The correlation between the precision of interpolation and data sampling density when estimating the distribution of the CaO grade in a limestone quarry using the kriging method was considered. At first, a reference data set with 160m × 160m area was generated using the grade measurement cuttings in an actually working limestone mine. This CaO grade distribution map was assumed as the reference distribution map. Then, eight testing data sets with 2 to 9m intervals (25.3 to 1.4% data density for the amount of original data) were prepared by thinning out some data points from the reference data set. Distribution maps of the CaO grade were estimated using each testing data set by ordinary kriging with the spherical variogram model. These testing distribution maps were compared with the reference map. As a result, favorable CaO grade distribution maps were obtained from the testing data sets with 2 to 6m interval data (25.3 to 3.0% data density for the amount of original data) that corresponded well with the reference map. It was confirmed that the precision of interpolation decreases as the data density decreases, but the decreasing tendency is not simple like a linear model. Actually, the grade distribution estimated with the testing data set with 5m intervals (4.2% data density for the amount of original data) shows a high interpolation accuracy with a less than 1% error range for more than 75% of the reference area of the face, while more than 50% of the area is beyond the 1% error range using the testing data set with 8m intervals (1.4% data density for the amount of original data). The considerations in this paper provide a guideline with a numerical basis regarding accuracy of interpolation in a limestone quarry.
Integration of multiple groundwater investigation data and precise modeling of hydrogeological structures including aquifers are indispensable to sustainable use of groundwater resources. GIS technology can be effectively applied to this purpose. This study selected the Kumamoto City area which depends on groundwater for all water supplies as a case study of such GIS application. Using the vertical geological cross-sections, the groundwater-level data at ten observation wells, digital elevation model, surface geological map, spring map, and ArcGIS (ESRI), the following hydraulic items were characterized: three-dimensional strata distribution, water-level distribution and its temporal change, correlation of the level with the precipitation, strata distribution at the water level, and the geological and topographic factors for spring formation. As the result, the general trend of annual average of water-level distribution was found to be unchanged despite the large change in precipitation. The zones with high changeability in water level were locally appeared due to the high permeability of strata along the vertical direction. Holocene Ariake clay layers and Pleistocene Aso-4 pyroclastic flow deposits were specified as main strata at the water levels in the first aquifer in the low land and terrace areas, respectively. The springs were clarified to be located at the steep change in topographic slope and at the boundaries of the surface and aquifer strata.