The influence of building interactions on seismic and elastic body waves

We outline some recent research advances on the control of elastic waves in thin and thick plates, that have occurred since the large scale experiment [S. Brule, Phys. Rev. Lett. 112, 133901 (2014)] that demonstrated significant interaction of surface seismic waves with holes structuring sedimentary soils at the meter scale. We further investigate the seismic wave trajectories of compressional body waves in soils structured with buildings. A significant substitution of soils by inclusions, acting as foundations, raises the question of the effective dynamic properties of these structured soils. Buildings, in the case of perfect elastic conditions for both soil and buildings, are shown to interact and strongly influence elastic body waves; such site-city seismic interactions were pointed out in [Gueguen et al., Bull. Seismol. Soc. Am. 92, 794-811 (2002)], and we investigate a variety of scenarios to illustrate the variety of behaviours possible.