134 



Using these linear wave theory estimates as the first guess, the full order optimiza- 

 tion, Eq. 6.7, is computed to determine the best full order fit to a global segment of 

 the record. The parameters of the potential function computed by this optimization 

 are then used as the initial estimate for the final optimization in each defined small 

 window in time. 



Phase Shift The phase parameters, Oi and 02 are adjusted to accommodate the 

 change in the time reference frame from the global to the local solution: 



On = — ^nAi + Q;n,global (6.23) 



where A^ is the difference between the time in the two reference frames. 



Nonlinear Optimization in Windows 



The established global solution is used as the first guess for the parameters in 

 each window, and these parameters are refined in the same manner as the previous 

 chapters by solving Eq. 6.7 with any standard nonlinear optimization routine. 



The resulting solution is then checked to see if is clearly spurious. Spurious solu- 

 tions can be identified by the same criteria used in the previous chapters: 



• Very large or systematically variable errors. 



• First order amplitude smaller than one of the higher order amplitudes. 



• Unrealistically large or small frequency or wave number. 



• Large discontinuity between the windows in the predicted kinematics. 



If no solution or a spurious solution is found, the parameters of the solution are 

 revised for another attempt. These revisions include increasing the width of the 

 window, and decreasing the order of the solution. If neither of these adjustments 

 result in an acceptable solution, the window is skipped, and future analysis must be 

 interpolated through that point. 



As with the analysis of a point pressure measurement, these adjustments are most 

 likely to be needed in the long, flat troughs of shallow water waves, or near zero 



