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A new approach for creating a non-ergodic $PSA$ ground-motion model (GMM) ispresented which account for the magnitude dependence of the non-ergodiceffects. In this approach, the average $PSA$ scaling is controlled by anergodic $PSA$ 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 $PSA$ factorsare based on $EAS$ non-ergodic effects and are converted to $PSA$ throughRandom Vibration Theory (RVT). The advantage of this approach is that it bettercaptures the non-ergodic source, path, and site effects through the smallmagnitude earthquakes. Due to the linear properties of Fourier Transform, the$EAS$ non-ergodic effects of the small events can be applied directly to thelarge magnitude events. This is not the case for $PSA$, as response spectrum iscontrolled by a range of frequencies, making $PSA$ non-ergodic effects dependedon the spectral shape which is magnitude dependent. Two $PSA$ non-ergodic GMMsare derived using the ASK14 and CY14 GMMs as backbone models, respectively. Thenon-ergodic $EAS$ effects are estimated with the LAK21 GMM. The RVTcalculations 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-durationmodel. The California subset of the NGAWest2 database is used for both models.The total aleatory standard deviation of the two non-ergodic $PSA$ GMMs isapproximately $30$ to $35\%$ smaller than the total aleatory standard deviationof the corresponding ergodic $PSA$ GMMs. This reduction has a significantimpact on hazard calculations at large return periods. In remote areas, farfrom stations and past events, the reduction of aleatory variability isaccompanied by an increase of epistemic uncertainty.

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