Inverse Distance Weighted Gridding Advanced Options (Multiple Channels)
Use the IDW Gridding Advanced Options dialog to specify advanced Inverse Distance Weighted gridding options.
IDW Gridding Advanced Options
Application Notes
Anti-aliasing
Prior to gridding (and after any log or log-linear transformation), data is pre-processed using an anti-aliasing technique. All values falling inside any single grid cell are averaged, and the data is then represented by the single averaged value at the grid cell centre. Any error in the spatial representation of features introduced by this step will never exceed one-quarter of the Nyquist wavelength, which is equal to 2 cell sizes.
The Inverse Distance Weighting Function: Defining the Weighting Slope and Power
The inverse distance weighting function assigns averaging weights based on distance, out to the defined search radius:
1 / (distance^power + 1/slope)
Where distance is in multiples of the horizontal cell size.
Using the default of 2 for the power, and 1 for the slope produces a bell-shaped weighting function. Requiring a slope > 0 ensures that the weight remains finite at zero distance. Decreasing the slope tends to flatten the bell, resulting in greater weighting of points away from the grid cell, and hence greater smoothing. Choosing a power less than 2, or a slope less than one, may result in over-smoothing the data.
The following table shows the effect of various slopes on the weighting given at various distances away from the centre cell. The weights have been normalized so the weight at the cell centre is equal to 1.
|
weighting of centre cell |
weighting 1 cell away |
weighting 2 cells away |
weighting 3 cells away |
weighting 4 cells away |
---|---|---|---|---|---|
P = 2, S = 0.2 |
1 |
0.83 |
0.55 |
0.36 |
0.24 |
P = 2, S = 0.5 |
1 |
0.67 |
0.33 |
0.18 |
0.11 |
P = 2, S = 1 |
1 |
0.5 |
0.2 |
0.1 |
0.56 |
P = 2, S = 2 |
1 |
0.33 |
0.11 |
0.053 |
0.03 |
Clearly, as the slope increases, the weighting is more tightly concentrated about the centre cell. The search radius should also be chosen based on the fall-off of the weighting function. Increasing the search radius beyond where the weighting function is significant will have little effect on the results, and may result in large increases in processing time, since the processing time varies in proportion to the cube of the search radius. (Remember that the search radius is specified in ground units, not as a multiple of cell sizes.)
The yellow asterisk icon () displayed in front of a parameter name indicates that this parameter is required.
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