Solution (source code)

= Solution

\b[In a zone with $dv/dz<0$, a descending ray bends towards the vertical instead of turning back towards the surface.] A ray cannot have its ordinary smooth diving-ray <turning point> within that decreasing-speed interval. There are rays turning above the zone and rays that penetrate it and turn deeper, after speed has increased sufficiently. The latter spend extra time traversing slower material, so their branch is delayed relative to a simple extrapolation of the original uniform-gradient curve.

Turning depths within the <low-velocity zone> are missing. In a piecewise-gradient example this can leave a range interval without a returning diving ray: a geometrical shadow zone between the shallow and deeper branches. The lower row of the original plot shows that situation, with the interrupted shallow branch and the delayed deeper branch. The boundaries are profile-dependent; reflected, refracted or diffracted <energy> can still arrive, and smoothing an idealized velocity maximum can change the branch limits. Thus the robust signature is the interruption/reorganization of the ordinary turning-ray family, not a universal claim of zero recorded signal. The supplied description alone does not specify unique numerical <travel times> or shadow-zone widths.