Coda reconstruction from cross-correlation of a diffuse field on thin elastic plates

This study contributes to the evaluation of the robustness and accuracy of Green's function reconstruction from cross-correlation of strongly dispersed reverberated signals, with disentangling of the respective roles of ballistic and reverberated ("coda") contributions. We conduct a suite of experiments on a highly reverberating thin duralumin plate, where an approximately diffuse flexural wave field is generated by taking advantage of the plate reverberation and wave dispersion. A large number of impulsive sources that cover the whole surface of the plate are used to validate ambient-noise theory through comparison of the causal and anticausal (i.e., positive- and negative-time) terms of the cross-correlation to one another and to the directly measured Green's function. To quantify the contribution of the ballistic and coda signals, the cross-correlation integral is defined over different time windows of variable length, and the accuracy of the reconstructed Green's function is studied as a function of the initial and end times of the integral. We show that even cross-correlations measured over limited time windows converge to a significant part of the Green's function. Convergence is achieved over a wide time window, which includes not only direct flexural-wave arrivals, but also the multiply reverberated coda. We propose a model, based on normal-mode analysis, that relates the similarity between the cross-correlation and the Green's function to the statistical properties of the plate. We also determine quantitatively how incoherent noise degrades the estimation of the Green's function.