The heterogeneous nature of Earth's crust is manifested in the scattering of propagating seismic waves. In recent years, different techniques have been developed to include such phenomenon in broad-band ground-motion calculations, either considering scattering as a semi-stochastic or purely stochastic process. In this study, we simulate broad-band (0–10 Hz) ground motions with a 3-D finite-difference wave propagation solver using several 3-D media characterized by von Karman correlation functions with different correlation lengths and standard deviation values. Our goal is to investigate scattering characteristics and its influence on the seismic wavefield at short and intermediate distances from the source in terms of ground motion parameters. We also examine scattering phenomena, related to the loss of radiation pattern and the directivity breakdown. We first simulate broad-band ground motions for a point-source characterized by a classic ω2 spectrum model. Fault finiteness is then introduced by means of a Haskell-type source model presenting both subshear and super-shear rupture speed. Results indicate that scattering plays an important role in ground motion even at short distances from the source, where source effects are thought to be dominating. In particular, peak ground motion parameters can be affected even at relatively low frequencies, implying that earthquake ground-motion simulations should include scattering also for peak ground velocity (PGV) calculations. At the same time, we find a gradual loss of the source signature in the 2–5 Hz frequency range, together with a distortion of the Mach cones in case of super-shear rupture. For more complex source models and truly heterogeneous Earth, these effects may occur even at lower frequencies. Our simulations suggests that von Karman correlation functions with correlation length between several hundred metres and few kilometres, Hurst exponent around 0.3 and standard deviation in the 5–10 per cent range reproduce the available observations.