Interpolation Surface Versus Graphical Method of Ray Construction . 

 Consideration of the above-mentioned surface-fitting programs led to the 

 choice of the linear surface of best fit as the most suitable one for use 

 in construction of wave rays. In general, it was found that rays run with 

 the linear surface of best fit compared most favorably with rays constructed 

 by graphical methods, and this is the case in the plotting example (Figure 9, 

 A and D) , An advantage of the least-squares linear-interpolation method 

 over the graphical method lies in the fact that ray curvature can be com- 

 puted at a number of points between contours. Aside from the absolute 

 validity of the two methods of wave-ray construction, the computer method 

 is estimated to be many times faster than the hand method when only the 

 terminal points are desired of a large number of rays. Where only a few 

 rays are desired, the hand method is clearly the most rapid and economical. 

 Because the practice of refracting only a few rays for a few wave periods 

 yields totally inadequate information upon which to assess wave heights and 

 energies at the shore, it seems clear that the real considerations are not 

 so much the man-hours involved in depth-grid and program-deck preparation 

 for the computer as they are in the necessity for the more realistic results 

 that can be afforded by the computer construction of wave rays for entire 

 wave spectra. 



Future Interpolation Schemes . A more valid interpolation scheme 

 would be obtained if a grid of depth values were input to MAIN 1620 or 

 MAIN 7094 instead of a grid of velocity values. The assumption, that the 

 grid interval be selected such that depth contours in any grid cell be 

 represented by straight and parallel contours, would then be perfectly 

 valid. In this case, a depth value would be obtained from the interpola- 

 tion surface at a given calculation point. Then, using the procedure used 

 by OOMPV (Appendix A), the depth value could be converted into a wave- 

 velocity value. It is noted that, in order to obtain curvature (FK) at a 

 calculation point, £l9 and "_ are needed. If a linear-interpolation program 



Bx 



By 



;re used with an input depth grid, expressions would be available for 



and -gy- The following, relationship (derived in Appendix F) could then 

 ! used to obtain 2^ and22: 

 9x By 



BC ^ 3d 2 9£ = 

 Bx Bx" ' By 



3d 

 By- 



where 



Z = 



Ck" 



Ck" 



l+k"C l-k"C 



+ In (l+k"C) -In (l-k"C) 



In this expression k' = T/4Tr and k" = ZVgT. If a quadratic surface were 

 to be used for interpolation similar relations could be derived to relate 



3^C , 3^C .^. B^d , B^d _ , 

 — - and — - with — - and — - , respectively. 



Bx 3y Bx By 



