Comparison Between Kriging Variance and Interpolation Variance as Uncertainty Measurements in the Capanema Iron Mine, State of Minas Gerais—Brazil

The Capanema Mine, an iron ore deposit, is located in the central portion of the Quadrilátero Ferrífero, State of Minas Gerais, southeastern Brazil. Mine development data from approximately 7000 drillholes were used for a comparative study between kriging variance and interpolation variance as uncertainty measurements associated with ordinary kriging estimates. As known, the traditional kriging variance does not depend on local data and, therefore, does not measure the actual dispersion of data. On the other hand, the interpolation variance measures adequately the local dispersion of data used for an ordinary kriging estimate. This paper presents an application of the concept of interpolation variance for measuring uncertainties associated with ordinary kriging estimates of Fe and silica grades. These data were selected for their distinct statistical characteristics with Fe presenting a negatively skewed distribution and, consequently, a low dispersion, and silica a positively skewed distribution and, therefore, a high variability. Comparative studies between the two uncertainty measurements associated with ordinary kriging estimates of Fe and silica proved the superiority of the interpolation variance as a reliable and precise alternative to the kriging variance.     

Relations Between Igneous and Metamorphic Rock Fracture Patterns and Groundwater Yield from the Variography of Water–Well Yields—Pinardville Quadrangle,New Hampshire

Exploratory variography was used to examine the spatial continuity of water–well yields in the Pinardville 7 Minute Quadrangle in southern New Hampshire and to link the variography to the characteristics of the fractured igneous and metamorphic rocks within the aquifer system. In addition to the analyses of variograms computed by using data from 939 wells, analyses were performed on subsets of the data that were stratified according to the level of yield and to five rock types. The stratification according to yield was defined by using the industry standard of a high-yield well that produces 40 gallons per minute or more. The stratification of the low-yield wells by rock type was defined by using the classification on the bedrock map for the State of New Hampshire. Although the variability is high in the low-yield wells, as indicated by the large nugget value, overall continuity ranges to 6000 feet in the fracture zones in which these wells have been drilled. This continuity is dominant in the northwesterly direction, as indicated by the directional variography. This result is consistent with the general trend in the larger tectonic configuration of the region. A lack of spatial correlation for 81 high-yield wells is consistent with the geologic interpretation that these wells occur in locally determined configurations of sheeting and steeply dipping fractures. Yield data in only three of the five rock types were sufficient for variography. Within these three, the dominant direction of the correlation structure ranged from northwesterly for the Massabesic Gneiss Complex to northeasterly for the Rangeley Formation to northerly for the Spaulding Granite, where the signature of the continuity in the low-yield wells is predominately attributed to the fracture system.