11 



Decision on G;rid Jntery^l a^d Nuimb.er of Points ^9 be Head 

 Fortunatel,Y thre^-iheoretical aspects of the problQrn Ixad bfeen carried out 

 to the point wl^ere tl;(,e methods for tJ-^e gnc^d^Tie^ipLB^xx!^} ayn^lys'QS Qi t{iioa^e series 

 developed by Tukey [l9'^-9] hpid bee^i c::r(j,a-A:i^;i3jd- t® ^1,€ twortdirnerisjonal v/aye 

 number analysis desired in t2iis problena, Thuo tap formuLas for reaolution^ 

 aliasing^ and, deg^ireos of freedoj.Ti -wj-nre ay:a,i.la';4e,. • They vviil be derived in- 

 Part o. It v/ao also jrealized tlv^it it was nqt es3ejTi^;aJ. tp ha.ve the dominant 

 wave direction roughly parallel to the gides of ^:^c recta^ngular grid of points 

 to be used. 



The leveling problem wag then studied and forniulas were derived for 

 determining the true zero reference plfiinei*. ft wa.s assumed that the spot 

 heights would be reportedi with refqrgnce to some; unknown a.r'bit.rary refer- 

 ence plane of the form z = ax + I y + c. If f) is th<? reported value,, then- 

 Yl^ * = Tl - a^' ^^by r c is the vaiuo. with ref^rqnce ip a true xerg) refajrence plane, 

 and SS(/l*)^ will be a rninimump, Ly atjcJ-jidard least squares tschniques,, the 

 values for a,, b and c can be determined, aj^d t^e data can be leveitd^ The 

 derivation and tlie procedures t.,T.ed a.re descr-^bod V* ^XQ following two parts 

 of this r oporto 



Since leveling was no longer a problem, t^Ae problanns of Gt£',ti:;tic?.l re- 

 liabilityj aliasinga and reso/lutdan were Et'-cliqd. Suppose that Ci'i spot heights 

 are read at an interval of A.vr. fe.:t on a square grid. Th|Sn, due to the nature 

 of the metliods of analysis^ sorae ;:pectrai components shorter than 2A::. and 

 all corxiponfiintG shorter than V^,\x v.dU be aliased ao that they appeal* as 



