Abstract
To address the issue of errors caused by ground vibrations in high-precision absolute gravity measurements, a vibration error correction method based on an Adam algorithm-optimized BP neural network is proposed. By constructing a vibration error model and analyzing the influence mechanism of vibration modes on the reconstruction error of falling body trajectories, the strong correlation between time errors and vibration signals is verified. A nonlinear relationship prediction model is proposed using a BP neural network to establish the relationship between vibration signals and time coordinate errors, thereby correcting time coordinate errors and calculating gravitational acceleration. The Adam algorithm was employed to replace the traditional stochastic gradient descent (SGD) algorithm for optimizing the backpropagation neural network, effectively enhancing the model’s convergence speed and prediction accuracy. Simulation results and practical applications demonstrate that this method effectively separates vibration interference components from interference signals. In field absolute gravity observation experiments, the measurement accuracies at the national gravity benchmark point (H03), the experimental office (H09), and the mountainous site (H20) reached 1.51, 1.30, and 3.01 µGal respectively.
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Data availability
Due to confidentiality requirements regarding the measured absolute gravity values, the data provided in this study are made available at the request of the corresponding author. Further investigation of this data will be conducted in the future.
Abbreviations
- BP:
-
Back propagation
- Adam:
-
Adaptive moment estimation
- SGD:
-
Stochastic gradient descent
- RMSE:
-
Root means square error
- DWT:
-
Discrete wavelet transform
- CG-6:
-
CG-6 relative gravity meter (manufactured by Scintrex, Canada)
References
Ben, Y. Y., Yang, X. L., Li, Q., Li, J. C. & Ruan, S. S. Damping strapdown inertial navigation system aided by gravity. Zhongguo Yi Qi Yi Biao Xue Bao. 35(7), 1482–1488. https://doi.org/10.19650/j.cnki.cjsi.2014.07.006 (2014).
E, F. J. The measurement of little g: A fertile ground for precision measurement science. J. Res. Natl. Inst. Stand. Technol. 110(6), 559–581. https://doi.org/10.6028/jres.110.082 (2005).
Liu, X., Li, H., Ban, S. F., Sun, H. P., Yi, G. Y., Huang, Z. Q. & Guo, J. Y., GGM inversion of seabed topography based on water depth zoning In Geomatics and Information Science of Wuhan University 1–15. https://doi.org/10.13203/j.whugis20250198 (2025).
Lu, B. J. & Zhang, X. B. Large-scale magnetic anomaly target state estimation method based on IAPO-CGLS-GCV algorithm. Clust. Comput. 29(1), 42–42. https://doi.org/10.1007/s10586-025-05839-3 (2025).
Pacôme, D. et al. GENESIS: Co-location of geodetic techniques in space. Earth Planets Space https://doi.org/10.1186/s40623-022-01752-w (2023).
Ren, M. S., Shang, Y. J., Zheng, W. K., Kang, S. J. & Zhao, P. Contrast test of domestic absolute gravimeter with FG5. Ce Hui Ke Xue. 45(09), 1–4+24. https://doi.org/10.16251/j.cnki.1009-2307.2020.09.001 (2020).
Zhang, W. M. et al. Experimental study on several interference factors in the development of absolute gravimeter. Prog. Geophys. 04, 1143–1148 (2008).
Huang, S. Research on vibration reduction technology of absolute gravimeter with reference prism Master’s degree, Institute of Earthquake Forecasting, China Earthquake Administration (2023).
Long, J. F., Huang, D. L., Teng, Y. T., Wu, Q. & Guo, X. Study on vibration scribing algorithm for anabsolute gravitational measurement. Acta Seismol. Sin. 34(6), 865–872. https://doi.org/10.3969/j.issn.0253-3782.2012.06.013 (2012).
Wu, Q., Teng, Y. T., Wang, X. M., Wu, Y. X. & Zhang, Y. Vibration error compensation algorithm in the development of laser interference absolute gravimeters. Geosci. Instrum. Methods Data Syst. 10(1), 113–122. https://doi.org/10.5194/gi-10-113-2021 (2021).
Wang, G., Hu, H., Wu, K. & Wang, L. J. Correction of vibration for classical free-fall gravimeters with correlation-analysis. Meas. Sci. Technol. 28(3), 035001-035001. https://doi.org/10.1088/1361-6501/aa54f7 (2017).
Li, G., Hu, H., Wu, K., Wang, G. & Wang, L. J. Ultra-low frequency vertical vibration isolator based on LaCoste spring linkage. Rev. Sci. Instrum. 85(10), 104502. https://doi.org/10.1063/1.4897488 (2014).
Nelson, P. G. An active vibration isolation system for inertial reference and precision measurement. Rev. Sci. Instrum. 62(9), 2069–2075. https://doi.org/10.1063/1.1142368 (1991).
Newell, D. et al. An ultra-low-noise, low-frequency, six degrees of freedom active vibration isolator. Rev. Sci. Instrum. 68(8), 3211–3219. https://doi.org/10.1063/1.1148269 (1997).
Richman, S. J. et al. Multistage active vibration isolation system. Rev. Sci. Instrum. 69(6), 2531–2538. https://doi.org/10.1063/1.1148954 (1998).
Guo, Y. G. et al. A transportable laser interferometry absolute gravimeter type NIM-II. Chin. J. Geophys. 31(1), 73–81 (1988) (121).
Canuteson, E., Zumberge, M. & Hanson, J. An absolute method of vertical seismometer calibration by reference to a falling mass with application to the measurement of the gain. Bull. Seismol. Soc. Am. 87(2), 484–493. https://doi.org/10.1785/BSSA0870020484 (1997).
Wen, Y., Wu, K., Li, Z. X., Yao, J. M., Guo, M. Y. & Wang, L. J. In Vibration Correction With Kalman Filtering Based Data Fusion for Absolute Gravimeters, ASME 2019 International Mechanical Engineering Congress and Exposition (2019).
Wen, Y., Wu, K., Guo, M. Y. & Wang, L. J. An optimized vibration correction method for absolute gravimetry. IEEE Trans. Instrum. Meas. 70, TIM.2020. https://doi.org/10.1109/tim.2020.3046084. (2021).
Xu, Q. Y., Ju, W. H., Lin, Y. S. & Zhang, T. L. Research on positioning error compensation of rock drilling manipulator based on ISBOA-BP neural network. Appl. Sci. 14(18), 8480. https://doi.org/10.3390/app14188480 (2024).
Yang, L. Gravity anomaly separation based on BP neural network. Chin. J. Eng. Geophys. 18(01), 90–97 (2021).
Fan, F. et al. Research on adjustment method of distance between center of mass and optical center of falling body in absolute gravimeter. Acta Metrol. Sin. 45(2), 231–237. https://doi.org/10.3969/j.issn.1000-1158.2024.02.13 (2024).
Wu, Q., Teng, Y. T., Huang, D. L. & Long, J. F. A new trajectory reconstruction algorithm for free-fall body in absolute gravimeter development. Acta Seismol. Sin. 34(04), 549–556+580 (2012).
Li, M., Liu, G. & Mao, Z. Phased-based motion estimation through short-distance Hilbert transform. Mech. Syst. Signal Process. 211, 111219-. https://doi.org/10.1016/j.ymssp.2024.111219 (2024).
D’Agostino, G. et al. The new IMGC-02 transportable absolute gravimeter: Measurement apparatus and applications in geophysics and volcanology. Ann. Geophys. 51(1), 39–49. https://doi.org/10.4401/ag-3038 (2008).
Wu, Q., Teng, Y. T., Zhang, B. & Huang, D. L. Calculation of measurement height in absolute gravimeter development. Geomat. Inf. Sci. Wuhan Univ. 42(12), 1773–1778. https://doi.org/10.13203/j.whugis20150529 (2017).
Niebauer, T. The effective measurement height of free-fall absolute gravimeters. Metrologia 26(2), 115. https://doi.org/10.1088/0026-1394/26/2/005 (1989).
Timmen, L. Precise definition of the effective measurement height of free-fall absolute gravimeters. Metrologia 40(2), 62. https://doi.org/10.1088/0026-1394/40/2/310 (2003).
Zumberge, M. A., Rinker, R. & Faller, J. A portable apparatus for absolute measurements of the Earth’s gravity. Metrologia 18(3), 145. https://doi.org/10.1088/0026-1394/18/3/006 (1982).
Murata, I. A transportable apparatus for absolute measurement of gravity. Bull. Earthq. Res. Inst. 53(1), 49–130. https://doi.org/10.15083/0000033181 (1978).
Liu, D.N., Shen, S. P., Dou, Z., Sun, H. R. & Sun, W. J. An OPGW multi-parameter ice thickness combination prediction method. In Study on Optical Communications 1–8. (2025). https://link.cnki.net/urlid/42.1266.TN.20250110.1530.004
Valle, M. E., Vital, W. L. & Vieira, G. Universal approximation theorem for vector- and hypercomplex-valued neural networks. Neural Netw. 180, 106632–106632. https://doi.org/10.1016/j.neunet.2024.106632 (2024).
Cao, L. On mine environmental gas concentration prediction model based on Adam algorithm BP neural network. J. Hunan Univ. Sci. Technol. (Nat. Sci. Edn.) 39(01), 18–23. https://doi.org/10.13582/j.cnki.1672-9102.2024.01.003 (2024).
Li, M., Li, H. J. & Chen, J. Adam optimization algorithm based on differential privacy protection. Comput. Appl. Softw. 37(06), 253–258+296 (2020).
Zhao, X. Q. & Song, Z. Y. Adam-optimized CNN super-resolution reconstruction. J. Front. Comput. Sci. Technol. 13(05), 858–865. https://doi.org/10.3778/j.issn.1673-9418.1809020 (2019).
Zhang, T. Z. A neural network training method based on Adam adaptive learning rate. Inf. Comput. 36(06), 44–46 (2024).
Duan, S. Q. et al. DSYOLO: A dynamic snake convolution-based segmentation model for tunnel lining cracks in complex environments. Eng. Struct. 344, 121325–121325. https://doi.org/10.1016/j.Engstruct.2025.121325 (2025).
Zhang, B. Evaluation method of carrying capacity of Xi’an-Shi’an high speed railway transportation road based on BP neural network. Microcomput. Appl. 38(06), 167–170 (2022).
Li, C. Y. X., R.G.; Chen, X.; Sun, H.B.; et al., Joint gravity survey using an absolute atom gravimeter and relative gravimeters. Metrologia arXiv preprint, arXiv:2504.00588, https://doi.org/10.48550/arXiv.2504.00588 (2025).
Araya, A., Kasai, K., Yoshida, M., Nakazawa, M. & Tsubokawa, T. Evaluation of systematic errors in the compact absolute gravimeter TAG-1 for network monitoring of volcanic activities. Int. Assoc. Geod. Symp. 18(1), 0. https://doi.org/10.1007/1345_2020_107 (1900).
Acknowledgements
We extend our gratitude to all faculty and students at the Institute of Geophysics, China Earthquake Administration for their assistance, with special thanks to my advisor for his invaluable guidance. We also thank the anonymous reviewers for their insightful and constructive suggestions that significantly improved the manuscript.
Funding
This study was funded by the Basic Research Operating Expenses of the Institute of Geophysics, China Earthquake Administration (DQJB24X26); China Earthquake Science Experimental Field Construction Project.
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Conceptualization, Y.N. and Q.W.; methodology, Y.N.; software, Y.N.; validation, Y.N. and Q.W.; formal analysis, Q.W. and Y.Z.; investigation, Y.Z., and Q.W., Y.Z. and Z.L.; resources, Q.W.; data curation, Y.N.; writing—original draft preparation, Y.N.; writing—review and editing, Y.N.; visualization, G.P.; supervision, Y.N.; project administration, Q.W. and Y.Z.; funding acquisition, Q.W. All authors have read and agreed to the published version of the manuscript.
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Niu, Y., Wu, Q., Zhang, Y. et al. Vibration error correction in absolute gravity measurement using BP neural network. Sci Rep (2026). https://doi.org/10.1038/s41598-026-43402-1
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DOI: https://doi.org/10.1038/s41598-026-43402-1
