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Smaller values of *q*^{'} result in higher quality
images. At equal values of *q*^{'}, it wins over the others by providing
predominance of the discontinuity's amplitude over the intensity of noise.
We shall restrict ourselves only to consideration of orders *q*^{'} for different
situations. Earlier we introduced the order of touching of a stacking line and a
travel-time curve in the case of a wave-field continuation operator. The same
definition is valid for an arbitrary IG-operator. If *r* is the order of touching,
then
| |
(140) |

In order to avoid some uncertainty we shall denote the symbol *v*
for each operator whose action depends on the choice of velocity. (This symbol
may mean a scalar value or a function and so on). In
particular, we shall write and
(*v*_{m}-migration velocity, *v*_{st}-stacking velocity)
. If , then operators and
do not change the order of discontinuity.
So the only reason for the inequality lies in action of operators
and .

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Stanford Exploration Project

1/13/1998