A Very Simple Example

%matplotlib widget
import matplotlib.pyplot as plt
plt.ioff()
# turn of warnings
import warnings
warnings.filterwarnings('ignore')

We are going to start with a very simple example of a spatial random field with an isotropic Gaussian covariance model and following parameters:

variance $\sigma^2=1$
correlation length $\lambda=10$

First, we set things up and create the axes for the field. We are going to need the SRF class for the actual generation of the spatial random field. But SRF also needs a covariance model and we will simply take the Gaussian model.

import gstools as gs

x = y = range(101)

Now we create the covariance model with the parameters $\sigma^2$ and $\lambda$ and hand it over to :any:SRF. By specifying a seed, we make sure to create reproducible results:

model = gs.Gaussian(dim=2, var=1, len_scale=10, nugget=0)
srf = gs.SRF(model, seed=20220425)

With these simple steps, everything is ready to create our first random field. We will create the field on a structured grid (as you might have guessed from the x and y), which makes it easier to plot.

field = srf.structured([x, y])
srf.plot()

Wow, that was pretty easy!

model.plot()

Covmodel

Additional Parameters

Random Field

Creating an Ensemble of Fields