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Metamaterials are artificially structured media that can focus (lensing) orreroute (cloaking) waves, and typically this is developed for electromagneticwaves at millimetric down to nanometric scales or for acoustics or thin elasticplates at centimeter scales. Extending the concepts of Kadic et al. 2013 weshow that the underlying ideas are generic across wave systems and scales bygeneralizing these concepts to seismic waves at frequencies, and lengthscalesof the order of hundreds of meters, relevant to civil engineering. By applyingideas from transformation optics we can manipulate and steer Rayleigh surfacewave solutions of the vector Navier equations of elastodynamics; this isunexpected as this vector system is, unlike Maxwell's electromagneticequations, not form invariant under transformations. As a paradigm of theconformal geophysics that we are creating, we design a square arrangement ofLuneburg lenses to reroute and then refocus Rayleigh waves around a buildingwith the dual aim of protection and minimizing the effect on the wavefront(cloaking) after exiting the lenses. To show that this is practicallyrealisable we deliberately choose to use material parameters readily availableand this metalens consists of a composite soil structured with buried pillarsmade of softer material. The regular lattice of inclusions is homogenized togive an effective material with a radially varying velocity profile that can bedirectly interpreted as a lens refractive index. We develop the theory and thenuse full 3D time domain numerical simulations to conclusively demonstrate thevalidity of the transformation seismology ideas: we demonstrate, at frequenciesof seismological relevance 3-10 Hz, and for low speed sedimentary soil ($v_s$:300-500 m/s), that the vibration of a structure is reduced by up to 6 dB at itsresonance frequency.

Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves