Difference between revisions of "Klauder filter"

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A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time ''t'' = 0 ms.  
 
A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time ''t'' = 0 ms.  
  
The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency ''f''<sub>l</sub> (perhaps 2–8 Hz), its upper frequency ''f''<sub>u</sub> (often about 100–200 Hz), and its duration ''T'', commonly about 6–12 s.  
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The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency ''f''<sub>lower</sub> (perhaps 2–8 Hz), its upper frequency ''f''<sub>upper</sub> (often about 100–200 Hz), and its duration ''T'', commonly about 6–12 s.  
  
 
:<math>A(t) = \mathrm{Re} \left[ \frac{\sin (\pi k t (T-t)}{\pi k t \mathrm{e}^{2 \pi \mathrm{i} f_0 t} } \right] </math>
 
:<math>A(t) = \mathrm{Re} \left[ \frac{\sin (\pi k t (T-t)}{\pi k t \mathrm{e}^{2 \pi \mathrm{i} f_0 t} } \right] </math>
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where ''k'' is the rate of change of frequency with time:
 
where ''k'' is the rate of change of frequency with time:
  
:<math>k = \frac{f_\mathrm{u} + f_\mathrm{l}}{T} \ </math>
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:<math>k = \frac{f_\mathrm{upper} - f_\mathrm{lower}}{T} \ </math>
  
 
and ''f''<sub>0</sub> is the mid-frequency of the bandwidth:
 
and ''f''<sub>0</sub> is the mid-frequency of the bandwidth:
  
:<math>f_0 = \frac{f_\mathrm{u} + f_\mathrm{l}}{2} \ </math>
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:<math>f_0 = \frac{f_\mathrm{upper} + f_\mathrm{lower}}{2} \ </math>
  
 
Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side.  
 
Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side.  
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==See also==
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* [[Ricker wavelet]]
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* [[Butterworth filter]]
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* [[Ormsby filter]]
  
 
==References==
 
==References==

Latest revision as of 00:06, 27 February 2014

A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time t = 0 ms.

The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency flower (perhaps 2–8 Hz), its upper frequency fupper (often about 100–200 Hz), and its duration T, commonly about 6–12 s.

where k is the rate of change of frequency with time:

and f0 is the mid-frequency of the bandwidth:

Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side.

See also

References

  • Ryan, 1994. A choice of wavelets. CSEG Recorder September 1994.

External links

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