Indicator kriging

The projection theory indicates that a projection estimator of the unknown I(2c z), such as a kriging estimator, is also a projection estimator (kriging) of its conditional expectation Fx(z (N)), (7) Consider then the indicator kriging estimator ... 

These various covariance models are Inferred directly from the corresponding indicator data i(3 z ), i-l,...,N. The indicator kriging approach is said to be "non-parametric, in the sense that it draws solely from the data, not from any multivariate distribution hypothesis, as was the case for the multi- -normal approach. 

Journel(7-9) provides a means for generating the desired mappings in situations such as the example site which are free from any undue assumptions regarding the distributional form of concentrations within blocks. This approach simply transforms the data into the sample cumulative probability distribution. This nonparametric geostatistical approach is sometimes called "indicator kriging."... 

The objective of indicator kriging is to estimate the local distribution of TCDD concentrations rather than the concentrations themselves. To apply indicator kriging, the data must be transformed from the original measurements of concentrations into indicator variables. This is accomplished by letting z(x ), a=l, N represent the initial data set... 

The goal of indicator kriging is to estimate the conditional distribution function of the unknown concentrations, Z(x) at... 

The indicator kriging estimator, I (x z), appears as a linear combination of the indicator data i(xa z), in the neighborhood, n," surrounding the point for which a prediction is to be made. This can be symbolized as ... 

Deutsch and Joumel, 1992) is applied. This method is based on an indicator kriging approach. It is able to honour extreme values and allows for consideration of soft information and of more than one spatial structme of the investigated data. Geological expert knowledge about facies distribution and composition, as well as information on aquifer specific sedimentation processes is helpful in this step (Vert et al., 1999). 

The cumulative distribution function at an unsampled location at threshold z can be estimated by krig-ing. This indicator kriging or IK requires a variogram measure of correlation corresponding to each threshold Zk, k=l,..., K. The IK process is repeated for all K threshold values that discretize the interval of variability of the continuous attribute Z. The distribution of uncertainty, built from assembling the K indicator krig-ing estimates, can be used for uncertainty assessment or simulation. 

Indicator Kriging This technique transforms the observations into integer valued quantities with the transformation... 

The weights Xf(z) are cut-off z-dependent, and are determined as solutions of a linear system ( ) In fact, the indicator estimators used for the case-study underlying Figures 3 were obtained by a- slightly more elaborate technique called probability kriging or PK (9, 10) ... 

Note that if the kriging weights Xi(z) are data values-independent, the indicator estimates (11) are not hence, the final estimate of the conditional cdf Fx(z (N)) is data values-dependent. For each cut-off Z], the kriging estimator (11) requires a different indicator covariance model ... 

Fig. 1. Kriged and contoured cross-section of sericite / (sericite + chlorite)) 100 Index (plotted in percent) along A - A on McIntyre grid line 3500E through the HMC deposit. White diamonds indicate sample locations. Specific rock units such as C15 are labeled with abbreviations. The Cu-Au zone is indicated cross-hatching.

Fig. 4. Kriged cross-section of 5 Occ along McIntyre grid line 3500E through the HMC deposit. White dots indicate sample locations.

Geostatistical processing is one of the most useful and practical methods for evaluation and estimation of a resource. Its BLUE (Best Liner Unbiased Estimator) Kriging not only can indicate the distribution and amount of ore in a resource, but also, based on variance and error of Kriging can identify some parts of ore body, that have lack of data and need more exploration. For a routine Geostatistical processing some issues should be considered ... 

An estimate of the conditional distribution of Z(x) can be obtained by an ordinary kriging of the indicator transformed data. 

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