Geodesic
Regularization algorithms of the statistical estimation of function in problem of geological modelling
Matematičeskoe modelirovanie, Tome 23 (2011) no. 4, pp. 23-40

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In paper various variants regularization algorithms are used for a solution of problems of a parameter estimation of geological model, namely position of layer roof and a layer sole, and also trends defining character of a modification of filtrational and capacity properties. Basic of methods is approximation of estimated functions by means of methods which are optimum from the informational point of view, i.e. ensure the given accuracy of expansion at the minimum number of parameters of approximation. In particular, for function of final smoothness is a spline-approximation. It is shown in paper that the spline-approximation, which parameters are defined by the maximum likelihood method, represents an estimation of average value of stochastic process. The average estimation of accuracy of method which shows is received that with magnification of number of parameters of approximation decreases the error of approximation and the error of statistical estimation increases. Thus, the number of parameters of approximation is regularization parameter. Convergence of algorithms to estimated magnitudes on probability is proved. The algorithm of definition of parameter of a regularization by means of criteria of check of statistical hypotheses is offered and realized. Results of modeling and real calculation are reduced.
Keywords: regularization, spline-approximation, stochastic process, geological modelling, least-squares method.
Mots-clés : filtration 
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     title = {Regularization algorithms of the statistical estimation of function in problem of geological modelling},
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D. A. Lavrik; I. R. Minniakhmetov; A. Kh. Pergament. Regularization algorithms of the statistical estimation of function in problem of geological modelling. Matematičeskoe modelirovanie, Tome 23 (2011) no. 4, pp. 23-40. http://geodesic.mathdoc.fr/item/MM_2011_23_4_a1/