The partial derivatives of the RMO function are directly derived from the partial derivatives of , taking into account that for flat reflectors only the vertical velocity component VV influences the image depth of normal incidence. The derivatives of can thus be written as follows:
The expressions for the derivatives of the slowness function with respect to the perturbation parameters depend on the particular form chosen to approximate the slowness function. Appendix C presents a particular approximation to the VTI group slowness function and derives the corresponding partial derivatives to be substituted in equations 21-23 and in equations 24-26. I used the same approximation to the VTI group slowness for the numerical experiments shown in this paper.