 Solution

For a P-to-S converted seismic head wave, set the transmitted S-wave angle to $90^{\circ }$, giving $\sin i_c=V_{P,\mathrm{incident}}/V_{S,\mathrm{transmitted}}$. At the limestone–sandstone boundary, $2500/1200>1$, so no transmitted S-wave head wave is possible for incidence from limestone.

At the sandstone–salt boundary, using the stated interpretation $V_{S3}=3000\mathrm{m}{\mathrm{s}}^{-1}$,The P-transmission seismic critical angle is lower, $30^{\circ }$, but this does not forbid the converted S branch: at $41.81^{\circ }$ the transmitted P field is evanescent while the S field reaches grazing incidence.