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Operator aliasing most often occurs when operator moveout across adjacent
traces exceeds the time sampling rate. Cycle skips can occur
when the operator is
aliased. For a moveout curve with slope
, and data with a spatial
Nyquist frequency of
, temporal frequencies above
are aliased.
In terms of the mesh spacing
and operator slope
,
operator aliasing will occur for all frequencies above
, where
is given by:
![\begin{displaymath}
f_{op} \; = \; \frac{1}{2 (\frac{dt}{dx}) \triangle x}.
\end{displaymath}](img7.png) |
(1) |
Defining the maximum stepout as
, the
highest dip frequency in the data is given by
![\begin{displaymath}
f_d \; = \; \frac{1}{2 p \triangle x}.
\end{displaymath}](img9.png) |
(2) |
When the stepout is captured by the mesh
spacing,
, and
, the
highest unaliased dip frequency is equal to the
Nyquist frequency
. In areas of
economic interest, steep dips are often
present in the data and
.
Anti-aliasing is called for when the frequency content of the data,
,
falls between
![\begin{displaymath}
f_{op} \; \leq \; f_s \; \leq \; f_d.
\end{displaymath}](img15.png) |
(3) |
This situation is illustrated in Figure 1.
spectrum
Figure 1. Operator aliasing, event dip, and
frequency content of the data.
|
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Previous: Introduction
2015-03-26