Understanding the Influence of Variograms

Up until now, we have only used very smooth Gaussian variograms for the underlying spatial random fields. Now, we will combine a smooth Gaussian field with a much rougher exponential field. This example should feel familiar, if you had a look at the previous examples.

import matplotlib.pyplot as plt
import numpy as np

import gstools as gs

dim = 2
# no. of cells in both dimensions
N = [200, 200]

x = np.arange(N[0])
y = np.arange(N[1])

Now, we generate fields with a Gaussian and an Exponential variogram.

model1 = gs.Gaussian(dim=dim, var=1, len_scale=[50, 25])
srf1 = gs.SRF(model1)
field1 = srf1.structured([x, y], seed=20170519)
model2 = gs.Exponential(dim=dim, var=1, len_scale=[40, 40])
srf2 = gs.SRF(model2)
field2 = srf2.structured([x, y], seed=19970221)

The lithotypes will consist of a circle which contains one category and the surrounding is the second category.

# no. of grid cells of the lithotypes
M = [200, 200]

# radius of circle
radius = 25

x_lith = np.arange(M[0])
y_lith = np.arange(M[1])
lithotypes = np.zeros(M)
mask = (x_lith[:, np.newaxis] - M[0] // 2) ** 2 + (
    y_lith[np.newaxis, :] - M[1] // 2
) ** 2 < radius**2
lithotypes[mask] = 1

With the two SRFs and the lithotypes ready, we can create the PGS.

pgs = gs.PGS(dim, [field1, field2])
P = pgs(lithotypes)

And now the plotting of the two Gaussian fields, the lithotypes, and the PGS.

fig, axs = plt.subplots(2, 2)

axs[0, 0].imshow(field1, cmap="copper", origin="lower")
axs[0, 1].imshow(field2, cmap="copper", origin="lower")
axs[1, 0].imshow(lithotypes, cmap="copper", origin="lower")
axs[1, 1].imshow(P, cmap="copper", origin="lower")

In this PGS, we can see two different spatial structures combined. We see large and rather smooth structures and shapes, which are surrounded by very rough and unconnected patches.