Local Segment 



Figure 1.2: Segment of record considered for local approximations 



1.2.1 Global Methods 



Spectral Methods 



The most commonly used global method for the analysis of irregular waves is 

 spectral analysis, coupled with superposition of linear waves. Spectral methods based 

 on a single point measurement seek to define the sea state with a variance spectrum, 

 E{ll>) which specifies the contribution to the variance of the water surface at each 

 frequency, u. In practice, the spectrum is defined in discrete form, with the water 

 surface described by the superposition of many linear waves, 



M 

 rj{x,y,t) — 22 am cos {km (xCOsOm. + ySmOm) - OJmi + OCm) (1-1) 



771=1 



where r] is the elevation of the water surface, Um and km are the frequency and wave 

 number of the mth wave, Om is the direction of propagation of the mth wave and am 

 is the phase of the mth wave at the origin of the coordinate system. 

 The amplitudes are found from the discrete variance spectrum, 



am = \/2E{Um)^iO 



(1.2) 



where Au is the frequency spacing of the discrete spectrum. The frequency and wave 

 number of each of the M waves are related by the linear dispersion relation. 



u;^ = gkmtd.rih.kmh 



(1.3) 



