Stochastic Signal Processing > Variograms
  • Step 1: Alpha example.
    The experimental variogram is computed from as the statistical variance of spatial increments for a lag h. We show how to compute the experimental variogram of the 895 ALPHA samples values displayed in figure a. Example of increments for lags 5 and 10 in the North South direction are shown in figure b and the corresponding experimental variogram values are shown in figure c. The experimental variogram shown in figure d supports the choice and specification of the variogram model.

  • Step 2: Geophysical example.
    Geophysical images consist in dense 1D, 2D or 3D regular grids, making it easier and faster to compute experimental variograms in all directions of space, that are called variograms maps. On a 1D profile as shown in figure a, variogram values are computed for each lag h by duplicating and shifting the profile by a distance h before computing the average of squared differences in the common part of the two shifted profiles.
    On a 2D section as shown in figure b, the same procedure is applied by duplicating and shifting the section by vector h and computing variance of difference inside the common intersection. Repeating the computation for each vector {hx, ht} within a given area leads to the experimental variogram map. This computation can be optimized up by using Fourier Transform.