Convolutional neural networks with SegNet architecture applied to three-dimensional tomography of subsurface electrical resistivity: CNN-3D-ERT

SUMMARY In general, the inverse problem of electrical resistivity tomography (ERT) is treated using a deterministic algorithm to find a model of subsurface resistivity that can numerically match the apparent resistivity data acquired at the ground surface and has a smooth distribution that has been introduced as prior information. In this paper, we propose a new deep learning algorithm for processing the 3-D reconstruction of ERT. This approach relies on the approximation of the inverse operator considered as a nonlinear function linking the section of apparent resistivity as input and the underground distribution of electrical resistivity as output. This approximation is performed with a large amount of known data to obtain an accurate generalization of the inverse operator by identifying during the learning process a set of parameters assigned to the neural networks. To train the network, the subsurface resistivity models are theoretically generated by a geostatistical anisotropic Gaussian generator, and their corresponding apparent resistivity by solving numerically 3-D Poisson's equation. These data are formed in a way to have the same size and trained on the convolutional neural networks with SegNet architecture containing a three-level encoder and decoder network ending with a regression layer. The encoders including the convolutional, max-pooling and nonlinear activation operations are sequentially performed to extract the main features of input data in lower resolution maps. On the other side, the decoders are dedicated to upsampling operations in concatenating with feature maps transferred from encoders to compensate the loss of resolution. The tool has been successfully validated on different synthetic cases and with particular attention to how data quality in terms of resolution and noise affects the effectiveness of the approach.