Task J: Sigma


  • To develop suites of standard deviation models applicable to CENA for:
    • ergodic within-event standard deviation (Phi, ϕ)
    • single-station within-event standard deviation (PhiSS, ϕSS)
    • between-event standard deviation (Tau, τ)

The standard deviation (sigma) of GMPEs quantifies the aleatory variability of ground motions and has a strong influence on the results of PSHA. The present state-of-the-practice of seismic hazard studies applies the standard deviations from ground-motion models developed using a broad range of earthquakes, sites, and regions to analyze the hazard at a single site from a single small source region. This is referred to as the ergodic assumption. The most promising approach to reducing the aleatory sigma is identifying the components of ground motion variability at a single site that are repeatable and removing them from the aleatory variability. These repeatable components are then transferred to the quantification of the epistemic uncertainty. A standard deviation term for which the site effects are systematically removed from the variability is referred to as single-station sigma.

The main objectives of the Sigma WG are to evaluate the ergodic within-event standard deviation (Phi), the single-station within-event standard deviation (PhiSS) and the between-event standard deviation (Tau) for CENA. These values will be compared to Phi, PhiSS and Tau evaluated for WUS and other regions around the world (Mexico, Japan, Turkey, Taiwan, Switzerland, China and Australia). The final product of the Sigma WG is a suite of parametric ergodic and single-station sigma models. These variability models will be adopted by the NGA-East TI team and assigned weights in the standard deviation logic tree (task L).

The sigma models will be developed using simulated data and the WUS data, which are much more complete than for CENA. The WG will compare the ergodic sigma and single-station sigma from small magnitude earthquakes from CENA and WUS to determine the applicability of the models to CENA. The TI team will then formally evaluate the applicability of the models to CENA. If needed, adjustments will be made to the within-event and between-event standard deviation terms. Final models for ergodic and single-station standard deviations will be developed and incorporated in the sigma logic tree (task L).