Laurent Stehly

Correlation of random wavefields: An interdisciplinary review

This paper presents an interdisciplinary review of the correlation properties of random wavefields. We expose several important theoretical results of various fields, ranging from time reversal in acoustics to transport theory in condensed matter physics. Using numerical simulations, we introduce the correlation process in an intuitive manner.We establish a fruitful mapping between time reversal and correlation, which enables us to transpose many known results from acoustics to seismology. We show that the multiple-scattering formalism developed in condensed matter physics provides a rigorous basis to analyze the field correlations in disordered media. We discuss extensively the various factors controllingandaffectingtheretrievaloftheGreen’sfunction of a complex medium from the correlation of either noise or coda.Acousticimagingofcomplexsamplesinthelaboratory and seismic tomography of geologic structures give a glimpse of the promising wide range of applications of the correlationmethod.

Correlation in ambient seismic noise and the reconstruction of Green function

Cross‐correlations between long continuous records of ambient seismic noise at distant stations are investigated. The dominant part of the Green function, namely Rayleigh waves, are reconstructed in a broad period range. This property reminds of the fluctuation‐dissipation theorem that relates the random fluctuations of a linear system and the system’s response to an external force. Ambient seismic noise is indeed not a thermal noise but it can be considered as a random and isotropic wave field both because the distribution of the ambient sources responsible for the noise randomizes when averaged over long periods and because of scattering from heterogeneities that occur within the Earth. The dispersion curves of Rayleigh waves for the paths between the stations are measured from the correlations. On paths where direct measurements between earthquake and station are available, we show that they are in good agreement with those deduced from noise correlation. The measurement of correlation along paths cros...

Imaging the solid Earth with seismic noise

The correlation of ambient vibrations of the Earth yields the impulse response between two passive sensors as if one was a source. This provides the opportunity to image the Earth beneath regional seismic arrays. In this paper, we present imaging of the lithosphere in Europe based on surface Rayleigh waves extracted from continuous record of the seismic noise. We also recall a brief history of passive imaging in seismology. The link between correlations and the green function is investigated from a mathematical point of view, and through laboratory experiments.