Correlation of random wavefields: An interdisciplinary review

Abstract

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 controlling and affecting the retrieval of the Green’s function of a complex medium from the correlation of either noise or coda. Acoustic imaging of complex samples in the laboratory and seismic tomography of geologic structures give a glimpse of the promising wide range of applications of the correlation method.