A Ground-Motion Model (GMM)'s apparent aleatory variability is inflated by errors in its predictor parameters, specifically the moment magnitude ( \({M}_{W}\) ). Multiple \({M}_{W}\) values can be available for an event (direct or deduced) and various \({M}_{W}\) definition approaches have been proposed to assign a unique \({M}_{W}\) value to an event. In this study, we investigate the impact of \({M}_{W}\) definition on a pan-European Engineering Strong Motion dataset based Fourier GMM, using two datasets with \({M}_{W}\) defined by two distinct approaches: [1] the ranking strategy of the Euro-Mediterranean Earthquake Catalogue (EMEC 2019) and [2] the multi-strategy (standardization, ranking, unification, averaging) approach to \({M}_{W}\) definition of Laurendeau et al., (Geophys J Int 230:1980–2002, 2022). Large discrepancies in \({M}_{W}\) values can be observed especially between \({M}_{W}\) ranging from 4.0 to 5.0. While the GMM median predictions remain unchanged irrespective of dataset, we report a large reduction in between-event variability of the GMM at low frequencies (< 1.8 Hz) when strategy [2] is adopted over [1] (18% at 0.35 Hz). This reduction applies to frequencies before the corner-frequency of the Fourier spectrum, as this part of the spectrum depends primarily on seismic moment. We attribute this reduction to the use of direct \({M}_{W}\) values in [2] instead of deduced \({M}_{W}\) values in [1], the priority scheme in the ranking strategy, and the unification strategy. Our study suggests that the approach used to define a unique \({M}_{W}\) in the GMM dataset may have a significant impact on its predictions in seismic hazard assessment.
