the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Jun 2026
Detecting Fault Structures from Earthquake Sequences via Unsupervised Learning
Abstract. This study develops a systematic framework to detect potential fault structures from earthquake sequences by integrating unsupervised learning and three-dimensional spatial analysis. Two major events in eastern Taiwan, EQ2018 and EQ2024, are analyzed using DBSCAN clustering, validated by the Silhouette Score, followed by Principal Component Analysis (PCA) to extract fault-plane geometries. The clustering results reveal both mapped and previously unrecognized fault orientations, with PCA-derived planes largely consistent with centroid moment tensor solutions of the largest-magnitude events. EQ2018 ruptures were confined to shallow crustal levels (<20 km), dominated by west-dipping planes, whereas EQ2024 exhibited greater depth variability, multiple dipping directions, and complex rupture geometries involving both onshore and offshore fault systems. Three-dimensional visualization further highlights the interplay between known active faults (e.g., Central Range, Milun, Lingding) and latent structures, underscoring the heterogeneous nature of rupture propagation in tectonically transitional zones. While PCA effectively captures dominant planar trends, limitations remain in representing curved or arc-shaped geometries. Overall, the proposed workflow demonstrates the utility of combining clustering and PCA to delineate subtle fault structures, offering a robust tool for advancing seismotectonic interpretation and improving seismic hazard assessment.
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Status: open (until 28 Jul 2026)
- RC1: 'Comment on egusphere-2026-3012', Anonymous Referee #1, 09 Jul 2026 reply
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RC2: 'Comment on egusphere-2026-3012', Anonymous Referee #2, 12 Jul 2026
reply
In this manuscript, the authors propose the combined use of DBSCAN and PCA to identify fault planes and compute the maximum moment magnitude associated with them. Although the study addresses an interesting topic with relevant implications for seismic hazard assessment, in my opinion there are several weak points that should be addressed before publication.
Major concerns
First, I have some concerns about originality. The combined use of DBSCAN and PCA to illuminate faults has already been proposed in the literature: Jian and Wang (2022) successfully used the unsupervised algorithms to characterize the 2018–2022 Hualien earthquake sequence and validated planar geometries from PCA using focal mechanisms and the two-dimensional back-projection method; Piegari et al. (2024) iteratively applied DBSCAN and PCA, with support from OPTICS, to illuminate faults and their hierarchical segmentation.
In the present manuscript, differently from previous study, the authors propose using the Silhouette score to evaluate clustering quality. However, the Silhouette score is an internal validation index that measures how compact a cluster is and how well it is separated from the others. Therefore, if the spatial distribution of earthquakes results in asymmetric or non-spherical clusters, the Silhouette score may not be the optimal choice. The authors should therefore better highlight the novelty of their approach by showing the advantages of using the Silhouette score, especially since, in at least one case, they do not use it to make their cluster selection. In my opinion, the authors should consider using at least a couple of validation indices to strengthen their approach and present it as a robust alternative to existing methods in the literature.
The second weak point is related to the estimation of the maximum seismic moment magnitude, Mw, associated with the rupture planes derived from PCA. The authors should report the formula used to calculate the length and width of the fault plane and clearly state the hypotheses and validity of the underlying assumptions. Since the maximum magnitude has important implications for hazard assessment, its computation must be rigorous and uncertainties should be quantified. Furthermore, since the PCA plane simplifies the rupture zone into a single planar surface, the discussion must explicitly acknowledge that actual faults possess intricate 3D geometries with segmented and branching structures. Such structural complexities can severely bias the estimation of the fault rupture area, which is a critical parameter in the accurate computation of Mw.
Another weak point is the lack of a quantitative comparison with studies analyzing the same seismicity. Although the authors devote a section to comparing their results with known fault systems, they fail to compare their findings with those of other studies, which are mentioned only as a list of references. A quantitative comparison of fault orientations and locations is therefore missing and should be added.
Minor comments
The choice to consider the same 30-day aftershock window to the two mainshocks, EQ2018 and EQ2024, despite their different moment magnitudes, should be motivated.
Fig. 1 is not clear because too many symbols are overlaid. The authors could consider splitting Fig. 1b into two figures, showing separately the seismicity related to the two large earthquakes.
Section 4.1 is redundant in many parts, with several lines that repeat the content of the legends of Fig. 3 and 4, which are unnecessary and should be removed.
The use of transparency in the histograms in Fig. 4b is strongly recommended, otherwise it is impossible to observe changes in the distribution over time.
The acronym PCA is defined in the Introduction, and its definition is repeated at the beginning of Section 3, in Section 3.2, in Section 4.2, and in Section 5, resulting in unnecessary redundancy.
The characteristic of each plane from PCA, not only in terms of strike and dip angles but also length and width, should be included in the text, and the use of tables is strongly suggested.
Section 4.3 should be rewritten to include a quantitative comparison between the obtained results and those reported in the literature.
The Discussion and Conclusions sections are redundant and can be shortened and merged.
Citation: https://doi.org/10.5194/egusphere-2026-3012-RC2
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Revision of
“Detecting Fault Structures from Earthquake Sequences via Unsupervised Learning”
Comments to the Author(s):
The manuscript presents a pipeline that combines DBSCAN unsupervised clustering and PCA analysis to identify potential fault structures from the 2018 and 2024 earthquake sequences in Taiwan. The topic is relevant, and the approach could be useful for analysing complex aftershock distributions, but the manuscript requires major revision before publication. The main weakness is that the proposed method is not sufficiently justified, validated, or tested. The authors should clarify some aspect such as how DBSCAN and PCA are combined, whether PCA is applied separately to each DBSCAN cluster, how the PCA-derived fault planes are defined, and how sensitive the results are to the selected DBSCAN parameters. This is particularly important because, in at least one case, the parameter set with the highest Silhouette Score was not adopted, and a more geologically plausible solution was chosen instead. This choice may be reasonable, but it reduces the objectivity of the workflow and requires a sensitivity analysis.
Another issue concerns also the use of PCA-derived fault-plane areas to estimate potential maximum magnitude. This step is not sufficiently motivated, and it is unclear why it is necessary for the clustering analysis. A PCA plane is a statistical approximation of an aftershock cloud, not necessarily a real rupture surface. Therefore, small variations in the inferred plane dimensions may strongly affect the estimated magnitude and could lead to misleading implications for seismic hazard. Also the location error could influence the PCA analysis results. The authors should either validate this approach using well-constrained earthquake sequences, provide uncertainty estimates, and cite previous studies using a similar method, or remove/reframe this part as a preliminary and exploratory analysis. The magnitude–area relationship should also be checked and clearly described.
The comparison with known fault systems also needs to be more rigorous. At present, it is mostly descriptive. An additional figure showing mapped faults, PCA-derived planes, clusters, and focal mechanisms would strengthen the validation of the method proposed. Also the visualization of only one focal mechanism per cluster is not sufficient to validate the inferred fault geometry; more focal mechanisms or additional independent constraints should be included.
The manuscript should also discuss uncertainties more explicitly, including earthquake-location errors (if available), uncertainty in PCA-derived strike and dip, uncertainty in plane dimensions, and the effect of using Min-Max normalization on the geometry of the inferred planes. Since longitude, latitude, and depth have different physical scales and uncertainties, normalization may influence clustering, PCA orientation, and the resulting magnitude estimastion.
The interpretation of temporal migration in the 2024 sequence should also be better supported. The distinction between T1 and T2 needs to be clearly defined in the text and figures, and any interpretation in terms of stress redistribution or secondary fault activation should be supported by references and more quantitative analysis. Finally, the manuscript needs clearer writing, more references in the introduction and seismicity description, improved figure captions, and better explanation of acronyms and plotted quantities. Several figures should be improved in readability, with larger fonts, clearer labels, visible acronyms, and a better representation of outlier/noise points.
Overall, the current version does not yet demonstrate that the DBSCAN–PCA workflow is robust enough to infer fault geometries and potential magnitudes. I therefore recommend major revision, with substantial methodological clarification and validation required before publication.
A few questions/comments/suggestions:
Lines 7-8: You start you abstract with the acronyms of the earthquakes. I suggest writing information about it and then refers it using the acronyms. EQ2018 and 2024 are cited the first time at lines 102.
Lines 49-50: I think that indicated date and magnitude of the mainshocks could help the reader in the understanding.
Lines 102-130: Please insert references when you describe the two seismic sequences.
Lines 144-146: Cite who create these algorithms.
Lines 209-212: You are using PCA to determine the length of the fault plane. A small variation in length can affect the expected Mw estimate. For this reason, the length must be as accurate as possible in order to avoid problems and unnecessary alarm. Are there any studies that have used this innovative approach? If so, I recommend citing them to strengthen your work; otherwise, I would first test the approach on a sequence for which I know the Mw values well and that has been thoroughly verified, to ensure the approach works before proposing it as a solution. Also, what values are being used—PC1, PC2, or PC3? Please specify this in the text. You should also specify why you compute the potential magnitude. What is its purpose in the seismicity clustering phase? Is the clustering spatial, or is there also clustering based on magnitude? Please specify.
Lines 264-265: Interval? Is the T1 and T2? It’s difficult to understand if you cite in one way in the figure and then in a different way in the text….
Lines 362-396: I would have expected a more rigorous comparison with the faults documented in the literature, rather than just a descriptive one (perhaps a new figure showing the overlay of the faults from the literature with those modeled using PCA). This paragraph does not seem to do justice to the work that was done, and a summary image showing the comparison would also be useful to support the procedure. Especially since the clustering changes when the epsilon and minpnt values are modified. There is also no geological interpretation of the faults modeled using these techniques...
Lines 404-406: The geometry of a fault is determined not by a single focal mechanism (as shown in Figure 6) but by many more. Either you create a diagram that includes many focal mechanisms to confirm the model you’ve developed, or—put that way—it does not serve as evidence that the work was successful.
Comments on Figures:
Figure 1: Increase the font and the dimension of the map on the right. I suggest also insert the acronyms in the Figure. I don’t understand the T1 and T2 meaning for 2024. Is it described in the text? You mean that in the EQ2024 the seismicity moved away from the mainshocks? You should explain the eventually migration in the text.
Figure 2: If I understood well, you divided the period T1 and T2 observing Fig. 1b. If yes, create two windows (maybe square shape) in the 1b and write “T1” and “T2”.
Figure 3: Why there are many number on the x axes? You can also show the outlier points in the map. Specify the acronymous name (Dstd, Dmean…)
Figure 4: Interval? Is T1 and T2? Specify.
Figure 6: I suggest to specity the magnitude of the focal mechanism in the figure and in the text.