Three-Dimensional Acoustic Wave Propagation in Complex Urban Environments Using the Spectral Element Method

Abstract

Accurate prediction of sound propagation in densely built urban environments requires numerical methods capable of resolving complex three-dimensional geometries, wave diffraction, and frequency-dependent scattering, phenomena that are often inadequately represented by conventional ray-tracing and empirical noise-mapping approaches. This study presents a high-resolution three-dimensional acoustic simulation of a real urban district in Kingston, Ontario, Canada, using the spectral element method (SEM) implemented in specfem3d. The study area encompasses the neighbourhood surrounding St. Mary’s Cathedral, where a bell tower located approximately 40 m above street level serves as an elevated acoustic source within a realistic urban geometry constructed from satellite imagery and GIS data. A 200 Hz Ricker wavelet is used to model acoustic excitation, and simulated receiver responses at
seven field-validated locations are evaluated in terms of arrival time, amplitude attenuation, and spectral characteristics. Receivers with a direct line of sight to the source reproduce theoretical free-field arrival times with relative errors below 0.11%, while obstructed receivers exhibit systematic delays consistent with diffraction around and over intervening buildings. Spectral centroid analysis reveals that enclosed urban environments preferentially retain higher-frequency energy, resulting in positive centroid shifts, whereas more open environments preserve the source spectrum more closely. Simulated amplitude attenuation agrees well with field observations, particularly between receivers C and D, where differences remain within three percentage points. These results demonstrate the capability of SEM to accurately model neighbourhood-scale acoustic wave propagation in complex urban settings and highlight its
potential for next-generation applications in urban noise assessment, soundscape analysis, and acoustic design. The study also establishes a benchmark for future investigations incorporating frequency-dependent material attenuation, atmospheric effects, extended simulation durations, and realistic source recordings.