Phase and Correlation in `Random' Seismic Fields and the Reconstruction of the Green Function |
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Authors: | Michel Campillo |
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Institution: | (1) Laboratoire de Géophysique Interne et Tectonophysique, Observatoire de Grenoble, Université Joseph Fourier and CNRS, BP 53, 38041 Grenoble, France |
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Abstract: | We first present a summary of recent results on coda interpretation. We emphasize the observation of the stabilization of
P to S energy ratio indicating the modal equipartition of the wavefield. This property clearly shows that the coda waves are
in the regime of multiple scattering. Numerical solutions of the elastic radiative transfer equation are used to illustrate
the evolution of the wave-field towards P-to-S energy stabilization, and asymptotically to complete isotropy. The energy properties
of the coda have been widely studied but the phase properties have often been neglected. The recently observed coherent backscattering
enhancement, an expression of the so-called `weak localization', demonstrates that interference effects still persist for
multiple diffracted waves. Another manifestation of the persistence of the phase is the possibility to reconstruct the Green
function between two stations by averaging the cross correlation of coda waves produced by distant earthquakes and recorded
at those two stations. This reconstruction is directly related to the properties of reciprocity and time reversal of any wavefield.
Using broadband seismic coda waves, we show that the dominant phases of the Green function in the band 2 s–10 s, namely fundamental
mode Rayleigh and Love waves, are reconstructed. We analyze the time symmetry of the cross correlation and show how the level
of symmetry evolves with the isotropization of the diffuse field with lapse time. Similarly we investigate the correlation
in continuous ambient noise records. Whereas the randomness of the coda results from multiple scattering by randomly distributed
scatterers, we assume that the seismic noise is random mostly because of the distribution of sources at the surface of the
Earth. Surface waves can be extracted from long time series. The dispersion curves of Rayleigh waves are deduced from the
correlations. On paths where measurements from earthquake data are also available, we show that they are in good agreement
with those deduced from noise correlation. The measurement of velocities from correlation of noise along paths crossing different
crustal structures opens the way for a `passive imaging' of the Earth's structure. |
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Keywords: | Random fields coda seismic noise imaging |
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