Time-shift imaging condition for converted waves

Time-shift angle decomposition for converted waves

Using the same definitions for $\vert{ \bf p}_{ \bf s}\vert$ and $\vert{ \bf p}_{ \bf r}\vert$ as in the preceding subsection, we can use equation  $\left( \ref{eqn:PmPh-b-cw} \right)$ to derive the relation

$$\cos^2 \theta = \frac{1}{\gamma } \frac{\vert{ \bf p}_{ \bf ... ...ert^2}{4s^2} - \frac{\left (1-\gamma \right)^2}{4\gamma } \;.$$ (15)

For PP reflections ($\gamma =1$), this expression reduces to

$$\cos \theta = \frac{\vert{ \bf p}_{ \bf m}\vert}{2s} \;.$$ (16)