TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC-EAUATION METHOD IN 

 UNDERWATER ACOUSTICS 



SOURCE MODELING — ASYMPTOTIC MATCHING 



Exact: 



r-^ + (z - z 



T~72 



z - z 



(8) 



Parabolic approximation: 



2 _ 



ill^l 



(9) 



(10) 



e.g. 



nz,o) = A e"^^ - ^o^'/^' -.A 



3/A A 



-^ , 0) = ^ (11) 



r ■f 



VTT OJ 



BOUNDARY CONDITIONS; 



IMAGE 

 SOURCE 



SOURCE 



"MUD" 



IMAGE BOTTOM 



SEAMOUNT 



BOTTOM 



"h,TTTr\" 



'MUD 



\v\\\\\\s\\\\\\ \\\\W\\ \\\\\\\\\N> 



Figure 2. INITIAL AND BOUNDARY CONDITIONS 



160 



