Simplified vibratory characterization of alluvial basins

For the analysis of seismic wave amplification, modal methods are interesting tools to study the modal properties of geological structures. Modal approaches mainly lead to information on such parameters as fundamental frequencies and eigenmodes of alluvial basins. For a specific alluvial deposit in Nice (France), a simplified modal approach involving the Rayleigh method is considered. This approach assumes a set of admissible shape functions for the eigenmodes and allows a fast estimation of the fundamental frequency of the basin. The agreement between modal numerical results and experimental ones is satisfactory. The simplified modal method then appears as an efficient mean for the global vibratory characterization of geological structures towards resonance.

💡 Research Summary

The paper presents a streamlined modal approach based on the Rayleigh method for estimating the fundamental vibration frequency of an alluvial basin, using the Nice (France) basin as a case study. Traditional wave‑propagation analyses of site effects require detailed numerical models (e.g., finite‑difference, boundary‑element) and considerable computational effort. In contrast, the Rayleigh quotient reduces the problem to a single‑degree‑of‑freedom approximation: the maximum elastic energy equals the maximum kinetic energy, leading to
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