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Potentiel de réserves d'un bassin pétrolier : modélisation et estimation

Abstract : The aim of this thesis is to build a statistical model of oil and gas fields' sizes distribution in a given sedimentary basin, for both the fields that exist in the subsoil and those which have already been discovered. The estimation of all the parameters of the model via estimation of the density of the observations by model selection of piecewise polynomials by penalized maximum likelihood techniques enables to provide estimates of the total number of fields which are yet to be discovered, by class of size. We assume that the set of underground fields' sizes is an i.i.d. sample of unknown population with Lévy-Pareto law with unknown parameter. The set of already discovered fields is a subsample without replacement from the previous which is "size-biased". The associated inclusion probabilities are to be estimated. We prove that the probability density of the observations is the product of the underlying density and of an unknown weighting function representing the sampling bias. An arbitrary partition of the sizes interval being set (called a model), the analytical solutions of likelihood maximization enables to estimate both the parameter of the underlying Lévy-Pareto law and the weighting function, which is assumed to be piecewise constant and based upon the partition. We shall add a monotonicity constraint over the latter, taking into account the fact that the bigger a field, the higher its probability of being discovered. Horvitz-Thompson-like estimators finally give the conclusion. We then allow our partitions to vary inside several classes of models and prove a model selection theorem which aims at selecting the best partition within a class, in terms of both Kullback and Hellinger risk of the associated estimator. We conclude by simulations and various applications to real data from sedimentary basins of four continents, in order to illustrate theoretical as well as practical aspects of our model.
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Contributor : Vincent Lepez <>
Submitted on : Tuesday, March 2, 2010 - 3:07:11 PM
Last modification on : Wednesday, September 16, 2020 - 5:06:28 PM
Long-term archiving on: : Friday, June 18, 2010 - 7:13:40 PM


  • HAL Id : tel-00460802, version 1



Vincent Lepez. Potentiel de réserves d'un bassin pétrolier : modélisation et estimation. Mathématiques [math]. Université Paris Sud - Paris XI, 2002. Français. ⟨tel-00460802⟩



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