In case of uniform scaling of velocity, the derivative of the slowness with respect to a uniform scaling of the velocity has a simple form:
The derivatives of the imaging depth and of the residual moveout with respect to the perturbation component have the following forms (refer to equations (53) and (55)):
The dependence of equation (30) on the group angles increases the complexity of its use. However, we showed in the preceding section that it is possible to compute the angle from . We first compute from by solving a system of two quadratic equations (equations (15) and (16)) then computes from by using equation (17). The computational cost of evaluating the group angles is negligible and it is important to introduce the distinction between the ``three aperture angles'': , and .
Equations (30) and (29) are consistent with the ones derived in the isotropic case with dipping reflectors Biondi and Symes (2003). Under the assumption that the medium is isotropic, and the derivatives of the imaging depth and of the residual moveout with respect to the perturbation component are