Journal of AE, Volume 23, 2005 (ca. 43 MB) - AEWG

Based on the results in Table 6, we note that the ranking in Table 5 (at a certain propagationdistance) of the best to worst SD for each frequency and mode generally correlates with theamount of relative dominance of that frequency/mode regardless of the propagation distance. Forexample at 60 mm, the best SD for case 9034 has a strong dominance for the 60 kHz/A 0 mode(4.3, see Table 6), and the worst SD for case 9002 is actually dominated by the 522 kHz/S 0 mode(1.3, see Table 6). Table 6 also provides a reason for the SD ranking (in Table 5) changing withthe propagation distance. The increase in 60 kHz/A 0 mode dominance (see Table 6) with increasingdistance correlates with the observation that at the larger propagation distances the 60kHz/A 0 mode generally has the best SDs, except for one case (we ignore case 9002 since bothmodes have about the same peak magnitude). The results for case (2791) rank as one of the bestat all the propagation distances due to the fact that the dominance of the 522 kHz/S 0 mode is verystrong since there is no A 0 mode for this midplane source.A question arises, why are the 522 kHz/S 0 mode results the best at the 60 mm distance eventhough there are two 60 kHz/A 0 cases (9034 and 9004) with strong dominance? The answer tothis question is likely due to the “spreading in time” of the WT results at lower frequencies. The“spreading in time” terminology refers to the signal at a specific time contributing to the WTmagnitudes over a range in time about that specific time. This characteristic at lower frequenciesis illustrated in Fig. 5. In this figure the input signal to the WT is a Dirac delta function. Thus wesuggest the 60 kHz/A 0 mode WT peak magnitude arrival time has larger errors since the WTpeak magnitude in that case reflects a wider time-range of the noise signal (see Fig. 5). In contrast,the 522 kHz/S 0 mode WT magnitude does not have the same range of arrival time errorsbecause the WT peak magnitude at that frequency does not result from as wide a time range ofthe noise signal. At the longer propagation distances, the drop in the dominance of the 522kHz/S 0 mode is evidently sufficient to allow the higher magnitude noise in the region of 522 kHz(see Fig. 2) to increase the SDs. This results in the 60 kHz/A 0 mode SDs being generally thelowest at the longer distances.9. Relative Fall-off of the 522 kHz/S 0 Mode with Increased Propagation DistanceThe 522 kHz/S 0 mode falls-off at a faster rate than the 60 kHz/A 0 mode with increasingpropagation distance as is shown in Table 6. Since the finite element modeling results did notincorporate the available frequency-based attenuation with propagation distance, the source ofthis frequency/mode fall-off is of interest. Since the frequency band is only 3 kHz wide in theWT computation, there should not be much dispersion with increasing propagation distance. Tocheck this assumption, the profile of the WT magnitude (at each of the two frequencies) as afunction of time was plotted for one of the cases (case 9002, noise-free signal) at the threepropagation distances. The normalized results in Fig. 6 show some potential dispersion for the522 kHz/S 0 mode. For example, at 60 % of the peak magnitude of the 522 kHz profile (in thelargest magnitude peak region) the width of the profile increases by 50 % as the propagationdistance increases from 60 mm to 180 mm. On the other hand, the change of width over thosepropagation distances at this level was not perceptible for the 60 kHz mode. It is suspected thatthis fall-off can be attributed to the following observations. In the 522 kHz region of the S 0mode, the group velocity curve makes nearly a “U-turn” (see Fig. 1 in reference 1) in the groupvelocity direction over a limited range of frequency change. Thus a range of frequencies in thisregion have about the same group velocity. This feature, in combination with the characteristic ofthe WT described next, likely causes this attenuation.11