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.

See also

• Ricker wavelet
• Butterworth filter
• Klauder filter

External links

• Ryan, 1994. A choice of wavelets. CSEG Recorder September 1994.
• Ormsby filter — Sheriff's Encyclopedic Dictionary

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