In this paper, a guided wave tomography method based on full waveform inversion (FWI) is developed for accurate and high-resolution reconstruction of the remaining wall thickness in isotropic plates. The forward model is computed in the frequency domain by solving a full-wave equation in a two-dimensional (2-D) acoustic model, accounting for higher order effects such as diffractions and multiple scattering. Both numerical simulations and experiments were carried out to obtain the signals of a dispersive guided mode propagating through defects. The inversion was based on local optimization of a waveform misfit function between modeled and measured data, and was applied iteratively to discrete frequency components from low to high frequencies. The resulting wave velocity maps were then converted to thickness maps by the dispersion characteristics of selected guided modes. The results suggest that the FWI method is capable to reconstruct the thickness map of a irregularly shaped defect accurately on a 10-mm-thick plate with the thickness error within 0.5 mm.

A quantitative study of the interaction of the T(0,1) torsional mode with an axial defect in a pipe is presented. The results are obtained from finite element simulations and experiments. The influence of the crack axial extent, depth, excitation frequency, and pipe circumference on the scattering is examined. It is found that the reflection from a defect consists of a series of the wave pulses with gradually decaying amplitudes. Such behavior is caused by the shear waves diffracting from the crack and then repeatedly interacting with the crack due to circumferential propagation. Time-domain reflection coefficient analysis demonstrates that the trend of the reflection strength for different crack lengths, pipe diameters, and frequencies from a through-thickness crack satisfies a simple normalization. The results show that the reflection coefficient initially increases with the crack length at all frequencies but finally reaches an oscillating regime. Also, at a given frequency and crack length the reflection decreases with the increase in pipe circumference. An additional scattering study of the shear wave SH0 mode at a part-thickness notch in a plate shows that the reflection coefficient, when plotted against depth of the notch, increases with both frequency and notch depth.