Abstract
The study compares the three deep learning approaches and assesses their relative performance solving the 1-D magnetotellurics (MT) inverse problem. MT data from a 1-D geothermal-type structure are used as an example to examine Variational Autoencoder (VAE), Residual Network (Res-Net), and U-Net architectures, adapted for 1-D MT inversion. Root Mean Square Error (RMSE) and Pearson correlation coefficient are applied as misfit measure and similarity criterion, and box plot tools are used to parameterize individual model parameters. The results show that the U-Net provides the most successful recovery of the 1-D resistivity models, even though all three approaches can produce accurate inversions of MT data. To investigate applicability of results to real data sets, the models performance are examined for the case of data containing noise. Three deep learning algorithms are robust with respect to data noise, although the U-Net is relatively superior. The study results provide a platform for more complex magnetotelluric inverse problems and ones involving real data sets.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Datasets for this research are available from the corresponding author on request.
Code availability
Name of the code/library: libraries in Python programming language. Contact: mehdi.rahmani.je@ut.ac.ir. The source codes are available for downloading at the link: https://github.com/MRjevinani/Mehdi_Rahmani_Jevinani.
Change history
24 February 2024
A Correction to this paper has been published: https://doi.org/10.1007/s12145-024-01254-1
References
Abbasnejad E, Dick A, Hengel AVD (2017) Infinite variational autoencoder for semi-supervised learning. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp 781-790. https://doi.org/10.48550/arXiv.1611.07800
Bergen KJ, Johnson PA, deHoop MV, Beroza GC (2019) Machine learning for data-driven discovery in solid earth geoscience. Science 363:6433. https://doi.org/10.1126/science.aau0323
Chen J, Hoversten GM, Key K, Nordquist G, Cumming W (2012) Stochastic inversion of magnetotelluric data using a sharp boundary parameterization and application to a geothermal site. Geophysics 77:E265–E279
Chen D, Hu F, Nian G, Yang T (2020) Deep residual learning for nonlinear regression. Entropy 22:193
Chi J, Liu Y, Wang V, Yan J (2022) Performance analysis of three kinds of neural networks in the classification of mask images. J Phys: Conf Ser 2181:012032. https://doi.org/10.1088/1742-6596/2181/1/012032
Fleuret F (2023) The little book of deep learning. Alanna Maldonado, Geneva
Gavrilov AD, Jordache A, Vasdani M, Deng J (2018) Preventing models overfitting and underfitting in convolutional neural networks. Int J Softw Sci Comput Intell 10(4):19–28
He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 770–778. https://doi.org/10.1109/CVPR.2016.90
Hsu WN, Zhang Y, Glass J (2017) Unsupervised domain adaptation for robust speech recognition via variational autoencoder-based data augmentation. IEEE Automatic Speech Recognition and Understanding Workshop (ASRU). https://doi.org/10.1109/ASRU.2017.8268911
Jones AG (1982) On the electrical crust—mantle structure in fennoscandia: no moho, and the asthenosphere revealed? Geophys J Int 68(2):371–388
Jones AG, Foster JH (1986) An objective real-time data-adaptive technique for efficient model resolution improvement in magnetotelluric studies. Geophysics 51(1):90–97
Kameoka H, Li L, Inoue S, Makino S (2019) Supervised determined source separation with multichannel variational autoencoder. Neural Comput 31:1891–1914
Kingma DP, Welling M (2014) Auto-encoding variational bayes. In: 2nd International Conference on Learning Representations, ICLR. https://doi.org/10.48550/arXiv.1312.6114
Lewis W, Vigh D (2017) Deep learning prior models from seismic images for full-waveform inversion. SEG Technical Program Expanded Abstracts, Houston. https://doi.org/10.1190/segam2017-17627643.1
Liao X, Zhiang Z, Yan O, Shi Z, Xu K, Jia D (2022) Inversion of 1-D magnetotelluric data using CNN-LSTM hybrid network. Arab J Geosci 15:1430
Liu Z, Chen H, Ren Z, Tang J, Xu Z, Chen Y, Liu X (2021) Deep learning audio magnetotellurics inversion using residual-based deep convolution neural network. J Appl Geophys 188:104309
Liu W, Wang He, Xi Z, Zhang R, Huang X (2022a) Physics-driven deep learning inversion with application to magnetotelluric. Remote Sensing 14:3218
Liu X, Craven JA, Tschirhart V (2022) Deep learning based one-dimensional inversion of magnetotelluric data, and an application in the southwestern Athabasca Basin Canada. Res Square. https://doi.org/10.21203/rs.3.rs-1599373/v1
Long J, Shelhamer E, Darrell T (2015) Fully convolutional networks for semantic segmentation. IEEE Conference on Computer Vision and Pattern Recognition (CVPR). https://doi.org/10.1109/CVPR.2015.7298965
Mao B, Han LJ, Feng O, Yin YJ (2019) Subsurface velocity inversion from deep learning-based data assimilation. J Appl Geophys 167:172–169
Oh S, Noh K, Seol SJ, Byun J (2020) Cooperative deep learning inversion of controlled-source electromagnetic data for salt delineation. Geophysics 85(4):E121–E137
Parker RL (1983) The magnetotelluric inverse problem. Geophys Surv 6:5–25
Pawar K, Attar VZ (2020) Assessment of autoencoder architectures for data representation. In: Kacprzyk, J. (Ed.), Deep Learning: Concepts and Architectures. Springer (ISBN 978–3–030–31756–0), pp. 101–132
Pintea SL, Sharma S, Vossepoel FC, van Gemert JC, Loog M (2022) Seismic inversion with deep learning. Comput Geosci 26:351–364
Puzyrev V (2019) Deep learning electromagnetic inversion with convolutional neural networks. Geophys J Int 218:817–832
Puzyrev V, Swidinsky A (2021) Inversion of 1D frequency- and time-domain electromagnetic data with convolutional neural networks. Comput Geosci 149:104681
Ronneberger O, Fischer P, Brox T (2015) U-Net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science, vol 9351. Springer, Cham. https://doi.org/10.1007/978-3-319-24574-4_28
Shahriari M, Pardo D, Picon A, Galdran A, Del Ser J, Torres-Verd C (2020) A deep learning approach to the inversion of borehole resistivity measurements. Comput Geosci 24:971–994
Sun Z, Sandoval L, Crystal-Ornelas R, Mousavi SM, Wang J, Lin C, Cristea N, Tong D, Carande WH, Ma X, Rao Y, Bednar JA, Tan A, Wang J, Purushotham S, Gill TE, Chastang J, Howard D, Holt B, Gangodamage C, Zhao P, Rivas P, Chester Z, Orduz J, Joun A (2022) A review of earth artificial intelligence. Comput Geosci 159:105034
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res 106(7):7183–7192
Wang He, Liu W, Xi Z (2019) Nonlinear inversion for magnetotelluric sounding based on a deep belief network. J Centr South Univ 26(9):2482–2494
Xu W, Sun H, Deng C, Tan Y (2017) Variational autoencoder for semisupervised text classification. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp 3358–3364. https://doi.org/10.1609/aaai.v31i1.10966
Ying X (2019) An overview of overfitting and its solutions. J Phys: Conf Ser 1168:022022
Yu S, Ma J (2021) Deep learning for geophysics: current and future trends. Rev Geophys 59:e2021RG000742
Funding
The authors have received no financial support for the research.
Author information
Authors and Affiliations
Contributions
Mehdi Rahmani Jevinani: conceptualization, development of the codes, writing of the primary draft. Banafsheh Habibian Dehkordi: conceptualization, supervision, a detailed review of the manuscript. Ian J. Ferguson: supervision, a detailed review of the manuscript. Mohammad Hossein Rohban: secondary supervision.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Communicated by: H. Babaie
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The original online version of this article was revised: Figure 10 has been updated with the correct image.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Rahmani Jevinani, M., Habibian Dehkordi, B., Ferguson, I.J. et al. Deep learning-based 1-D magnetotelluric inversion: performance comparison of architectures. Earth Sci Inform 17, 1663–1677 (2024). https://doi.org/10.1007/s12145-024-01233-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-024-01233-6