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	The degree of the filter sharpness at the cutoffs (default = 8.0).

Application Notes

The Butterworth Bandpass filter allows passing the desired mid-wavenumber range while attenuating the low and high extremes of the wavenumber continuum. The Filter Order controls the degree of the sharpness of the cutoff wavenumbers; the higher the number the closer the shape of the operator is to the ideal bandpass operator. However one is cautioned not to apply the ideal bandpass filter as it manifests a ringing artefact. A common, but more complicated alternative is the Cosine Bandpass roll-off filter (FFTCOSNB).

Butterworth Bandpass Filter

Where:

k0	Low wavenumber cutoff in cycles/ ground unit.
k1	High wavenumber cutoff in cycles/ground unit.
n	Positive integer value determining the degree of sharpness of the cutoff.

Wavenumber Domain Variable Definition

k	Wavenumber domain increment, used to depict a radially symmetrical variable.	where: np is the number of points cs is the cell size
u	X component in the wavenumber domain.	k = 2π ( i μ+j ν )
v	Y component in the wavenumber domain.
r	Radial component in the wavenumber domain.	also 2πk
θ	Polar component in the wavenumber domain.

Ground_unit is the survey ground units as defined in your grid (e.g. metre or feet). Ground units may be left undefined.