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The challenging translation from the laboratory scale to the geophysics scale

29 September 2016 ( maj : 5 October 2016 ), by Administrateur

The translation of the required physics from the laboratory scale to the geophysics scale is highly challenging. In the plate, only one plate mode was excited in the kHz range (the A0 flexural mode). The A0 mode is vertically polarized, and as no leakage was possible, the elastic wave was forced to interact with the vertical rods. At the geophysics scale, the medium is no longer 2D as in the plate, but is fully 3D, with the possibility of leakage of surface waves deep into the bedrock. Indeed, the elastic waves will no longer propagate confined within a thin plate, but within a semi-infinite substrate, some at the air-soil interface, other ones deep inside the substrate. We thus cannot be sure that the Rayleigh surface waves will interact with trees in the same manner as the flexural waves did interact with the rods (Fig. 1). There is also the natural question about the role played by transverse shear waves (also-called Love waves) and body waves at the subsurface, as they will probably overlap with surface waves in the case of an active-source experiment. Indeed, body waves are solutions of the full Navier equations that do not retain their form under geometric transform, what makes the design of a seismic cloak for body waves more challenging than for surface Rayleigh waves (that can be modeled with simplified, transformation invariant, governing equations, similarly to Lamb waves in plates). So there is a considerable amount of fundamental science that needs to be understood and explored here.

Figure 1.
Comparison between metamaterial wave physics at the lab scale and in geophysics. (a) Dispersion curves measured (black) and computed with Bloch theory (red) for the case of vertical beams attached to the plate. Arrows point to the respective modal deformation. (b) Same as (a) but for the case of the trees on a semi-infinite geophysics half space. The S-wave line bounds the radiative zone on the left, which is not involved in the analysis.