Deep Learning Inversion of Electrical Resistivity Data

The inverse problem of electrical resistivity surveys (ERSs) is difficult\nbecause of its nonlinear and ill-posed nature. For this task, traditional\nlinear inversion methods still face challenges such as suboptimal approximation\nand initial model selection. Inspired by the remarkable nonlinear mapping\nability of deep learning approaches, in this article, we propose to build the\nmapping from apparent resistivity data (input) to resistivity model (output)\ndirectly by convolutional neural networks (CNNs). However, the vertically\nvarying characteristic of patterns in the apparent resistivity data may cause\nambiguity when using CNNs with the weight sharing and effective receptive field\nproperties. To address the potential issue, we supply an additional tier\nfeature map to CNNs to help those aware of the relationship between input and\noutput. Based on the prevalent U-Net architecture, we design our network\n(ERSInvNet) that can be trained end-to-end and can reach a very fast inference\nspeed during testing. We further introduce a depth weighting function and a\nsmooth constraint into loss function to improve inversion accuracy for the deep\nregion and suppress false anomalies. Six groups of experiments are considered\nto demonstrate the feasibility and efficiency of the proposed methods.\nAccording to the comprehensive qualitative analysis and quantitative\ncomparison, ERSInvNet with tier feature map, smooth constraints, and depth\nweighting function together achieve the best performance.\n