RMO function with arbitrary scaling of velocity

The derivatives of $z_{\tilde{\gamma}}$ and $\Delta z_{\rm RMO}$ with respect to arbitrary perturbations of the individual velocity components (i.e. V_V, V_H, and V_N) have no simple form in the case of dipping reflectors and depend on the particular form chosen to approximate the slowness function. The derivatives of $z_{\tilde{\gamma}}$ are

$$\begin{eqnarray} \frac{\partial z_\gamma}{\partial \rho_V_V} = -\frac{z_\xi}{2} ... ...(\alpha_x-\gamma)} \frac{\partial S_r}{\partial \rho_V_N} \right).\end{eqnarray}$$ (33) (34) (35)