# Deep Learning Inversion of Electrical Resistivity Data

arXiv: https://arxiv.org/abs/1904.05265 · HTML: https://mlsanity.com/paper/1904.05265/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2019.

## Built on by (most cited first, 8 of 8)

- [Inversion of Time-Lapse Surface Gravity Data for Detection of 3D CO2 Plumes via Deep Learning](https://mlsanity.com/paper/2209.02850/) (2022)
- [A Test-Time Learning Approach to Reparameterize the Geophysical Inverse Problem with a Convolutional Neural Network](https://mlsanity.com/paper/2312.04752/) (2023)
- [Towards Understanding the Benefits of Neural Network Parameterizations in Geophysical Inversions: A Study With Neural Fields](https://mlsanity.com/paper/2503.17503/) (2025)
- [Joint inversion of Time-Lapse Surface Gravity and Seismic Data for Monitoring of 3D CO2 Plumes via Deep Learning](https://mlsanity.com/paper/2310.04430/) (2023)
- [Assesment of material layers in building walls using GeoRadar](https://mlsanity.com/paper/2208.12064/) (2022)
- [A Noise-robust Multi-head Attention Mechanism for Formation Resistivity Prediction: Frequency Aware LSTM](https://mlsanity.com/paper/2406.03849/) (2024)
- [3-D Magnetotelluric Deep Learning Inversion Guided by Pseudo-Physical Information](https://mlsanity.com/paper/2410.09388/) (2024)
- [Enhancing Deep Learning based RMT Data Inversion using Gaussian Random Field](https://mlsanity.com/paper/2410.19858/) (2024)

## Abstract (arXiv)

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