This article introduces two analytical methods that aim at investigating the effect of the urban environment on seismic motions. We regard cities as a periodic distribution of simple oscillators. The response to a vertical incident SH wave is analyzed by considering the city with a macroscopic point of view. As a first approach, the effect of buildings is described by a mean impedance on the soil–city interface. This enables us to identify a mechanical soil–city coupling parameter that governs the magnitude of the interaction and to determine a characteristic time of the soil–city response. A second, more refined model based on approximated wave fields radiated by each building leads to introducing a boundary layer to describe the multiple interactions effect. This provides an assessment of both free soil motion and building basement motion. Applications are given for monofrequency and multifrequency cities in the case of homogeneous and stratified substratums.

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