Observational data of asteroids can be explained by considering them as an agglomerate of granular material. Understanding the mechanical properties of these objects is relevant for many scientific reasons: space missions design, evaluation of impact threats to our planet, and understanding the nature of asteroids and their implication in the origin of the solar system. In-situ measurements of mechanical properties require complex and costly space missions. Here a laboratory-scale characterization of wave propagation in granular media is presented using a novel experimental setup as well as numerical simulations. The pressure inside an asteroid is still a matter of debate, but it definitely presents a pressure gradient towards the interior. This is why impact characterization needs to be performed as a function of the confining pressure. Our experimental setup allows for the simultaneous measurement of the external confining pressure, internal pressure, total strain, and acceleration in a 50 cm side squared box filled up with a billion grains. We study the propagation of impact-generated and shaker-born seismic body waves in the 500 Hz range. Through subsequent compression-relaxation cycles, it was observed that the granular media behaves on average like a solid with a constant elastic modulus during each compression. Effective medium theory (EMT) for granular media explains the data at low pressure. After each compression-relaxation cycle, the elastic modulus increases, and a high hysteresis is observed: relaxation shows a more complex behavior than compression. We show that seismic waves generated by both impact and vibration travels at the pressure wave speed. Thanks to a numerical model, we measure a strong wave attenuation α ∼ 3.4 Np/m. We found that the wave speed increases with the confining pressure with a p1/2 dependency, in disagreement with theoretical models that predicts a shallower dependency. The dependency of the elasticity with the confining pressure can be explained by a modified EMT model with a coordination number proportional to the pressure, or equivalently by a mesoscopic nonlinear model based on third-order nonlinear elastic energy. The interpretation of these models is a deep reorganization in the particle contact network.