| A priori interpolation functions, such as 1/dx, do not incorporate
any structure inherant in your response variable. With inverse distance,
when trying to estimate a response variable's (like density) magnitude
at an unknown location, the weight (or significance) the interpolating
routine gives to the variable's value at each known (sampled) location
decays rapidly as the distance between the known and unknown points increases.
How rapidly this occurs can be adjusted to best fit your real world situation
by adjusting the value of the exponent. This graph illustrates the
influence on inverse distance weighting for exponents 1 - 6. |