Grid-Fitting: A Method For Improved Financial And Physical Analysis Of Coal And Other Mineral Deposits

Much progress has been made in the application of geostatistics to hard rock ore deposits.1,2,3 4,8 Progress in the application of geostatistics to coal deposits has developed over a period of time out of hard rock technology.5,7 Exploratory drilling in many hard rock deposits is frequently significantly more productive than exploratory drilling in coal deposits. For example, hundreds of feet of drilling and/or many drill setups are frequently necessary to obtain a few samples from a typical 4 to 6 foot thick coal seam. With hard rock deposits, which are frequently thick or volumetric, less drilling dead work is involved in sampling the deposit. To produce a variogram, which is the basic element needed for geostatistical analysis, a few well positioned holes drilled into a hard rock deposit where the core(s) can be divided into many sections can produce a detailed variogram. To produce a similar type variogram in coal, it is necessary to drill many dozens of holes with much of the core length consisting of overburden data which is frequently of only secondary importance. To apply geostatistics to coal, not only are many separate sample sites needed, but frequently a problem exists in that the interval distance between samples cannot be controlled with the ease that hard rock drilling intervals can be controlled where it is only necessary to cut core segments according to some preassigned interval of distance. Because the uses of existing coal deposit samples are frequently handicapped by irregular sample distances and lack of sampling density along certain directions needed for the development of variograms, the application of geostatistics to coal deposits frequently does not proceed with the same efficiency and rapidity as when these techniques are applied to ore deposits. Grid-fitting was developed by the writers, as a logical and evolutionary improvement over the long and successful application of geostatistics to coal seams.6,9 Grid-fitting combines the trending of variance as well as other aspects of probability theory to optimize informational yields from the commonly less productive data derived from coal exploratory programs. Grid-fitting is basically a technique where a hypothesis involving numerous grid patterns, where each pattern is of a given geometry, size and direction is repeatedly matched against actual sample data to determine which match results in the closest fit of the hypothesis to the data. To determine the closest fit, a special index known as a selectivity index was developed. The selectivity index is basically the product of the mean and variance of the variances contained within each of the grids. hence, if SI is the selectivity index then [SI = Xs E (S i - Xs) /N] where [X]s is the mean of individual grid variances Si2 for any pattern of given geometry, direction and size.