APPENDIX C 

 FOURIER TRANSFORM OF THE THREE-DIMENSIONAL GREEN FUNCTION 



Equation (36) can be expressed as 



G(x 



,y,z) = -77 J e-^^dk J 



i 2 2^/2 



^ 1/2 ^+ ^ ^^Pt^(^^+^^) ^il^} d£ (CD 



-- (k^+£^) I (kVa^) - K 



where 



(oH-kU) • 



(C.2) 



The first double integral of Equation (C.l) Is known. Therefore, we rewrite Equation 

 (C.l) as 



G(x,y,z) = - 



2^- S^^'^'"^ 



(C.3) 



2 2 2 2 

 where R = x + y + z and G„ Is given as 



G3(x,y,z) =^ J 



-Ikx 



dk< 



2 2 1/2 

 exp[z(k +£ ) -ly£] 



2 2^/2 22 1/2 

 -~ (k +£ ) [(k^+£^) -k] 



2^ J 



d2, 



> (C.4) 



If we assume y and z become very small. Equation (0.3) Is expressed as 



G(x,0,0) = - 



2 2 

 2tt(x +r ) 



YJ^- G3(x,0,0) 



(C.5) 



1. 2 2^2 

 where r = y + z , 



55 



