Citation: | Qingkui Meng, Lianghui Guo, Shuai Zhang, Hanyu Lou, Rui Li. Deep Learning in Gravity Research: A Review. Journal of Earth Science, 2025, 36(4): 1808-1819. doi: 10.1007/s12583-023-1926-x |
This study explores the application of deep learning (DL) to gravity research, which is a promising intersection of earth science and information science. DL provides new methods and ideas for exploring and solving problems related to multiple solutions and uncertainty in the study of gravity. We focus on the application of convolutional neural networks, recurrent neural networks, and other DL technologies to gravity data denoising, interpolation, anomaly inversion, field modelling, and geological interpretation. However, importantly, the application of DL to the field of gravity research is still in its initial stage. There is significant potential for development and widespread application in overcoming limitations in sample size, network framework optimization, and generalization ability.
Bayram, T., 2016. Application of Back Propagation Artificial Neural Networks for Gravity Field Modelling. Acta Montanistica Slovaca, 21(3): 200–207 |
Bengio, Y., 2009. Learning Deep Architectures for AI. Foundations and Trends® in Machine Learning, 2(1): 1–127. https://doi.org/10.1561/2200000006 |
Bengio, Y., Lamblin, P., Popovici, D., et al., 2007. Greedy Layer-Wise Training of Deep Networks. In: Schölkopf, B., Platt, J., Hofmann, T., eds., Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference. The MIT Press. 153–160. |
Cao, H., 2020. Fundamentals of Earth Gravity. Science Press, Beijing. 252 (in Chinese) |
Chen, B., 2020. Research on Denoising of Potential Field Data Based on Deep Convolutional Neural Network: [Dissertation]. China University of Geosciences, Beijing (in Chinese with English Abstract) |
Chen, H. Y., Zhang, J. L., 2022. What Is the Future Road for Mineral Exploration in the 21st Century? Journal of Earth Science, 33(5): 1328–1329. https://doi.org/10.1007/s12583-022-1744-8 |
Chen, J., Schiek-Stewart, C., Lu, L. G., et al., 2020. Machine Learning Method to Determine Salt Structures from Gravity Data. SPE Annual Technical Conference and Exhibition, October 26–29, 2020. Virtual. SPE, D041S046R007. https://doi.org/10.2118/201424-ms |
Cheng, L., Wang, Z. B., Song, Y., et al., 2020. Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks. Acta Astronautica, 170: 66–79. https://doi.org/10.1016/j.actaastro.2019.11.039 |
Cheng, Y., Li, T. L., Zhou, S., 2022. Error Transfer Model and Error Compensation for Dynamic Measurement of Rotating Accelerometer Gravity Gradiometer. Chinese Journal of Geophysics, 65(3): 1125–1134 (in Chinese with English Abstract) |
Cho, K., van Merriënboer, B., Gulcehre, C., et al., 2014. Learning Phrase Representations Using RNN Encoder-Decoder for Statistical Machine Translation. arXiv preprint arXiv: 1406.1078. |
Cordell, L. E., 1992. A Scattered Equivalent-Source Methods for Interpolation and Gridding of Potential-Field Data in Three Dimensions. Geophysics, 57(4): 629–636. https://doi.org/10.1190/1.1443275 |
Deng, Y. F., Chen, Y., Li, P. F., et al., 2022. A Synthesis of Geophysical Data in Southeastern North China Craton: Implications for the Formation of the Arcuate Xuhuai Thrust Belt. Journal of Earth Science, 33(3): 552–566. https://doi.org/10.1007/s12583-021-1584-y |
Evstifeev, M. I., 2017. The State of the Art in the Development of Onboard Gravity Gradiometers. Gyroscopy and Navigation, 8(1): 68–79. https://doi.org/10.1134/S2075108717010047 |
Furfaro, R., Barocco, R., Linares, R., et al., 2021. Modeling Irregular Small Bodies Gravity Field via Extreme Learning Machines and Bayesian Optimization. Advances in Space Research, 67(1): 617–638. https://doi.org/10.1016/j.asr.2020.06.021 |
Gao, A., Liao, W. T., 2019. Efficient Gravity Field Modeling Method for Small Bodies Based on Gaussian Process Regression. Acta Astronautica, 157: 73–91. https://doi.org/10.1016/j.actaastro.2018.12.020 |
Goodfellow, I., Pouget-Abadie, J., Mirza, M., et al., 2020. Generative Adversarial Networks. Communications of the ACM, 63(11): 139–144. https://doi.org/10.1145/3422622 |
Guo, L. F., Chen, Y. Q., Zhao, B. B., 2021. Application of Singular Value Decomposition (SVD) to the Extraction of Gravity Anomalies Associated with Ag-Pb-Zn-W Polymetallic Mineralization in the Bozhushan Ore Field, Southwestern China. Journal of Earth Science, 32(2): 310–317. https://doi.org/10.1007/s12583-020-1352-4 |
Guo, L. H., Meng, X. H., Shi, L., et al., 2012. Preferential Filtering Method and Its Application to Bouguer Gravity Anomaly of Chinese Continent. Chinese Journal of Geophysics, 55(12): 4078–4088. https://doi.org/10.6038/j.issn.0001-5733.2012.12.020 (in Chinese with English Abstract) |
Hansen, R. O., 1993. Interpretive Gridding by Anisotropic Kriging. Geophysics, 58(10): 1491–1497. https://doi.org/10.1190/1.1443363 |
He, K. M., Zhang, X. Y., Ren, S. Q., et al., 2016. Deep Residual Learning for Image Recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 27–30, 2016, Las Vegas, NV, USA. IEEE: 770–778. |
Hinton, G. E., Salakhutdinov, R. R., 2006. Reducing the Dimensionality of Data with Neural Networks. Science, 313(5786): 504–507. https://doi.org/10.1126/science.1127647 |
Hochreiter, S., Schmidhuber, J., 1997. Long Short-Term Memory. Neural Computation, 9(8): 1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735 |
Huang, M. T., Deng, K. L., Ouyang, Y. Z., et al., 2022. Development and Study in Marine and Airborne Gravimetry and Its Application. Geomatics and Information Science of Wuhan University, 47(10): 1635–1650 (in Chinese with English Abstract) |
Huang, R., Zhang, Y., Vatankhah, S., et al., 2022. Inversion of Large-Scale Gravity Data with Application of VNetFree. Geophysical Journal International, 231(1): 306–318. https://doi.org/10.1093/gji/ggac190 |
Huang, Z. Y., Wang, Q. B., Zhao, D. M., et al., 2021a. Gravity Data Denoising and Reconstruction Based on Deep Residual Network. Journal of Chinese Inertial Technology, 29(4): 443–450. https://doi.org/10.13695/j.cnki.12-1222/o3.2021.04.004 (in Chinese with English Abstract) |
Huang, Z. Y., Wang, Q. B., Li, S. Z., et al., 2021b. Using Kmeans-RBF Neural Network to Improve the Accuracy of Grid Gravity Data. Hydrographic Surveying and Charting, 41(4): 43–47 (in Chinese with English Abstract) |
Jessell, M., Guo, J. T., Li, Y. Q., et al., 2022. Into the Noddyverse: a Massive Data Store of 3D Geological Models for Machine Learning and Inversion Applications. Earth System Science Data, 14(1): 381–392. https://doi.org/10.5194/essd-14-381-2022 |
Jiang, T., Li, J. C., Dang, Y. M., et al., 2014. Regional Gravity Field Modeling Based on Moment Harmonic Analysis. Chinese Science: Earth Science, 44(1): 82–89 (in Chinese) |
Krizhevsky, A., Sutskever, I., Hinton, G. E., 2017. ImageNet Classification with Deep Convolutional Neural Networks. Communications of the ACM, 60(6): 84–90. https://doi.org/10.1145/3065386 |
LeCun, Y., Bengio, Y., Hinton, G., 2015. Deep Learning. Nature, 521(7553): 436–444. https://doi.org/10.1038/nature14539 |
LeCun, Y., Bottou, L., Bengio, Y., et al., 1998. Gradient-Based Learning Applied to Document Recognition. Proceedings of the IEEE, 86(11): 2278–2324. https://doi.org/10.1109/5.726791 |
Li, J. C., 2012. Topographic Gravimetric Effects in Earth Sciences: Review of Origin, Significance and Implications. Education of Geography, (S2): 1. https://doi.org/10.3969/j.issn.1005-5207.2012.07.002(in Chinese) |
Li, J., 1993. Spectral Method in Physical Geodesy: [Dissertation]. Wuhan Technical University of Surveying and Mapping, Wuhan (in Chinese) |
Li, N., Xu, B. S., Wu, H. L., et al., 2021. Application Status and Prospects of Artificial Intelligence in Well Logging and Formation Evaluation. Acta Petrolei Sinica, 42(4): 508–522. https://doi.org/10.7623/syxb202104008 |
Li, Y. G., Oldenburg, D. W., 1998. 3-D Inversion of Gravity Data. Geophysics, 63(1): 109–119. https://doi.org/10.1190/1.1444302 |
Li, Y., Han, L. G., Zhou, S., et al., 2023. Gravity Data Density Interface Inversion Based on U-Net Deep Learning Network. Chinese Journal of Geophysics, 66(1): 401–411. https://doi.org/10.6038/cjg2022Q0362 (in Chinese with English Abstract) |
Liu, L. T., Xu, H. Z., 2004. Wavelets in Airborne Gravimetry. Chinese Journal of Geophysics, 47(3): 490–494 (in Chinese with English Abstract) doi: 10.3321/j.issn:0001-5733.2004.03.019 |
Liu, S., Hu, X. Y., Liu, T. Y., 2014. A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization. Pure and Applied Geophysics, 171(7): 1531–1555. https://doi.org/10.1007/s00024-013-0712-8 |
Luo, Z. C., Zhong, B., Zhou, H., et al., 2022. Progress in Determining the Earth's Gravity Field Model by Satellite Gravimetry. Geomatics and Information Science of Wuhan University, 47(10): 1713–1727. https://doi.org/10.13203/j.whugis20220537 (in Chinese with English Abstract) |
Lv, M., Zhang, Y., Liu, S., 2023. Fast Forward Approximation and Multitask Inversion of Gravity Anomaly Based on UNet3+. Geophysical Journal International, 234(2): 972–984. https://doi.org/10.1093/gji/ggad106 |
Ma, G. Q., Wu, Q., Xiong, S. Q., et al., 2021. Ratio Method for Calculating the Source Location of Gravity and Magnetic Anomalies Based on Deep Learning. Earth Science, 46(9): 3365–3375 (in Chinese with English Abstract) |
Ma, G. W., Wang, Z., Li, L., 2022. Gridding and Filtering Method of Gravity and Magnetic Data Based on Self-Attention Deep Learning. Oil Geophysical Prospecting, 57(1): 34–42 (in Chinese with English Abstract) |
Martin, J., Schaub, H., 2022. Physics-Informed Neural Networks for Gravity Field Modeling of the Earth and Moon. Celestial Mechanics and Dynamical Astronomy, 134(2): 13. https://doi.org/10.1007/s10569-022-10069-5 |
Mousavi, S. M., Ellsworth, W. L., Zhu, W. Q., et al., 2020. Earthquake Transformer—An Attentive Deep-Learning Model for Simultaneous Earthquake Detection and Phase Picking. Nature Communications, 11: 3952. https://doi.org/10.1038/s41467-020-17591-w |
Nabighian, M. N., Ander, M. E., Grauch, V. J. S., et al., 2005. Historical Development of the Gravity Method in Exploration. Geophysics, 70(6): 63ND–89ND. https://doi.org/10.1190/1.2133785 |
Nagihara, S., Hall, S. A., 2001. Three-Dimensional Gravity Inversion Using Simulated Annealing: Constraints on the Diapiric Roots of Allochthonous Salt Structures. Geophysics, 66(5): 1438–1449. https://doi.org/10.1190/1.1487089 |
Pallero, J. L. G., Fernández-Martínez, J. L., Bonvalot, S., et al., 2015. Gravity Inversion and Uncertainty Assessment of Basement Relief via Particle Swarm Optimization. Journal of Applied Geophysics, 116: 180–191. https://doi.org/10.1016/j.jappgeo.2015.03.008 |
She, Y. W., Fu, G. Y., 2021. Estimation of Gravity Anomaly Data Based on Recurrent Neural Network. Journal of Geodesy and Geodynamics, 41(3): 234–237. https://doi.org/10.14075/j.jgg.2021.03.003 (in Chinese with English Abstract) |
Simonyan, K., Zisserman, A., 2014. Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv preprint arXiv: 1409. 1556. https://doi.org/10.48550/arXiv.1409.1556 |
Singer, D. A., 2021. How Deep Learning Networks Could Be Designed to Locate Mineral Deposits. Journal of Earth Science, 32(2): 288–292. https://doi.org/10.1007/s12583-020-1399-2 |
Sun, H. P., Li, Q. Q., Bao, L. F., et al., 2022. Progress and Development Trend of Global Refined Seafloor Topography Modeling. Geomatics and Information Science of Wuhan University, 47(10): 1555–1567 (in Chinese with English Abstract) |
Sun, H. P., Sun, W. K., Shen, W. B., et al., 2021. Research Progress of Earth's Gravity Field and Its Application in Geosciences—A Summary of Annual Meeting of Chinese Geoscience Union in 2020. Advances in Earth Science, 36(5): 445–460 (in Chinese with English Abstract) |
Sun, H., 2021. Preface to the Special Issue of "Earth's Gravity Field and Its Geological Application". Advances in Earth Science, 36(5): 443–444 (in Chinese with English Abstract) |
Szegedy, C., Liu, W., Jia, Y. Q., et al., 2015. Going Deeper with Convolutions. In: Proceedings of 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 7–12, 2015, Boston. IEEE: 1–9. |
Valentín, M. B., Bom, C. R., Coelho, J. M., et al., 2019. A Deep Residual Convolutional Neural Network for Automatic Lithological Facies Identification in Brazilian Pre-Salt Oilfield Wellbore Image Logs. Journal of Petroleum Science and Engineering, 179: 474–503. https://doi.org/10.1016/j.petrol.2019.04.030 |
Wang, F., Chen, S. C., Liu, Y. N., 2019. Deep Learning for Gravity and Magnetic Data Interpolation. In: SEG Technical Program Expanded Abstracts 2019, Society of Exploration Geophysicists, San Antonio, Texas. 2533–2537. |
Wang, J. B., Xiong, S. Q., Guo, Z. H., et al., 2012. Kalman Smoothing for Airborne Gravity Data. Progress in Geophysics, 27(4): 1717–1722. https://doi.org/10.6038/j.issn.1004-2903.2012.04.052 (in Chinese with English Abstract) |
Wang, J., Zhou, Z. W., Meng, X. H., et al., 2023. A Novel Method for Eliminating the Strip-Shaped Interferences in Aeromagnetic Anomaly Based on Convolutional Neural Network. IEEE Transactions on Geoscience and Remote Sensing, 61: 5902211. https://doi.org/10.1109/TGRS.2023.3239345 |
Wang, W. Y., Qiu, Z. Y., Liu, J. L., et al., 2009. The Research to the Extending Edge and Interpolation Based on the Minimum Curvature Method in Potential Field Data Processing. Progress in Geophysics, 24(4): 1327–1338. https://doi.org/10.3969/j.issn.1004-2903.2009.04.022 (in Chinese with English Abstract) |
Wang, Y. C., Liu, L. T., Xu, H. Z., 2020. The Identification of Gravity Anomaly Body Based on the Convolutional Neural Network. Geophysical and Geochemical Exploration, 44(2): 394–400. https://doi.org/10.11720/wtyht.2020.1504 (in Chinese with English Abstract) |
Wang, Y. C., Liu, L. T., Xu, H. Z., 2022. Noisy Gravity Data Reconstruction Using the Convolutional Autoencoder. Geomatics and Information Science of Wuhan University, 47(4): 543–550. https://doi.org/10.13203/j.whugis20190410 (in Chinese with English Abstract) |
Wu, X. M., Ma, J. W., Si, X., et al., 2023. Sensing Prior Constraints in Deep Neural Networks for Solving Exploration Geophysical Problems. Proceedings of the National Academy of Sciences of the United States of America, 120(23): e2219573120. https://doi.org/10.1073/pnas.2219573120 |
Yang, J. Y., Zhang, X. H., Zhang, F. F., et al., 2012. On the Accuracy of EGM2008 Earth Gravitational Model in Chinese Mainland. Progress in Geophysics, 27(4): 1298–1306. https://doi.org/10.6038/j.issn.1004-2903.2012.04.003 (in Chinese with English Abstract) |
Yang, M., 2022. Study on Gravity and Magnetic Geological Interpretation Methods Based on Deep Learning: Taking Benxi-Xiuyan Area, Liaoning Province as a Case: [Dissertation]. Jilin University, Jilin |
Yang, Q. G., Hu, X. Y., Liu, S., et al., 2021. 3-D Gravity Inversion Based on Deep Convolution Neural Networks. IEEE Geoscience and Remote Sensing Letters, 19: 3001305. https://doi.org/10.1109/LGRS.2020.3047131 |
Yang, Y., Li, D., 2017. Research and Experiment of Gravity Gradient Measurement Technology Based on Rotary Accelerometer Principle. Navigation Positioning and Timing, 4(4): 20–28. https://doi.org/10.19306/j.cnki.2095-8110.2017.04.003 (in Chinese with English Abstract) |
Yu, S. W., Ma, J. W., 2021. Deep Learning for Geophysics: Current and Future Trends. Reviews of Geophysics, 59(3): e2021RG000742. https://doi.org/10.1029/2021RG000742 |
Zeng, H., 2005. Gravity Field and Gravity Exploration. Geological Publishing House, Beijing. 273 (in Chinese) |
Zhang, J., Wang, C. -Y., Shi, Y. L., et al., 2004. Three-Dimensional Crustal Structure in Central Taiwan from Gravity Inversion with a Parallel Genetic Algorithm. Geophysics, 69(4): 917–924. https://doi.org/10.1190/1.1778235 |
Zhang, L. Z., Zhang, G. B., Liu, Y., et al., 2022. Deep Learning for 3-D Inversion of Gravity Data. IEEE Transactions on Geoscience and Remote Sensing, 60: 5905918. https://doi.org/10.1109/TGRS.2021.3110606 |
Zhang, S., Yin, C. C., Cao, X. Y., et al., 2022. DecNet: Decomposition Network for 3D Gravity Inversion. Geophysics, 87(5): G103–G114. https://doi.org/10.1190/geo2021-0744.1 |
Zhang, Z. H., Liao, X. L., Cao, Y. Y., et al., 2021. Joint Gravity and Gravity Gradient Inversion Based on Deep Learning. Chinese Journal of Geophysics, 64(4): 1435–1452 (in Chinese with English Abstract) |
Zhang, Z. H., Yao, Y., Shi, Z. Y., et al., 2022. Deep Learning for Potential Field Edge Detection. Chinese Journal of Geophysics, 65(5): 1785–1801 (in Chinese with English Abstract) |
Zhao, J. M., Chen, S. Z., Deng, G., et al., 2019. Basement Structure and Properties of the Western Junggar Basin, China. Journal of Earth Science, 30(2): 223–235. https://doi.org/10.1007/s12583-018-1207-4 |
Zhdanov, M. S., 2015. Inverse Theory and Applications in Geophysics. Elsevier Science RM.https://doi.org/10.1016/C2012-0-03334-0 |
Zhou, X. Y., Chen, Z. X., Lv, Y. D., et al., 2023. 3-D Gravity Intelligent Inversion by U-Net Network with Data Augmentation. IEEE Transactions on Geoscience and Remote Sensing, 61: 5902713. https://doi.org/10.1109/TGRS.2023.3241310 |
Zhou, Z. W., Wang, J., Meng, X. H., et al., 2023. High-Precision Intelligence Denoising of Potential Field Data Based on RevU-Net. IEEE Geoscience and Remote Sensing Letters, 20: 7501105. https://doi.org/10.1109/LGRS.2023.3241295 |