Pitney Bowes MapInfo Vertical Mapper - Manual (Page 158)

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Vertical Mapper 3.7
Semivariogram Analysis
Grid creation is a valuable way to visualize how data, represented by points, changes through
space. The change in value between known locations can easily be shown. However, one thing a
grid does not show very well is how values change in any given direction and how strong that
directional trend is. This can be particularly valuable to know in some fields. For example, in mineral
exploration applications this information is important when trace elements have been transported to
their present location from the source by stream, landslide, glacier, or wind. The transportation of the
mineral often produces linear orientation in the landscape, and if it can be properly modeled, the
source can be found. Direction can also be important in understanding the geographic relationships
of demographic data such as average family income and population density.
A directional trend is the tendency for data points with similar values to be arranged in a linear
fashion or in a particular direction. Often there is more than one directional trend; however, generally
one trend dominates. The most popular technique for examining directional trends is variance
analysis.
Example of data that does not vary crosswise but varies greatly along the y-axis of the
data.
Semivariance expresses the degree of relationship between points on a surface. The semivariance
is simply half the variance of the differences between all possible points spaced a constant distance
apart.
The semivariance at a distance d = 0 will be zero because there are no differences between points
that are compared to themselves. However, as points are compared to increasingly distant points,
the semivariance increases. At some distance, called the range, the semivariance will become
approximately equal to the variance of the whole surface itself. This is the greatest distance over
which the value at a point on the surface is related to the value at another point. The range defines
the maximum neighbourhood over which control points should be selected to estimate a grid node,
taking advantage of the statistical correlation among the observations.
The calculation of semivariance between sample pairs is performed at different distances until all
possible distance combinations have been analyzed. The initial distance used is called the lag
distance, which is increased by the same amount for each pass through the data. For example, if the
lag distance is 10 metres, the first pass calculates the variance of all sample pairs that are 10 metres
apart. The second pass calculates the variance of all sample pairs 20 metres apart, the third at 30
metres and so on until the last two points that are the farthest apart have been examined.