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Slant stacks are commonly applied to unsorted data, one
shot at a time. This form is well suited to deconvolution
of multiple reflections from flat reflectors. Such multiple
reflections are periodic at zero-offset, but not at a single
finite offset *h*.
A slant stack attempts to describe our recorded data as
a sum of dipping lines.
A dip *p*_{s} will measure the slope of
time with offset holding a source position constant.

| |
(1) |

With ideal sampling and infinite offsets,
this equation would describe a plane-wave
source on the surface. A plane wave reflecting from
flat reflectors would produce periodic multiples at any *p*_{s}.
Predictive deconvolutions can detect this periodicity and
remove multiple reflections.
The simplest slant-stack sums data over all lines within
a feasible range of dips.
Let be the intersection at zero offset of our imaginary
plane wave in the shot gather.

| |
(2) |

In practice the integral over offset *h* must be a discrete
sum with a limited range of offsets.
The inverse of this transform looks much like another slant
stack, with some adjustments of the spectrum. Papers
are readily available to explain this inverse. I will concentrate
instead on the conversion of one type of slant stack to another.

** Next:** The Fourier version
** Up:** NOTES FROM TIEMAN's SEMINAR
** Previous:** The data
Stanford Exploration Project

11/12/1997