Summarizing the GRF’s correlation structure

The semivariogram can be computed with geoR::variog().

Some arguments:

• option:
  • "bin" (default) returns values of binned semivariogram
  • "cloud" returns the semivariogram cloud
    • i.e. points \((h_{ij},v_{ij})\) with:
      \(h_{ij}=||s_i−s_j||\)
      \(v_{ij} = \frac{1}{2} \cdot (Z(s_i) - Z(s_j))^2\)
  • "smooth" returns the kernel smoothed semivariogram
• uvec: to define the variogram binning (option = "bin").
  • if a scalar is provided, this is the default number of bins
  • if not provided: 13 bins are calculated
• max.dist: maximum distance for the semivariogram
• trend: specifies the mean part of the model. By default, trend = "cte" so the mean is assumed constant over the region.

A trend can be fitted using ordinary least squares: then variograms are computed using the residuals.