Random fields based on autocorrelation models

If there are no or not enough measurements available, field variations can be depicted using autocorrelation models. These models are based on the assumption that points being spatially close to each other are strongly correlated (i.e. may even have similar values), and points that are farther away are less or not correlated.

This can be represented by autocorrelation functions, which depend on the distance between two points and calculate the correlation. The degree of distance dependence can be controlled by a parameter (correlation length).

In SoS, these models are implemented as parametric models. There are two variants:

1. Synthetic random field model
An autocorrelation function is determined for each point on the network and then a minimum number of parameters is determined by Karhunen-Loeve decomposition to obtain predetermined statistical properties (mean, standard deviation, correlation length).

2. Free-form variation model
Here a range of points is selected in advance (or is determined automatically) and, for these points, an autocorrelation function (interpolation) is then directly linked to a scaling parameter.

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