Intrinsic material absorption, as exemplified in the attenuation of seismic waves, is a key parameter in several seismological fields, in particular earthquake engineering. The advances of the last few decades in the theory of wave propagation in linear anelastic materials provide an opportunity to examine more completely the implications of intrinsic material absorption on seismic wave propagation. In the present paper, we analyze the records of two near-surface open quarry explosions of recently rescued, unexploded World War II bombs dropped by Allied air raids and recovered at a few meters depth close to the Milano Centrale railway station. Recordings obtained at epicentral distances of 1.4 km and 2.5 km show clear separation of body and surface waves and strong evidence for elliptical prograde particle motions for P waves. Classic elasticity theory predicts linear longitudinal motions for P waves. Hence, synthetic seismograms computed using computer codes that are based both on elasticity theory and on homogeneous attenuating waves (Herrmann and Ammon, 2002) do not account for observed particle motions. On the contrary the theory of wave propagation in homogeneous isotropic linear viscoelastic media (Borcherdt, 1971, 1973, 2009) accurately accounts for the observed characteristics of the recorded motion. Application of the theory provides empirical estimates of the inhomogeneity γ values (0≤γ<π/2) and evidence of intrinsic material absorption at low strain levels (less than 10-6), as quantified by independent empirical estimates of Q-1.