Practical Geostatistics For The Lognormal-De Wijsian Model - 2.1 General

The term geostatistics was introduced by Matheron (1960) to cover the development and application of mathematical and statistical models which take specific account of the spatial structure of a 'regionalised' variable. In ore valuation the relative positions of available ore values within an ore body or portion thereof, can only be ignored in the unlikely case where there is no significant pattern of association or correlation between them - that is, if they do not disclose any significant spatial structure. A structure might not be evident in the available data, e.g. where the spacing of the available values is relatively wide such as in surface drilling on a new deep gold mine. However, practical selective mining considerations could dictate the need for eventual underground valuation on a scale much smaller than that represented by this spacing and the possibility of a significant structure on such a smaller scale cannot then be ignored. Some spatial structure must be present wherever the average variability among the values of check ore samples from the same, adjacent or nearby grooves or of borehole cores from the deflections in the same borehole, is lower than the overall variability for ore values within the whole ore body. Another practical check on the presence of a spatial structure is where it is evident that there is or will be a significant variation in the ore grades for individual ore blocks. Any correlation between peripheral and follow-up internal ore block values also provides evidence of a spatial structure, and hence the regression techniques covered in §1.16-1.2 1 can be accepted as the first application of the geostatistical procedures. The spatial structure of a regionalised variable can be studied and measured by the pattern, usually a decreasing function, in the level of correlation or of the covariance between pairs of values as the distance or lag between the values increases, that is, by the correlogram or covariogram (Krige, 1968, 1969, 1976; and Fig. 18). In geostatistics, for various practical and theoretical reasons (Matheron, 1960, 1971), the measure most commonly used is the semivario- gram, which increases as the lag increases. The semivariogram and covariance values are interrelated and for the lognormal- de Wijsian pattern used extensively for gold ore valuation both measures as well as their relationship can be defined on a fairly straightforward basis. Provided the underlying as- sumptions are realistic, the choice of measure - correlogram, covariogram or semivariogram - will be dictated mainly by convenience. Paragraph 2.2 will cover some general geostatistical terms and $2.3-2.12 will deal mainly with the theoretical side of the lognormal-de Wijsian model for spatial structures. Wherever the relevant variable lends itself to normalisation via the 3-parameter lognormal distribution (see 51.9) the de Wijsian semivariogram model is also likely to be suitable and will provide substantial advantages in application. Various practical applications will be covered in Section 3. Although confined to the lognormal-de Wijsian model, much of the theory covered and the general approach is applicable to all spatial structures. [ ]