APMEG: Quadratic Time–Frequency Distribution Analysis of Energy Concentration Features for Unveiling Reliable Diagnostic Precursors in Global Major Earthquakes Towards Short-Term Prediction

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study presents a TFD-based method for short-term earthquake prediction using energy concentration features. By analyzing magnitude-time series data from five major earthquakes(including the Turkey–Syria, Sulawesi, Luzon, Kaikōura, and Noto events)using STFT, WVD, CWD, and CWT following linear interpolation, the authors identified distinct energy peaks 11–66 hours before each mainshock, patterns often undetectable in time-domain analysis. The work is innovative in applying nonlinear TFDs to capture the non-stationary, multi-spectral nature of seismic signals. However,  considerable modifications are required before publishing.

Major comments:

1. The manuscript currently equates diagnostic precursors with peaks in mean energy concentration, but the criteria for identifying such a peak are not specified. For instance, was a threshold applied? Were statistical tests conducted to verify its significance? It is recommended that a clearer definition and quantitative metrics be provided.
2. Although linear interpolation is a reasonable preprocessing method, its impact on preserving the original signal's dynamic features has not been sufficiently demonstrated. The authors are encouraged to include comparative illustrations of pre- and post-interpolation signal segments—both in the time and frequency domains—to assess whether critical dynamic information is retained.
3. The study focuses solely on cases where major earthquakes occurred, without including control examples where no mainshock followed minor seismicity. This omission prevents assessment of false positive rates and specificity. It is recommended that the authors include at least one control case to evaluate the method’s generalizability and robustness.
4.  Although the manuscript notes efforts to reduce endpoint effects in TFD analysis, it does not specify the techniques used. The authors should clearly describe the method applied and justify its appropriateness and effectiveness in addressing endpoint artifacts.
5.  While Figures 3-7 provide comparisons between TFDs and mean energy concentration, the following improvements are suggested: unify the color scale legends across figures; explicitly mark the mainshock timing and energy peaks; reduce the number of main text figures by selecting only the most representative results and moving the rest to supplementary materials.

Author Response

Comment 1: The manuscript currently equates diagnostic precursors with peaks in mean energy concentration, but the criteria for identifying such a peak are not specified. For instance, was a threshold applied? Were statistical tests conducted to verify its significance? It is recommended that a clearer definition and quantitative metrics be provided.

Response: Noted, we have included a statistical definition of what we consider a peak. You may refer to the updated manuscript, under Discussions on page 10, line 254.

 

Comments 2: Although linear interpolation is a reasonable preprocessing method, its impact on preserving the original signal's dynamic features has not been sufficiently demonstrated. The authors are encouraged to include comparative illustrations of pre- and post-interpolation signal segments—both in the time and frequency domains—to assess whether critical dynamic information is retained.

Response: Noted. We have included a comparison with using Weighted Wavelet Z Transform (WWZ) against the raw data. WWZ is an application of CWT which do not require interpolation. This is added under a new subsection of Discussions "Necessity of Data Interpolation", on page 13.

 

Comments 3: The study focuses solely on cases where major earthquakes occurred, without including control examples where no mainshock followed minor seismicity. This omission prevents assessment of false positive rates and specificity. It is recommended that the authors include at least one control case to evaluate the method’s generalizability and robustness.

Response: Noted. As we have the dataset of Turkey-Syria earthquake spanning 1 month, we will be using a different 1-week window of the dataset as a control. We have added the comparison in Discussions, page 10, line 266.

 

Comments 4: Although the manuscript notes efforts to reduce endpoint effects in TFD analysis, it does not specify the techniques used. The authors should clearly describe the method applied and justify its appropriateness and effectiveness in addressing endpoint artifacts.

Response: Noted, we have included the method used in Discussion: Endpoint Effect, as well as a comparison of before and after application of said method, as well as justifications of using the method. Page 14, line 340 onwards.

Comments 5: While Figures 3-7 provide comparisons between TFDs and mean energy concentration, the following improvements are suggested: unify the color scale legends across figures; explicitly mark the mainshock timing and energy peaks; reduce the number of main text figures by selecting only the most representative results and moving the rest to supplementary materials.

Response: Thank you for these improvement suggestions. We will adjust accordingly.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a novel short-term earthquake prediction method using Time-Frequency Distributions (TFDs), which effectively identify consistent precursory patterns in seismic signals hours to days before major earthquakes. The approach demonstrates strong potential for improving the reliability and timeliness of earthquake forecasting.

I agree the method proposed in this paper can be used to identify precursors to major earthquakes, and therefore this research will be meaningful to the society. However, I find it difficult to call this a “prediction”. Earthquake prediction involves comprehensive forecasting of the time, location, and magnitude, whereas this method only indicates the possibility of a precursor.

The studies of several typical earthquakes in this paper support the conclusions; however, this only falls within the scope of True Positives (TP). Additionally, I am unclear whether there are False Positives (FP). There are cases where similar precursors appear, but no earthquake ultimately occurs. These two points must be discussed.

Other minor comments are as follows:

1. The invention of the seismoscope by Zhang Heng does not fall within the scope of modern science and including it in this paper is inappropriate. It should be removed.
2. In Line 89, the author could also mention the earthquake that occurred in southern Peru in June 2024, which was also a magnitude 7+ event and holds significant academic value.

Reference: https://doi.org/10.1016/j.oceaneng.2025.121325

3. I understand that WVD (Section 2.5) is known to suffer from cross-term interference, what specific steps or techniques have the authors implemented to mitigate these effects, and how do they ensure the reliability of the extracted precursory patterns?
4. How does the study quantitatively define and validate the “mean energy concentration” metric in the time-frequency distributions for reliably detecting earthquake precursors?

Author Response

Major Comments 1: I agree the method proposed in this paper can be used to identify precursors to major earthquakes, and therefore this research will be meaningful to the society. However, I find it difficult to call this a “prediction”. Earthquake prediction involves comprehensive forecasting of the time, location, and magnitude, whereas this method only indicates the possibility of a precursor.

Response: Perhaps the language used in introduction and conclusion were unclear, apologies on our part. The aim of this research is as you've mentioned, to provide a possible diagnostic precursor for the purpose of earthquake prediction, not to provide an earthquake prediction method itself. We will adjust where earthquake prediction is mentioned accordingly.

 

Major Comment 2: 

The studies of several typical earthquakes in this paper support the conclusions; however, this only falls within the scope of True Positives (TP). Additionally, I am unclear whether there are False Positives (FP). There are cases where similar precursors appear, but no earthquake ultimately occurs. These two points must be discussed.

Response: Noted. At this point of the research we are not able to account for TN, FP and FN, due to lack of dataset for analysis. We will include this in the subsection "Limitations and Further Research", page 15, line 378.

 

Comments 1: The invention of the seismoscope by Zhang Heng does not fall within the scope of modern science and including it in this paper is inappropriate. It should be removed.

Response: Noted, we will remove this.

 

Comments 2: In Line 89, the author could also mention the earthquake that occurred in southern Peru in June 2024, which was also a magnitude 7+ event and holds significant academic value.

Response: We thank you for your suggestion, and so we have mentioned this earthquake in introduction instead of the Data Sources subsection, as we were not able to obtain sufficient open data for said earthquake for analysis.

 

Comments 3: I understand that WVD (Section 2.5) is known to suffer from cross-term interference, what specific steps or techniques have the authors implemented to mitigate these effects, and how do they ensure the reliability of the extracted precursory patterns?

Based on documentation of one of our tools for WVD, this issue had been raised up, and a simple solution was provided which we deem was enough to retain and enhance the precursory patterns, especially since the patterns that we observe are not directly on the TFDs themselves, but rather the mean energy concentration diagram of respective TFDs. We will mention the method involved in the same subsection (2.5).

 

Comments 4: How does the study quantitatively define and validate the “mean energy concentration” metric in the time-frequency distributions for reliably detecting earthquake precursors?

Response: For this analysis, we had used a statistical definition for a threshold of the mean energy concentration to obtain peaks. You may refer to the updated manuscript, under Discussions on page 10, line 253.

 

Reviewer 3 Report

Comments and Suggestions for Authors

2.2 Data interpolation: by applying data interpolation you are messing with the “ground truth” i.e. you introduce events that never occurred. In other words, you are “forcing” earthquakes to occur at regular intervals in time. This fact and its consequences have to be elaborated on in the text. Why don’t you simply use zeros between two adjacent points, as indeed there are no events between two adjacent points?

2.7 CWT: If I understood correctly CWT can work without equal spacing. Then why don’t you process the datasets with CWT twice; first with equal spacing, and second with natural spacing to see the difference, thus evaluating the effect of forcing the data to be of equal spacing?

Table 8: What is the criterion you have used to consider a spike as peak? Explain this in the text, and indicate the peaks in the corresponding Figures 3 to 7. Also indicate or explain in the text how you calculate the “Estimate time between peaks” - between neighboring peaks, or between first and last.

What is the guarantee that even when there are patterns of mean energy concentration like the ones you have discovered, a major earthquake will follow? Have you studied catalogues months and even years long trying to prove that such patterns never occur, unless a major earthquake occurs after them? Please elaborate on this in the text. 

In the attached file I have made a few suggestions on the English language.

Comments for author File: Comments.pdf

Author Response

Comment 1: 

2.2 Data interpolation: by applying data interpolation you are messing with the “ground truth” i.e. you introduce events that never occurred. In other words, you are “forcing” earthquakes to occur at regular intervals in time. This fact and its consequences have to be elaborated on in the text. Why don’t you simply use zeros between two adjacent points, as indeed there are no events between two adjacent points?

Response: Noted, we will elaborate on this in the manuscript, in a new subsection called Necessity of Data Interpolation under Discussions (page 13). Off the manuscript, zero-insertion would introduce a different set of issues, e.g. the active span of an earthquake over time is not accounted for, unrecorded minor earthquakes of below 2 (or 3 depending on dataset) in magnitude would be forced to 0, and lastly computation time and resources, especially for the more complex TFDs (WVD and CWD).

 

Comments 2: 

2.7 CWT: If I understood correctly CWT can work without equal spacing. Then why don’t you process the datasets with CWT twice; first with equal spacing, and second with natural spacing to see the difference, thus evaluating the effect of forcing the data to be of equal spacing?

Response: Traditional CWT cannot work on unevenly spaced data. The "constant windowing" on CWT's subsection refers to the windowing used in STFT. There is however a method called Weighted Wavelet Z, which is an application of CWT which can account for unevenly spaced data, however it is not a good solution, as these sort of techniques (there are others, like Least-Squared Wavelet Analysis) require a third parameter, "weight", which we can only assume unless a better definition of weight can be derived from the available dataset. We will include this comparison in discussion. Page 13, line 317.

 

Comments 3: 

Table 8: What is the criterion you have used to consider a spike as peak? Explain this in the text, and indicate the peaks in the corresponding Figures 3 to 7. Also indicate or explain in the text how you calculate the “Estimate time between peaks” - between neighboring peaks, or between first and last.

Response: Noted. We used a statistical definition of sum of mean and 2 standard deviation as a threshold to consider if a spike is a peak. This is included in the new manuscript on page 10 line 254. We have also made the indication as you mentioned on Table 8 regarding Estimate time between peaks.

 

 Comments 4:

What is the guarantee that even when there are patterns of mean energy concentration like the ones you have discovered, a major earthquake will follow? Have you studied catalogues months and even years long trying to prove that such patterns never occur, unless a major earthquake occurs after them? Please elaborate on this in the text. 

Response:  At this point of the research, we are not able to guarantee or provide a robust statistical proof (TP, FP, TN, FN) for the precursory pattern. We will elaborate this in the text, under the limitations and further research subsection, page 15 line 378.

 

Comment 5: 

In the attached file I have made a few suggestions on the English language.

Response: Thank you very much for your suggestions, we will make edits.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I cannot find the response to my review reports. 

Author Response

Comments 1: I cannot find the response to my review reports. 

Response: I apologise for any inconvenience. Will make sure the responses to the first round of comments are included in the next resubmission cover letter.

Reviewer 2 Report

Comments and Suggestions for Authors

I thank the authors’ efforts in carefully revising the manuscript. Some of my comments were well responded. I believe that the manuscript has been well improved.

First, I thank the authors for explaining the goal of this manuscript. They state that they provide a possible diagnostic precursor for the purpose of earthquake prediction. I agree with the diagnostic precursor, but the direct relationship between the precursor and the earthquake is still controversial. It is not appropriate to say that it is the purpose, because the earthquake is unpredictable. The authors should revise the title and clearly discuss this problem.

Second, it is a pity that they are not able to account for TN, FP and FN, due to lack of dataset for analysis. This could be another reason that I cannot agree with the direct relationship between the precursor and the earthquake.

Third, regarding the Response to Comment 2, I agree that the authors mentioned this earthquake in introduction instead of the Data Sources subsection. However, they should cite the following reference:

Reference: https://doi.org/10.1016/j.oceaneng.2025.121325

Therefore, I believe that a major revision is required before we can consider proceeding with the manuscript.

Author Response

Comments 1: First, I thank the authors for explaining the goal of this manuscript. They state that they provide a possible diagnostic precursor for the purpose of earthquake prediction. I agree with the diagnostic precursor, but the direct relationship between the precursor and the earthquake is still controversial. It is not appropriate to say that it is the purpose, because the earthquake is unpredictable. The authors should revise the title and clearly discuss this problem.

Response: I understand that the topic of earthquake prediction is still a highly controversial one, and perhaps at this point it may be correct to state that earthquakes are unpredictable. We believe however, that we can make progress towards earthquake prediction, if not all earthquakes, at least major earthquakes; with the identification of diagnostic precursory patterns within earthquake data leading to major earthquakes. We will update the title to include "-towards short-term prediction" to reflect this, as well as texts in the abstract, Introduction, subsection "Limitations and Further Research", and Conclusion.

Comments 2: Second, it is a pity that they are not able to account for TN, FP and FN, due to lack of dataset for analysis. This could be another reason that I cannot agree with the direct relationship between the precursor and the earthquake.

Response: Perhaps it is correct to point out that the inability to fully account for TN, FP, and FN due to dataset limitations is a primary reason why a direct relationship between the observed precursors and earthquakes cannot be definitively established. We have clarified this in the 'Limitations and Further Research' subsection of the manuscript, explicitly stating this as a key limitation and emphasizing that future work with more comprehensive datasets will be required to assess the statistical robustness of these precursory patterns. Page 15, Lines 378 - 389

Comments 3: 

Third, regarding the Response to Comment 2, I agree that the authors mentioned this earthquake in introduction instead of the Data Sources subsection. However, they should cite the following reference:

Reference: https://doi.org/10.1016/j.oceaneng.2025.121325

Therefore, I believe that a major revision is required before we can consider proceeding with the manuscript.

Response: Thanks for the suggestion. We have carefully reviewed the recommended reference "Tsunami characteristics and source estimation of the 2024 Yauca (Peru) earthquake". While the paper is an interesting study on the tsunami caused by the Yauca earthquake (the effect of an earthquake), its focus does not directly align with the seismological characteristics or precursory signal analysis, which is the context of our discussion (the precursor of an earthquake). To ensure our introduction remains focused and that all citations are directly relevant to the specific points being made, we have opted to retain the current references. We hope our reasoning can be accepted.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The authors did not address my comments and questions thoroughly. The replies are not convincing to me.

Author Response

Comment 1: The authors did not address my comments and questions thoroughly. The replies are not convincing to me.

Response: We have now included a comparison of time domain and frequency domain of the raw data vs the interpolated data of the Turkey-Syria earthquake, in the same section "Necessity of Data Interpolation" page 13, line 316.

Reviewer 2 Report

Comments and Suggestions for Authors

I thank the authors for carefully responding to my comments. This version is suitable for publication. I am glad to accept it.

Author Response

Comments 1: I thank the authors for carefully responding to my comments. This version is suitable for publication. I am glad to accept it.

Response: We thank you for your time and effort in reviewing and highlighting concrete changes which we can take to enhance our paper. We also thank you for your acceptance.