Inverse Distance

Inverse Distance is a simple interpolant that can often yield satisfactory results. The basic premise of inverse distance is that data points are weighted by the inverse of their distance to the estimation point. This approach has the effect of giving more influence to nearby data points than those farther away. Additionally, the inverted distance weight can be raised to further reduce the effect of data points located farther away. This approach is mathematically expressed as:

where v₀ is the estimated concentration at (x₀, y₀, z₀), v_i is a neighboring data value at (x_i, y_i, z_i), D_I is the distance between (x₀,y₀,z₀) and (x_i,y_i,z_i), P is the power, and N(v₀) is the number of data points in the neighborhood of v₀.

In addition to the power parameter P, SADA requires a definition of the neighborhood around v₀. The issue of neighborhood definition is important to ordinary kriging and indicator kriging, as well. For this reason, a discussion of neighborhood definitions is consolidated in Defining A Neighborhood.

To utilize inverse distance, select Inverse Distance from the drop down box in the Geo tab of the Control Panel. Enter the Power value and define the neighborhood parameters. SADA is now ready to use inverse distance method in its mapping functions. Press the Estimates or Risk mapping buttons on the main toolbar.