The simulation of near-source ground motion requires the calculation of ground motion in a very broad-band frequency range (typically from 10 s to 0.1 s). However, the calculation of complete Green's function is too time consuming for high-frequency simulations. We present a method to obtain very broad-band synthetic seismograms, combining the kinematic spectral source model of Bernard et al., [1996>, and an algorithm, based on the wavenumber technique of Bouchon and Aki, [1977>. High-frequency radiations are evaluated with ray theory and a broad-band dislocation defined on a finely discretized fault plane. The low-frequency radiations due to the near- and intermediate-fields are calculated with the complete field algorithm on a low-wavenumber filtered dislocation. This dislocation is defined on a coarse grid over the fault, hence significantly reducing the computing time. We apply this method to compute the ground motion at a station located near an extended fault, where the near-, intermediate- and far-field radiations are important. ¿ 1998 American Geophysical Union