Spatial Statistics, Covariogram And Semivariogram Definition And Calculation - 3.1 General

The statistical methods described in the previous chapter permit the estimation of the average value p of a deposit, and the calculation of confidence limits for this value. They are based on the assumption of independence of sample values. As soon as a reasonable number of samples has been obtained from a deposit, local valuation, or estimation of blocks of ore within the mineral deposit, becomes necessary. The assumption of independence of values must then be rejected. Local valuation is possible only if there is a relationship between the value of a sample and the value of the surrounding ore, provided this relationship is a function of the position of the sample with respect to the blocks of ore to be valued. Whichever method is used for the valuation of a block of ore, the following assumptions are always made: ? The values of samples located near or inside the block are related to the value of the block. ? The values of the samples located closest to the block are most closely related to the value of the block. These assumptions will hold true only if the following assumption can also be made: ? There exists a relationship between sample values which is a function of the distance between samples. We are saying that the value x (z) of a sample centred at a point z has properties which are functions of this point. A certain spatial structure exists in the sample distribution. We are therefore dealing with a regionalized phenomenon, and we must treat x (z) as a regionalized variable. This can be done statistically by means of a model chosen to represent the spatial structure of the phenomenon. We shall see that the relationship between block values and sample values can be deduced from the relationship between sample values, and all local valuation problems can be solved using the statistical model obtained from the analysis of the sample values. It is important to realize that this statistical model is obtained by analysing the properties of known sample values, and will be used for the estimation of unknown block values. Such a statistical inference is valid only if the model developed represents the properties of both the sampled section of the ore body and the section to be valued: some stationarity conditions must be satisfied, and the model with the least restrictive conditions is preferred. In the following chapters, the most important models used in spatial geostatistics are presented. The models which can be used when there is no significant drift (trends) in values are described in Chapters 3-1 1. These models can also be used to solve some specific valuation problems when a linear drift is present. A general study of the more difficult problem of analysis of an ore body whose values present a drift is described in Chapter 12. Note that the area considered for local valuation of a block of ore is often small enough for any drift which might be present to be ignored.