The change in the horizontal displacement due to the wave particle velocity with 

 respect to depth, which is related to tilt angle, is 



j£ = ak sinh k ( d - z ) sin (kx-qt) (29) 



3z sinh(kd) 



Now, the wave profile is represented by 



n = a cos(kx-ujt) (30) 



and the wave slope follows as : 



-iD = - aksin(kx-o)t) (31) 



3x 



If we assume linear wave theory, then Equations (29) and (31) can be combined to 

 relate the measured tilt angle to the desired wave slope as 



_3_£ _ f3_rn sinh k(d-z) 

 3z 3x sinh(kd) 



or rearranging, ill = - i& sinh(kd) (32) 



3x 3z sinh k(d-z) 



where i£ = tancj) for the Wave Track buoy and where <J> is the vertical tilt angle. 

 3z 



Initially, the tilt angles are converted to surface slope in the raw data file. 

 Once the auto and cross spectra have been computed for the spectral analysis, the 

 depth effect, i.e., hyperbolics, are applied if necessary. 



The phase correction and the magnetic declination are also applied in this 

 process. Phase corrections must be applied since wave buoys do not follow waves 

 precisely, nor do their electronics respond instantly. Hydrodynamic and electronic 

 lags are inherent. At this time there are no hydrodynamic phase corrections 

 to the buoy known to the authors. However, the manufacturer, ENDECO, has provided 

 the authors with electronic phase corrections that were developed from rotating arm 

 tests. Ideally, the corrections consist of electronic phase lags of the heave 



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