358 



EXPLORATION GEOPHYSICS 



L x^WX'^ + 'f- + Z'^ y \/x'? + 3;- + z-^ 



- tan-i 



X'l \/x2~ + y^ + zi^ 

 + tan-i m 



ysi , , _i X2Z1 



— + tan ^ 7:==z 



y \/x-^ + 7- + ^1^ 



— tan ^ 



•^1 V'1^1^ + y^ + Zf^ 



£i£i 



y ^/x-^ + 3^^ + z^ 



-tan-i ^ -^'"- + tan-i ''"^^- 1 (124) 



•^1 V-*"!^ + y- + ^2^ y V'^'l^ + y^ + Z-l" J 



(f) Same as (e) except y — y\ and 3/2 where | 3'2 | =7^ | yi I 



U xz= Cro lOge - =r "— • 



L V-'^'i^ + y2^ + ^1" + y2 yx^ + yi^ + Z-^ 



+ 



-^1 (125) 

 y^A 



L_ V -*1 "J" 3'2 ~T~ •'^l ' 3'2 V'*'l "^yi ~t~ -^2" I" 3'l 



. 1 \A'2^ + A'2^ + ^1^ + ^2 ^Jx-^ + Vi^ + ^2^ + V 

 + loge - ^ ^ "— • =^ 



\/-^'2^ + A'l" + Z^ + 3'i \/-^'2^ + >'2^ + ^2^ + 3': 



IJyg obtained from U ^z by interchanging x and y 



Uxy — Gct loge • 



L V-tV + 3-1^ + ^2^ + ^2 ' 



U^ = - G(t\ tan-i - 



L X 



3'!^ + 5^o2 + Zo V-*"!^ + 3^2^ + ^1^ + ^1 

 V^to-TTi- 4-52^ + ^^2 ^ \/r2^ + 72^ + Z-j- + Zi (\2C\ 



\/X2^ + yi' + ^^1^ + Zx \/x^ + 3/2^ + Z<^ + ,22 



; ^JX'? + 3^2 



+ tan-1 



xo\/ x^r -r 3'2^ + 2^2^ 



A' 12-1 



- tan-1 



■y2.g2 



tan~ 



L 1 



X2 V-^'2" + 3^1" + ^1^ 



+ tan ^ -=====^ — tan 



^1 V-^'i^ + y'^ + "1" 



+ tan ^ — tan- 



-ri V't'i^ + 3'i^ + Z'^ 



— tan ^ 



tan-i 



- tan-i 



- tan-i 



7===^= + tan 



===== +tan 



xi V-^'i" + 3'2^ + -2" 



• + tan 



X2 ^/xo^ + 3'i" + ^2^ 



+tan 



X2 V-^'2" + 3^2^ + ^1" 



3'2 \/x2^ + 3'2" + Z2^ 



3'i V-^2^ + 3'!^ + ^i^ 



X\Zx 



3^2 V-^'i" + 3'2^ + ■s^i^ 

 ,ri^2 



3'i V^i^ + yi^ + 



Z2' 



3'i V-'^i^ + 3'i" + -2^1^ 



.Tl£^2 



3'2 V-'-'l" + 3^2" + ^2^ 



Vl V'^'2^ + 3'!^ + ^2^ 

 XoZx "I 



3'2 V-*'2^ + 3'2^ + '^l^J 



(127) 



