We present a new approach for performing broad-band ground motion time histories (0.1–30 Hz) of a future earthquake in a sedimentary basin. Synthetics are computed with an hybrid scheme combining reciprocity-based 3-D-spectral element method simulations at low frequencies and empirical Green's functions (EGF) at high frequencies. The combination between both deterministic and empirical parts results in a set of hybrid Green's functions, summed according to a new k−2 kinematic model algorithm. The summation technique enables to remove the high-frequency artefacts that appear above the EGF corner frequency. The ground motion variability is assessed by generating a variety of source parameter sets selected from a priori probability density functions. This leads to a population of response spectra, from which the median spectral acceleration and standard deviation values are derived. The method is applied to simulate a MW 5.5 event in the deep Grenoble basin (French Alps). The comparison with EC8 regulations suggests the need of specific design spectra in the Grenoble valley.