Prepare Grid

Use the FFT2PREP GX to prepare your grid for FFT processing.

FFT2 Grid Pre-processing dialog options

Name of Input (Original) Grid File	Name of Input Grid File (Original Grid) Script Parameter: FFT2PREP.INGRD
Name of Output (Pre-processed) Grid File	Name of Output Grid File (Pre-processed Grid) Script Parameter: FFT2PREP.OUTGRD
Type of trend surface to remove	Select order of trend to remove. (Default - first order) Options are: remove mean first order second order third order Script Parameter: FFT2PREP.TORDER
Trend based on	Select which grid points to base the trend surface to remove. (Default - edge points) Options are: edge points all points Script Parameter:FFT2PREP.TBASE
% expansion	Type the percent grid expansion. (Default - 10) Script Parameter:FFT2PREP.PEX
Square or rectangular expansion	Select the form of grid expansion. (Default - square) Options are: square rectangular Script Parameter:FFT2PREP.TEX
Grid fill method	Select the grid fill method. (Default - multi-step expansion) Options are: multistep expansion maximum entrophy inverse distance Script Parameter:FFT2PREP.FILL
Roll off to zero at distance of (cells)	Specify the number of cells beyond the valid area at which to roll-off to zero. Script Parameter:FFT2PREP.ZDIST
Limit all amplitudes to be less than	Specify an amplitude limit. High amplitude anomalies can cause problems in filtering systems such as MAGMAP. With this option, anomalies that exceed half the specified limit are smoothly attenuated. The attenuation is started at half the limit, with no values allowed to exceed the limit. This option should only be used on trend-removed grids. Script Parameter:FFT2PREP.ALIM
Edge amplitude limit	Specify an edge amplitude limit High amplitude anomalies on the edges of the valid area can produce oscillations in the extrapolated areas. With this option, a limit may be placed on anomalies along the edges of the grid. Script Parameter:FFT2PREP.ELIM

Application Notes

Grid preparation consists of the following basic processes:

Removing a trend from a grid. The trend which is removed is stored in the user area of the grid header and is filtered together with the zero wave number.
Expanding the dimensions of a grid by adding dummy areas to the grid edges to produce either a square or a rectangular grid. By default, the grid size is increased by a minimum of 10%, then the next largest acceptable dimension is chosen. The system uses the Winograd FFT algorithm for dimensions up to 2520 X 2520. Beyond this dimension, it switches to a power of 2 FFT methods.
Replacing all dummies in a grid with interpolated values from the valid parts of the grid. The FFT routines require a completely filled grid which is periodic at its edges.

Trend Removal

Trend removal, removes up to a third order trend surface from a grid. When calculating the trend surface to remove, it may be calculated either by using all the valid points in the grid , or by using only the edge points along the valid edge of the grid. Using the edge points is often better, especially if there are any large amplitude anomalies within the grid.

Grid Expansion

The expansion should be about the half the size of the broadest features of interest in the map. If you are tapering the data to 0, the expansion need not be larger than the taper distance. If the grid is small, or if the wave numbers of interest approaches the size of the grid, we recommend square expansion because this minimizes side-effects that result from having different wave number samples in the X and Y directions. Rectangular grids can save significant processing time and disk space when working with large grids.

Grid Filling

The dummy areas are extrapolated using the real data that is located in their immediate vicinity. The extrapolation method is one of: inverse distance weighting, maximum entropy prediction and multi-step expansion.

The default is the Multi-step Expansion method. This method produces an outcome that has a natural feel to it. In order to fill the dummy areas of the grid, the Multi-step expansion applies the four steps in the order described below. The Multi-step expansion produces an filled grid that has a more natural feel, however it is the slowest of the three methods since it is performed in more steps that the other two:

Extend the grid margin by 3 grid cells using a radial weighted sum of up to the 8 closest data points.
Fill the inner dummy segments (inlets and islands) by mirror-imaging the adjacent real data onto the dummy segments. This is done in an iterative approach alternating in the X & Y directions. At each iteration the size of the segment to be filled increases until there are no remaining dummies.
Using the Minimum curvature algorithm, the grid is then extended to the edges of the bounding rectangle of the real data. There is however a stipulation; periodicity is a fundamental requirement of the FFT process. Thus the assumption that the real data is repeated at an interval equal to 4 times the expanded MAGMAP dimensions, helps control the extrapolation at both ends. This process ensures that the extrapolation at this step is constrained within the wavelengths and amplitudes present in the original data.
Using a Linear Prediction algorithm, extrapolate the data from the bounding rectangle of the original data to the full size required by the MAGMAP FFT process. Once again in order to ensure the continuity between each 2 opposite edges, the periodicity of the data is implied.

The Multi-step Expansion method extends the data inside the bounding rectangle within the same range of signal wavelength and amplitude as the real data. As we retreat further from the real data, the extrapolated data has longer wavelengths and lower amplitudes, however these extrapolated data is located further away from the grid and does not produce artifacts in the filtered data.

The Maximum Entropy Method extends the data along one dimension and then along the other. Although on a grid line to grid line basis the nature of the real data is reflected in the extrapolated data and thus the spectrum of the latter has the same character as the former, a high frequency line to line noise is introduced across grid lines. A certain level of smoothing is applied to the extended data in order to attenuate this chatter. In principle the outcome of the MAGMAP process applied to grids filled with the ME method, is most of the time satisfactory, however the filled grid does not show a natural texture.

Depending on the nature of the input grid, the prediction function may yield unreasonable extrapolated data at large distances from the valid parts of the grid. This is when the tapering should be applied. The default however is not to apply any tapering. This option should only be used on trend-removed grids. High amplitude anomalies can accentuate this potential problem. If turned on, anomalies begin to be attenuated beyond half the specified roll-off limit. The attenuation is started at half the limit, with no values allowed to exceed the limit. High amplitude anomalies on the edges of the valid area can produce oscillations in the extrapolated data.

For more information see the 2D Filtering Learning Path.