Inversion of 2D and 3D DC resistivity imaging data for high contrast geophysical regions using artificial neural networks / Ahmad Neyamadpour - Neyamadpour, Ahmad (2010)
In electrical resistivity imaging surveys, the field data along a profile are normally acquired as a subsurface distribution of apparent resistivity. One common method to obtain the true resistivity distribution is by inverting the apparent resistivity values. However, the inversion of DC resistivity imaging data is complex due to its non-linearity. This is especially true for regions with high resistivity contrast. For the complicated subsurface structure, especially when regions of high resistivity contrast exist, a conventional inversion technique based on least squares methods may not be able to invert the DC resistivity data with adequate accuracy. Therefore, in this study, we investigate the applicability of artificial neural networks in the inversion of 2D and 3D electrical resistivity imaging data obtained with five common electrode arrays, i.e.,Wenner-Schlumberger, Wenner, dipole-dipole, pole-dipole, and pole-pole arrays. The basics of the DC resistivity survey and that of the 1D, 2D and 3D surveys are discussed in this thesis. The common arrays used for the 2D and 3D surveys are compared using the following characteristics: (i) the signal strength, (ii) the horizontal data coverage, (iii) the sensitivity of the array to horizontal structures, (iv) the sensitivity of the array to vertical structures, and (v) the depth of investigation for each array. In order to study the numerical simulation of the measured data for a given subsurface parameter, the basis of the finite difference method and the various boundary conditions are explained here. By comparing the common non-linear least square inversion methods (i.e., the steepest descent method, the nonlinear conjugate gradients method, Newton-type methods and smoothness-constrained least squares methods), the L1_ norm smoothness-constrained optimization method (or robust inversion technique) has been recognized as the most efficient of the least squares methods mentioned here, because it sometimes gives relatively better results in high resistivity zones with sharp boundaries. In order to study the effect of data pool formation in training the neural network, two methods have been used to generate the synthetic data. These methods are M1 and M2, and they basically differ in the type of input-output data used to train the artificial neural network. The effect of the input-output data type is investigated by 2D and 3D study. The results suggest that the synthetic data generated by M2_2D and M2_3D methods may be the best data type for training and testing the neural networks in this study. The effect of the number of nodes in each layer of the network (for 2D and 3D cases) have been studied which determined the simplest architecture for the neural network that can reach the desired threshold error for each array. The effect of the training data pool volume in the 2D and 3D parts of this study has also been evaluated, and the sufficient volume for each data type is selected.Furthermore, five common training paradigms, i.e., batch training with weight and bias learning rules, conjugate gradient with Fletcher reverse updates, resilient propagation,gradient descent with momentum and adaptive learning rate and Levenberg-Marquardt with weight and bias learning rules, are compared for both 2D and 3D. These results show that,for all the arrays (2D and 3D) except 3D pole - dipole data, resilient propagation is the most efficient algorithm for training the DC resistivity data. In the case of 3D study of pole - dipole data, the gradient descent with momentum and an adaptive learning rate algorithm is found to be the most efficient paradigm. In addition, an interpolation and extrapolation properties of the neural network have been studied using another 24 synthetic datasets generated for each array. The RMS errors for all the interpolation and extrapolation test sets related to each array are in the range of 0.3 - 9.0%. It is therefore, concluded that the networks are properly designed and trained. The ability of the trained neural networks to invert the 2D and 3D DC resistivity imaging data is also checked using real field datasets from a site with high resistivity contrast. The inverted field data from the neural network is then compared with inverted results from the conventional robust inversion method for each array. Further study using a synthetic example similar to the field data is conducted for each array in order to evaluate the reliability and accuracy of the inversion results using both the neural network and the robust inversion technique. All the subsurface features were nearly resolved by the results of both these methods. However, the neural network results are found to be more realistic, especially for the vertical columns and horizontal pipes. In contrast, the robust inversion method produced a relatively smaller vertical dimension than the actual size of the real field data. When the inversion results of both the neural network and the robust inversion methods for the synthetic test models were compared with their corresponding physical resistivity models, it has been found that the depths of the anomalies in the results of the robust inversion method results are less pronounced than their actual values. In addition, the robust inversion method produced smaller resistivity values than their actual values, but in comparison the result from neural network produced better physical models. It is thus,concluded that the neural network results are more accurate than the results from robust inversion method.