Influence of the site-specific component of kappa on the magnitude-dependency of within-event aleatory variabilities in ground-motion models

The aleatory-variability component (standard deviation) of a ground motion has a large influence on results of a probabilistic seismic hazard assessment. kappa, a measure of high-frequency attenuation, has site- and record-specific effects that have been suggested as reasons for observing heteroscedastic aleatory variability within earthquake ground motions. Specifically, kappa has been proposed as a reason why ground motions from small earthquakes are more variable than those from large earthquakes, which is modeled by magnitude-dependent within-event standard deviations in ground-motion prediction equations (GMPEs). In this study, we use ground motions simulated using the stochastic method to examine the influence of the site-specific component of kappa on aleatory variability of earthquake ground motions and examine the hypothesis that this could be a cause of the observed heteroscedasticity in this variability. We consider simulations with both fixed and continuous stress drop distributions and the site-specific component of kappa to demonstrate that variation in the stress drop parameter contributes minimally to magnitude-dependency, unlike the site-specific component of kappa, which causes significant magnitude-dependency. Variation in the site-specific component of kappa is, therefore, proposed to be at least partially responsible for the magnitude-dependency captured in the aleatory-variability components of some recent GMPEs. It is found, however, that the expected impact of the site-specific component of kappa on aleatory variability is much greater than modeled in these GMPEs, which suggests that there could be a mitigating effect that is not captured within the simulations (e.g., correlated inputs to the simulations).