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references > kriging
What is Ordinary Kriging (OK)?
Ordinary Kriging (OK) is a geostatistical method, often used
in mining for block modelling; i.e. local estimation by interpolation.
It is a linear method and is thus based on a linear weighted
average.
The basic principles of OK (as used for block modelling) are:
- A search is made around the block to be estimated. Samples
located within the search 'neighbourhood' are utilised for
estimation of the block in question, whereas samples outside
this neighbourhood are not used.
- The samples within the search are assigned weights that
reflect the spatial variability of grade (as characterised
by the relevant variogram model).
Kriging
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- A weighted average is calculated to produce the block
estimate.
The advantages of OK over other, non-geostatistical interpolations
(for example inverse distance weighting) are:
- OK weights are based on the data themselves (via the variogram
model) rather than being arbitrary (as is the case for inverse
distance).
- Because of this, OK estimates correctly account for nugget
variance and short-range structures.
- OK weights reflect better the anisotropy of spatial grade
distribution, compared to non-geostatistical interpolators.
- OK estimates reflect the support of the estimated block
and the informing data.
- A major, well-known advantage of OK is that the optimal
interpolation weights assigned to data are calculated in
such a way that they minimise the variance of the estimation
error.
At its simplest, kriging is just a weighted average, where the
weights are chosen in this 'best' possible way.
As for IDW, in a kriging we allocate weights to the samples
found within a defined search neighbourhood in order to obtain
a linear estimate. These are the kriging weights.
What makes kriging different to other linear weighted averages
is that it is firmly based upon a probabilistic model.
In particular, kriging employs the variogram model as the weighting
function. Because of this, kriging weights are assigned in a
way that reflects the spatial correlation of the grades themselves.
This represents a real step forward from using arbitrary weighting
functions that bear little relation to the nature of grade distribution
(like IDW).
References on basic geostatistics
Armstrong, M., (Ed.), 1998.
Basic linear geostatistics. Springer-Verlag (Berlin), 256pp.
David, M., 1977. Geostatistical
ore reserve estimation. Developments in Geomathematics 2. Elsevier
(Amsterdam), 364pp.
Isaaks, E.H., and Srivastava, R.M.,
1989. An introduction to applied geostatistics. Oxford
University Press (New York) 561pp.
Journel, A.G., 1989. Fundamentals
of geostatistics in five lessons. Short Course in Geology: Volume
8. American Geophysical Union (Washington), 40pp.
Journel, A.G., and Huijbregts, Ch.J.,
1978. Mining geostatistics. Academic Press (London),
600pp.
Wackernagel, H., 1995. Multivariate
geostatistics. Springer-Verlag (Berlin), 256pp. |
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