  In this work, we experimentally and numerically investigate the propagation
and attenuation of vertically polarized surface waves in an unconsolidated
granular medium equipped with small-scale metabarriers of different depths,
i.e., arrays composed of one, two, and three embedded layers of sub-wavelength
resonators. Our findings reveal how such a multi-layer arrangement strongly
affects the attenuation of the surface wave motion within and after the
barrier. When the surface waves collide with the barriers, the wavefront is
back-scattered and steered downward underneath the oscillators. Due to the
stiffness gradient of the granular medium, part of the wavefield is then
rerouted to the surface level after overcoming the resonant array. Overall, the
in-depth insertion of additional layers of resonators leads to a greater and
broader band wave attenuation when compared to the single layer case.
