Pseudo-isotropy about the Z axis

The condition is that

<I>WI>_<I>zI> = <I>WI>_<I>xnmoI> (13)

For P waves this means

$$\begin{eqnarray} W_{33} & = & W_{44} + \frac{(W_{13} + W_{44})^2}{W_{33} - W_{44}} \end{eqnarray}$$ (14)

which is

(<I>W₁₃I> + <I>W₄₄I>)² = (<I>W₃₃I> - <I>W₄₄I>)² (15)