Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate

Giraldi, Loïc; Maître, Olivier Le; Mandli, Kyle T.; Dawson, Clint; Hoteit, Ibrahim

doi:10.1007/s10596-017-9646-z

Cited by 31 publications

(32 citation statements)

References 29 publications

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“…We focused in the previous sections on the case of a linear problem where X, A(X) and E follow the multivariate normal distribution. In [13], we showed that when A is nonlinear and X is drawn according to a uniform distribution, the PCA-YN is an appropriate dimensionality reduction method. The reason is that the probability density function of the posterior distribution of X is…”

Section: Application To Nonlinear Problemsmentioning

confidence: 99%

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Optimal projection of observations in a Bayesian setting

Giraldi

Maître

Hoteit

2018

Computational Statistics & Data Analysis

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Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback-Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.

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Section: Application To Nonlinear Problemsmentioning

confidence: 99%

“…In future works, the method will be applied to extreme hydrological flow problems (e.g. [13,30]). In particular, we plan to apply the approach to the framework of Ensemble Kalman filters (EnKF) [11] for large datasets.…”

Section: Perspectivesmentioning

confidence: 99%

Optimal projection of observations in a Bayesian setting

Giraldi

Maître

Hoteit

2018

Computational Statistics & Data Analysis

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“…Bayesian inversion frameworks for tsunami inversion have been carried out recently [ 11 , 12 ]. These approaches, in principle, thoroughly quantify uncertainties in the inversion.…”

Section: Introductionmentioning

confidence: 99%

Uncertainties in the 2004 Sumatra–Andaman source through nonlinear stochastic inversion of tsunami waves

et al. 2017

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Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems.

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“…To this end, we utilize the polynomial chaos (PC) approach (Ghanem and Spanos, 1991;Xiu and Karniadakis, 2002;Le Maître and Knio, 2010) to build functional representations of PGV responses of an original source model. Thanks to the significant reduction in computational cost of the PC surrogate models (in comparison with both the original source model and a Bayesian analysis based on Markov chain Monte Carlo (MCMC) sampling, which requires a prohibitive number of model runs; Minson et al, 2014), it is suitable to utilize the PC surrogates in a Bayesian inference framework (Sudret and Mai, 2013;Sraj et al, 2016;Giraldi et al, 2017). This enables us to quantitatively rank different kinematic source models given by the PGVs they produce and identify the most likely one that fits a chosen reference GMPE (expectation).…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference of earthquake rupture models using polynomial chaos expansion

Cruz-Jiménez

Martin

et al. 2018

Geosci. Model Dev.

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Abstract. In this paper, we employed polynomial chaos (PC) expansions to understand earthquake rupture model responses to random fault plane properties. A sensitivity analysis based on our PC surrogate model suggests that the hypocenter location plays a dominant role in peak ground velocity (PGV) responses, while elliptical patch properties only show secondary impact. In addition, the PC surrogate model is utilized for Bayesian inference of the most likely underlying fault plane configuration in light of a set of PGV observations from a ground-motion prediction equation (GMPE). A restricted sampling approach is also developed to incorporate additional physical constraints on the fault plane configuration and to increase the sampling efficiency.

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Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate

Cited by 31 publications

References 29 publications

Optimal projection of observations in a Bayesian setting

Optimal projection of observations in a Bayesian setting

Uncertainties in the 2004 Sumatra–Andaman source through nonlinear stochastic inversion of tsunami waves

Bayesian inference of earthquake rupture models using polynomial chaos expansion

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