Identification of i kz with converts
the dispersion relations of Table .2
into the differential equations of Table .3.
The differential equations in Table 4.3 were based on a dispersion relation that in turn was based on an assumption of constant velocity. So you might not expect that the equations have substantial validity or even great utility when the velocity is depth-variable, v = v(z). The actual limitations are better characterized by their inability, by themselves, to describe reflection.
Migration methods based on equation (9) or on Table .3 are called phase-shift methods.