How Many Samples are Enough? Theoretical Determination of the Critical Sampling Density for a Greek Clay Quarry.

According to recently established theoretical analysis and under certain conditions, a critical sampling density can be determined for an earth-related space-distributed natural variable. Sampling above this critical limit adds little to the mapping results. The objective of this paper is the application of the above theory to the Sesklo clay quarry in Greece, where Heracles General Cement Company had conducted a sampling campaign to estimate its reserves. The structural analysis of Al2O3 values generated a variogram model, from which the critical sampling density was identified. This critical number was by far lower than the existing sampling density. Clay reserves were then estimated using geostatistics and inverse distance squares in different data schemes with variable densities. The results of the comparisons between the various models revealed that, when the sampling density was greater than its critical value, geostatistics and deterministic interpolation gave similar estimations, which is also in agreement to the theory. The optimal sampling grid finally proposed here, will result to significant cost savings in the next drilling program which is now in plan by the company.