Non-destructive sub-surface inspection by A0-mode Lamb-wave measurement with opt-acoustical Spatio-gradient analysis

This paper proposes the third-largest eigenvalue imaging is proposed which has an ability to classify the Lamb´s wave field through the rank of the covariance matrix defined over the 4-dimensional vector space which is spanned by following components:(1) a vertical (z-directional) displacement, (2) its vertical particle velocity, (3) x-directional and (4) y-directional out-of-plane strains. Focusing the rank of the covariance matrix, we can find following facts in the far field: (1) rank=2: when no-defect exists over the Lamb wave field, or even when defects exist only on the line colinearly with a pair of acoustic transmitter and receiver, (2)rank=3: in other cases, and in the near field of the defects (3) rank=3.