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The CMP gather *G* can be viewed as a sum of gathers *G*_{tx}, each containing
only one non-zero amplitude:
| |
(4) |

where *G*_{tx} is a gather containing a spike at (*t*,*x*) and *A*(*t*,*x*) is the
amplitude of a trace with offset *x* at time *t*.
Because the image of *G*_{tx} is a -space containing a parabola,
we can write

| |
(5) |

i.e., the -space can be viewed as a sum of panels, each containing
one parabola. For a constant offset *x*, the resulting sets of parabolas are shown
in Figure .
Let us denote as *V*_{x} the panel that we get for one offset *x*:

| |
(6) |

*V*_{x} is an image of a trace with offset *x*. Finally we have
| |
(7) |

*V*_{x} consists of horizontal lines for *x*=0. For increasing offset *V*_{x}
consists of parabolas with increasing slopes (Figure ).

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Stanford Exploration Project

1/13/1998