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The Dabaghi and Der Kiureghian stochastic near-fault ground motion model requires information about the source, site, and source-to-site geometry, including directivity parameters. Directivity parameters entail often unavailable knowledge of the rupture geometry and hypocenter location. This article presents methods to randomize the directivity parameters required to simulate near-fault ground motions. A first procedure is proposed where only the contributing fault, earthquake magnitude, and site location are known. Possible rupture directivity conditions are accounted for by randomizing the rupture geometry and hypocenter location. For this purpose, new predictive models of the rupture geometry parameters are developed for shallow crustal earthquakes with magnitudes between 5.2 and 7.9. To allow validation of synthetic motions with NGA-West2 models, a second procedure randomizes the rupture geometry …