In an attempt to improve the ground motion modelling, the characteristics of the slip velocity functions (SVF) generated using the kinematic k−2 source are investigated and compared to the dynamic solutions proposed in the literature. Several numerical simulations were performed to test the influence of the model parameters on the SVF modelling. Overall, the shapes of SVF are very complex and exhibit a large variability in time and space. However, we found out that the mean SVF is a simple boxcar with duration equal to the largest rise time value. In the areas of weak slip, the SVFs are characterized by the existence of negative values, whereas in large slip areas, the SVF is more impulsive. Overall, on the examples investigated, the SVFs modelled with this k−2 source model are different from a typical Kostrov's solution. The critical analysis of the kinematic k−2 source led us to identify the Fourier decomposition of the slip to be responsible for these difficulties, and to propose a new recombination scheme. It consists of adding a positive correction to the Fourier slip components. The slip is described as the sum of positive contributions at various scales. The SVFs modelled using this new scheme are greatly improved. Moreover, through several parametrical analyses performed to qualify this new approach, we show that the SVF are corrected while preserving the essential quality of the k−2 modelling, that is, the ω2 spectral shape and Cd apparent directivity of the synthetic accelerograms. Strong ground motion modelling in the near-fault region was made and numerical ground motion parameters were compared to the empirical relationships. We show that predicted peak ground motion is consistent with near-source attenuation laws