Seismic wave interaction with buried cavity networks: Analytical modeling and resonance effects

We study the scattering of elastic waves by a periodic array of cavities buried in an elastic half-space. This configuration is relevant in seismology, where shallow voids can locally amplify ground motion. Building on homogenized interface models developed for infinite media, we extend the approach to account for the presence of a stress-free surface. The resulting model yields an analytical solution to the 2D elastodynamic problem for incident longitudinal L and transverse T waves. A semi-analytical multimodal solution is used for validation. The analysis reveals the conditions under which resonances occur in the soil layer between the cavity tops and the surface, with particular emphasis on the low-frequency resonance that dominates in seismic contexts. The model identifies the key parameters governing resonance and provides insights into the transition from infinite to finite cavity arrays. It offers a simplified yet accurate framework for assessing site-specific seismic amplification.