Urban Attenuation Lengths in City-Like Environments: Insights from 3D Numerical Simulations of Site–City Interaction

ABSTRACT Estimating seismic ground motion in urban environments requires consideration of site–city interaction effects, which involve coupling between incident seismic wavefields and kinematic and inertial interactions with buildings. Although both observational data and numerical simulations have addressed this issue, the attenuation of seismic waves in urban settings remains poorly understood. In this study, we use 3D numerical simulations to examine the evolution of the wavefield in urban-like environments for frequencies up to 12 Hz. The simulations are conducted using the spectral element method. The model consists of a layered half-space with a flat surface, where the shear-wave velocity of the upper layer is 200 m/s and that of the half-space is 650 m/s. The urban configuration includes 30 buildings, each 100 m in height with a footprint of 25 m in both the x and y directions spaced 100 m apart. The building foundations are modeled as blocks with a depth of 15 m and horizontal dimensions identical to the superstructure. We perform three sets of simulations considering (1) free-field conditions, (2) foundations only, and (3) full buildings. The attenuation of seismic waves with distance is quantified by the amplitude decay of the ballistic wavefield. Our results indicate that at high frequencies (>5 Hz), seismic wave attenuation is primarily governed by scattering, driven by interactions with the foundations acting as diffractors. At lower frequencies, attenuation is mainly controlled by the buildings’ dynamics, leading to energy band gaps at the resonant frequencies of the buildings. Furthermore, the scattering attenuation length is found to be of the same order as the spacing between foundations. Finally, by analyzing the spatial variability of the ground motion within the urban cluster, we observe that the distance at which ground motion becomes uncorrelated is determined by the urban attenuation length, which we introduce as the urban mean free path.