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Single-Station Sigma

¹ Department of Earth Sciences
Carleton University
Ottawa, Ontario K1S 5B6, Canada

Is the random variability of ground motions for a single station less than that obtained by regression analyses of ground-motion data recorded over a broad network of sites? This question has important implications for seismic design of critical facilities because of the influence of this variability (commonly referred to as "sigma") on probabilistic seismic-hazard computations at low probabilities. I address this question using ShakeMap data recorded at a group of 21 stations, all in the Los Angeles region, for which the shear-wave velocity in the upper 30 m (V₃₀) is known. Ground-motion prediction equations are derived from a database of site- corrected amplitudes compiled for the group of stations as a whole. The standard deviation of residuals (sigma) for the regression of the entire database is then compared with the standard deviation of residuals at individual stations. Regressions of single-station databases are also performed.

The sigma for an individual station is less than the overall sigma. The results of this study suggest that when computing hazard at a specific site for which the site amplification has been estimated based on either an empirical correction or on V₃₀, the site sigma can be taken as 90% of the corresponding sigma for the applicable ground-motion prediction equation, if the problem under consideration is one of multiple earthquake sources. If hazard from a single source at a fixed azimuth is considered (such as a single fault), the site sigma is 60% of the corresponding sigma for regional ground-motion relations. Further study with additional datasets is warranted to determine whether these results apply to hazard computations in a general sense, beyond the limited range of conditions studied here.

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