Difference between revisions of "Ormsby filter"

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(added see also)
(corrected and simplified expression (had incorrect extra pi in sinc function))
 
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A common type of synthetic wavelet in reflection seismology.
 
A common type of synthetic wavelet in reflection seismology.
  
:<math>A(t) = \left[ \frac{(\pi f_4)^2}{\pi f_4 - \pi f_3} \mathrm{sinc}^2(\pi f_4 t) - \frac{(\pi f_3)^2}{\pi f_4 - \pi f_3} \mathrm{sinc}^2(\pi f_3 t) \right]
+
:<math>A(t) = \frac{\pi f_1^2 }{f_2 - f_1} \mathrm{sinc}^2(f_1 t) - \frac{\pi f_2^2 }{f_2 - f_1} \mathrm{sinc}^2(f_2 t)
  - \left[ \frac{(\pi f_2)^2}{\pi f_2 - \pi f_1} \mathrm{sinc}^2(\pi f_2 t) - \frac{(\pi f_1)^2}{\pi f_2 - \pi f_1} \mathrm{sinc}^2(\pi f_1 t) \right] </math>
+
  - \frac{\pi f_3^2 }{f_4 - f_3} \mathrm{sinc}^2(f_3 t) \frac{\pi f_4^2}{f_4 - f_3} \mathrm{sinc}^2(f_4 t) </math>
  
 
where
 
where

Latest revision as of 15:16, 10 August 2020

A common type of synthetic wavelet in reflection seismology.

where

  • f1 = low-cut frequency
  • f2 = low-pass frequency
  • f3 = high-pass frequency
  • f4 = high-cut frequency

An example might have frequencies of 5–10–40–45 Hz. This defines a trapezoidal shape in the frequency spectrum.

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

See also

External links

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