Mean and modal ϵ in the deaggregation of probabilistic ground motion

An important element of probabilistic seismic-hazard analysis (PSHA) is the incorporation of ground-motion uncertainty from the earthquake sources. The standard normal variate ϵ measures the difference between any specified spectral-acceleration level, or SA₀, and the estimated median spectral acceleration from each probabilistic source. In this article, mean and modal values of ϵ for a specified SA₀ are defined and computed from all sources considered in the USGS 1996 PSHA maps. Contour maps of ϵ are presented for the conterminous United States for 1-, 0.3-, and 0.2-sec SA₀ and for peak horizontal acceleration, PGA₀ corresponding to a 2% probability of exceedance (PE) in 50 yr, or mean annual rate of exceedance, r, of 0.000404.

Mean and modal ϵ exhibit a wide variation geographically for any specified PE. Modal ϵ for the 2% in 50 yr PE exceeds 2 near the most active western California faults, is less than –1 near some less active faults of the western United States (principally in the Basin and Range), and may be less than 0 in areal fault zones of the central and eastern United States (CEUS). This geographic variation is useful for comparing probabilistic ground motions with ground motions from scenario earthquakes on dominating faults, often used in seismic-resistant provisions of building codes. An interactive seismic-hazard deaggregation menu item has been added to the USGS probabilistic seismic-hazard analysis Web site, http://geohazards.cr.usgs.gov/eq/, allowing visitors to compute mean and modal distance, magnitude, and ϵ corresponding to ground motions having mean return times from 250 to 5000 yr for any site in the United States.