Capabilities of multivariate Bayesian inference toward seismic hazard assessment
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Capabilities of multivariate Bayesian inference toward seismic hazard assessment Somayajulu L. N. Dhulipala1 · Madeleine M. Flint2 Received: 24 August 2019 / Accepted: 16 June 2020 © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2020
Abstract Multivariate Bayesian inference can bring significant benefits to seismic hazard analysis: its multivariate feature enables computing scalar and vector hazard without making any approximations; Correlations between intensity measures are implicitly modeled, permitting direct simulation of ground motion selection tools such as the conditional mean spectrum and the generalized conditioning intensity measure. Its updating feature enables a seamless integration of new ground motion data into the hazard results. In this paper, we first develop a multivariate Bayesian ground motion model through the NGA-West2 database. The model functional form considers fault type, magnitude and distance dependencies, and also the linear and the rock intensity-dependent site response. We use a hybrid Markov chain Monte Carlo sampling to perform Bayesian inference consisting of Gibbs step and a multilevel Metropolis–Hastings step. We then perform several checks on the model to ensure that it is unbiased. Finally, we illustrate the merits of this multivariate Bayesian analysis through practical and contemporary examples, which include: ground motion model updating with ground motion data recorded in the last four years and not part of the NGA-West2 database; computation of scalar and vector seismic hazard using the un-updated and updated ground motion models for Los Angeles, CA; and simulation of the conditional mean spectrum under scalar and vector IM conditioning while accounting for different sources of aleatoric and epistemic uncertainties. Keywords Ground motion modeling · Bayesian inference · Markov chain Monte Carlo · Seismic hazard · Performance-based earthquake engineering List of symbols yijk Predicted value of SA at period k, event i and station j FP (.) Path term Mi Magnitude of event i RJB,ij Joyner–Boore distance of station j event i 𝜂ik Within-event residual at period k event i * Somayajulu L. N. Dhulipala [email protected] 1
Idaho National Laboratory, Idaho Falls, ID 83402, USA
2
Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA
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e(.) Event term coefficient U Unspecified fault type NS Normal slip fault c(.) Path term coefficient Mref Reference magnitude blin Linear site response coefficient Vref Reference Vs30 No Number of ground motion recordings Np Number of model coefficients Y No × Nt matrix of log SA (observations) 𝛼 Nt × Np matrix of model coefficients p(.) Probability density 𝛷 No × No matrix of correlations across No observations 𝜙 i Sub-matrix of correlations for event i 𝜌 Correlation between two periods at the same site Δ Multivariate normal covariance matrix 𝜈 Inverse Wishart degrees of freedom a, b Beta distribution pa
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