## 3 Experimental Procedures
The start time of this WT was at 169 \(\upmu\)s and the A\({}_{\text{o}}\) peak corresponded to 1.18 mm/\(\upmu\)s velocity, subtracting the signal risetime of 6 \(\upmu\)s. This matched the predicted A\({}_{\rm o}\) velocity of 1.18 mm/\(\upmu\)s. On this spectrogram, a notable non-A\({}_{\rm o}\)-mode signal was found from 530 to 600 kHz, starting at 180 \(\upmu\)s. This part was due to the S\({}_{\rm o}\) mode and was excluded from further processing. WT analysis was conducted for each propagation distance for the set of S\({}_{\rm o}\)-mode and A\({}_{\rm o}\)-mode signals. WT intensity was obtained as a function of time and frequency. The frequency step used was typically 7.5 kHz. For a given frequency, WT intensity values were summed over a selected duration that covers the expected mode arrival times. When the range of frequency was wide, the summed values were sometimes aggregated over two or three frequency steps, doubling or tripling the frequency step to 15 or 22.5 kHz. Next, the summed WT intensity values at all propagation distances were arranged in a table, from which attenuation coefficients were determined. The WT intensity, I, obtained by AGU-Vallen Wavelet software is given as the square of amplitude multiplied by time interval. Because wave attenuation is defined in terms of wave motion, or vertical displacement, D, of Lamb waves [2] (p. 91), we have  
\[\sqrt{I}=aD=D_{\rm o}\exp(-\alpha^{\prime}x), \tag{1}\]  
where a and D\({}_{\rm o}\) are constants, \(\alpha^{\prime}\) is attenuation coefficient in Np/m, and x is the wave propagation distance in m. For planer waves, geometrical spreading reduces displacement by the square-root of x [2] (p. 89). Combining these, one obtains  
\[D=D_{\rm o}\exp(-\alpha^{\prime}x)/\sqrt{x}. \tag{2}\]  
Figure 3: _Cont._  
Figure 3: _Cont_. In practice, we use attenuation coefficient \(\alpha\) using the unit of dB/m. This comes from the slope of a plot of 20 log (D\(\surd\)/x) vs. x. This means that D\(\surd\)/x is expressed in dB scale. This D\(\surd\)x term is denoted here as the WT intensity sum. An example is given in Figure 3e. This dataset produced Figure 3a,c plus six more test data for x between 125 and 275 mm. In particular, this plot is for symmetric mode waves at 496 kHz. A linear regression fit was obtained with \(\alpha\)-S\({}_{\rm o}\) = 49.3 dB/m and R\({}^{2}\) = 0.993. The values of \(\alpha\)-S\({}_{\rm o}\) were determined from 206 to 600 kHz and are plotted in Figure 3f. Average R\({}^{2}\) value was 0.921, which indicates a satisfactory fit. Only one R\({}^{2}\) value was below 0.8 at 0.795 for the data in Figure 3f. Below 200 kHz, R\({}^{2}\) values decreased to below 0.7, or no attenuation was detected. Above 600 kHz, the I value decreased to below 30% of the peak, and the \(\alpha\)-S\({}_{\rm o}\) value started to decline with frequency. This is caused by a slow decrease in I values at larger x, apparently due to higher contributions from background  
Figure 3: **(a)** Displacement amplitude (in pm) of symmetric Lamb waves detected on front side (blue curve), back side (green curve) and summed (halved, red curve) on 1.4-mm PS sheet. Propagation distance: 200 mm. Signal arrival: 97 μs, Transmitter (Tx): NDT C16 (normal incidence), Receiver (Rx): KRN-BB-PC. **(b)** Displacement amplitude (in pm) of asymmetric Lamb waves. Same sample and transducers as above except halved signal difference is shown as red curve, Tx incident angle of 60\({}^{\circ}\) used and signal arrival at 169 μs (plotted from 170 μs). **(c)** Wavelet transform spectrogram of the summed signal (red curve, **(a)**). Transform start time was shifted by 97 μs. Red and blue represent high and low WT intensities. Dispersion curves for S\({}_{\rm o}\) and A\({}_{\rm o}\) modes are also plotted. Insert shows a partial WT spectrogram at propagation distance of 125 mm, shifted by 60 μs. **(d)** Wavelet transform spectrogram of the difference signal (red curve, **(b)**). Transform start time was shifted by 169 μs.