Abstract
Random sampling of a known covariance function can be used during the process of estimating the variance of means or totals for a spatial random variable in blocks of variable size. One advantage of this method is that the precision of any block variance can be determined at the same time as the integral itself. In two-dimensional space this approach yields sufficiently precise results for continuous spatial random variables with exponential, Gaussian, and spherical covariance functions, as well as for point patterns with exponential covariance density or power-law-type, second-order intensity function. Practical examples of application deal with the areal distribution of felsic volcanic rocks and gold deposits in the Abitibi Volcanic Belt, Canadian Shield. The exponential model yields good results in both cases, but, as an overall fit, the fractal (power-law) model performs better in the characterization of the two-dimensional distribution of the gold deposits.
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Agterberg, F.P. Calculation of the variance of mean values for blocks in regional resource evaluation studies. Nat Resour Res 2, 312–324 (1993). https://doi.org/10.1007/BF02257541
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DOI: https://doi.org/10.1007/BF02257541