  In this work, an unconsolidated granular medium, made of silica microbeads,
is experimentally tested in a laboratory setting. The objective is to
investigate the attenuation mechanisms of vertically polarized seismic waves
traveling at the surface of unconsolidated substrates that are characterized by
power-law rigidity profiles. Both geometric spreading and material damping due
to skeletal dissipation are considered. An electromagnetic shaker is employed
to excite the granular medium between 300 and 550 Hz, generating linear modes
that are localized near the surface. A densely sampled section is recorded at
the surface using a laser vibrometer. The explicit solution of the geometric
attenuation law of Rayleigh-like waves in layered media is employed to
calculate the geometric spreading function of the vertically polarized surface
modes within the granular material. In accordance with recent studies, the
dynamics of these small-amplitude multi-modal linear waves can be analysed by
considering the granular medium as perfectly continuous and elastic. By
performing a non-linear regression analysis on particle displacements,
extracted from experimental velocity data, we determine the frequency-dependent
attenuation coefficients, which account for the material damping.
  The findings of this work show that laboratory-scale physical models can be
used to study the geometric spreading of vertically polarized seismic waves
induced by the soil inhomogeneity and characterize the material damping of the
medium.
