Linear regression models for estimating true subsurface resistivity from apparent resistivity data

• Published in: Journal of Earth System Science 2018-07, Vol.127 (5), p.1-10, Article 64
• Main Authors: Muhammad, Sabiu Bala, Saad, Rosli
• Format: Article
• Language: English
• Subjects: Algorithms; Aquatic reptiles; Arrays; Calibration; Coefficients; Computer memory; Datasets; Dependent variables; Dipoles; Earth and Environmental Science; Earth Sciences; Electrical resistivity; Estimation; Independent variables; Mathematical models; Model accuracy; Regression analysis; Regression models; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Standard error; Statistical methods
• ISSN: 0253-4126; 0973-774X
• DOI: 10.1007/s12040-018-0970-z

Simple linear regression (SLR) models for rapid estimation of true subsurface resistivity from apparent resistivity measurements are developed and assessed in this study. The objective is to minimize the processing time and computer memory required to carry out inversion with conventional algorithms. The arrays considered are Wenner, Wenner–Schlumberger and dipole–dipole. The parameters investigated are apparent resistivity ( ρ a ) and true resistivity ( ρ t ) as independent and dependent variables, respectively. For the fact that subsurface resistivity is nonlinear, the datasets were first transformed into logarithmic scale to satisfy the basic regression assumptions. Three models, one each for the three array types, are thus developed based on simple linear relationships between the dependent and independent variables. The generated SLR coefficients were used to estimate ρ t for different ρ a datasets for validation. Accuracy of the models was assessed using coefficient of determination ( R 2 ) , F -test, standard error ( SE ) and weighted mean absolute percentage error ( wMAPE ). The model calibration R 2 and F -value are obtained as 0.75 and 2286, 0.63 and 1097, and 0.47 and 446 for the Wenner, Wenner–Schlumberger and dipole–dipole array models, respectively. The SE for calibration and validation are obtained as 0.12 and 0.13, 0.16 and 0.25, and 0.21 and 0.24 for the Wenner, Wenner–Schlumberger and dipole–dipole array models, respectively. Similarly, the wMAPE for calibration and validation are estimated as 3.27 and 3.49%, 3.88 and 5.72%, and 5.35 and 6.07% for the three array models, respectively. When compared with standard constraint least-squares (SCLS) inversion and Incomplete Gauss–Newton (IGN) algorithms, the SLR models were found to reduce about 80–96.5% of the processing time and memory space required to carry out the inversion with the SCLS algorithm. It is concluded that the SLR models can rapidly estimate ρ t for the various arrays accurately.