Butterworth Bandpass (BTWRB)

Use the Butterworth Bandpass option to apply a Butterworth bandpass filter.

Butterworth Bandpass Filter dialog options

Long wavelength cutoff	Long-wavelength central cutoff, in ground units.
Short wavelength cutoff	Short-wavelength central cutoff, in ground units.
Filter order	Controls the sharpness of the filter at the cutoff wavelengths. The default is 8.

Application Notes

The Butterworth bandpass filter passes the desired mid-wavenumber range while attenuating the low and high extremes of the wavenumber spectrum. The Filter order controls the degree of the sharpness of the cutoff wavenumbers:

• Higher values make the filter shape closer to an ideal bandpass operator.

• However, an ideal bandpass filter is not recommended because it produces ringing artifacts (Gibbs’ Phenomenon).

A common—but more complex—alternative is the Cosine Bandpass roll-off filter (FFTCOSNB).

Butterworth Bandpass Filter

Where:

k0	Low wavenumber cutoff (cycles per ground unit).
k1	High wavenumber cutoff (cycles per ground unit).
n	Positive integer determining the sharpness of the cutoff.

Wavenumber Domain Variable Definitions

The following variables are used in the wavenumber domain:
k	Wavenumber increment, used to depict a radially symmetrical variable.	Where: np: number of points cs: cell size
μ	X-component of the wavenumber.
v	Y-component of the wavenumber.
r	Radial component of the wavenumber.
θ	Angular (polar) component of the wavenumber.

Ground unit refers to the survey ground units defined in your grid (e.g., metres or feet). Ground units may be left undefined.