Seismic wave attenuation in urban environments: insights from 3D numerical simulations of site-cityinteraction

Seismic wave characteristics are influenced by several physical processes, including the
earthquake source, geometrical effects such as topography, and local amplification phenomena.
In urban environments, civil structures introduce an additional complexity in the wavefield
evolution. While earthquake engineers have traditionally regarded buildings as passive
recipients of seismic waves, diverse seismological studies have demonstrated that building
clusters can significantly alter the ground motion (e.g. Guéguen et al. 2002; Kham et al.
2006; Semblat et al. 2008; Guéguen & Colombi, 2016). This phenomenon is known as
site-city interaction (SCI) effects. Key signatures of SCI include elongated ground motion
duration, increased spatial variability, and wave amplitude decay. SCI arises from two primary
mechanisms: kinematic and inertial interactions. In kinematic interaction, seismic waves are
scattered due to the impedance contrast between the soil and the building foundations. In
inertial interaction, the wavefield is perturbed at frequency bands near the resonant frequencies
of the buildings, often converting surface into body waves or adding some harmonics. Despite
extensive studies using numerical simulations and observations either from active shots or
earthquake records, the contribution of SCI mechanisms to seismic wave attenuation remains
insufficiently quantified.
In this work, we use 3D numerical simulations to study the wavefield evolution in urban
environments at the local scale, for frequencies up to 10 Hz. Simulations are performed by
using the spectral element method code EFISPEC (De Martin, 2011). The model consists of a
layered half-space with a flat surface, where the shear wave velocity of the layer is 200 m/s
and that of the half-space is 650 m/s. The urban configuration includes 30 buildings spaced
100 m apart, each 100 m high. The building foundations are modeled as rigid blocks with size
25 m. We perform three sets of simulations: (1) free-field conditions, (2) with foundations
only, and (3) with complete buildings. Attenuation is quantified from the amplitude decay
of the ballistic wavefield with distance. Our results reveal that at high frequency (> 5 Hz),
seismic wave attenuation is primarily controlled by scattering, driven by interactions with
foundations acting as diffractors. At lower frequencies, attenuation is dominated by the
building dynamics, resulting in energy band gaps near the modal frequencies of the buildings.
Additionally, the scattering attenuation length is found to be of the same order as the spacing
between foundations.