FFT Space -> Fourier

Use the 1D FFT > Advanced Settings > FFT Space -> Fourier menu option (FFTIN GX) to transform a channel from the space domain to the frequency domain.

FFT Space -> Fourier dialog options

Channel to transform	Specify the name of the channel to transform. Script Parameter: FFTIN.IN
[Trend Removal>]	Click to set trend removal parameters.
[Expansion>]	Click to set grid expansion parameters.

FFT Space -> Fourier - Trend Removal dialog options

Type of trend line to remove

Select one of the following options: Remove mean value Remove trend line based on all data points (default) Remove trend line based on two edge points Do not remove trend Script Parameter: FFTIN.DETRD [0 - do not remove trend; 1 - remove trend line based on two edge points; 2 - remove trend line based on all data points (default); 3 - remove mean value]

FFT Space -> Fourier - Expansion dialog options

Minimum expansion (%)

Specify the minimum data expansion percentage before FFT processing. Default: 10%. Script Parameter: FFTIN.EXP

Application Notes

This GX creates three output channels:

• Real component of the transform

• Imaginary component of the transform

• Wavenumber channel

All three channels inherit the base name of the input channel and are appended with _r, _i, and _w, respectively.

• Fiducials are expressed in cycles per fiducial.

• The wavenumber channel is expressed in radians per fiducial.

Key Processing Details

• In the space domain, an observed signal has only a real component. Therefore, its transform in the wavenumber domain is symmetrical, and the negative spectrum is the conjugate of the positive spectrum:

  H(−f)=[H(f)]*

  Consequently, only the positive spectrum (signal) needs to be saved.

• FFT requires constant sampling intervals in the space domain. To meet this requirement, the data is re-fiducialized to a constant spacing before transformation.

• To satisfy the assumption of signal periodicity, a first-order trend is removed prior to FFT. This ensures continuity at the edges (the signal is cyclical). The removed trend is restored later by the FFTOUT GX.

• The data is padded by at least 10% (default) before FFT. This buffer, combined with trend removal, ensures smooth extrapolation and continuity. The extended array size is rounded up to the next power of 2.

  Example: If the original data has 60 points and the user specifies 10% padding, the final size of the array will be 128 (the smallest power of 2 greater than 66).

Expansion Fill Methods

The padded segment is interpolated using one of the following methods:

• Maximum Entropy Prediction (MEP):

  Determines the spectral content or the preceding real data segment and predicts a data function with the same spectral signature as the original data. As a result, the predicted data does not significantly alter the energy spectrum of the original data.

• Constrained Linear Prediction (CLP):

  Calculates a series of linear prediction coefficients based on a segment of real data, then uses these coefficients to recursively extrapolate the data. The nature of geophysical data, with its wide range of distributions, generally yields coefficients that produce a reasonable extrapolation. However, if the data contains undamped oscillations, such as superimposed aircraft systematic noise, LP may produce an unstable outcome. An additional constraint on the calculation of the coefficients pushes the results back into the stable zone. The details of constrained LP are outside the scope of this topic. For further information, see the reference below.

Reference