A Non-ergodic Spectral Acceleration Ground Motion Model for California Developed with Random Vibration Theory

Abstract

A new approach for creating a non-ergodic $PSA$ ground-motion model (GMM) is presented which account for the magnitude dependence of the non-ergodic effects. In this approach, the average $PSA$ scaling is controlled by an ergodic $PSA$ GMM, and the non-ergodic effects are captured with non-ergodic $PSA$ factors, which are the adjustment that needs to be applied to an ergodic $PSA$ GMM to incorporate the non-ergodic effects. The non-ergodic $PSA$ factors are based on $EAS$ non-ergodic effects and are converted to $PSA$ through Random Vibration Theory (RVT). The advantage of this approach is that it better captures the non-ergodic source, path, and site effects through the small magnitude earthquakes. Due to the linear properties of Fourier Transform, the $EAS$ non-ergodic effects of the small events can be applied directly to the large magnitude events. This is not the case for $PSA$, as response spectrum is controlled by a range of frequencies, making $PSA$ non-ergodic effects depended on the spectral shape which is magnitude dependent. Two $PSA$ non-ergodic GMMs are derived using the ASK14 and CY14 GMMs as backbone models, respectively. The non-ergodic $EAS$ effects are estimated with the LAK21 GMM. The RVT calculations are performed with the V75 peak factor model, the $D_{a0.05-0.85}$ estimate of AS96 for the ground-motion duration, and BT15 oscillator-duration model. The California subset of the NGAWest2 database is used for both models. The total aleatory standard deviation of the two non-ergodic $PSA$ GMMs is approximately $30$ to $35\%$ smaller than the total aleatory standard deviation of the corresponding ergodic $PSA$ GMMs. This reduction has a significant impact on hazard calculations at large return periods. In remote areas, far from stations and past events, the reduction of aleatory variability is accompanied by an increase of epistemic uncertainty.