ABSTRACT

We integrate the information of multiple tomographic models acquired from the earth’s surface by modifying a statistical approach recently developed for the integration of cross-borehole tomographic models. In doing so, we introduce spectral cluster analysis as the new core of the model integration procedure to capture the spatial heterogeneity present in all considered tomographic models and describe this heterogeneity in a fuzzy sense. Because spectral cluster algorithms analyze model structure locally, they are considered relatively robust with regard to systematically and spatially varying imaging capabilities typical for geophysical tomographic surveys conducted on the earth’s surface. Using a synthetic aquifer example, a fuzzy spectral cluster algorithm can be used to integrate the information provided by 2D tomographic refraction seismic and DC resistivity surveys. The integrated information in the fuzzy membership domain is then used to derive an integrated zonal geophysical model outlining the major structural units present in both input models. We also explain how the fuzzy membership information can be used to identify optimal locations for sparse logging of additional target parameters, i.e., porosity information in our synthetic example. We demonstrate how this sparse porosity information can be extrapolated based on all tomographic input models. The resultant 2D porosity model matches the original porosity distribution reasonably well within the spatial resolution limits of the underlying tomographic models. Consecutively, we apply this approach to a field data base acquired over a former river channel. Sparse information about natural gamma radiation is available and extrapolated on the basis of the fuzzy membership information obtained by spectral cluster analysis of 2D P-wave velocity and electrical resistivity models. This field data shows that the presented parameter extrapolation procedure is robust, even if the locations of target parameter acquisition have not been optimized with regard to the fuzzy membership information.

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