Keywords: acoustics, diffusion, fractal analysis, architectural morphology, urban scattering, multiscale distribution.

The aim of this work is to define an acoustic diffraction pattern computation model from varying geometry complexities. To do this, we develop both analytical and numerical approaches of the far-field diffraction models, based on X-ray diffraction analogy. Founding this approach, Bragg's law and Fraunhofer's model describe the field conditions for constructive and desctructive interferences, which is produced from strong diffraction. Considering diffusive structures as families of parallel planes running in different directions, each plane acts like a slightly reflective mirror, reflecting a tiny fraction of the incident acoustic wave. When in phase, those reflections lead to diffraction interferences production.

Wave coherence has two domains: spatial and temporal. Consequently, knowledge of the phase of the field at some point in space and/or time determines the phase at other points in space and/or time. Those "near-" and "far field region" will be defined through a Rayleigh distance calculation. The near-field Fresnel diffraction law describes spatially coherent sound when distances between the structure and the reception plane are small compared to the size of the reception structure (hemispheric wavefront), uncoherent incoming waves defining a non-deterministic acoustic field into twice spatial and temporal domains.

Otherwise, if viewed at a large distance compared to the extent of the object, the sound may be accurately modeled as plane waves with different wavefront tilts. This occurs in the Fraunhofer diffraction region which phases differences defines the time coherence behaviour through diffracted energy density distribution. This Fraunhofer diffraction region involves the diffracted sound pattern as variable in proportion to the reciprocal of the structure dimensions. Consequently, structure angular distribution, defines angular repartition of the sound energy with X-rays diffraction patterns (Miller indices). As Parceval's Theorem enables the computation of the scattering behaviour from the structure factor of the scattering structure: this allows the deduction of the frontage diffractance from the Fourier transform of the frontage surface scatterers. As an indicator of the indentation frequency, this Fourier transform discriminates clearly the structure of the reflection surface, revealing the spatial occurences of the roughness peaks.

Then, the angular scattering distribution function is defined through the structure factor computation of the surface, and indicates the fractal scattering behaviour for a particular direction of the incident wave. This calculation implies multiscale densitometrical distribution vertexes quantification at each incidence angle, provided through a fractal evaluation technique, the closing operation called Minkowski sausage. The resulting densitometry computation reveals the characteristic directions of scattering, which has to be calculated through the scattering pressure function along the lateral active diffraction zone. Scattering experimental results will then be compared to the fractal angular estimation of diffusivity. At this aim, multisensor method of measurement will be described, with performing an experimental validation of this angle dependent scattering fractal-characterization model. To do this, two approaches to measure the angular response of the frontage will be compared. The first is applied to a 1/5th scale model and the second will take a real into account. Both have in common the same measurement techniques based on impulse response exploiting maximum-lenght sequences stimulus (MLS).

Conclusion will state on diffractance qualification of an indented surface according to its scattering distribution function. As a consequence, a good evaluation of the acoustical reaction of an urban surface can be processed with using morphological attributes of an architecture.

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