Seismic metasurface on an orthorhombic elastic half-space

The article is studying a seismic meta-surface in the case of an oscillatory system arranged on the surface of an orthorhombic elastic half-space. The approach is based on the asymptotic hyperbolic-elliptic formulation for the Rayleigh wave excited by prescribed surface loading. The latter results in hyperbolic equations for surface displacements, with the right-hand sides involving the loading components. The derived model allows a formulation for the meta-surface in the form of a periodic spring-mass system attached to the surface as a hyperbolic equation for the horizontal displacement, with smooth contact stresses emerging from averaging the effect of a regular array of oscillators. The associated dispersion relation is constructed and illustrated numerically for both cases of exponential and oscillatory decay.