The resonant nature of surface motion above a soft semi-circular cylindrical basin subjected to SH plane waves is demonstrated theoretically from the rigorous formulation and solution of the problem. The connection of the resonances of this “open structure” with a nonrigid bottom is established with those of the “closed structure” having a rigid bottom. The resonances are shown to be the manifestation of the excitation of the normal modes of the bedrock-basin system. The form of these modes is established. Exact as well as approximate procedures are given for computing the characteristic frequencies Ω. The rigorous approach shows that the Ω are generally complex. The rigorously computed Ω are used to validate the 1D, Bard and Bouchon, Rial, and new approximate procedures for computing the (real part of the) Ω. Dropping the rigid bottom assumption enables a computation to be made of the response at resonance, which includes all basin-bedrock interactions. The latter can be dangerously underestimated if the resonances are assumed to be located where the rigid bottom assumption predicts them to be. The main features of the ground motion are explained by the modal analysis, notably those concerning the spatial variability along the ground in different frequency ranges and its dependence on the driving field. Many of these features apply to basins of more general shape.

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