Appendix A: Details of the Application of the Source Identification Scheme‪.‬

The 19 signals in the database (three source types at six or seven depths each) were analyzed according to the scheme described in section eight. The analysis was done for both the 45/0 and 67.5/0[degrees] angle ratios. Table A-1 outlines the key results for each case (a source type and source depth defined a case) of the three-source-type database when 45[degrees] was the second radiation angle. In this table the logic of the analysis scheme outlined in section eight flows from left to right. The first column identifies the known source type. The scheme and calculations proceed starting from the third column as if the source type was unknown. The next-to-last column shows the source type that was "determined" for comparison with the known information. Table A-2 gives the same results for the choice of 67.5' for the second angle. The last column (called the "reduction factor") in each of these tables records the ratio of the peak WT magnitude of the primary frequency from the zero degree direction divided by the peak WT magnitude of the lowest peak magnitude at the second angle (primary or secondary as required) to uniquely determine the source type. The tables also record the percentage difference from the calculated primary and as needed secondary angle ratios for each signal case as compared to the average angle ratios (table 1) from the nearest source type(s) eliminated at each step. At first glance, a comparison of the two tables seems to indicate that the choice of 67.5[degrees] as the second angle would be best. The reason for this tentative conclusion is that the percentage differences between the angle ratios for the selected source(s) versus the angle ratios for the source(s) rejected for a given case is considerably greater in the 67.5[degrees] case. Thus with this second angle, errors in angle ratio values due to the effects of the presence of noise might be expected to be less likely to lead to incorrect selection or rejection of source types. But upon closer examination, there are several reasons why the choice of 45' seems to be better. First, the last column (reduction factor) in the two tables indicates that for most of the depths of the in-plane dipole source, the loss in the WT peak magnitudes at 67.5[degrees] [table A-2(a)] for the lowest peak WT magnitude required for unique source identification is considerably greater than that for 45' [table A-1(a)]. Thus the advantage of potential tolerance to angle ratio errors could be overpowered by a substantial increase in the size of the noise-induced errors because of a considerably lower S/N ratio at 67.5[degrees]. Second, when the two tables [A-1(c) and A-2(c)] are compared for the microcrack initiation source, there are problems of a different type. In certain cases (depths of 2.35 to 1.723 mm) the frequency/mode combination at 67.5[degrees] is not the same as that at zero degrees for either the primary and/or the secondary angle ratio. Thus a relevant angle ratio could not be determined, and it was not possible to identify the source type using the scheme described in section eight. For the shear source, a comparison of the two tables [A-1(b) and A-2(b)] does show a genuine opportunity to experience reduced effects from errors in peak WT magnitudes caused by noise if the 67.5[degrees]angle is used for most depths (except 1.097 and 0.783 mm). The reason for the potential advantage is that the WT mode peak magnitudes decrease only moderately between 45' and 67.5', while the difference in the average angle ratio value between alternate source type(s) selections has increased markedly. This potential advantage for the shear source type is outweighed by the potential difficulties of the other two sources types. Further, the practicality of implementing angle ratios at different angles for different source types does not make sense when the problem is to identify unknown source types. Thus, the 45/0[degrees] angle ratio was used in the signal-plus-noise considerat