Kappa ( ) Scaling of Ground-Motion Prediction Equations Using an Inverse Random Vibration Theory Approach

Abstract

Abstract A method for deriving kappa ( κ ) scaling factors that can be applied to ground‐motion prediction equations (GMPEs) to account for site‐specific κ estimates is described. This method relies on inverse random vibration theory as implemented in the computer program Strata (Kottke and Rathje, 2008a,b) to derive a Fourier amplitude spectrum (FAS) that is consistent with the response spectrum from the GMPE. The GMPE host κ values are estimated by fitting the high‐frequency FAS with the Anderson and Hough (1984) κ scaling function. The derived FAS are then scaled from their host κ value to a target κ . Random vibration theory (Cartwright and Longuet‐Higgins, 1956) is then used to convert the κ scaled FAS to response spectra, and κ scaling factors are computed by the ratio of the κ scaled response spectra to the GMPE response spectra. In contrast to the commonly used hybrid empirical method (Campbell, 2003), the proposed approach does not require a full seismological model for the stochastic parameters (stress drop, whole‐path attenuation, etc.) of the host and target regions and does not assume that response spectral shape of GMPE is consistent with that of the representative point‐source stochastic model for the host region, which can lead to inappropriate response spectral scaling factors. Finally, the effects of the well‐known trade‐off between κ and stress drop scaling are reduced. The method, when applied within the frequency limitations discussed in this paper, can be used to incorporate κ scaling into GMPEs.