Impact of a real terrain on the sonic boom signature at the ground has been little studied in the literature. In the current prediction schemes, a flat and perfectly reflecting ground is usually assumed and the reflected boom is obtained by multiplying the incident boom by a constant factor. In this paper, the effects of a non-flat and absorbing ground are investigated. For this, a numerical study is conducted. The 2-D Euler equations are solved in curvilinear coordinates using high-order finite difference schemes. Signatures of the incident boom typical of a classical N-wave and of a low boom are considered. The variability on the waveform at the ground induced by the terrain irregularities is studied for different characteristic length scales of the terrain.