RANGE 



X 



I— 



a. 



LU 



Q 



Figure 9. The Principal Ray Types 



solving the depth dependent wave equation and evaluating the ray type integrals. 

 If WKBJ and stationary phase techniques are used, respectively, the classical 

 ray theoretic solution is obtained. MurphylO replaced the WKBJ technique with 

 a Weber function representation in order to treat the two-turning-point problem. 

 Brekhovskikh replaced the method of stationary phase with an Airy integral 

 modification in order to investigate r-austics. 



At present, our propagation model uses the following modified WKBJ ex- 

 pression to solve the depth dependent wave equation: 



F+(z;X,«j)= T^/^w^/^ exp|+iwQ(z^, z^;\) + iir/4^ 



g(z;X) (Bil" p(z;X)J + iAijw 



2/3 



p(z;x)}). 



Q (z 





2/3 



(3 V'^/-^ 



p(z;X) = --J- Q (z, z^;X)J ,andg(z;X) 



ap(z;X) 



az 



-1/2 



107 



