This study represents an attempt to unravel the complex relationship between the propagated wave-field and the statistical properties of the regional medium (e.g. the correlation model and length of the heterogeneities and the intrinsic attenuation). This objective is pursued by inspecting the broad-band (0-30 Hz) synthetic wave-forms obtained by source-to-site 3-D numerical simulations in regional-size scenarios. A narrow heterogeneous domains (of a few tens of meters width) is embedded inside a homogeneous half-space, between the source depth and the free-surface (where the wave-field is monitored by a dense array of stations). The presented numerical benchmark compares the major differences obtained when including or not the heterogeneous domain in the model. The high-frequency attenuation is assessed by computing the κ coefficient for different source-station configurations.