and analysis of multivariate observations.” Proc., 5th Berkeley Symp. on Mathematical Statistics and Probability, Volume 1: Statistics, Univ. of California, Berkeley, CA, 281–297.
Manzour, H., Davidson, R. A., Horspool, N., and Nozick, L. K. (2016). “Seismic hazard and loss analysis for spatially distributed infrastructure in Christchurch, New Zealand.” Earthquake Spectra, 32(2), 697–712.
McGuire, R. K. (1976). “Fortran computer program for seismic risk analysis.”, USGS, Reston, VA.
McGuire, R. K. (2004). Seismic hazard and risk analysis, Earthquake Engineering Research Institute, Oakland, CA.
McGuire, R. K. (2008). “Probabilistic seismic hazard analysis: Early history.” Earthquake Eng. Struct. Dyn., 37(3), 329–338.
Miranda, M. J., and Bocchini, P. (2015). “A versatile technique for the optimal approximation of random processes by functional quantization.” Appl. Math. Comput., 271, 935–958.
Musson, R. (1999). “Determination of design earthquakes in seismic hazard analysis through Monte Carlo simulation.” J. Earthquake Eng., 3(4), 463–474.
Musson, R. (2000). “The use of Monte Carlo simulations for seismic hazard assessment in the UK.” Ann. Geophys., 43(1), 1–9.
Padgett, J. E., DesRoches, R., and Nilsson, E. (2010). “Regional seismic risk assessment of bridge network in Charleston, South Carolina.” J. Earthquake Eng., 14(6), 918–933.
Park, J., et al. (2007). “Modeling spatial correlation of ground motion intensity measures for regional seismic hazard and portfolio loss estimation.” Applications of statistics and probability in civil engineering, Taylor & Francis Group, London, 1–8.
Peterson, D. M., et al. (2014). “Documentation for the 2014 update of the United States National Seismic Hazard Maps.”, USGS, Reston, VA.
Rhoades, D. A., and McVerry, G. H. (2001). “Joint hazard of earthquake shaking at two or more locations.” Earthquake Spectra, 17(4), 697–710.
Sokolov, V., and Wenzel, F. (2011a). “Influence of ground-motion correlation on probabilistic assessments of seismic hazard and loss: sensitivity analysis.” Bull. Earthquake Eng., 9(5), 1339–1360.
Sokolov, V., and Wenzel, F. (2011b). “Influence of spatial correlation of strong ground motion on uncertainty in earthquake loss estimation.” Earthquake Eng. Struct. Dyn., 40(9), 993–1009.
Tesfamariam, S., and Goda, K. (2013). Handbook of seismic risk analysis and management of civil infrastructure systems, Woodhead Publishing, Cambridge, U.K.
Vaziri, P., Davidson, R., Apivatanagul, P., and Nozick, L. (2012). “Identification of optimization-based probabilistic earthquake scenarios for regional loss estimation.” J. Earthquake Eng., 16(2), 296–315.
Wang, M., and Takada, T. (2005). “Macrospatial correlation model of seismic ground motions.” Earthquake Spectra, 21(4), 1137–1156.
Wells, D. L., and Coppersmith, K. J. (1994). “New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement.” Bull. Seismol. Soc. Am., 84(4), 974–1002.
Wesson, R. L., and Perkins, D. M. (2001). “Spatial correlation of probabilistic earthquake ground motion and loss.” Bull. Seismol. Soc. Am., 91(6), 1498–1515.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4 • Issue 1 • March 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 6, 2017
Accepted: Jul 5, 2017
Published online: Nov 27, 2017
Published in print: Mar 1, 2018
Discussion open until: Apr 27, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.