The physics-based numerical simulation is a reliable tool to build-up source-to-site strong ground motion earthquake scenarios. In this paper, we enhance those forward simulations by including (1) the hysteretic non-linear behaviour of geomaterials and (2) the heterogeneous nature of soils. Scattering-induced damping, ground motion spatial incoherence and de-amplification may therefore be reproduced. A classical case study is considered herein: a seismic wave generated by a localized double-couple earthquake propagating towards the surface through layered elastic homogeneous bedrock, underlying a heterogeneous non-linear soil stratum. 3D numerical simulations were performed by means of a Spectral Element Method (SEM) code. The latter was coupled with a highly scalable random field generator to reproduce the media heterogeneity. Moreover, an extension to J 2 elasto-plasticity numerical integration was introduced. Time-histories and lagged-coherency curves at the surface show the ground motion de-amplification (mainly related to soil non-linearity) and loss of coherency (due to the wave-scattering caused by soil heterogeneity).