Multiple Linear Regression Models For Estimating True Subsurface Resistivity From Apparent Resistivity Measurements
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Date
2018-06
Authors
Bala, Muhammad Sabiu
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
Multiple linear regression (MLR) 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 required to
carry out inversion with conventional algorithms. The arrays considered are Wenner,
Wenner-Schlumberger and Dipole-dipole. The parameters investigated are apparent
resistivity ( a ), horizontal location (x) and depth (z) as independent variable; while
true resistivity ( t
) is dependent variable. To address the nonlinearity in subsurface
resistivity distribution, the datasets were first transformed into logarithmic scale to
satisfy the basic regression assumptions; normality, linearity, multicollinearity, axis
balance, heteroscedasticity and outliers. Four models, each for the three array types,
were developed based on hierarchical multiple linear relationships between the
dependent variable and the independent variables. The generated MLR coefficients
were used to estimate t
for different a , x and z datasets for validation. Accuracy
of the models was assessed using coefficient of determination (R2), adjusted coefficient
of determination (R2
adj), root-mean-square error (RMSE) and weighted mean absolute
percentage error (wMAPE). The model calibration, R2 values were obtained as 0.75-
0.76 for Wenner array models, 0.63-0.71 for Wenner-Schlumberger array models and
0.47-0.66 for Dipole-dipole array models. Similarly, the RMSE and wMAPE obtained
for all the models developed were in the range of 3-8 %. One best model each for the
three arrays was thus selected based on the accuracy assessment.
Description
Keywords
Multiple linear regression true subsurface resistivity , from apparent resistivity measurements