| Available from UMI in association with The British Library. Requires signed TDF.; The aim of this thesis is to investigate and develop statistical techniques that could be used by the petroleum industry in the assessment of the economic viability of oil and gas reservoirs. Specifically we consider the geostatistical technique of kriging, which was developed and refined in the mining industry; the petroleum industry has far fewer data points.; Kriging estimates spatially varying quantities, such as porosity and permeability, by assuming a known model for a random surface. One problem we consider is the sensitivity of the method to the assumed model. We demonstrate that if kriging is to be used as an exploratory tool then some form of sensitivity analysis is necessary to show how and where the fitted surface will change when the assumed model is perturbed. An exact sensitivity analysis is too complicated to be useful and very demanding computationally for large data sets, so we develop a simple approximate analysis.; As kriging is a model based approach it is necessary to estimate any parameters of the model from the data, but there is no formal way of doing this. Maximum likelihood has frequently been suggested; however we show by some simple examples that the profile likelihood can be multimodal even in quite large data sets and that the global maximum may not correspond to a sensible value of the parameters.; There are many methods available for the estimation of spatially varying quantities in the presence of geological faults (including kriging), provided the fault location and displacement are known. Often this information may not be available and so estimation will not be possible. We propose maximum a posteriori (M.A.P.) estimation (a Bayesian technique used in image analysis) as a means of overcoming this problem. It provides a general framework for both modelling and estimation of faults and as a by-product we establish the equivalence of M.A.P. estimation and kriging.; Finally we analyse a data set supplied by British Petroleum in order to compare the techniques developed in this thesis with those currently in use in the petroleum industry. |
