Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances.

We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.