Uncertainty, Variability, and Earthquake Physics in Ground-Motion Prediction Equations

Residuals between ground-motion data and ground-motion prediction equations (GMPEs) can be decomposed into terms representing earthquake source, path, and site effects. These terms can be cast in terms of repeatable (epistemic) residuals and the random (aleatory) components. Identifying the repeatable residuals leads to a GMPE with reduced uncertainty for a specific source, site, or path location, which in turn can yield a lower hazard level at small probabilities of exceedance. We illustrate a schematic framework for this residual partitioning with a dataset from the ANZA network, which straddles the central San Jacinto fault in southern California. The dataset consists of more than 3200 1: 15 <= M <= 3 earthquakes and their peak ground accelerations (PGAs), recorded at close distances (R <= 20 km). We construct a small-magnitude GMPE for these PGA data, incorporating V-S30 site conditions and geometrical spreading. Identification and removal of the repeatable source, path, and site terms yield an overall reduction in the standard deviation from 0.97 (in ln units) to 0.44, for a non-ergodic assumption, that is, for a single-source location, single site, and single path. We give examples of relationships between independent seismological observables and the repeatable terms. We find a correlation between location-based source terms and stress drops in the San Jacinto fault zone region; an explanation of the site term as a function of kappa, the near-site attenuation parameter; and a suggestion that the path component can be related directly to elastic structure. These correlations allow the repeatable source location, site, and path terms to be determined a priori using independent geophysical relationships. Those terms could be incorporated into location-specific GMPEs for more accurate and precise ground-motion prediction.