During the last decade modelling the subsurface in the 2.5^th (structural surfaces), 3^rd (volumetric models) or even 4^th (time dependent models) dimension developed into a proper method to readily identify complex geological structures. Especially the oil and mining industry or hydrogeologists designed powerful modelling methods and associated software packages. The results, however, can not be adopted unconfined for 3D modelling in regional land survey projects. The structure and quality of respective datasets as well as much larger areas to model and the high diversity of potential applications require different basic approaches. Data from the land survey archives commonly constitute the main input when modelling the subsurface. These are composed of maps on different scales, inhomogeneous databases, site investigation reports and particular information details, that were collected over the recent years. The result is a high spatial heterogeneity of the data density, data accuracy and data validity which must be considered with the geological interpretation and also, must be analysed in detail before constructing volumetric property models. The knowledge about uncertainties, natural and artificial variabilities and references of each geoscientific parameter is essential to select the proper interpolation algorithms and visualisation methods. Such initial structural data and uncertainty analysis will produce not only more accurate 3D models, but will also enable more effective predictions of unmeasured properties.

To clarify the described discrepancies we will transfer two 2.5D lithostratigraphical subsurface models of quaternary units in Manchester (modelled by the British Geological Survey, Great Britain) and Ostfriesland  (modelled by the University of Cologne, Germany) into 3D volumetric models by attributing geotechnical, hydrological and geochemical parameters. The structural analysis of the multiparameter dataset and its uncertainties will be realised using multivariate geostatistics with a fuzzy logic approach. The quantified coherences and dependencies among one another of the different properties will be used to evaluate unmeasured data. In this context a program has already been developed to calculate estimations of permeability values (kf values in m/s), granular uniformity classes and mean grain sizes (mm) using qualitative lithological descriptions of bore logs. Furthermore these results will be compared with additional measurements from the field, such, that the algorithm can be verified.

The spatial structure for each parameter will be deduced with proper interpolation algorithms (e.g. Inverse Distance To Power, Fuzzy Kriging, Indicator Kriging etc.). The allocation of the empty spaces will be made on the basis of a 3D octree multiresolution grid. Here the cell volume behaves inversely proportional to the data density, so it can be used for quantifying geometrical uncertainties. The cells will be allocated with soft data derived from fuzzy and multivariate analysis, e.g., fuzzy c-means clustering. The outcome will be a geological 3D fuzzy subsurface model, which is controlled by natural phenomena on the one hand and uncertainties in data structure and interpretation on the other hand. The visualisation techniques and the data formats are discussed in correspondence with Prof. Dr. Lang at the Institute for Computer Science in Cologne.

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Sara Schade, Dipl. Geol. Institute for Geology and Mineralogy University of Cologne Zülpicher Straße 49 a 50674 Köln sara@scharasade.de www.scharasade.de
GEOSUM: A Step towards an integrated concept in three dimensional subsurface modelling (GeoLeipzig Meeting 2004)