Zastosowanie krigingu zwyczajnego do rekonstrukcji i wizualizacji reliefu w miejscach odkrywkowej eksploatacji piasku

W niniejszym artykule zaprezentowano jeden ze sposobów odtwarzania rzeźby (sprzed rozpoczęcia eksploatacji piasku na cele podsadzkowe) czterech pól piaskowych dawnego wyrobiska „Siemonia”. Morfologia analizowanego terenu została zwizualizowana w oparciu o archiwalną mapę geologiczną (arkusz Wojkowice) z zastosowaniem metod geostatystycznych, w tym m.in. krigingu zwyczajnego. Jest to jedna ze znanych technik estymacji (szacowania), nazywana B.L.U.E. (best linear unbiased estimator). Zgodność dopasowania matematycznych modeli sferycznych do wariogramu empirycznego potwierdzono w procedurze kross-walidacji. Uzyskane wartości błędów (błąd średni, błąd średni kwadratowy oraz błąd średni kwadratowy standaryzowany) są w znacznym stopniu zgodne z notowanymi w literaturze naukowej. Wygenerowana rzeźba badanego terenu pod postacią modelu trójwymiarowgo w wyniku przeprowadzonej pełnej analizy geostatystycznej jest dość mocno uwydatniona w porównaniu do modelu otrzymanego bez zastosowania analizy strukturalnej i kross-walidacji.

Extraction of mineral resources, including rocks, usually causes some significant changes of the landscape. Transformation of the relief which character and scale can be analysed by means of cartographic materials seems to be the most interesting. Reconstruction of the relief of the period prior to the exploitation is a starting point for such investigation. It can be done basing on archival cartographic materials which are difficult to obtain. However, too varied morphological material of the area can lead to erroneous conclusions which suggests interpretation of three-dimensional models of the relief. Hence, the paper deals with reconstruction and visualisation of the relief (in the period before the exploitation) of four sand fields of the old sand mine excavation “Siemonia”. A geological map of Poland (Wojkowice sheet) has been used for the purpose. A geostatical analysis by means of the programmes Surfer 8. and ArcGIS 10.1. has been performed on the map. An estimation method called ordinary kriging, which is related to B.L.U.E. (best linear unbiased estimator), where the condition of the lack of weight of the measurement (the sum of weight is equal to 1) is fulfilled, has been applied. The calculated values of errors (mean error, mean squared error and mean squared standardised error) obtained as a result of application of the cross-validation procedure are, to a large extent, in agreement with predetermined values of errors given by numerous authors in the scientific literature. It confirms proper “manual” adjustment of two mathematical models of spherical variograms and empirical variograms. The generated contour map of the investigated area (based on estimated points of sampling in nodes of the interpolation grid) together with its three-dimensional digital model are more adequate (due to significant marking of the relief) to the previous state of the investigated area than the two other presented types of cartographic visualisations made without application of the geostatistical methods. Hence, the graphic presentation of results, mentioned as the last one, can be only applied to visualise the relief without any detailed geomorphological interpretations due to its inaccuracy. It seems to be obvious that detailed analyses can be performed basing on a digital model of the terrain accompanied by its contour map obtained when reconstruction of the relief is made by means of geostatistical methods (especially ordinary kriging).