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| Effective AMO implementation in the log-stretch,
frequency-wavenumber domain | |
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Up: Vlad and Biondi: Log-stretch
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As it can be seen in Fig. 4, 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.
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impresp2
Figure 4. AMO impulse response artifacts
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Suppose we want to attenuate all spatial frequencies that are larger than a certain threshold , where
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with , and being the coordinates in the frequency-wavenumber domain (without logstretch), and being the minimum apparent velocity of the events that we want the filtered data cube to contain. Thus, the data cube will become:
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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 and axes: since the exponential needs to be dimensionless, we have
where
Thus, the final expression of is
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(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. 5:
the slices through the cube are taken at exactly the same locations as
those in Fig. 4, but now the artefacts are gone.
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fkfilter
Figure 5. AMO impulse response after f-k filtering
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| Effective AMO implementation in the log-stretch,
frequency-wavenumber domain | |
|
Next: Cost-cutting avenues
Up: Vlad and Biondi: Log-stretch
Previous: Stretching and aliasing
2013-03-03