Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 6 / b

The reflected P wave remains in the upper layer. Conservation of horizontal seismic ray parameter gives $\sin i_r/V_{P1}=\sin 30^{\circ }/V_{P1}$, so the reflected P angle is $30^{\circ }$ from vertical. This is specular reflection at the horizontal interface.

For the converted reflected S wave, Snell law for elastic waves givesThus $i_{S1}=17.46^{\circ }$ from vertical, in the upper layer. The converted in-plane mode is SV; an isotropic planar P incidence does not generate an independent SH mode.

The required transmitted P wave angle would satisfyTherefore there is no real transmitted P-ray angle. The incidence exceeds the P critical angle $\arcsin (1500/3500)=25.38^{\circ }$; the transmitted P contribution is evanescent away from the interface rather than a propagating body ray. Reporting $90^{\circ }$ would describe critical incidence, not the stated $30^{\circ }$ incidence.

The transmitted converted S wave obeysHence $i_{S2}=41.81^{\circ }$ from vertical. A propagating transmitted SV mode can exist even though the transmitted P mode is already supercritical.