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In a laterally homogeneous model, the NMO equation 6
flattens primary events on a CMP gather with offset
and time
to its zero-offset traveltime
. Brown and Guitton (2005) use an analogous
NMO equation for pegleg multiples under locally 1D earth assumption. For
example, first-order pegleg can be kinematically approximated by
pseudo-primary with the same offset but with an additional zero-offset
traveltime
. The NMO equation for an
th-order pegleg multiple
is generalized to
![\begin{displaymath}
t_m(x) = \sqrt{(t_0+m\tau)^2 + \frac{x^2}{v_m^2(t_0)}}\;,
\end{displaymath}](img52.png) |
(8) |
where
is the corresponding multiple traveltime recorded at
offset
and the effective RMS velocity
is
defined according to Dix's equation as:
![\begin{displaymath}
v_m(t_0) = \sqrt{\frac{t_0v^2(t_0)+m\tau\,v^2(\tau)}{t_0+m\tau}}\;.
\end{displaymath}](img55.png) |
(9) |
In marine seismic data,
is constant water velocity, and
it assumes that we are able to pick zero-offset traveltime
of the water bottom. According to the definition of slopes for
primaries (equation 7), slopes for pegleg multiples can be
calculated analogously by:
![\begin{displaymath}
\sigma_m(t,x) = {\frac{x}{t_m(x)\,v_m^2(t_0,x)}}\;.
\end{displaymath}](img57.png) |
(10) |
Equation 10 provides the estimation of multiple slopes,
which we use to define VD-seislet frame for representing pegleg
multiples of different orders.
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Next: Separation of primaries and
Up: Theory
Previous: VD-slope pattern for primary
2015-10-24