Estimation of layered earth conductivity with electromagnetic induction data in the low induction number range using the genetic algorithm method

Estimating the electromagnetic parameters of the subsurface is crucial for the non-invasive characterization of soil properties such as clay content, water content, contaminants, and aquifers. It is also of significant importance in agriculture for managing water resources. In this context, several geophysical methods, including electromagnetic (EM) techniques, have been developed to measure parameters such as the conductivity of subsurface layers. In this study, the conductivity of horizontal subsurface layers within the exploration depth of the EM-38 device was estimated using electromagnetic data in the low induction number (LIN) range. The data were acquired using the EM-38 device, depending on the horizontal and vertical orientation of the transmitter and receiver dipoles, and were received at the receiver coil. Additionally, the combined data obtained from both horizontal and vertical modes could be used as combined-mode data. To perform the inversion process, synthetic data for three modes (horizontal, vertical, and combined) were first generated. Subsequently, the electrical conductivity of the horizontal layers in the model was estimated using linear inversion for each of these three datasets in the low induction number range. Ordinary least squares, Tikhonov regularization (of zeroth, first, and second orders), and genetic algorithms (GA) were employed to estimate the parameters. The results demonstrated that, for this problem, Tikhonov regularization of zeroth, first, and second orders does not significantly improve the solution, and the model obtained using these techniques deviates considerably from the true model. Genetic algorithms, which are intelligent optimization techniques, have been applied to solve nonlinear inverse problems in various fields of geophysics. Genetic algorithms (GA), inspired by the concept of evolution, represent a class of search and optimization methods. These algorithms encode potential solutions to a specific problem in chromosome-like data structures. By applying recombination operators to these chromosomal data structures, genetic algorithms preserve the critical information stored within these structures. The inversion results showed that, for the employed model, genetic algorithms and the ordinary least squares method with combined-mode data provided the conductivity of the layers with errors of less than 4% and 5%, respectively. In the inversion using both the ordinary least squares method and genetic algorithms, the parameters estimated using combined-mode data exhibited the lowest root mean square error (RMSE) compared to the other two modes, while the horizontal mode had the highest error. Therefore, for this problem, the genetic algorithm was identified as a more robust and accurate method compared to ordinary least squares, and the combined-mode data proved to be more suitable than the other two modes. The data resolution matrix and the model resolution matrix were both identity matrices, indicating the uniqueness of the data and the model parameters. Moreover, the model covariance matrix revealed that noise in the data is strongly mapped, particularly onto the second parameter of the model.