Analysis of repeatable source and path effects on the ground-motion median and standard deviation based on an empirical dataset from the Central and Eastern United States

Abstract

In this article, we analyzed the repeatable source and path effects on ground-motion median and standard deviation using an empirical dataset from the Central and Eastern United States (CEUS). For this purpose, we used the ground-motion models (GMMs) developed by Pezeshk et al. and Akhani et al. for areas outside and inside the Coastal Plain to calculate a set of empirical residuals of the response spectral values. We calculated total residuals as the natural logarithm of the observed ground motion (horizontal peak ground acceleration (PGA) and pseudo-spectral acceleration (PSA) at periods ranging from 0.01 to 10 seconds) minus the natural logarithm of the ground motion predicted by the GMMs. The total residuals and the results of the single-station standard deviation are used to identify the repeatable source and path effects by removing the ergodic assumption. We employed a mixed-effects regression algorithm to decompose the total residuals into relevant components. The ergodic standard deviations (between-event ( $\tau$ ) and within-event ( $\varphi$ ) standard deviations) from this study are generally higher than those reported in previous studies. The resulting standard deviations for areas inside and outside the Coastal Plain are similar at longer periods, while at shorter periods, standard deviations are higher outside the Coastal Plain than inside. The results indicate that non-ergodic standard deviations are lower than those obtained using the ergodic assumption. There is a noticeable reduction in aleatory variability, ranging from 30% to 50%, between ergodic and non-ergodic standard deviations, with shorter periods showing a greater reduction than longer periods. Using an illustrative example, we demonstrate that the results of the study can be used in a non-ergodic probabilistic seismic hazard analysis (PSHA) and present the epistemic uncertainties related to each component, alongside the aleatory variabilities.