frequency to one previously selected. This usually resulted in an unreason- 

 ably large increase in amplitude and a large phase change for the previously 

 selected constituent as an interference pattern was set up between the two 

 frequencies. Such occurrences are considered an artifact of the attempt to 

 fit a particular field record. Since they destroy amplitude and phase infor- 

 mation for previously selected constituents, it is expected that they can only 

 obscure any meaningful physical processes. Therefore, the constituent which 

 gave rise to the first such occurrence and all subsequently selected constit- 

 uents were ignored. 



Between 10 and 21 constituents were retained in each MRS analysis which, 

 in the final run, accounted for between 53 and 81 percent of the variance in 

 the field data. Figure 11 illustrates how the explained variance increases 

 as more constituents are added for one South Haven record. The figure also 

 illustrates the improved effectiveness of the constituents as their frequen- 

 cies are tuned in successive MRS runs. Figure 12 shows similar results for 

 one Columbia Light record. 



The veracity of constituents returned by the MRS was tested by analyzing 

 an artificial 512-second record made up of three fundamental frequencies and 

 their second and third harmonics (Table 2). Frequencies used in the first MRS 

 run were intentionally offset from the true frequencies. The second MRS run 

 included frequencies nearly identical to the true frequencies. The MRS analy- 

 sis returned excellent estimates of both amplitude and frequency for the three 

 fundamentals (Fig. 13). In all three cases the MRS points plotted closest 

 to the actual constituents were from the second MR^S run. Second harmonic 

 frequencies were also included in the MRS and were successfully identified for 

 two of the three frequencies, as indicated in the figure. The frequency line 

 spacing from the standard FFT analysis of a 512-second record (Fig. 13) 

 clearly indicates that MRS allows a frequency resolution superior to FFT 

 analysis. 



The absence of MRS constituents near the second harmonic of the middle 

 actual frequency in Figure 13 bears further discussion. This second harmonic 

 has the smallest amplitude of the three included in the artificial record. 

 MRS eventually selected a constituent appropriate to this second harmonic, but 

 the selection occurred after the normal termination point. Similarly, it is 

 expected that the MRS analysis of field records will omit some constituents 

 which may be important in identifying structure in the records. However, it 

 also seems clear that dominant constituents will be properly identified and 

 retained. 



Phases returned from MRS analysis of the artificial record were within 4° 

 of the actual phases of the fundamentals (Fig. 14). The ability to identify a 

 meaningful phase, demonstrated in the figure, is a vast improvement over the 

 uncertainty in phase obtained in FFT analysis . 



34 



