Test.* The first test compares the maximum variance to the sum of all of the 

 neighboring variances, while the second allows a more complicated comparison 

 through on F-test. A significance level of .05 was used in both cases. It turned 

 out that in the inner region (0-50 nautical miles from the coast) a stretch of sea 

 surface approximately 3 miles long could be considered as weakly homogeneous , 

 For the outer region (distances greater than 50 nautical miles) this length increased 

 to approximately 7 miles. Obviously, the transition from the 3 to 7 mile length was 

 not abrupt. By considering it as such, we give up some spectral confidence in the 35- 

 50 mile range, but this is made up for by the gain in uniformity of analysis. 



6.0 THE SPECTRAL TRANSFORMATION 



6.1 The Frequency Transformation 



The problem of relating the frequency and direction of a free wave to its 

 apparent frequency and direction, as observed from a moving platform, has been 

 discussed in detail by St. Denis and Pierson (1953) and also by Snyder and Cox (1966). 

 The practical aspects of the frequency mapping and spectral transformation have been 

 put forth by Cartwright (1963). Cartwrights paper was of considerable assistance in 

 the mathematical formulation of this section. 



U IS 



The relation between real wave frequency a and the apparent wave frequency 

 w =o-_ o- V cos f' ^ ^5) 



where V is the speed of the moving platform and 4^ is the angle between the direction 

 of platform motion and the direction of wave propagation. The basic equation (5) 

 will give a unique value of w for any fixed values of a and ^ . On the other hand, 

 the inverse relation 



^ ^ 1 ±-\/ 1 - (4a;V COS xP )/g^ 



2Vcos ^/g (6) 



is non-unique. The speed of the platform and the value of ^ determine which branch 

 of (6) is to be considered. Cartwright gives a very succinct discussion of the various 

 possibilities of this determination, therefore, such a summary will not be repeated here. 

 It will suffice it to say, the problem is a bit complicated for the general situation in 

 which the speed of the platform can be less than the speed of the fastest wave. In this case. 



*The generous assistance of Dr. H. C. S. Thom in making these choices is gratefully 

 acknowledged . 



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