Pitney Bowes MapInfo Vertical Mapper - Manual (Page 159)

Chapter 9: Data Analysis
User Guide
157
Put simply, every point is compared to every other point to determine which points are approximately
the first lag distance apart. When points this distance apart are found, the variance between their
values and their geographical orientation is determined. Once the first lag distance has been
analyzed the process is repeated using the second lag distance and then the third, and so on until all
distance possibilities are exhausted. When the variance analysis is completed, the information is
displayed in a semivariogram.
A semivariogram is a graph that plots the semivariance between points on the y-axis and distance at
which the semivariance was calculated on the x-axis. An example of a semivariogram is shown in
the next figure. The undulating line on the graph is the plot of calculated semivariances, plotted on
the y-axis, and their corresponding lag distances on the x-axis. This plot is given the term
experimental semivariogram. The jagged nature of the experimental semivariogram makes it
unsuitable for use in applications such as calculating kriging weights, so a smooth mathematical
function (model) must be fit to the variogram. The model is shown as the smooth line on the graph.
An example of an omni-directional semivariogram.
Although the strength of semivariogram analysis is its ability to account for directional trends of the
data, it is possible to analyze variance with respect to distance only and disregard how points are
geographically oriented. The above experimental semivariogram is an example of this, called an
omni-directional experimental semivariogram. If the geographic orientation is important, then a
directional semivariogram should be calculated such as the one shown in the next figure.