The Inverse Distance to a Power gridding method is a weighted average interpolator, and can be either an exact or a smoothing interpolator. Gridding methods are used with MapViewer's contour, gradient, and vector maps.
With Inverse Distance to a Power, data are weighted during interpolation such that the influence of one point relative to another declines with distance from the grid node. Weighting is assigned to data through the use of a weighting power that controls how the weighting factors drop off as distance from a grid node increases. The greater the weighting power, the less effect points far from the grid node have during interpolation. As the power increases, the grid node value approaches the value of the nearest point. For a smaller power, the weights are more evenly distributed among the neighboring data points.
Normally, Inverse Distance to a Power behaves as an exact interpolator. When calculating a grid node, the weights assigned to the data points are fractions, and the sum of all the weights are equal to 1.0. When a particular observation is coincident with a grid node, the distance between that observation and the grid node is 0.0, and that observation is given a weight of 1.0, while all other observations are given weights of 0.0. Thus, the grid node is assigned the value of the coincident observation. The Smoothing parameter is a mechanism for buffering this behavior. When you assign a non-zero Smoothing parameter, no point is given an overwhelming weight so that no point is given a weighting factor equal to 1.0.
One of the characteristics of Inverse Distance to a Power is the generation of "bull's-eyes" surrounding the position of observations within the gridded area. You can assign a smoothing parameter during Inverse Distance to a Power to reduce the "bull's-eye" effect by smoothing the interpolated grid.
Inverse Distance to a Power is a very fast method for gridding. With less than 500 points, you can use the All Data search type and gridding proceeds rapidly.
Inverse Distance to a Power Math
Specifying Inverse Distance to a Power Options
In the Property
Manager Gridding page, select Inverse
Distance to a Power as
the Gridding
method and then click
the Advanced Options
button to display the Inverse
Distance Options dialog.
Specifiy the power, smoothing, and anisotropy in the Inverse Distance
Options dialog.
On the General page, the weighting Power parameter determines how quickly weights fall off with distance from the grid node. As the power parameter approaches zero, the generated surface approaches a horizontal planar surface through the average of all observations from the data. As the power parameter increases, the generated surface is a "nearest neighbor" interpolator and the resultant surface becomes polygonal. The polygons represent the nearest observation to the interpolated grid node. Power values between 1.2e-038 and 1.0e+038 are accepted, although powers should usually fall between one and three.
The Smoothing factor parameter allows you to incorporate an "uncertainty" factor associated with your input data. The larger the smoothing factor parameter, the less overwhelming influence any particular observation has in computing a neighboring grid node.
You can also set the Anisotropy parameters on the General page. For more information about anisotropy options, see the Anisotropy.
Specify the search options on the Search page.
Inverse Distance to a Power References
Davis, John C. (1986), Statistics and Data Analysis in Geology, John Wiley and Sons, New York.
Franke, R. (1982), Scattered Data Interpolation: Test of Some Methods, Mathematics of Computations, v. 33, n. 157, p. 181-200.
See Also
