 Seismic layer transfer matrix

At normal incidence, a uniform lossless elastic wave layer of thickness $h_j$, speed $c_j$ and seismic impedance $q_j={\rho }_j{c}_j$ has wave phase thickness ${\delta }_j=\omega h_j/c_j$. With phasors proportional to $e^{-i\omega t}$, particle velocity $V$ and compressive traction $P=-T$, the displayed matrix maps $(V,P)$ from the top to the bottom. It has determinant one. Multiplying these matrices in physical order accounts for all coherent multiple reflections. Continuity of $V,P$ connects adjacent layers without another propagation factor.