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The impulse response of AMO is described by a saddle in the output
midpoint domain. The shape of the saddle depends on the offset vector of the
input data
and on the output offset vector
,where the unit vectors and
point respectively in the in-line direction and the cross-line
direction. The analytical expression of the AMO saddle, as given in
Appendix A, is,

| |
(1) |

The traveltimes *t*_{1} and *t*_{2} are the traveltime of
the input data after normal moveout correction
and the traveltime of the results before inverse NMO. The midpoint
vector is the difference
between the input and output midpoint location vectors.
The surface represented by equation amo_surf.eq is a skewed
saddle; its shape is controlled by the values of
the absolute offsets *h*_{1} and *h*_{2}, and by the azimuth
rotation .
The spatial extent of the operator has a maximum for rotation of 90
degrees and vanishes when offsets and azimuth rotation tend to zero.
Figure impulse-big shows the surface of the AMO
impulse response when *t*_{1} is equal to 1 s, *h*_{1} is
equal to 2 km, *h*_{2} is equal to 1.8 km,
is equal to zero degrees, and is equal to 30
degrees.

**impulse-big
**

Figure 1 The full AMO impulse response
when
,,
,,.

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Stanford Exploration Project

1/18/2001