Estudo comparativo de métodos geoestatísticos de estimativas e simulações estocásticas condicionais / Comparative study of geostatistical estimation methods and conditional stochastic simulations

AUTOR(ES)

Rafael de Aguiar Furuie

DATA DE PUBLICAÇÃO

2009

RESUMO

Different geostatistical methods present themselves as the optimal solution to different realities according to the characteristics displayed by the data in analysis. Some of the most popular estimation methods include ordinary kriging and lognormal ordinary kriging, this last one involving the transformation of data from their original space to a Gaussian distribution. However, these methods present some limitations, one of the most prominent ones being the smoothing effect observed in the resulting estimates. Some recent algorithms have been proposed as a way to correct this effect, and are tested in this work for their effectiveness, as well as some methods for the backtransformation of the lognormal converted values. Another approach to the problem is by means of the group of methods known as stochastic simulation, some of the most popular ones being the sequential Gaussian simulation and turning bands simulation, which although do not present the smoothing effect, lack the local accuracy characteristic of the estimation methods. This work seeks to assess the effectiveness of the different estimation (ordinary kriging, lognormal ordinary kriging, and their corrected estimates) and simulation (sequential Gaussian simulation and turning bands simulation) methods for different scenarios. Twenty seven exhaustive data sets (in a 50x50 grid) have been sampled at 90 points based on simple random sampling. These data sets started from a Gaussian distribution (Log1) and had their variation coefficients increased progressively, up to a highly asymmetrical distribution (Log27). Experimental semivariograms have been computed and modeled for geostatistical estimation and simulation processes. The resulting estimates or realizations were then compared to the original exhaustive data in order to assess how well these reproduced the original data. This was done by comparing statistical parameters of the original data and the ones of the reconstructed data, as well as graphically. Results showed that the method that presented the best correlation with the exhaustive data was lognormal ordinary kriging, even better when the backtransformation technique by Yamamoto is applied, which much improved the results for the more asymmetrical data sets. Ordinary kriging and its correction had some severe limitations in reproducing the lower tail of the more asymmetrical data sets, with worst results than those for the uncorrected estimates. Both simulation methods used presented a very small degree of correlation to the exhaustive data, their results also progressively less representative as the variation coefficient grew, even though it has the advantage of presenting several scenarios for decision making.

ASSUNTO(S)

krigagem ordinária lognormal ordinary kriging krigagem ordinária lognormal turning bands simulation sequential gaussian simulation simulação gaussiana sequencial simulação estocástica stochastic simulation ordinary kriging efeito de suavização smoothing effect simulação por bandas rotativas

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