# gstools.variogram.vario_estimate_axis

gstools.variogram.vario_estimate_axis(field, direction='x', estimator='matheron', no_data=nan)[source]

Estimates the variogram along array axis.

The indices of the given direction are used for the bins. Uniform spacings along the given axis are assumed.

The algorithm calculates following equation:

$\gamma(r_k) = \frac{1}{2 N(r_k)} \sum_{i=1}^{N(r_k)} (z(\mathbf x_i) - z(\mathbf x_i'))^2 \; ,$

with $$r_k \leq \| \mathbf x_i - \mathbf x_i' \| < r_{k+1}$$ being the bins.

Or if the estimator “cressie” was chosen:

$\gamma(r_k) = \frac{\frac{1}{2}\left(\frac{1}{N(r_k)}\sum_{i=1}^{N(r_k)} \left|z(\mathbf x_i) - z(\mathbf x_i')\right|^{0.5}\right)^4} {0.457 + 0.494 / N(r_k) + 0.045 / N^2(r_k)} \; ,$

with $$r_k \leq \| \mathbf x_i - \mathbf x_i' \| < r_{k+1}$$ being the bins. The Cressie estimator is more robust to outliers [Webster2007].

Parameters
Returns

the estimated variogram along the given direction.

Return type

numpy.ndarray

Warning

It is assumed that the field is defined on an equidistant Cartesian grid.

Notes

Internally uses double precision and also returns doubles.

References

Webster2007

Webster, R. and Oliver, M. A. “Geostatistics for environmental scientists.”, John Wiley & Sons. (2007)