In this paper, we give a proof of the observability inequality from a portion of the boundary for the viscoelastic wave equation (also called the wave equation with memory kernel) in an arbitrary space dimension. Previous approaches have been limited to one dimension with a recent extension to dimension three by Pandolfi. We complete these results arguing by perturbation from the standard wave equation to show that the corresponding harmonic system is a Riesz sequence. Also, our result preserves the control/observation time from the wave equation. We include a new proof of the boundary observability inequality for the wave equation in line with this Riesz sequence perspective, but again, in arbitrary space dimensions, since it is the crucial result from which ours is derived.