The hypothesis that particular physical properties of the earth at the source can affect the radiation of high-frequency waves was numerically investigated. Two factors have been considered: a non-elastic behavior of the material at the crack tip (i.e presence of a cohesive zone) and the kinematics of the rupture front. Using the discrete wave number method, we calculated complete near-source synthetic spectra radiated by a circular shear crack model. The two processes can explain an exponential decrease of the aceleration spectrum at high frequencies. Moreover, they can be differentiated. In the case of a final smooth deceleration of the rupture front, the rate of decay of the acceleration spectra is equivalent in all the azimuths. A clear azimuthal dependence exists in the presence of a cohesive zone, with the maximum rate of decay being observed in the direction of the fault strike. The parameter fmax varies as the ratio of the rupture velocity over the length of the cohesive zone for the nonelastic model and as the inverse of the duration of the deceleration of the rupture front when the rupture front stops smoothly. These two models result in a decay of spectral amplitude at high frequency the mimics the effect of the anelastic attenuation. ¿ American Geophysical Union 1989