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As it can be seen in Fig. 3, the impulse response of
the AMO computed in the log-stretch, frequency-wavenumber domain has
some artifacts: high amplitude, large saddle corners. Low temporal
frequencies and high spatial slopes are also present. These artifacts can be eliminated easily
using a f-k filter, which is described below.
**impresp2
**

Figure 3 AMO impulse response artifacts

Suppose we want to attenuate all spatial frequencies *k* that are larger than a certain threshold , where

| |
(10) |

with , *k*_{x} and *k*_{y} being the coordinates in the frequency-wavenumber domain (without logstretch), and *v* being the minimum apparent velocity of the events that we want the filtered data cube to contain. Thus, the data cube will become:
| |
(11) |

Too small an will result in an abrupt transition in the f-k domain, and thus ringing artifacts in the t-x domain. An which is too big will result in no visible filtering of the targeted artifacts. Moreover, depends on the choice of units and the number of samples for the *m*_{x} and *m*_{y} axes: since the exponential needs to be dimensionless, we have
where
Thus, the final expression of is
| |
(12) |

where is a value that is hand-picked only once, and embedded in the code. This way, we will not have to change anything at all in the code or in the parameters in order to set , no matter what the units of the data cube may be.
The result of the filtering can be seen in Fig. 4:
the slices through the cube are taken at exactly the same locations as
those in Fig. 3, but now the artefacts are gone.

**fkfilter
**

Figure 4 AMO impulse response after f-k filtering

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** Up:** Vlad and Biondi: Log-stretch
** Previous:** Stretching and aliasing
Stanford Exploration Project

9/18/2001