In solving eq.uation (l^*-) the following assiraptions have been made: 



(1) Coherence peaks greater than O.kk (the lower limit of the 95 

 percent confidence level) are assumed to be meaningfial. The periods and 

 phase angles associated with these peaks are given in figures 8b and 9b. 

 (in one case, the 25-second peak, although falling slightly below the 95 

 percent confidence line, has also been used in these computations to pro- 

 vide continuity in the spectra.) 



(2) The waves obey classical gravity wave theory. For the period 

 range considered, it was assumed as Robin (I963) had done, that the veloc- 

 ities and wavelengths of the waves were essentially unaffected by ice cover. 



1/2 

 Thus the velocity C ^ [ gX tanh ^ 1 ^"^^^ 



1/2 

 and X= Xd rtanh 277_H-j ' (16) 



where C = wave velocity (m/sec) 

 g = gravity (9.83 m/sec2) 

 H = water depth(m) 



T = period (sec) 

 (3) Although the array was located in deep water (approximately 

 l,600m) the presumed direction of incoming waves was across the wide and 

 shallow continental shelf north of Siberia. Since tne greatest portion of 

 the total distance traveled was across this shelf, an average depth of 150m 

 was used in the computations of X . 



The solutions for a computed from equation (lU) and corresponding to 

 waves from the west are plotted in figure 12. The values of q for periods 

 of 25 seconds or more are unique. As the wave periods become shorter than 

 25 seconds, two, three, four, and finally five solutions become possible. 

 For periods shorter than 25 seconds, there is no real guide for the choice 

 of solution or solutions. In the analysis of Munk et al. (1963), the exten- 

 sion of the unique solutions, i.e., when j = 0, was preferred, because a 

 sense of continuity was maintained. This was justified because their plot 

 of coherences vs frequency, upon which their solutions of a were based, was 

 itself fairly continuous. No such continuity was observed in the plot of 

 coherences versus frequency in this study, rather there were discrete coher- 

 ence peaks emerging from the noise level. Thus, it appears just as likely 

 to have short-period solutions of a coming from the higher order branches 

 as from the j = branch. This problem cannot be resolved without an 

 additional element in the array. 



The peak at 167- second period (figure 9h) poses an interesting problem. 

 With its computed phase angle of 176° no solution of equation (l^) exists. 



2k 



