The aim of the paper is the comparison of the least squares prediction presented by Heiskanen and Moritz (1967) in the classical handbook “Physical Geodesy” with the geostatistical method of simple kriging as well as in case of Gaussian random fields their equivalence to conditional expectation. The paper contains also short notes on the extension of simple kriging to ordinary kriging by dropping the assumption of known mean value of a random field as well as some necessary information on random fields, covariance function and semivariogram function. The semivariogram is emphasized in the paper, for two reasons. Firstly, the semivariogram describes broader class of phenomena, and for the second order stationary processes it is equivalent to the covariance function. Secondly, the analysis of different kinds of phenomena in terms of covariance is more common. Thus, it is worth introducing another function describing spatial continuity and variability. For the ease of presentation all the considerations were limited to the Euclidean space (thus, for limited areas) although with some extra effort they can be extended to manifolds like sphere, ellipsoid, etc.

Bełchatów lignite deposit is located in the central partof Poland in the tectonic Kleszczów graben. It is dividedinto several parts, which are mining fields: Kamieńsk area (eastern part of the deposit), Bełchatów area (central partof the deposit) and Szczerców area (western part of the deposit). The subject of this study was the Belchatow area.The main issue of the investigations was the dependence of local, regional and global, horizontal variability of selected lignite qualitative parameters (moisture, ash content, calorific value and sulfur content in the as receivedstate) is a function of viewing direction. There was applied the geostatistical analysis of the lignite variability parameters with use of semivariograms.

The researches which were conducted at different scales of observation: in the locale scale – in small field size8 ́8 m called experimental area (local analysis), in larger homogeneous separated parts of the Belchatow area(regional analysis) and in the whole Bełchatów area scale (general analysis). The results proved the visible anisotropy of variability mine lignite parametres. Anisotropy structure observed in regional and global scale isconnected with tectonic structure of the Bełchatów Graben. The detailed studies show the variated level of anisotropy observed in different areas of Bełchatów field.

However, no dependence of the relative level of ash and total sulfur content anisotropy on the environment of sedimentation of the main coal deposit in different parts of the Belhchatów field has been observed. Both parameters characterize with strong or medium anisotropy level in examined fields. Moreover, anisotropy is alsovisible in the local scale. Conducted researches confirmed the thesis that zonal anisotropy is prevalent kind of anisotropy in the regional scale. In the range of the whole deposit the total sulfur content showed zonal anisotropy,whereas the ash content revealed geometric anisotropy