Arithmetic map operations are very common procedures used in GIS to combine raster maps resulting in a new and improved raster map. It is essential that this new map be accompanied by an assessment of uncertainty. This paper shows how we can calculate the uncertainty of the resulting map after performing some arithmetic operation. Actually, the propagation of uncertainty depends on a reliable measurement of the local accuracy and local covariance, as well. In this sense, the use of the interpolation variance is proposed because it takes into account both data configuration and data values. Taylor series expansion is used to derive the mean and variance of the function defined by an arithmetic operation. We show exact results for means and variances for arithmetic operations involving addition, subtraction and multiplication and that it is possible to get approximate mean and variance for the quotient of raster maps.
ou iguais às distâncias Euclidianas, pode-se calcular uma razão entre elas a ser utilizada como um fator.Com o uso desse fator, é possível estimar a função covariância e, portanto, a solução do sistema de equações de krigagem. Para aplicar o método proposto, um estudo de caso foi considerado na Mina de Capanema (MG). Dados de testemunho de sondagem foram usados para derivar o modelo geométrico e, dessa maneira, calcular o variograma e estimativas por krigagem para a unidade denominada hematita intemperizada. Os resultados são compatíveis com o modelo geométrico e estão restritas à unidade estratigráfica.
Sequential indicator simulation realizations contain unavoidable artifacts that are geologically unrealistic. This happens because unlikely types can be drawn randomly from the cumulative distribution and be assigned to a cell in the simulated model. This cell may then be used as previously simulated data when a cell in its neighborhood is visited during a random walk. The sequential process sometimes results in geologically unrealistic realizations. However, different realizations can reveal hidden features. Each realization contains both reliable geological information and noise that is displayed as unlikely types. This paper proposes applying the averaging filter that is commonly used in seismic reflection data to improve the signal to noise ratio. After applying this filter, all L realizations will be condensed into a single geological model that contains certain and uncertain cells. This average model is then exhaustively sampled for the certain cells, and this new sample is used to post-process the uncertain cells to reduce the uncertainty. This resampling and post-processing procedure can be repeated until the final model is considered to be good enough. The proposed method is tested with a model of a dike that crosscuts two sedimentary units. The synthetic geologic model was sampled with 24 drill holes. The resultsshow that the final geological model with reduced uncertainty reproduces very well the sedimentary units and the orientation of the dike as well. The dike shape is not fully reproduced and still presents uncertainties because of lack of neighbor data.
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