Poster #092, Earthquake Forecasting and Predictability (EFP)
Covariance Analysis of the UCERF3-TI Logic Tree
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Poster Presentation
2020 SCEC Annual Meeting, Poster #092, SCEC Contribution #10566 VIEW PDF
class” C_k to be the set of rate-vector pairs (lambda, lambda') that share the same branch up to level k, and we compute the class covariance Cov_k [lambda, lambda'] by taking the expectation of (lambda – E_k[lambda]) (lambda'– E_k [lambda'])^T over the connection class. According to this definition, the only members of C_K are the self-pairs lambda = lambda'. Hence, Cov_K [lambda, lambda] is just the sample covariance matrix for the event-rate vector lambda, and its diagonal elements are the rate variances, (sigma_i)^2 = Var [lambda_i], which are the most basic measures of the UCERF3-TI epistemic uncertainty. For k < K, the class covariance matrix provides information about the correlations imposed by the model-component choices below the branching level k. We show that Cov_k [lambda_i, lambda_i'] ≤ (sigma_i)^2 and that the expected value of the difference vector lambda – lambda' for a pair in class C_k is 2(Cov_K [lambda, lambda] – Covk [lambda, lambda']). The diagonal elements of this difference matrix thus measure the variance due to epistemic uncertainties in the model-component choices at branching levels of k and above. We use this graph-theoretic construction to evaluate the relative contributions of each logic-tree level to the overall UCERF3-TI epistemic variance.
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