Regularization - 5.1 Introduction

In the previous chapters we did not concern ourselves with the fact that the geostatistical properties of the regionalized variable x (z) are affected by the size of the support w. Ideally, when analysing an ore body O, we would like to determine the properties of point values in O, i.e. the properties of a regionalized variable with an infinitely small support, say w°. In practice, point values are never known. To measure the value of x at a point z we must take a sample of size w centred at z. For example, if we are interested in the grade at point z, w will be the volume of the sample 'centred in z; if we are interested in the metal accumulation at point z, w will be the area of the cross-section of the sample centred in z. We say that the measured property is a regularized variable, and so the semivariogram (or covariogram) calculated from the values obtained is also regularized. In the majority of the mining problems which can be solved by geostatistical methods, we are interested in the properties of blocks of ore and of samples with a finite non-point support. It will be shown in the following chapters that these problems can be solved by calculating the average value of the point sernivariogram in volumes or areas of finite dimension, or between such volumes or areas. These calculations would be simple if we knew the point semivariogram. This means that the point semivariogram has to be estimated from the observed regularized semivariogram(s).