Sigma: Issues, Insights, and Challenges

The prediction of ground-motion levels at a site is one of the key elements of seismic hazard assessment. This prediction is commonly achieved using equations derived through regression analysis on selected sets of instrumentally recorded strong-motion data, hereafter referred to as empirical ground-motion prediction equations (GMPE). Reviews and compilations of equations published to date have been presented by, among others, Campbell (1985), Joyner and Boore (1988), and Douglas (2003, 2004, 2006). These equations relate a predicted variable ( Z pred) characterizing the level of shaking, most commonly the logarithm of a peak ground-motion parameter ( e.g. , PGA, PGV) or response spectral ordinate (SA, PSA, PSV, SD), to a set of explanatory variables { Xk }= X 1, X 2,... describing the earthquake source, wave propagation path, and site conditions: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[ Z\_{\mathrm{pred}}=f(\{X\_{k}\})\] \end{document}(1) The explanatory variables { Xk } usually include the earthquake magnitude, M ; a factor describing the style-of-faulting of the causative event; a measure of the source-to-site distance, R ; and a parameter characterizing the site class. Recent equations sometimes also include additional terms to characterize the location of the site with respect to the rupture plane (hanging-wall factor), to distinguish between ground motions from surface-faulting events and buried ruptures, or to include the effects of sediment depth in the case of deep alluvial basins. Other factors that are known to influence the motion (and many others that are not yet known) are not included in the equation because the information is not readily available or not predictable in advance. For instance, anisotropy effects resulting from the dynamic propagation of rupture (including directivity effects) are currently not included in predictions, although back-analyses of ground motions from past earthquakes have shown that such effects may have a strong influence on the spatial distribution of ground motions. …