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Let us denote as the operator of summation along hyperbolas.
The operator transforms (t,x)-space into -space:
| |
(2) |
An adjoint operator transforms -space into
(t,x)-space:
| |
(3) |
We can also define a stacking operator in -space. Because
maps a point onto a parabola (Jedlicka, 1989b), it is natural
to define an operator as an operator of summation along parabolas:
| |
(4) |
The adjoint operator ,
| |
(5) |
may serve as an alternative operator for velocity analysis.
Here each point in (t,x)-space is spread onto a parabola
in -space.
Both operators and are linear.
The relationship between them is shown in Appendix A.
Next: VELOCITY ANALYSIS
Up: Jedlicka: Velocity analysis by
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Stanford Exploration Project
1/13/1998