Cross-correlation of random fields:: mathematical approach and applications

Random field cross-correlation is a new promising technique for seismic exploration, as it bypasses shortcomings of usual active methods. Seismic noise can be considered as a reproducible, stationary in time, natural source. In the present paper we show why and how cross-correlation of noise records can be used for geophysical imaging. We discuss the theoretical conditions required to observe the emergence of the Green's functions between two receivers from the cross-correlation of noise records. We present examples of seismic imaging using reconstructed surface waves from regional to local scales. We also show an application using body waves extracted from records of a small-scale network. We then introduce a new way to achieve surface wave seismic experiments using cross-correlation of unsynchronized sources. At a laboratory scale, we demonstrate that body wave extraction may also be used to image buried scatterers. These works show the feasibility of passive imaging from noise cross-correlation at different scales.