<< Click to Display Table of Contents >> Navigation:  Chapter 10 Gridding and Contouring > Contour Maps > Editing a Contour Map > Grids > Gridding Algorithms > Inverse Distance

Inverse distance is a very fast and common gridding algorithm. The Inverse Distance algorithm uses a weighted average to interpolate the data at regularly spaced intervals.  This method uses a power parameter to control how the weighting drops off with distance from the grid node. At higher powers, closer points are much more highly weighted. And at lower powers, the weights are more evenly distributed amongst the data points. A typical power is 2, that is the inverse distance squared.

 

When calculating the value of a grid node, the weight given to a data point is proportional to the inverse of the distance between the data point and grid node raised to the specified power. The assigned weights of the data points used to calculate a grid node are fractions that are adjusted to sum to one.

 

If a data point is at the same location as a grid node within a supplied tolerance, than the grid node is assigned the value of the data point and the other data points are not used. Occasionally, this approach can lead to "bull's eyes" in the contours surrounding a data point that is coincident with a grid node. To avoid this a smoothing parameter can be assigned to ensure that no one data point is given all of the weight for a grid node. The higher the smoothing factor the less weight will be placed to a data point that is coincident with the grid node. This will reduce the "bull's eye" effect and smooth the interpolated grid.

 

When calculating a grid node not all of the data points need to be used for the calculation since the ones farthest away will have minimal impact. The maximum number of data points can be specified to limit the impact of very distant data points and speed up the grid calculation. In addition, the maximum distance that a data point can be away from a grid node can also be specified to limit the impact of very distant data points.

 

In situations where the data points are closed spaced along specific lineaments (such as with seismic lines), it is possible that only the data points in one or two quadrants of a grid node will be used to calculate the node value. This may lead to a false anisotropy being imparted to the map from the gridding algorithm. To prevent this it is possible to perform a quadrant search where at least one data value must be used from each quadrant around a grid node.

 

Anisotropy refers to data that has a preferred direction of higher or lower continuity. In the gridding process, anisotropy can be applied by using a different weight factors for distances in the X direction versus distances in the Y direction. Typically, anisotropy is not used for most grids.