Next: The slopes of the
Up: STRUCTURE OF A VELOCITY
Previous: Image of a point
The CMP gather G can be viewed as a sum of gathers Gtx, each containing
only one non-zero amplitude:
| |
(4) |
where Gtx 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 Gtx 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 Vx the panel that we get for one offset x:
| |
(6) |
Vx is an image of a trace with offset x. Finally we have
| |
(7) |
Vx consists of horizontal lines for x=0. For increasing offset Vx
consists of parabolas with increasing slopes (Figure ).
Next: The slopes of the
Up: STRUCTURE OF A VELOCITY
Previous: Image of a point
Stanford Exploration Project
1/13/1998