Hierarchical Multiple Linear Regression for Fast Estimation of Subsurface Resistivity from Apparent Resistivity Measurements Based on Dipole-Dipole Array

Abstract

Multiple linear regression (MLR) models for fast estimation of true subsurface resistivity from apparent resistivity field measurements are developed and assessed in this study, based on Dipole-dipole array. The parameters that have been investigated are apparent resistivity (ρa) horizontal location (X) and depth (Z) of measurement as the independent variables; and true resistivity (ρt) as dependent variable. To achieve linearity in both resistivities, datasets were first transformed into logarithmic domain following diagnostic checks of normality of the dependent variable and heteroscedasticity to ensure accurate models. Four MLR models namely; DD1, DD2, DD3 and DD4 were developed based on hierarchical combination of the independent variables. The generated MLR coefficients were applied to another dataset to estimate ρt values for validation. The accuracy of the models was assessed using coefficient of determination (R2), standard error (SE) and weighted mean absolute percentage error (wMAPE). It is concluded that the MLR models can estimate ρt for the Dipole-dipole array with high level of accuracy, with the DD4 model being the best.