 Seismic ray parameter in horizontal layering

In horizontally layered isotropic media, horizontal slowness is conserved along a ray. The incidence angle $i$ is measured from vertical. A smooth turning depth satisfies $pv=1$. The range and travel time are $x=2\int pvdz/\sqrt{1-p^2{v}^2}$ and $T=2\int dz/[v\sqrt{1-p^2{v}^2}]$ for a symmetric surface-to-surface turning ray.