AN APPLICATION OF EMPIRICAL D-POSTERIOR BAYESIAN APPROACH TO THE PROBLEM OF STATISTICAL ESTIMATION OF ROCK POROSITY AND PERMEABILITY

One of the common ways for estimating porosity and permeability based on well logs is to apply some form of linear regression with regard to prior knowledge of the rock type. However, accurate determination of the rock type might be difficult and expensive, and there it might be inaccurate if the cheaper methods are applied. In this paper a procedure for porosity estimation is presented which might be used in the absence of knowledge of the rock type (the same methods are applicable for permeability estimation). The estimation is done from well logs: gamma ray, neutron porosity, bulk density, and formation resistivity. The procedure is based on basic application of d-posterior approach in Bayesian paradigm, and possesses some optimal properties with respect to the d-risk. A discrete model was considered for the problem. The rock porosity was treated as an unknown parameter with a prior distribution. The well logs were supposed to compose a random vector with joint distribution which depends on the value of the unknown parameter, the rock porosity. The procedure chooses the estimate for the porosity as the one which brings maximum to the posterior probability of porosity for given values of well logs. The performance of the procedure was tested on real data, the well logs of Cretaceous carbonate sediments. The resulting d-risks of the procedure calculated on the dataset are provided showing viability of the approach. Some ways on procedure improvement are suggested: Examination of more complex normal-normal model for the problem; estimation of porosity based on logs of neighboring beds.