NMO

The first-anelliptic example in Figure  would have been more realistic if we had simply omitted the depth scale entirely. Mathematically this means rewriting equation () explicitly in terms of vertical traveltime, finding the first-anelliptic equivalent of equation (). To do this, replace M_z C by T(0)², S by x², and M_x by $F_W M_{\mbox{\rm\scriptsize NMO}}$,obtaining the first-anelliptic processing-NMO equation:  

$$T(x)^2 = {{ T(0)^4 + ( F_W + 1 ) T(0)^2 M_{\mbox{\rm\scripts... ...2 x^4 \over T(0)^2 + F_W M_{\mbox{\rm\scriptsize NMO}} x^2 }} .$$ (25)

The anellipticity parameter F_W controls the deviation from normal moveout; if $F_W \equiv 1$ the moveout is exactly hyperbolic. Note that one should not try to define $F_W = M_x / M_{{\mbox{\rm\scriptsize NMO}}}$using a measured value for M_x. F_W and $M_{{\mbox{\rm\scriptsize NMO}}}$are both vertical paraxial measurements; there is no reason to suppose they should be strictly related to M_x, a horizontal measurement.