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In practice, integration of discrete data is performed by stacking,
which requires special caution in the case of spatial aliasing
Claerbout (1992). In theory, it is convenient to
represent a stacking operator in the form of a continuous integral:

| |
(1) |

Function *M*(*z*,*x*) is the input of the operator, *S*(*t*,*y*) is the
output, represents the summation path, and *w* stands for the
weighting function. The range of integration (the
operator aperture) may also depend on *t* and *y*. Allowing *x* to be
a two-dimensional variable, we can use definition (1) to
represent an operator applied to three-dimensional data. Throughout
this paper, I assume that *t* and *z* belong to a one-dimensional
space, and that *x* and *y* have the same number of dimensions.
The goal of inversion is to reconstruct some function
for a given *S*(*t*,*y*), so that is in a
particular sense close to *M* in equation (1).

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** Up:** Fomel: Stacking operators
** Previous:** Introduction
Stanford Exploration Project

11/12/1997