Truncated Power Law Variograms
GSTools also implements truncated power law variograms, which can be represented as a superposition of scale dependant modes in form of standard variograms, which are truncated by a lower- and an upper length-scale .
with Stable modes on each scale:
which gives Gaussian modes for
or Exponential modes for
For this results in:
import numpy as np import gstools as gs x = y = np.linspace(0, 100, 100) model = gs.TPLStable( dim=2, # spatial dimension var=1, # variance (C is calculated internally, so variance is actually 1) len_low=0, # lower truncation of the power law len_scale=10, # length scale (a.k.a. range), len_up = len_low + len_scale nugget=0.1, # nugget anis=0.5, # anisotropy between main direction and transversal ones angles=np.pi / 4, # rotation angles alpha=1.5, # shape parameter from the stable model hurst=0.7, # hurst coefficient from the power law ) srf = gs.SRF(model, mean=1.0, seed=19970221) srf.structured([x, y]) srf.plot()
Total running time of the script: ( 0 minutes 15.390 seconds)