Abstract
SUMMARY We analyse the statistics of phase fluctuations of seismic signals obtained from a temporarysmall aperture array deployed on a volcano in the French Auvergne. We demonstrate thatthe phase field satisfies Circular Gaussian statistics. We then determine the scattering meanfree path of Rayleigh waves from the spatial phase decoherence. This phenomenon, observedfor diffuse wavefields, is found to yield a good approximation of the scattering mean freepath. Contrary to the amplitude, spatial phase decoherence is free from absorption effects andprovides direct access to the scattering mean free path. Key words: Surface waves and free oscillations; Coda waves; Statistical Seismology; Wavescattering and diffraction. 1 INTRODUCTION In heterogeneous media, after a sufficient amount of time of prop-agation, waves enter the multiple scattering regime. In this regimewaves bounce on several heterogeneities before reaching the re-ceivers. The characteristic length (resp. time) after which such aregime can be observed is the scattering mean free path (resp.time), defined as the distance (resp. time) between two succes-sive scattering events. This distance also refers to the characteristicdistance of attenuation of the coherent wave front. The coherentwave, rigorously defined as the wave that resists ensemble aver-aging, roughly corresponds to the direct (or ballistic) wave. Thescattering mean free path reflects the degree of heterogeneity ofthe medium: the longer the scattering mean free path, the weakerthescattering. dependsontwofeatures:theintensityofthefluctu-ations of the mechanical properties in the medium, and the spatialextension of the fluctuations. In nature, is found to vary over sev-eral orders of magnitude, depending on the frequency, and also onthe nature of the material at test.The multiple scattering regime can be observed in many fieldsof wave physics. It was, for instance, demonstrated in optics andin acoustics with the observation of the coherent backscattering ef-fect (or weak localization; van Albada & Lagendijk 1985;WolfM Tourin
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