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We should prefer a transform of a single source gather
because these gathers correspond to a physical experiment
that can be modeled easily by wave-equation methods.
Unfortunately,
reflections from dipping layers and point scatters may have
a very complicated expression in a source gather.
We may be obliged to use many dips to capture their coherence.
Worse, many reflections will have minimum times at finite offset,
and a slant stack will alias some of their energy.
If the data are first sorted by midpoint *y* and half-offset *h*,
then reflections from dipping lines and from points will
still remain symmetric about zero offset. A slant
stack of a midpoint gather will better capture the
coherence of the reflections:

| |
(7) |

where
| |
(8) |

The Fourier version of a common-midpoint slant stack
can be derived exactly as before.
Let *f*_{y} be the Fourier frequency of :
| |
(9) |

Unfortunately, this slant stack does not correspond to any
single seismic experiment, and wave-equation modeling is much
more awkward.

** Next:** Conversion of midpoint to
** Up:** NOTES FROM TIEMAN's SEMINAR
** Previous:** The Fourier version
Stanford Exploration Project

11/12/1997