Wiener Optimum (OPTM)

Use the Wiener Optimum option to apply the Wiener optimum filter.

Wiener Optimum Filter dialog options

Inclination

Geomagnetic inclination in degrees from the horizon (I).

Declination

Geomagnetic declination in degrees azimuth (D).

Minimum depth of sources

The depth (h) at which to interpret an optimum filter from the observed energy spectrum (in ground unit). By default, the depth is taken as the flying height in the control file, or the continuation depth if specified by the "Downward Continuation" or "Apparent Susceptibility" filter options.

Roll-off start (longer) wavelength

The wavelength (in ground unit) at which to start the short-wavelength roll-off (1/k0). This parameter must be given together with parameter 4. By default, this k0 is calculated by finding the point at which the slope of the observed energy spectrum rises above the slope defined by the depth (1/[4*p*h]).

Roll-off end (shorter)
wavelength

The wavelength (in ground unit) at which to end the short-wavelength roll-off (1/k1). By default, k1 is set to be two times k0.

Noise level
(log spectral density)

Spectral density estimate of noise (θ) to be removed by the Wiener filter. This is in terms of the log of spectral density as reported in the second column of the energy spectrum. By default this is calculated as the average of the spectral density between k0 and k1.

Application Notes

Optimum Wiener

The Wiener optimum filter is intended to remove the effect of white noise from the magnetic data. White noise is high-wavenumber background noise present in the data. Because magnetic signal is stronger in the direction of the inducing field, the signal to noise ratio will vary as a function of both inclination and declination. The optimum Wiener filter takes the variation of signal to noise ratio into account when applying the filter.

for k < k0
for k0 ≤ k ≤ k1
for k > k1

Where:

I

 geomagnetic inclination.

D

geomagnetic declination.

h

the depth at which to interpret an optimum filter from the observed energy spectrum. By default, the depth is taken as the flying height in the control file, or the continuation depth if specified by the "Downward Continuation" or "Apparent Susceptibility" filter options (in ground_units).

k0

the wavenumber (cycles/ground_unit) at which to start the high-wavenumber roll-off. This parameter must be given together with parameter 4. By default, this point is calculated by finding the point at which the slope of the observed energy spectrum rises above the slope defined by the depth (1/4h).

k1

the wavenumber (cycles/ground_unit) at which to end the high wavenumber roll-off. By default, this point is set to be two times k0.

φ

spectral density estimate of noise to be removed by the Wiener filter. This is in terms of the log of spectral density as reported in the second column of the energy spectrum. By default this is calculated as the average of the spectral density between k0 and k1.
 

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.

    • The optimum filter is most often used to remove the theoretical effect of all sources that would lie above a specified depth. The filter parameters can be specified or calculated automatically based on analysis of the energy spectrum.

    Although FILTER can calculate the parameters of the filter, we recommend that you confirm that the interpreted parameters are reasonable. When the energy spectrum is not smooth, the filter can choose the wrong point at which to start the noise calculation. Most often, this point is chosen to be too low and the resulting maps will appear too smooth.

    The optimum filter can be quite complicated to use and understand. A good alternative is to use the Butterworth filter as a low-pass filter. Determine the wavenumber at which sources appear too shallow by interpreting the depth estimate in the energy-spectrum plot

    See Also: