130 



the chances that the optimization will converge to a spurious minimum. 



Global Solution 



As with arrays of water surface measurements, a single short segment of the mea- 

 sured pressure records often may not contain sufficient information to identify the 

 directional trend of the wave field. As a result, it is necessary to examine a larger 

 segment of the record, for example an entire wave from crest to crest or trough to 

 trough, to get a general sense of the directional trend of the wave field. This global 

 solution can then be refined to fit a small segment very closely. This approach is used 

 to establish the initial estimate for the optimization procedure in each window. 



The procedure for computing the initial estimate to the global solution for an 

 array of pressure measurements is virtually identical to that used in the previous 

 chapter for arrays of water surface measurements. It will be outlined here. For more 

 detail, see section 5.3.2. 



For the initial estimate, it is assumed that the pressure records can be approxi- 

 mated with linear wave theory: 



Pd = a cos {k:,;Xn -\- kylfn — iOtm + «) (6.8) 



for the single wave method, and 



Pd - ai cos {kj:^iXn + ky^iljn - iOitm + Oti) 

 -1-02 cos {kx,2Xn + ^^,2?/^ " "^2^™ + <^2) 



for the two wave method, where: 



(6.9) 



a„ = AnPtOn 



cosh.Kn{h + Zp) 

 cosh Knh 



l\n — \ k -\- k 



(6.10) 



An is the amplitude of the linear potential function of the nth wave, and z-p is the 

 elevation of the pressure array. 



