Suppose a number of acoustic sensors distributed over a city detect a gunshot. Where did it originate? Sound propagation in an urban environment is complicated by the presence of buildings. Buildings act as obstacles to sound propagation and introduce multiple propagation paths, reflections, diffraction, and scattering. This behaviour will depend on the building façades, their configuration and other scattering by the atmosphere, wind and ground terrain. The environment contains both known features such as buildings and unknown (effectively random) features such as moving vehicles and wind.

For this CASE award, we are interested in propagation over distances of up to 1km, and frequencies up to 1kHz. The specific objective is the inverse problem of the localisation of a single source of sound, which may be impulsive or continuous. Because of the many propagation paths and echoes it is difficult for a listener to locate the source of the sound, especially when this source is not in the line of sight. In this application, the listener is a distribution of sensors, whose optimal positioning is of interest.

An initial workshop has revealed the following possible research avenues:

1. Wave equation methods, in particular the use of ray tracing, reciprocity and numerics, and acoustic propagation in the presence of wind.
2. Averaged theories: these include analogies with radiative heat transfer (which leads to a nonlinear diffusion model), analogies with diffusion models for optical propagation in a multimode fibre with lossy boundaries, and homogenisation theory for waves in deterministic and random media.

Project staff and support

David Hewett (Postgraduate Associate, University of Oxford)
John Ockendon (Academic supervisor, University of Oxford)
Duncan Williams (Industrial supervisor, Dstl Winfrith)
David Allwright (Technology Translator, Industrial Mathematics KTN)

This project is being carried out at the University of Oxford, in conjunction with Dstl. It is supported by an EPSRC industrial CASE award, made available through the Knowledge Transfer Network for Industrial Mathematics. Start date: June 2006; duration: 3.5 years.