Predictive kappa ( κ ) models for Turkey: Regional effects and uncertainty analysis

Abstract

High-frequency attenuation of ground motions is commonly characterized by the κ parameter. κ and its value at zero distance, ${\kappa }_0$ , are critical parameters for site characterization, ground motion simulations, and adjustment of ground motion models for different site conditions. In this study, we derive regional κ models for Eastern, Western, and Northwestern Turkey, using a ground motion data set of 3212 strong ground motion records with 9636 components from 1053 earthquakes, recorded at 178 stations with varying site conditions. Initially, models with linear functional forms are derived with distance and site conditions as predictor variables. Residual analyses showed that these models have non-normal residuals with heterogeneous variances (heteroscedasticity). Box–Cox transformations on κ values are performed to address these two issues. Models using these transformations resulted in normal residuals with homogeneous variances (homoscedasticity). Effects of earthquake magnitude on the κ value are also investigated, and a linear adjustment for magnitudes is proposed. A constant vertical-to-horizontal ratio of 0.78 is proposed to estimate the vertical κ values instead of deriving separate models for the vertical component. This approach does not result in significant decreases in accuracy and is preferred due to its simplicity. Next, the physical implications of logarithmic transformations for the κ values are discussed. Finally, regional differences in κ models are highlighted.