Geostatistics Overview
Geostatistics Overview
When a volumetric model is created, we generally use geostatistics to estimate (interpolate and extrapolate) data into the volume based on sparse measurements. The algorithm used is called kriging, which is named after a South African statistician and mining engineer, Danie G. Krige who pioneered the field of geostatistics. Kriging is not only one of the best estimation methods, but it also is the only one that provides statistical measures of quality of the estimate.
The basic methodology in kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point. The method is mathematically related to regression analysis. Both derive a best linear unbiased estimator, based on assumptions on covariances and make use of Gauss-Markov theorem to prove independence of the estimate and error.
The combination of kriging and volumetric modeling provides a much more feature rich model than is possible with any model that is limited to external surfaces and/or simpler estimation methods such as IDW or FastRBF. It allows us to perform volumetric subsetting operations and true volumetric analysis, and we can defend the quality of our models based on the limitations of our data.
In the coal mining industry, we can determine the quantity and quality of coal and its financial value. We can assess the amount and extraction cost of excavating overburden layers that must be removed or whether it is more cost effective to use tunneling to access the coal.
In the field of environmental engineering, where our software was born, volumetric modeling allows us to determine the spatial extent of the contamination at various levels as well as compute the mass of contaminant that is present in the soil, groundwater, water or air. During remediation efforts, this is critical, since we must confirm that the mass of contaminant being removed matches the reduction seen in the site, otherwise it is a clue that during the site assessment we have not found all the sources of contamination. This can result in remediation efforts which create contamination in some otherwise clean portions of the site.
The kriging algorithm provides us with only one direct statistical measure of quality, and that is Standard Deviation. However, C Tech uses Standard Deviation to compute three additional metrics which are often more meaningful. These are:
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