Earthquake Swarm Activity in the Tokara Islands (2025): Statistical Analysis Indicates Low Probability of Major Seismic Event

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The literature review presented in this paper is superficial and does not represent the state of the art in this field.

Moreover, the chosen methodology and presentation of results are of low quality.

Therefore, the paper cannot be accepted for publication.

Author Response

I sincerely thank Reviewer 1 for their feedback on our manuscript. I acknowledge their concerns regarding the literature review, methodology, and presentation of results, and I appreciate the opportunity to clarify and address these points.
Regarding the literature review, I respectfully disagree that it is superficial. The review focuses on key studies relevant to the Tokara Islands earthquake swarm and its statistical characterization, including references to the Gutenberg-Richter law [7] and regional seismic activity [1, 2, 3, 4, 5]. To ensure it reflects the state of the art, I have included citations to recent datasets (e.g., JMA public datasets [12, 13, 14]) and comparative analyses of volcanic and seismic interactions [16, 17]. I are happy to expand the review to incorporate additional references suggested by the reviewer to further contextualize our work within the field.

Concerning the methodology, I believe the application of Exploratory Data Analysis (EDA) using quantile-quantile (QQ) plots represents a novel and robust approach to characterizing earthquake inter-event times and magnitudes. While traditional statistical methods, such as those based on the Gutenberg-Richter law, dominate seismological research, our study demonstrates the efficacy of modern statistical techniques (e.g., robust linear regression via R’s lm() function [6, 15]) in identifying distributional patterns (e.g., exponential and normal distributions). This approach, as shown in Figures 1–4, provides precise parameter estimates (λ, μ, σ) and enables predictive modelling, which I argue advances the field. I welcome specific suggestions for enhancing the methodology to address any perceived shortcomings.

Finally, I regret that the presentation of results was perceived as low quality. I have structured the Results section (Sections 3, 3.2, 3.2.3) to clearly present findings through QQ plots, epicentral migration maps, and parameter estimates (Figures 1–4, Table 1), with detailed explanations of distributional deviations and their geological implications. To improve clarity, I are prepared to revise the figures, captions, and text based on specific feedback to ensure the results are communicated effectively.

I believe these points address the reviewer’s concerns and demonstrate the manuscript’s contribution to understanding the Tokara Islands earthquake swarm. I are committed to making revisions to strengthen the paper and appreciate any further guidance to meet the journal’s standards.

Reviewer 2 Report

Comments and Suggestions for Authors

General Comments

This paper provides a thorough analysis of the 2025 earthquake swarm in the Tokara Islands, using Exploratory Data Analysis (EDA) to examine seismic patterns and their relationship with volcanic activity. The study offers valuable insights into the statistical properties of earthquake swarms, highlighting key differences from previous seismic events. Overall, the paper is well-structured and presents an important contribution to understanding volcanic-induced seismic activity. Nonetheless, there are several aspects that need to be addressed to improve clarity, robustness, and reproducibility. The following suggestions provide further details:

Main comments

1. Consider adding a brief summary of key findings in the abstract, as currently, it focuses more on the methodology than on the results.
2. The introduction would benefit from more detail, particularly on the historical context of seismic activity in the Tokara Islands and the significance of the 2025 swarm.
3. The Materials and Methods section should provide more detail on the statistical techniques used and clarify the data collection process.
4. Expand the explanation of statistical methods used, especially EDA, to make it accessible to readers who may not be familiar with advanced statistical analyses. A brief justification of why EDA was selected would be valuable.
5. Figures 1 and 3 are well-presented, and the comparisons across different earthquake swarms are informative. However, the captions could be more detailed to provide additional context to the reader, especially for those less familiar with seismic data visualization.
6. Figure 2: The spatial analysis is a key part of this study. I would recommend including more details on how the epicentral migration was tracked (e.g., temporal resolution of data points) to ensure clarity for readers not directly familiar with seismic event tracking.
7. While the results are solid, the discussion could benefit from a more explicit connection to real-world applications, particularly how these findings could influence future earthquake monitoring or volcanic eruption prediction efforts.
8. Line 196-200: The conclusion is concise, but a stronger statement about the broader implications of your findings for volcanic hazard assessment would strengthen it. How might this study influence future seismic monitoring efforts in the region?
9. Including references to more recent studies that utilize EDA for seismic analysis could help position this paper within the current state of research.

Author Response

"Consider adding a brief summary of key findings in the abstract, as currently, it focuses more on the methodology than on the results.
The introduction would benefit from more detail, particularly on the historical context of seismic activity in the Tokara Islands and the significance of the 2025 swarm."

I sincerely thank Reviewer 2 for their constructive and detailed feedback, which has significantly helped us strengthen the manuscript. Below, I address each comment and outline the revisions made to improve the clarity, context, and impact of the study.

I appreciate the suggestion to balance the abstract by including a summary of key findings. The methods section of this summary was 150 characters long. The results section was 688 characters long, but I added 345 characters.  I deleted some of the duplicated parts, but I think it is clear that the results are the main focus. The revised abstract now clearly highlights the study’s findings while retaining a concise description of the methodology.

"The Materials and Methods section should provide more detail on the statistical techniques used and clarify the data collection process.
Expand the explanation of statistical methods used, especially EDA, to make it accessible to readers who may not be familiar with advanced statistical analyses. A brief justification of why EDA was selected would be valuable."

I thank Reviewer 2 for the positive feedback on Figures 1 and 3. To enhance clarity, I have revised the captions to provide more context for readers less familiar with seismic data visualization. For Figure 1 (lines 150–160), I added details explaining the exponential distribution of inter-event times and the normal distribution of magnitudes, including their divergence from the Gutenberg-Richter law [7], with a brief note on the geological implications of the March 2025 data. For Figure 3 (lines 180–200), I expanded the caption to describe the significance of epicentral migration and the two populations of inter-event times and magnitudes (e.g., λ = 5 and λ ≈ 1.43 in Figure 3B), linking these to volcanic activity at Suwanose Island.

"Figures 1 and 3 are well-presented, and the comparisons across different earthquake swarms are informative. However, the captions could be more detailed to provide additional context to the reader, especially for those less familiar with seismic data visualization."

I have expanded the introduction to provide greater detail on the historical seismic activity in the Tokara Islands, incorporating references to past earthquake swarms (e.g., 2021 events, as shown in Figure 4) and the 2015 Kuchinoerabu Island eruption to contextualize the 2025 swarm’s significance [1, 16]. A new paragraph (lines 25–40) discusses the region’s geological setting, including the Kikai Caldera and Nankai Trough, and highlights the 2025 swarm’s relevance due to its correlation with volcanic activity at Suwanose Island. This addition strengthens the historical and geological context, as suggested.

"Figure 2: The spatial analysis is a key part of this study. I would recommend including more details on how the epicentral migration was tracked (e.g., temporal resolution of data points) to ensure clarity for readers not directly familiar with seismic event tracking."

I appreciate the emphasis on the spatial analysis in Figure 2. To address the suggestion for more details on epicentral migration, I added a note in Section 3.2 (lines 210–215) clarifying that epicentral locations were tracked using JMA data [13, 14] with daily temporal resolution, though specific time resolution details are not publicly disclosed by the JMA. I also revised the Figure 2 caption (lines 165–175) to emphasize that the observed changes (e.g., deviations at points A and B) reflect distinct seismic events rather than gradual migration, aligning with the interpretation in Section 3.2.3 that these are separate swarm events driven by different geological factors.

"While the results are solid, the discussion could benefit from a more explicit connection to real-world applications, particularly how these findings could influence future earthquake monitoring or volcanic eruption prediction efforts."

To strengthen the connection to real-world applications, I have revised the Discussion (Section 4, lines 250–270) to explicitly link the findings to earthquake monitoring and volcanic eruption prediction. A new paragraph discusses how the estimated parameters (λ, μ, σ) and epicentral migration patterns (Figures 1–4) can improve hazard assessment. 

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript demonstrates the volcanic origin of the Tokara Islands earthquake swarm through exploratory data analysis (EDA) and excludes its possibility as a precursor to a major earthquake in the Nankai Trough. The research question has clear public safety significance, the method selection is more reasonable, and the conclusion is also supported by data. But there are still some parts that need to be improved.

1. There is a problem of confusion in some terms in the manuscript. Please check and unify the terms in the full text, such as ' earthquake cluster ' and ' swarm '.
2. In the introduction, the Nankai Trough earthquake is mentioned, but not described. This is a highly relevant and important background. It is recommended to briefly explain the background risk of the ' Nankai Trough earthquake ' in the introduction.
3. In the second part of the manuscript, there is no mention of data screening criteria, such as magnitude threshold, hypocentral uncertainty bounds, declustering methods, etc. Is there? Please explain.

4.σ is described as ' magnitude scale ', and its physical meaning is not clear in the manuscript. Represents standard deviation? Scale parameter? In addition, can you explain the physical sense of the change of μ value in Fig.1?

5. Figure 2A, right figure, only marked ' 7 / 8 ', should indicate the complete period.
6. In Section 3.3, the author mentions ' statistically identical ', but does not provide the results of hypothesis testing, which should be supplemented to confirm that there is no significant difference in the interval distribution of earthquake swarms between 2025 and 2021, making the manuscript logic more rigorous.

7.It is recommended to supplement the fitting index of the quantile-quantile (QQ) plot in the figure.

8. In the discussion section, can other volcanic earthquake cases be properly introduced for comparative analysis?

Author Response

"1 There is a problem of confusion in some terms in the manuscript. Please check and unify the terms in the full text, such as ' earthquake cluster ' and ' swarm '."

I sincerely thank Reviewer 3 for highlighting the inconsistency in terminology, specifically the use of "earthquake cluster" and "swarm" in the manuscript. To address this concern, I have conducted a thorough review of the full text and unified the terminology to ensure clarity and consistency. Additionally, I have ensured that related terms, such as "interval" and "magnitudes," remain consistent with the established framework (e.g., exponential and normal distributions, respectively). I believe these changes eliminate confusion and enhance the manuscript’s readability. I appreciate any further guidance on additional terms that may require unification.

"2 In the introduction, the Nankai Trough earthquake is mentioned, but not described. This is a highly relevant and important background. It is recommended to briefly explain the background risk of the ' Nankai Trough earthquake ' in the introduction."

I sincerely thank Reviewer 3 for their valuable suggestion to include a description of the Nankai Trough earthquake in the introduction to provide essential background context. To address this, I have added a paragraph to the introduction that briefly outlines the Nankai Trough’s significance as a major subduction zone along Japan’s Pacific coast, which pose substantial seismic and tsunami risks. I appreciate any further guidance on refining this background information to ensure its relevance and clarity.

"3 In the second part of the manuscript, there is no mention of data screening criteria, such as magnitude threshold, hypocentral uncertainty bounds, declustering methods, etc. Is there? Please explain."

I sincerely thank Reviewer 3 for their insightful comment regarding the absence of data screening criteria in the Materials and Methods section. To address this, I have revised Section 2.1 (Data Collection, lines 80–90) to explicitly state that no data screening criteria, such as magnitude thresholds, hypocentral uncertainty bounds, or declustering methods, were applied. All earthquake data from the Japan Meteorological Agency (JMA) datasets, including occurrence times, magnitudes, and epicentral locations [12, 13, 14], were used in their entirety to ensure a comprehensive analysis of the Tokara Islands earthquake swarm. This approach aligns with the study’s objective to characterize the full range of seismic activity using Exploratory Data Analysis (EDA), as described in Section 2.2, without introducing bias through selective filtering. Historically, selective data screening has been used in seismology to fit models like the Gutenberg-Richter law [7], but I opted for an inclusive approach to maintain scientific integrity and capture the true distributional patterns (e.g., exponential for inter-event times, normal for magnitudes, Figures 1–4). I appreciate any further guidance on additional details that could enhance the clarity of our data handling procedures.

"4.σ is described as ' magnitude scale ', and its physical meaning is not clear in the manuscript. Represents standard deviation? Scale parameter? In addition, can you explain the physical sense of the change of μ value in Fig.1?"

I sincerely thank Reviewer 3 for their valuable feedback regarding the unclear description of the parameter σ and the need for a physical interpretation of changes in μ in Figure 1. To address these concerns, I have made the following revisions to the manuscript to enhance clarity and provide a robust explanation of the parameters’ meanings and implications. Regarding the description of σ as a "magnitude scale," I acknowledge that this term was ambiguous. I have revised Section 2.2 (Data Analysis, lines 100–110) and the caption for Figure 1B (lines 155–160) to clarify that σ is the standard deviation of the normal distribution used to model earthquake magnitudes in the Tokara Islands earthquake swarm. In this context, σ quantifies the variability of earthquake magnitudes around the mean (μ), reflecting the spread of seismic energy release. While σ is mathematically equivalent to the standard deviation in a normal distribution, I have avoided the term "scale parameter" to prevent confusion with other statistical contexts (e.g., exponential distributions). Instead, I explicitly describe σ as the standard deviation, calculated using robust statistical methods in R’s lm() function [15], to characterize the dispersion of magnitudes observed in March 2025 (Figure 1B).For the physical significance of changes in μ in Figure 1B, I have added a detailed explanation in Section 3 (Results, lines 145–150) and the Figure 1B caption (lines 155–160). The parameter μ represents the mean magnitude of earthquakes in the normal distribution. An increase in μ, as observed in Figure 1B, indicates a shift in the average seismic energy release, often associated with the occurrence of larger earthquakes within the swarm. This phenomenon is common in Japan, particularly in tectonically active regions like the Tokara Islands, where episodic increases in seismic activity (e.g., triggered by volcanic processes at Suwanose Island) can elevate the mean magnitude. For example, the data in Figure 1B (March 2025) show a μ of approximately 3, with slight increases potentially linked to larger events influenced by regional tectonic stress or volcanic activity [1, 16]. These changes reflect the dynamic interplay between tectonic and volcanic processes, as discussed in Section 4 (lines 250–270). I believe these revisions clarify the physical meaning of σ and μ and their relevance to the study’s findings. I appreciate any further guidance on enhancing these explanations.

"5 Figure 2A, right figure, only marked ' 7 / 8 ', should indicate the complete period."

I sincerely thank Reviewer 3 for their feedback regarding the incomplete labeling of the time period in the right panel of Figure 2A, marked only as “7/8” (8 July 2025). To address this concern, I have revised the caption for Figure 2 to clarify that the center panel specifically depicts the epicentral distribution on 8 July 2025, capturing a distinct seismic event characterized by a northward migration of epicentres towards Suwanose Island, as described in Section 3. This event was a transient phenomenon observed on that day, with similar intermittent occurrences every few days thereafter, but it becomes less prominent when data are aggregated over a longer period.To provide a broader temporal context, I have added a new panel at the right, which illustrates the epicentral distribution of the Tokara Islands earthquake swarm over an extended period. These revisions complement the existing analysis in Figure 2A and Section 3, enhancing clarity for readers. I appreciate any further guidance on refining these additions.

"6 In Section 3.3, the author mentions ' statistically identical ', but does not provide the results of hypothesis testing, which should be supplemented to confirm that there is no significant difference in the interval distribution of earthquake swarms between 2025 and 2021, making the manuscript logic more rigorous."

Section 3.3 and the suggestion to include hypothesis testing to confirm the similarity of earthquake inter-event time distributions between the 2021 and 2025 Tokara Islands earthquake swarms. I acknowledge that the term “statistically identical” may imply a formal statistical equivalence test, which was not conducted, and I appreciate the opportunity to clarify this point.To address this concern, I have revised Section 3.3 and the caption for Figure 4 to replace “statistically identical” with “practically indistinguishable,” reflecting that the quantile-quantile (QQ) plots for the 2021 and 2025 swarms (29 June–4 July 2025, 10–12 April 2021, 4–7 December 2021) show highly similar distributional patterns (e.g., exponential distributions for inter-event times) without claiming strict statistical equivalence. I recognize the reviewer’s point about hypothesis testing to enhance rigor. However, testing for statistical equivalence (i.e., proving distributions are identical) is challenging, as it requires demonstrating that differences are negligible across all possible data, often referred to as the “devil’s proof” in statistical literature. Instead, our analysis relies on visual and quantitative comparisons via QQ plots, which show nearly identical slopes and intercepts for the 2021 and 2025 datasets (Figure 4), suggesting consistent parameters (e.g., λ for inter-event times). I believe these revisions strengthen the manuscript’s logic and clarity. I welcome any further guidance on incorporating specific statistical tests or additional analyses to enhance the comparison.

’

"7.It is recommended to supplement the fitting index of the quantile-quantile (QQ) plot in the figure."

I sincerely thank Reviewer 3 for their valuable suggestion to supplement the fitting index for the quantile-quantile (QQ) plots in the manuscript’s figures. To address this, I have revised the captions for Figures 1, 3, and 4, which contain QQ plots for earthquake inter-event times and magnitudes in the Tokara Islands earthquake swarm. 

"8  In the discussion section, can other volcanic earthquake cases be properly introduced for comparative analysis?"

We sincerely thank Reviewer 3 for their insightful suggestion to introduce other volcanic earthquake cases for comparative analysis in the Discussion section. To address this, I have revised the third paragraph of Section 4. It may be a somewhat unique phenomenon (third paragraph of Discussion).

 

Reviewer 4 Report

Comments and Suggestions for Authors

The study only analyzed earthquake swarm data from June to July 2025 (approximately 40 days), while volcanic related seismic activity typically lasts for several months or even years. It is recommended to supplement at least 6 months of continuous data to quantify frequency changes (such as an increase in daily earthquake frequency from 5 to 50) and their lag relationship with volcanic activity (such as a peak occurring X days after an eruption).

Although the difference between σ=0.37 in 2025 and σ=1.3 before the 2011 Northeast earthquake was pointed out, no significance test (such as t-test p-value) was conducted. Suggest supplementing hypothesis testing results to clarify whether the differences exceed the natural fluctuation range (such as the 95% confidence interval).

Figure 2 shows that the epicenter migrated from Akuseki Island to Suwanose Island (approximately 10km), but the migration rate (such as 0.5km/day) or directional concentration (such as compass variance<15 °) was not calculated. Suggest adding spatial autocorrelation analysis (such as Moran's I index).

The cumulative energy released by earthquake clusters has not been converted into equivalent magnitude (such as ∑ E=10 ¹² J ≈ Mw4.5), nor has it been compared with volcanic eruption energy (such as VEI2 ≈ 10 ¹¹ J). Suggest supplementing energy balance analysis and quantifying the contribution rate of magmatic activity (such as ≥ 70%).

The interval between earthquakes follows an exponential distribution while the magnitude follows a normal distribution, which is inconsistent with the classical G-R law, but the degree of deviation has not been quantified (such as K-S test D value>0.3). Suggest analyzing the abnormality of b value (such as b=0.8 ± 0.1 vs typical value 1.0).

The conclusion of 'low probability' lacks numerical basis. Suggest calculating conditional probabilities based on historical data (such as P (M>7 | σ<0.5)=0.1%) and providing an error range (± 0.05%).

Mentioning the similarity of activities in 2021/2025, but without quantifying the eruption scale (such as SO ₂ emission differences<20%) or magma volume changes (such as InSAR deformation ± 5cm). Suggest supplementing geochemical or deformation data for cross validation.

Not deducting the regional background seismic rate (such as Tokara baseline once per week). Suggest calculating Z-score to quantify the intensity of anomalies (e.g. Z=15 corresponds to p<0.001).

The JMA catalog has incomplete detection of earthquakes with M<1.5 (omission rate of about 30%), which may underestimate σ. It is recommended to conduct a comprehensive magnitude analysis (Mc=1.2).

Only comparing with the 2000 Miyake Island event (tectonic type), there is a lack of similar volcanic earthquake groups (such as the 2015 Ko'ei Ryobu Island). Suggest adding 3-5 case comparison matrices for σ/μ parameters.

The use of daily average frequency masks key sub daily variations (such as tidal modulation). Suggest displaying the relationship between hourly frequency and solid tide phase (such as correlation coefficient r>0.6).

The parameter estimation (such as σ=0.37 ±?) does not provide uncertainty. Suggest using bootstrap method to calculate 95% CI (such as σ ∈ [0.33, 0.41]).

Not utilizing synchronous geomagnetic data (such as EM variation>50nT) or water temperature data. Suggest using a contingency table to analyze multi parameter coupling (e.g. Cramer's V>0.4).

The introduction section is missing some latest relevant literature, please supplement. References: Landslide Displacement Prediction Based on Time Series and PSO-BP Model in Three Georges Reservoir, China; Assessment of landslide susceptibility based on the two-layer Stacking model-A case study of Jiacha County, China.

The epicenter positioning error of ± 2km may confuse the migration path. Suggest conducting Monte Carlo simulation to evaluate the probability of the impact of positioning error on the conclusion (e.g.<5%).

Author Response

I thank Reviewer 4 for their detailed feedback. I have addressed the suggestions by adding clarifications to the manuscript, as outlined below, while noting that some recommendations do not align with the study’s objectives.

>The study only analyzed earthquake swarm data from June to July 2025 (approximately 40 days), while volcanic related seismic activity typically lasts for several months or even years. It is recommended to supplement at least 6 months of continuous data to quantify frequency changes (such as an increase in daily earthquake frequency from 5 to 50) and their lag relationship with volcanic activity (such as a peak occurring X days after an eruption).

Data duration (6 months recommended): The study focuses on the June–July 2025 Tokara Islands earthquake swarm as a preliminary report to provide timely data for public reassurance, given the swarm’s ongoing subsidence (Figures 3D–E). Extending the analysis to 6 months is beyond the scope of this rapid communication. I have added this rationale to the Introduction and supplemented Figures 3D–E with data showing the swarm’s decline.

>Although the difference between σ=0.37 in 2025 and σ=1.3 before the 2011 Northeast earthquake was pointed out, no significance test (such as t-test p-value) was conducted. Suggest supplementing hypothesis testing results to clarify whether the differences exceed the natural fluctuation range (such as the 95% confidence interval).

Significance testing for σ differences: I appreciate the suggestion for hypothesis testing. However, in line with modern statistical practice, particularly in EDA, we prioritize visual analysis (e.g., quantile-quantile plots) over significance tests, which can be misleading due to multiple testing issues [Wasserstein and Lazar, 2016, American Statistician, 70(2):129–133]. The large difference in σ (0.37 in 2025 vs. 1.3 pre-2011) is evident in Figure 1B, rendering further testing unnecessary. I have clarified this in Section 2.2 (lines 105–110).

>Figure 2 shows that the epicenter migrated from Akuseki Island to Suwanose Island (approximately 10km), but the migration rate (such as 0.5km/day) or directional concentration (such as compass variance<15 °) was not calculated. Suggest adding spatial autocorrelation analysis (such as Moran's I index).

Epicentral migration analysis: I do not interpret the epicentral changes from Akuseki to Suwanose Island (Figure 2) as migration but as distinct seismic events with different characteristics. I have added this explanation to Section 3.2 (lines 210–215), noting that recent micro-seismic activity has shifted to another location, further supporting this interpretation.

>The cumulative energy released by earthquake clusters has not been converted into equivalent magnitude (such as ∑ E=10 ¹² J ≈ Mw4.5), nor has it been compared with volcanic eruption energy (such as VEI2 ≈ 10 ¹¹ J). Suggest supplementing energy balance analysis and quantifying the contribution rate of magmatic activity (such as ≥ 70%).

Energy balance analysis: Due to the absence of volcanic eruption energy data from the Japan Meteorological Agency, as noted in Section 4, we cannot quantify cumulative earthquake energy or its relation to volcanic activity. I have expanded the third paragraph of the Discussion to explain that while the 2025 swarm is likely driven by magma movement, its relationship to eruption energy varies by location and does not always correlate with large eruptions.

>The interval between earthquakes follows an exponential distribution while the magnitude follows a normal distribution, which is inconsistent with the classical G-R law, but the degree of deviation has not been quantified (such as K-S test D value>0.3). Suggest analyzing the abnormality of b value (such as b=0.8 ± 0.1 vs typical value 1.0).

This is explained in a previous paper [6]. The classical G-R rule was simply a misunderstanding. It was a misinterpretation of a coincidence in the graph. Therefore, the b value itself is a misobserved value, and there is no point in comparing it. Please refer to the previous paper for the graph. It is still in printing, but a preprint is available on arxiv. https://arxiv.org/abs/2302.02326

>The conclusion of 'low probability' lacks numerical basis. Suggest calculating conditional probabilities based on historical data (such as P (M>7 | σ<0.5)=0.1%) and providing an error range (± 0.05%).

I don't understand the meaning of P (M>7 | σ<0.5)=0.1%). σ<0.5)=0.1% is not a concept that is normally used to specify something. Magnitude follows a normal distribution. Hence if you want to specify that distribution, you should determine the values of σ and μ. Regardless of the probability of σ<0.5, it is impossible to estimate P (M>7) without determining μ; this is obvious.
Additionally, this reviewer has repeatedly pointed out the error range (± 0.05%), which is a concept used when presenting an estimated value. Since no estimated value is proposed here, it cannot be calculated.

The term ‘low probability’ is only used in the title of this paper. I have explained using P-values that M=4.5 rarely occurs under this swarm of earthquakes (3.3).  

>Mentioning the similarity of activities in 2021/2025, but without quantifying the eruption scale (such as SO ₂ emission differences<20%) or magma volume changes (such as InSAR deformation ± 5cm). Suggest supplementing geochemical or deformation data for cross validation.

This is something that concerns me as well, but it seems that the Japan Meteorological Agency does not measure such data, or at least it is not publicly available.

>Not deducting the regional background seismic rate (such as Tokara baseline once per week). Suggest calculating Z-score to quantify the intensity of anomalies (e.g. Z=15 corresponds to p<0.001).

Energy balance analysis: Due to the absence of volcanic eruption energy data from the Japan Meteorological Agency, as noted in Section 4, we cannot quantify cumulative earthquake energy or its relation to volcanic activity. I have expanded the third paragraph of the Discussion to explain that while the 2025 swarm is likely driven by magma movement, its relationship to eruption energy varies by location and does not always correlate with large eruptions.
>
>The JMA catalog has incomplete detection of earthquakes with M<1.5 (omission rate of about 30%), which may underestimate σ. It is recommended to conduct a comprehensive magnitude analysis (Mc=1.2).

I am also interested in this, but unfortunately the data has not been published. The only data that has been published is that which has been recorded as a perceptible earthquake at a certain location (I have added an explanation to the method).
When measuring magnitude, some kind of threshold is necessary. Here, it is determined by whether or not it was a ‘perceptible earthquake.’ It is not based on the magnitude itself. However, at least within this range, the normal distribution functions very effectively, that much is certain (e.g., Fig. 1B). Considering this characteristic, such small magnitude earthquakes probably occur only rarely.

>Only comparing with the 2000 Miyake Island event (tectonic type), there is a lack of similar volcanic earthquake groups (such as the 2015 Ko'ei Ryobu Island). Suggest adding 3-5 case comparison matrices for σ/μ parameters.

I don't think that's necessary here. This swarm earthquake is somewhat unique. If I can show that it has the same characteristics as earthquakes that have occurred in the past, I can assume that nothing major will happen in the future. And that fulfils the purpose of this paper. If you are interested, please refer to the previous paper [6]. There are more examples there. The R code is also available to the public, so anyone with the data can investigate it.

I did not know which country and which island Ko'ei Ryobu Island referred to. Based on the closest possible pronunciation and date, I think it refers to Kuchinoerabu Island, which erupted in May of that year, but no swarm earthquakes were observed before or after this eruption. It seems that either magma movement was not necessary, or there was no structure that was prone to swarm earthquakes along the way. I added an explanation for this as well (third paragraph of the discussion).

>The use of daily average frequency masks key sub daily variations (such as tidal modulation). Suggest displaying the relationship between hourly frequency and solid tide phase (such as correlation coefficient r>0.6).

This is probably irrelevant. The fluctuations caused by the Tokara earthquake swarm are extremely large. If the hourly occurrence rate and solid tidal phase are examined over a sufficiently large range, it is trivial that r = 0, which is meaningless.

>The parameter estimation (such as σ=0.37 ±?) does not provide uncertainty. Suggest using bootstrap method to calculate 95% CI (such as σ ∈ [0.33, 0.41]).
>The epicenter positioning error of ± 2km may confuse the migration path. Suggest conducting Monte Carlo simulation to evaluate the probability of the impact of positioning error on the conclusion (e.g.<5%).

Sub-daily variations and tidal modulation: The large fluctua
tions in the Tokara Islands earthquake swarm’s frequency (Figure 3D–E) overshadow sub-daily variations, rendering tidal modulation analysis (e.g., hourly frequency vs. solid tide phase) negligible, with expected correlation near zero. I have clarified this in Section 3.2

Along with bootstrapping, Monte Carlo simulation is also a kind of attempt, but basically the data is not refreshed. Therefore, it does not reinforce the accuracy of the measurement. This is also true in terms of determining measurement error. I think that those should not be used in situations where scientific rigour is required.

>Not utilizing synchronous geomagnetic data (such as EM variation>50nT) or water temperature data. Suggest using a contingency table to analyze multi parameter coupling (e.g. Cramer's V>0.4).

Geomagnetic and water temperature data: Due to unavailable synchronous geomagnetic and water temperature data, multi-parameter coupling analysis is infeasible. I have noted this limitation in Section 4, emphasizing that daily fluctuations (Figure 2, Table 1) reflect seismic variability.

>The introduction section is missing some latest relevant literature, please supplement. References: Landslide Displacement Prediction Based on Time Series and PSO-BP Model in Three Georges Reservoir, China; Assessment of landslide susceptibility based on the two-layer Stacking model-A case study of Jiacha County, China.

Latest literature: The suggested landslide studies are unrelated to our seismic swarm analysis using simple EDA models, guided by Occam’s razor. I have clarified our focus on straightforward statistical models in the Introduction.

 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The author has substantially improved the quality of the paper.

The paper can now be accepted for publication.

Author Response

Thank you very much for your positive feedback and for recognizing the improvements made to the manuscript. I greatly appreciate your time and valuable input throughout the review process. I am pleased to hear that the revised explanation has been well-received and that the paper is now suitable for publication. Please let me know if there are any further steps or minor revisions required before final acceptance.

Reviewer 2 Report

Comments and Suggestions for Authors

Thanks for the edits. Please improve references

Author Response

Thank you for your valuable feedback and for suggesting improvements to the references. I appreciate your careful review and have addressed the issues by correcting several errors in the reference list, ensuring accuracy and consistency in formatting. Additionally, I have reviewed all citations to confirm they align with the journal’s guidelines. Please let me know if there are specific references or further improvements you would like me to address.

Reviewer 4 Report

Comments and Suggestions for Authors

The introduction section is missing some latest relevant literature, please supplement. References: Landslide Displacement Prediction Based on Time Series and PSO-BP Model in Three Georges Reservoir, China; Assessment of landslide susceptibility based on the two-layer Stacking model-A case study of Jiacha County, China.

Author Response

Thank you for your continued feedback and for suggesting additional references to strengthen the introduction section. I greatly appreciate your effort to ensure the manuscript is comprehensive and up-to-date. Regarding the two suggested papers—"Landslide Displacement Prediction Based on Time Series and PSO-BP Model in Three Georges Reservoir, China" I have carefully reviewed this relevance to the current study.

As previously noted, I respectfully believe these papers are not directly relevant to the scope and focus of my manuscript. The proposed studies utilize highly sophisticated and complex modeling approaches, which differ fundamentally from the methodological framework and objectives of my work. Following the principle of Occam’s Razor, which emphasizes simplicity and clarity in scientific explanations, my study prioritizes a more straightforward approach to ensure robustness and generalizability. While the suggested papers are valuable in their own right, their focus on complex models does not align closely with the goals of this paper, which are centered on the Tokara Swarm is almost the same that occured in past, and will not cause huge earthquakes.

Had the manuscript’s objective been to critically compare modeling approaches, I would have considered citing these works to discuss their methodologies. However, given the current focus, I believe introducing this reference might lead to an unnecessary digression that could detract from the paper’s clarity. I hope this explanation clarifies my rationale for not including these citations. Please let me know if there are other relevant studies or specific aspects of the introduction that you feel require further enhancement, and I will be happy to address them.