We study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency "pump" wave induces a strain field in the sample and modulates the propagation of a high-frequency "probe" wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists of the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) P and (shear) S waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.
The METAFORET experiment was designed to demonstrate that complex wave physics phenomena classically observed at the meso- and micro-scales in acoustics and in optics also apply at the geophysics scale. In particular, the experiment shows that a dense forest of trees can behave as a locally resonant metamaterial for seismic surface waves. The dense arrangement of trees anchored into the ground creates anomalous dispersion curves for surface waves, which highlight a large frequency band-gap around one resonant frequency of the trees, at ∼45 Hz. This demonstration is carried out through the deployment of a dense seismic array of ∼1000 autonomous geophones providing seismic recordings under vibrating source excitation at the transition between an open field and a forest. Additional geophysical equipment was deployed (e.g. ground-penetrating radar, velocimeters on trees) to provide essential complementary measurements. Insights and interpretations on the observed seismic wavefield, including the attenuation length, the intensity ratio between the field and the forest and the surface wave polarization, are validated with 2D numerical simulations of trees over a layered halfspace.
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