gstools.variogram.vario_estimate_axis

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

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:

• field (numpy.ndarray or numpy.ma.MaskedArray) – the spatially distributed data (can be masked)

• direction (str or int) – the axis over which the variogram will be estimated (x, y, z) or (0, 1, 2, …)

• estimator (str, optional) –

  the estimator function, possible choices:

  • “matheron”: the standard method of moments of Matheron

  • “cressie”: an estimator more robust to outliers

  Default: “matheron”

• no_data (float, optional) – Value to identify missing data in the given field. Default: numpy.nan

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)