the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Feb 2026
Pre-Seismic Geomagnetic Fusion Anomaly Extraction Based on Spatially Weighted Non-Negative Tensor Factorization
Abstract. Earthquake preparation processes are known to generate geomagnetic anomalies, Existing methods for extracting pre-seismic geomagnetic anomalies from multi-station observations are limited by the lack of physically meaningful constraints. Considering that electromagnetic signal propagation is related to epicentral distance, we incorporate spatial relationships between observation stations and potential seismic source regions into non-negative tensor factorization (NTF), and propose a Spatially Weighted Non-negative Tensor Factorization (SW-NTF) method to extract fused pre-seismic geomagnetic anomalies from multi-station data. SW-NTF was applied to daily 1 Hz Z-component geomagnetic data recorded at seven stations from 90 days before to 30 days after the 2021 Ms 7.4 Madoi earthquake. Compared with traditional NTF, SW-NTF captures a more pronounced accelerated growth in the pre-seismic geomagnetic anomalies. The extracted anomalies exhibit two phases of S-shaped accelerated growth (day −85 to −60 and day −40 to −17). Spatially, anomalous signals initially appear at stations farther from the epicenter and progressively migrate toward the epicentral region as the earthquake approaches. The potential influence of space weather activity is examined, suggesting that the detected anomalies are not dominated by external geomagnetic disturbances. Temporal comparisons show that the two-phase acceleration of geomagnetic anomalies precedes similar acceleration in cumulative Benioff strain. Observed variation patterns are also consistent with magnetic field changes in rock loading experiments, and the spatiotemporal correspondence with b-values indicates that the anomalies likely reflect stress evolution in the crust during earthquake preparation.
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RC1: 'Comment on egusphere-2026-317', Anonymous Referee #1, 26 Feb 2026
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AC1: 'Reply on RC1', Baiyi Yang, 01 Mar 2026
hank you for your invaluable suggestions. We will take them into careful consideration and incorporate them into the subsequent revision.
Citation: https://doi.org/10.5194/egusphere-2026-317-AC1 -
RC2: 'Reply on AC1', Anonymous Referee #1, 01 Mar 2026
Thank you for your prompt response. I hope the suggestions help you improve your valuable manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-317-RC2 -
AC3: 'Reply on RC2', Baiyi Yang, 29 Mar 2026
Thank you once again for your valuable suggestions on how to improve this study. The revisions are as follows:
1.The Madoi earthquake data (including date, magnitude, coordinates, etc.) have been added to Figure 1.
2.In Section 5.1 (Discussion), an analysis of the impact of space weather activity on geomagnetic anomalies has been included. Based on an investigation of parameters such as DST and Kp during the periods when anomalies occurred, we conclude that the appearance of these anomalies is unrelated to space weather activity.
3.In Section 5.2 (Discussion), we have supplemented the study by linking the frequency of pre-earthquake signals to the seismic source. The skin depth of the dominant frequency of the anomalies was calculated and found that it closely matches the focal depth of the Madoi earthquake.
4.Several formatting errors in the manuscript have also been corrected.
If any further issues remain, we would greatly appreciate your continued guidance and will promptly address them accordingly.
Best regards!
Citation: https://doi.org/10.5194/egusphere-2026-317-AC3
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AC3: 'Reply on RC2', Baiyi Yang, 29 Mar 2026
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RC2: 'Reply on AC1', Anonymous Referee #1, 01 Mar 2026
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AC1: 'Reply on RC1', Baiyi Yang, 01 Mar 2026
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RC3: 'Comment on egusphere-2026-317', Anonymous Referee #2, 03 Mar 2026
Yang et al. proposed a new method to extract geomagnetic anomalies from a network of ground geomagnetic stations based on a spatially weighted non-negative matrix factorisation (NTF). The authors applied this method to analyse from 3 months before up to 1 month after the Madoi 2021 earthquake in China. They selected 7 ground observatories and combined them in a tensor for a common analysis of the vertical component Z of the geomagnetic field. They compared the results with the standard (not weighted) NTF method, showing a clear improvement. The authors compared the temporal trend with seismicity variations, finding an extremely interesting similarity between the geomagnetic anomalous trend, especially from -40 to 0 days, and cumulative Benioff strain. Both of them provide the same curvature (i.e., trend) strongly suggesting a strict connection between them, i.e., supporting the seismo-induced nature of the extracted anomalies. The geomagnetic trend slightly preceded the seismic trend. Furthermore, the authors also provided a very interesting analysis of the variation of seismic b-value. The peak of b-value over time coincides with the higher rate of geomagnetic anomalies (for -73 and -30 days), further suggesting a correlation between the two quantities. A third peak of b-value is present at -52 days without a corresponding magnetic clear signal (the authors can integrate this as a limitation of the study). Finally, the authors performed a spatial investigation of b-value that showed a clear drop in epicentral area before the earthquake, suggesting a lock of the fault that preceded the Madoi earthquake.
Finally, considering that the proposed method provides an improvement over existing ones, the results strongly support the hypothesis of seismo-induced anomalies and considering the extremely interesting contribution for the analysis and understanding of the preparation phase of the Madoi 2021 earthquake, I suggest this paper for publication after minor clarifications and improvements.
As a general point, I would suggest to the authors to consider this very recent and wide review paper on their topic:
- Yu, Z., Jing, X., Yang, M. et al. A Review of Earthquake Precursor Anomaly Extraction Techniques for Geophysical Time-Series Observations. Surv Geophys (2026). https://doi.org/10.1007/s10712-026-09927-w
Furthermore, the authors could include some limitations of the present work in the conclusions, such as the lack of stations closer than 100 km to the epicentre and the angular gap of distributions of the available stations, mainly on the northern side of the epicentre. Future studies can also investigate longer time periods.
Minor points and specific comments:
- Line 7. Not always the earthquake produce geomagnetic anomalies before their occurrence. So please, add some moderation words such as: [...] generate geomagnetic anomalies “in some cases”.
- Line 7. Please change the comma with a dot (anomalies. Existing)
- Line 21. I think it’s better to add “seismological” before “b-value” (seismological b-value) to make it clear to a broader readership.
- Lines 24-25. The sentence requires to cite the source. I think the authors are referring to this one:
- So Much More to Know..., 2005. Science 309, 78–102. https://doi.org/10.1126/science.309.5731.78b
- Lines 28-30. The sentence “Among these... prediction” could be supported by the following review paper:
- Chen, H., Han, P., Hattori, K., 2022. Recent Advances and Challenges in the Seismo-Electromagnetic Study: A Brief Review. Remote Sensing 14, 5893. https://doi.org/10.3390/rs14225893
- Line 38. What do you mean by “trams”? Do you refer to “railways”?
- Lines 43-46. The same author applied a similar approach also to geomagnetic ground data on the occasion of the Ludin 2022 earthquake in China. I think that a comparison with your study would be very interesting.
- Yu, Z., Jing, X., Wang, X., Chi, C., Zheng, H., 2024. The Study on Anomalies of the Geomagnetic Topology Network Associated with the 2022 Ms6.8 Luding Earthquake. Remote Sensing 16. https://doi.org/10.3390/rs16091613
- Line 58. I suggest inserting “possible” or “eventual” before “anomalous geomagnetic changes” because, in principle, you could not even find any anomalies... so in the introduction, I suggest saying “possible anomalous geomagnetic changes...”
- Lines 59-62. When you refer to section numbers used a consistence notation (section II, III IV and later you said section 5... So use only one notation.
- Line 72. The frequency range can reach up to 0.5 Hz sampling at 1 Hz for Nyquist theorem, so please revise the frequency range.
- Line 84. Please specify “one of the most seismically active region” of what. I think you want to say “of the Earth”
- Line 100. I suggest specifying that the earthquake under investigation by Fan et al., 2024, is the same as the one in the present study.
- Lines 126-132. This concept was also applied in the paper you already cited by De Santis et al., 2015, where they introduced a weight for the distance of pre-earthquake to the target earthquake to study. However, considering that the list of citations in line 127 is quite long, I suggest adding another sentence with the reference comment if you agree.
- Line 154. Why did you select the Z component? In some paper the Z/H ratio is used (see for example Hobara, 2004). I ask you for a comment or cite the alternative option, not to change your method.
- Hobara, Y.; Koons, H.C.; Roeder, J.L.; Yumoto, K.; Hayakawa, M. Characteristics of ULF Magnetic Anomaly before Earthquakes. Physics and Chemistry of the Earth, Parts A/B/C 2004, 29, 437–444, doi:10.1016/j.pce.2003.12.005.
- Line 159. Maybe this local time (0-4 AM) is from local midnight to pre-sunset?
- Line 179. Why is the maximum iteration 200? For example, 1000 requires too much computing time? Overall, generally the analysis stopped for reaching the maximum number of iterations or precision criteria (i.e, the required tolerance)?
- Line 225. Please ensure that if you use a subscript for tmin and tmax, you use the same notation outside and inside the brackets.
- Line 232. I would suggest expressing this concept in a different way if the authors agree: Looking at Figure 5, it’s possible to identify two distinct phases…
- Lines 52-53. Please cite the paper describes the claimed effect of pause of acoustic emission prior to rock failure experiment in laboratory.
- Line 291. I think it’s necessary to specify the word “Seismo” (the seismo-geomagnetic observations) or, alternatively, change the verb “susceptible” as for other research topics, the geomagnetic storm and solar activity are the objects of investigation.
- Line 306. What do you mean for fused anomaly? Maybe just anomaly? Please explain or revise the sentence
- Line 311. Please delete “Overall” (typed 2 times).
- Line 316. If the authors agree, I would suggest specifying the release in the form of electromagnetic radiation (not seismic energy).
- Lines 321-336.The proposed theoretical explanation by the comparison with lab experiment is very interesting and in my opinion is plausible. I would just suggest a further final comment that is the possibility that in the reality the scale of these processes could be even longer, as for example Scholz used a scale of several years before the earthquake, and it depends on the earthquake magnitude (Scholz et al., 1973 in your reference list).
- Line 346. I would suggest replacing “sequences” with “number” or “rate” as a seismic sequence is itself the space-time close concatenation of seismic events increasing toward a mainshock and decreasing after.
- Lines 366-379. I agree with the description and interpretation proposed by the authros in these lines. The authors may even add if they think that in this case the recorded anomaly trends look as a possible precursor also of the smaller seismicity trends that preceded the Madoi earthquake. It’s mostly what is already affirmed by the author, adding the concept that the geomagnetic anomalies extracted by the author could be interpreted either as a precursor of smaller seismicity or the mainshock.
- Line 386. Please change “probability” with “rate” as b-value is calculated over the real earthquake so it’s not a probability.
- Line 387. Please check the family name of the reference (K. ?)
- Line 412. I would suggest to specify that this is the expected standard behaviour with b-value approximately one.
- Line 432. If you agree with my previous suggestion revise please “local midnight”
Citation: https://doi.org/10.5194/egusphere-2026-317-RC3 -
AC2: 'Reply on RC3', Baiyi Yang, 05 Mar 2026
Thank you for your valuable comments and suggestions on this paper. We will make additions and revisions based on the areas you have pointed out for improvement.
Citation: https://doi.org/10.5194/egusphere-2026-317-AC2 -
RC4: 'Reply on AC2', Anonymous Referee #2, 05 Mar 2026
Thank you for your prompt reply! I hope my suggestions may help improve the manuscript, which is already very interesting! I look forward to the revised version!
Best regards!
Citation: https://doi.org/10.5194/egusphere-2026-317-RC4 -
AC4: 'Reply on RC4', Baiyi Yang, 29 Mar 2026
We greatly appreciate your detailed and professional comments on the manuscript. The specific revisions are as follows:
1.In the conclusion, we have summarized the limitations of this study and outlined directions for future research.
2.Regarding the specific revisions to the manuscript, we have made the modifications in accordance with your comments.
If any further issues remain, we would greatly appreciate your continued guidance and will promptly address them accordingly.
Best regards！
Citation: https://doi.org/10.5194/egusphere-2026-317-AC4
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AC4: 'Reply on RC4', Baiyi Yang, 29 Mar 2026
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RC4: 'Reply on AC2', Anonymous Referee #2, 05 Mar 2026
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The manuscript addresses important scientific and technical issues both within the NHESS and within Earth Sciences. The study of earthquakes, from a deterministic forecasting perspective, has only recently begun to gain acceptance, thanks to the work and scientific contributions of international teams. Given the nature of the topics covered, the study fits into an international context and is of interest for the methodology used, also thanks to the delineation of scientific assumptions. The results refer to a specific case, but they can be applied to other experiments, especially multidisciplinary ones. Despite the study relating to an earthquake, the conclusions are substantial. The outcome of the experiment, the calculations performed, and the results are such that they can be reproduced by fellow scientists in other tectonic settings, in seismically active zones around the world. Returning to the manuscript, the title clearly reflects the content of the document, and the abstract is comprehensive and provides an overview of the study. However, both the title and abstract are aimed at a specialist audience, given its technical nature. Mathematical formulas, symbols, and abbreviations are correctly defined. The size and readability of the figures are relevant and appropriate for the data presented. The authors give due credit to previous work, spanning a sufficient period of time. In this regard, both the number and quality of references are appropriate, and the references are accessible for use by other scientists. The overall presentation is well-structured, clear, and easy to use, especially for scientists in the field. The length of the paper is appropriate and balanced for an international scientific context. However, the technical language is precise and easily understood by other scientists, thanks to the use of good-quality English, which is fluent, simple, and easy to read and understand, even by a broad and diverse audience. The document is not accompanied by supplementary material.
If the authors wish, they could supplement the manuscript with:
Madoi Earthquake data (date, magnitude, coordinates, etc.)
An index map to more easily frame the studied area and enhance Figure 1.
Mention other studies based on geomagnetic anomalies regarding time windows between the anomaly and the earthquake of 90, 60, 30 days, and even a few hours before the main shock. Similarly, there are also publications that address the search for candidate seismic precursors in frequencies below 1 Hz.
Specifying that the anomalies are geomagnetic and not solar in nature is important because numerous studies, including those available online, link solar activity to the triggering of major geophysical events.
Among the references the authors could add are those regarding studies that have linked the frequency of pre-seismic signals to the hypocenter.
There are spacing errors on page 7, while in the references, is the capitalization of the first citation correct?