Generate Gaussian random fields and threshold them to obtain structures.

A Gaussian random field describes a volume field with correlated noise. This means the probability of similarity between two values decreases exponentially with their distance. In the Gaussian Random Field Generator in GeoDict, several Gauss functions can be combined to define a random field.

In the image below, a scalar Gaussian random field in a jet color gradient is shown. The corresponding Gaussian function has a standard deviation of 3.

The Gaussian random field can then be segmented to a structure as shown here:

In the following example observe different forms of noise.

1. Uncorrelated noise, all values are independent.
2. Noise following a spatial correlation. The values are correlated with their spatial neighborhood.
3. Noise following a spatial correlation with a large correlation length.

The spatial correlation can be specified with an autocorrelation graph. For each distance between two voxels the probability of similarity, also called covariance, is described.

In the Gaussian Random Field Generator, you may define several autocorrelation functions to generate a custom random field.