Ormsby filter

A common type of synthetic wavelet in reflection seismology.


 * $$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]

- \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] $$

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.