ArcGIS Tutorial: Semi-variant function modeling

When modeling a semivariogram, self-correlation can be checked and quantified. In Geostatistical, this is called spatial modeling, also known as structural analysis or mutation analysis. In the spatial modeling of Semivariogram, we can start with the empirical semivariogram graph and calculate

Semivariogram (distance h) = 0.5 * Average [(Value at location i–value @ location J) 2]

(The distance between all paired positions is h). The formula involves calculating half of the squared difference between the paired positions. Quickly drawing all the pairings becomes difficult to handle. Instead of drawing each pair, the pairing is grouped into individual step bar cells. For example, the average half-variance of all point pairs with distances greater than 40 meters but less than 50 meters are calculated. The empirical semivariogram is a graph of the distance or stride length on the x-axis of the average semivariogram value on the y-axis (see).

　　

In addition, allowing replication is an intrinsic stationarity hypothesis. Therefore, you can use the averaging in the above Semivariogram formula.

After creating the empirical Semivariogram, the empirical semivariogram can be formed according to the point-fitting model. Semivariogram modeling and fitting the least squares line in regression analysis are similar. You can select a function as a model, for example, a spherical type that starts rising and then tends to smooth over a larger distance outside a certain range.

The goal is to calculate the parameters of the curve to minimize deviations from the points according to certain criteria. There are several variants of the Semivariogram model to choose from.

ArcGIS Tutorial: Semi-variant function modeling