Abstract. This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method ± wavelet analysis residual kriging (WARK) ± is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses arti®cial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.
The Australian machine-learning workflows apply fusion, clustering, and estimation operations to hydrogeophysical data for deriving hydrostratigraphic units (HSUs). Data fusion is performed by training a self-organizing map (SOM) with these data. The application of Davies-Bouldin criteria to K-means clustering of SOM nodes determines the number and location of HSUs. Estimation is handled by iterative least-squares minimization of the SOM quantization and topographical errors. Two workflows provide 3D characterization of HSUs (and related attributes) from different hydrogeophysical data (measured, derived, interpolated, and estimated values) sets. In Workflow 1, the SOM learns to recognize relationships among a subset of borehole geophysical and hydrogeologic data. Using the data-fusion approach described above, the missing hydrological data are estimated using these learned relationships and HSUs determined at borehole sample locations resulting in a low lateral density and high vertical density spatial distribution. Variogram modeling of the regional field data and HSU estimates is undertaken to evaluate the spatial statistical structure of selected attributes. In workflow 2, the learned relationships between borehole data and the more spatially extensive AEM conductivity model are used to estimate the key attributes and HSUs at a number of locations away from the borehole. The AEM conductivity profile at a number of random locations are mapped to the SOM network and estimation performed to arrive at a set of continuous HSUs with high lateral density and medium vertical density (based on m-layer modelled structure). Performance metrics and validation are used to test each step of both workflows.
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