“…We detail the analytical computation of the two functions G and H introduced in Section II, the following equations and notations being largely borrowed from [9]. Denoting by c, c O , c 1 , c 2 , c 3 the sound speed, respectively, at the source depth z, the observer depth z O , the sea surface depth z 1 = 0, the minimum of celerity depth z 2 , and at the bottom depth z 3 (assuming c 1 > c 3 > c 2 , otherwise exchange the bottom and the surface, and z positive downwards), and by g 1 , g 2 the algebraic gradients of celerity in the surface layer and in the deep layer (note that these gradients are taken positive in [9], thus introducing minor changes of sign in the sequel), one recalls the expressions obtained in [9] for the eigenrays…”