The operator measuring semblance differentially is

Then where is the arrival (horizontal) slowness of the ray passing offset
This observation is due to Hua Song. As a result, within accuracy
limitations already built into the asymptotic linearized model, *a*
might as well be replaced by 1!. That is, to leading order in
frequency, differential semblance is insensitive to wave dynamics
(amplitude), and responds only to kinematic model changes,
i.e. changes in traveltime. Thus minimization of differential
semblance will amount to a sort of traveltime tomography.

Fons ten Kroode (personal communication) has pointed out that
replacement of *G*[*v*] by an asymptotically unitary operator with
the same kinematics also yields an asymptotocally identical
objective without leading order amplitude dependence, and without
application of the forward modeling operator, thus at lower computational
cost.

The computations above are correct when the map is smooth and invertible. This is so inside the mute zone defined above, uniformly for . Therefore application of the inverse square root Helmholtz operator following will bring the spectral content back into alignment with that of the data, uniformly over . Thus

The ray slowness4/20/1999