Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 82 / 4 / b / Solution

For downward-phase reversal, the P-SV displacement potentials instead produceEliminating the potentials as before givesThe Hermitian part is negative definite, and consequentlyfor a nonzero backward displacement field. The P potential must use vertical wavenumber $k_{\alpha }$ and the S potential $k_{\beta }$, as in the original PDF; the TeX incorrectly gives the shear wavenumber for both.