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A velocity analysis panel is obtained by transformation of a CMP gather. In this
paper an operator of summation will be used. This operator transforms
(t,x)-space into -space; i.e., it is an operator of transformation
from the time-offset domain into the time-sloth domain.
We are interested in the image in -space of a point
in (t,x)-space.
Let a gather Gtx contain only one non-zero amplitude
that is located at time t of a trace with the offset x (Fig. a).
Let us apply the operator on the gather Gtx.
The operator gives non-zero results only for hyperbolas passing through
the point (T,X) (Fig. ). Each hyperbola is determined by
the time and the sloth m, which satisfy the equation
| |
(1) |
which can be written
| |
(2) |
This is the equation of a parabola, so we have
| |
(3) |
A parabola corresponding to the point (T,X) is shown in Figure b.
Next: Representation of a velocity
Up: STRUCTURE OF A VELOCITY
Previous: STRUCTURE OF A VELOCITY
Stanford Exploration Project
1/13/1998