Geostatistical modeling of sound propagation: Principles and a field application experiment.

The assessment of noise sources for environmental purposes requires reliable methods for mapping. Numerical models are well adapted for sophisticated simulations and sensitivity analyses; however, real-time mapping of large frequency bands must be based on fast and acceptable computations and honor in situ measurements. In this paper, a real-time mapping procedure of noise exposure is proposed. The procedure is based on geostatistical modeling of spatial variations and applied to a case study taken from an experimental campaign, where a point source was placed on a flat meadow. An analytical approximation of the acoustic field was first computed with the Embleton model. The difference between this approximation and the actual measurements (L(eq15 min) 1/3-octave bands samples from 19 microphones spread over the meadow) showed spatial structure, which has been modeled with a variogram. Finally, the geostatistical technique of kriging with external drift provided an optimal interpolation of the acoustic field data while encapsulating the first approximation from the Embleton model. Systematic geostatistical inference and real-time mapping with the proposed procedure can be envisaged in simple cases.

Sound propagation above a porous road surface with extended reaction by boundary element method.

Acoustic impedance of an absorbing interface is easily introduced in boundary element codes provided that a local reaction is assumed. But this assumption is not valid in the case of porous road surface. A two-domain approach was developed for the prediction of sound propagation above a porous layer that takes into account the sound propagation inside the porous material. The porous material is modeled by a homogeneous dissipative fluid medium. An alternative to this time consuming two-domain approach is proposed by using the grazing incidence approximate impedance in the traditional single-domain boundary element method (BEM). It can be checked that this value is numerically consistent with the surface impedance calculated at the interface from the pressure and surface velocity solutions of the two-domain approach. The single-domain BEM introducing this grazing incidence impedance is compared in terms of sound attenuation with analytical solutions and two-domain BEM. The comparison is also performed with the single-domain BEM using the normal incidence impedance, and reveals a much better accuracy for the prediction of sound propagation above a porous interface.

Sound-field modeling in architectural acoustics by a transport theory: application to street canyons.

The transport theory of sound particles is applied to the sound field modeling in architectural acoustics. A theoretical description is proposed for empty enclosures with complex boundary conditions, including both specular and diffuse reflections. As an example, the model is applied to street canyons. Therefore, an asymptotic approach is proposed to reduce the transport equation to a diffusion equation defined by only one parameter, the diffusion coefficient. This coefficient is a function of the reflection law of the building façades, the ratio of specular and diffuse reflections, as well as the street width. The model is then compared to Monte Carlo simulations of the propagation of sound particles in complex enclosures. As expected by the asymptotic approach, the model is in agreement with numerical results, but mainly for small street width and very diffuse reflections. Finally, a discussion is proposed in the conclusion, on the model's capabilities.

Traffic noise prediction with the parabolic equation method: validation of a split-step Padé approach in complex environments.

This study deals with sound propagation in typical traffic noise conditions. The numerical results are obtained through the split-step Padé method and the discrete random Fourier modes technique. These are first evaluated qualitatively, by color contour maps showing noise propagation, diffraction by an impedance discontinuity or a screen edge, and scattering by atmospheric turbulence. Next, our numerical results are quantitatively validated by comparison with analytical models and other parabolic equation models. For all the atmospheric conditions and geometrical configurations available in literature, the agreement between the different methods is very good, except for some cases involving the atmospheric turbulence. However, in those particular cases, the split-step Padé results are shown to be more consistent with physical theory. Finally, our method seems to be very powerful and reliable for traffic noise prediction.