Multivariate Multiple Linear Regression for Jointly Modeling of Petrophysical Properties

Abstract

This paper introduces a solid procedure for multiple linear regression of petrophysical properties by estimation the linear association between the predictors and two response factors together. The common procedure is to consider only one response (univariate regression) given a set of predictors; however, the core porosity has been jointly modeled with core permeability given three continuous variables (well logs) and one discrete variable (Lithofacies) in sandstone formation. In a prior step, the core permeability and core porosity have been corrected given the neutron porosity measurements. The least squares estimator is adopted for coefficient estimation, multiple responses prediction, and residuals computing. The t-distribution test is used to validate the overall joint modeling of petrophysical modeling in order to check the null hypothesis rejection for all the variables and attain confidence interval to be greater than 95%. The backward stepwise elimination has been used to delete the non-influential predictors that have no impact on the two responses. Since there is a colinearity between the water saturation and shale volume predictors, the stepwise elimination has taken the shale volume a way in permeability modeling ad water saturation in porosity modeling when they fail to reject the null hypothesis of their coefficients being zero.