Scattering Cross-Section Estimation Using Passive Imaging in Reverberating Elastic Plates: Case Study of Rigid Isotropic Inclusion

Abstract

We investigate here how passive imaging based on noise correlation can serve to retrieve the scattering strength in a reverberating elastic plate. In previous works, we demonstrated the possibility to detect and localize passively a single scatterer in a reverberating elastic plate combining a transducer array and beamforming imaging, when a diffuse flexural wave field is approximately generated. In particular, when the noise is non uniformly distributed over the plate surface, we can take benefit from reverberations to accelerate the convergence towards the Green's functions. A continuity is addressed here to passively characterize a single scatterer in a thin plate. Numerical simulations are conducted in the presence and absence of a defect within the plate. We calculate the differential correlation matrix obtained in these cases (i.e., with versus without the scatterer) as a measure of the temporal variations in the Green's function due to the defect. By back-propagating the differential matrix, an image is obtained with a maximum intensity on the defect location. We also develop a formula that relates this focal spot on the defect position to the scattering strength of the scatterer. The formula are numerically validated using simulations in an aluminum plate. We substantiate the reliability of this approach through a classical method for the measurement of the scattering cross-section based exclusively on direct arrivals. Finally, some defect localization images are shown where the amplitude represents the scattering cross-section of the defect at 5 kHz and 25 kHz.