It is shown how, given a fuzzy formulation of the variogram of a soil property, a fuzzy set of grid spacings that will achieve a target kriging variance can be derived. This fuzzy set of grid spacings can then be defuzzified in a more or less conservative way to define a sampling scheme. The method is illustrated in three examples. The first uses a hypothetical fuzzy variogram. The second is a ...

to enhance the certainty of the grade block model, it is necessary to increase the number of exploratory drillholes and collect more data from the deposit. the inputs of the process of locating these additional drillholes include the variogram model parameters, locations of the samples taken from the initial drillholes, and the geological block model. the uncertainties of these inputs will lead...

Nowadays, kriging has been accepted as the most common method of grade estimation in mineral resource evaluation stage. Access to the crisp assay data and a variogram model are the necessary means for the utilization of this method. Since fitting a crisp variogram model is generally difficult, if not impossible, the fitted theoretical model is usually tainted with uncertainty due to various rea...

To enhance the certainty of the grade block model, it is necessary to increase the number of exploratory drillholes and collect more data from the deposit. The inputs of the process of locating these additional drillholes include the variogram model parameters, locations of the samples taken from the initial drillholes, and the geological block model. The uncertainties of these inputs will lead...

Due to the nature of the geological and mining activities, different input parameters in the grade estimation and mineral resource evaluation are always tainted with uncertainties. It is possible to investigate the uncertainties related to the measurements and parameters of the variogram model using the fuzzy kriging method instead of the kriging method. The fuzzy kriging theory has already bee...

This work deals with spatial interpolation and problems related to the imprecision and the uncertainty of the data. Previous works led us to define a semantic-based aggregation process, which allows the combination of spatial data defined by fuzzy sets and possibility degrees. This article proposes to modify this aggregation process, in order to take into account a fuzzy variogram describing th...

The variogram model is one of the most relevant parameters in geostatistical estimation and simulation methods. The sample variogram is inferred from available data, which may be subject to spatial bias and proportional effect. Over this sample variogram, a licit variogram model is fit and is carried through the process of estimation and/or simulation of the random function usually without rega...

Before optimal linear prediction can be performed on spatial data sets, the variogram is usually estimated at various lags and a parametric model is fitted to those estimates. Apart from possible a priori knowledge about the process and the user’s subjectivity, there is no standard methodology for choosing among valid variogram models like the spherical or the exponential ones. This paper discu...

In this paper we propose an extended version of a model-based strategy for clustering spatial functional data. The strategy, we refer, aims simultaneously to classify spatially dependent curves and to obtain a spatial functional model prototype for each cluster. The fit of these models implies to estimate a variogram function, the trace variogram function. Our proposal is to introduce an altern...

The variogram is a critical input to geostatistical studies. It is the most widely used tool to investigate and model spatial variability of lithofacies, porosity, and other petrophysical properties. In addition, 90% of geostatistical reservoir characterization studies use variogram-based geostatistical modeling methods. Furthermore, the variogram reflects our understanding of the geometry and ...