Linear Discriminant Analysis for Bayesian Estimation of Continuous Facies Distribution

摘要

Precisely prediction of rock facies leads to adequate reservoir characterization by improving the porosity-permeability relationships to estimate the properties in non-cored intervals.It also helps to accurately identify the spatial facies distribution to perform an accurate reservoir model for optimal future reservoir performance. In this paper,the conditional posterior probabilities of continuous facies distribution has been estimated through Bayesian linear discriminate analysis(BLDA)with respect to the well logs and core data in a well in sandstone formation in West Africa.The independent variables are caliper log(CCL),deep induction log,medium induction log,gamma rays,neutron porosity,core porosity,deep resistivity,medium resistivity,spontaneous potential(SP),density&corrected density,in addition to core permeability. The BLDA has been chosen to estimate the maximum likelihood and minimize the standard error for the nonlinear relationships between facies&core and log data. The Linear discriminate Analysis seeks a linear transformation(discriminate function)of both the independent and dependent variables in order to produce a new set of transformed values that provides a more accurate discrimination with dimensionality reduction.Beta distribution of facies has been consid-ered as prior knowledge and the resulted predicted probability(posterior)has been estimated from LDA based on Baye’s theorem that represents the relationship between predicted probability(posterior)with the conditional probability and the prior knowledge. The linear discriminant analysis has been accomplished considering the cross-validation in addition to splitting the data into train and test.Through assessing the LDA models,the cross-validation has been chosen as optimal solution to estimate the continuous facies distribution because the total true correct summation is more than it value through splitting data method.