Geostatistics without tears. A practical guide to surface interpolation, geostatistics, variograms and kriging / Геостатистика без слез. Практическое руководство по интерполяции поверхности, геостатистике, вариограммам и кригингу

Geostatistics (also known as kriging) was developed for the mining industry during the 1960s and 1970s to estimate changes in ore grade. The principles of geostatistics are now applied to many applications that require statistically based interpolation techniques. Geostatistics provides a data value estimate for locations that cannot be sampled directly by examining data taken at locations that can be sampled. If a model of spatial correlation can be established for the sampled data then this model is used to interpolate data values for those locations that cannot be sampled directly. The effectiveness of geostatistics depends upon how well the observation points represent the phenomenon under study as well as the appropriate selection of the model parameters.
Matheron introduced the term geostatistics in 1962 with this definition: “Geostatistics is the application of the formalism of random functions to the reconnaissance and estimation of natural phenomena” (Journel and Huijbregts, 1978). Oliver and Webster (1991) said, “. . . there is to be no geostatistics without tears”.
The intent of this paper is to provide the reader with an introduction and understanding of surface interpolation techniques and geostatistics (kriging). Hopefully no tears will be shed.  <...>