WKBJ Solution and Transparent Propagators

2 For acoustic media Newton’s Law in frequency domain is � � �P � �i��v . (2) From equation (2) we get � P � i��v . (3) �z 1 �P � . (4) i�� z Assume the plane wave pressure field � P exp[ i( k x � k z � )] . (5) We have � � ik P � ik cos P (6) �z where k � � c � is the angle of wave propagating direction with respect to vertical direction (see Figure 1). Substituting equation (6) into (4) we get �cv P � � cv