Calculation of Theoretical Travel Time and Automatic Picking of Actual Travel Time in Seismic Data
Round 1
Reviewer 1 Report
The article is undoubtedly of interest, but for their research, the authors could turn to a more modern velocity model of the Earth.
Author Response
Point 1:The article is undoubtedly of interest, but for their research, the authors could turn to a more modern velocity model of the Earth.
Response 1: We are grateful to you for your effort reviewing our paper. Thank you very much for your comments, and we will move to a more modern Earth velocity model in our follow-up work.
Reviewer 2 Report
The manuscript "Calculation of theoretical travel time and automatic picking of actual traveltime in seismic data" presents a methodology for automatically picking seismic phases based on a correlation metric. The subject is of great interest to seismologists who work with big data. Although the article deals with a topic worthy of investigation, the manuscript should be improved. The introduction is well presented but needs a slight improvement. The methodology and results need to be presented more accurately. Please see some comments below.
(1) The word "Earth" is sometimes capitalized, but not in others. Both styles are acceptable, but using just one style throughout the manuscript is most suitable. See line 32, for instance.
(2) In lines 32-33, what does "three elements of an earthquake" mean? Do the authors refer to the strike, dip, and rake parameters to describe a focal mechanism? Please clarify it.
(3) Regarding the abbreviations, they must be inserted in parentheses right after the written-out means when defined for the first time. This one should be made at its first appearance in the main text. I suggest that the authors review the abbreviations entered in the manuscript. For example, please replace "AIC" with "Akaike Information Criterion (AIC)" in line 65. In line 75, what does "MCCC" mean? Please double-check the abbreviations.
(4) The authors did not mention the most popular method for seismic phase picking, namely the short-term average/long-term average (STA/LTA) technique proposed by Allen R. V. (1978) Automatic earthquake recognition and timing from single traces. Bulletin of the Seismological Society of America, 68(5): 1521-1 533. I suggest two works to be referenced in which the STA/LTA technique is used to perform automatic picking: (i) da Silva, S.L.E.F. ; Corso, G. (2022) Microseismic event detection in noisy environments with instantaneous spectral Shannon entropy. Physical Review E, 106, 014133; and (ii) Wu, H.; Xiao, W.; Ren, H. (2022) Automatic Time Picking for Weak Seismic Phase in the Strong Noise and Interference Environment: An Hybrid Method Based on Array Similarity. Sensors, 22, 9924. In addition, authors should also mention works involving automatic picking through techniques based on Machine Learning; follow the suggestions: (i) Dimililer, K.; Dindar, H.; Al-Turjman, F. (2021) Deep learning, machine learning and internet of things in geophysical engineering applications: An overview. Microprocessors and Microsystems, 80, 103613; and (ii) Wang, J.; Xiao,Z.; Liu, C.; Zhao, D.; Yao, Z. (2019) Deep Learning for Picking Seismic Arrival Times. Journal of Geophysical Research: Solid Earth. 124(7), 6612.
(5) Lines 79-85: In the last paragraph of the introduction, the authors must inform which methods they used in this work and if they are applying existing methods or proposing new strategies. Detail this paragraph more to guide readers better.
(6) Figure 1 represents the Earth model used in this work. However, this figure is not mentioned in the body of the text. Authors should further develop the first paragraph of Section 2, providing more details of the IASP91 model illustrated in Figure 1.
(7) After Equation (1), the spatial dependence of τ and v must be explained. Also, it is essential to clarify that travel time τ refers to the first arrival.
(8) In lines 99 and 103, are x, y, z angles or spatial coordinates? This seems ambiguous.
(9) Please provide more details on how the authors obtained Equation 3.
(10) In this case, the authors must clarify that the 2D model is composed of concentric circles similar to the one illustrated on the right side of Figure 1 (or Figure 2). Are the earthquakes analyzed in Section 4 contained in an x-z plane?
(11) In line 117, v_x and v_z are only valid for P-waves? S-waves? All seismic phases?
(12) Figure 2 is in low resolution. Please provide a higher-resolution figure.
(13) The paragraph in lines 125-129 should be transferred to line 110.
(14) Consider removing—repeated information—the expression "The Earth model used in this paper is the IASP91 velocity model." in line 125.
(15) The term "the corresponding" in line 135 seems to be incorrect.
(16) Please explain what v_0 means in Equation 5.
(17) In the last paragraph of Section 2, please explain in detail the numerical methodology used; several computational techniques exist in the literature. What methodology was used by the authors? Please justify the methodological choice.
(18) Line 155: What does the index j mean in x_ij? The time? Please clarify.
(19) Lines 155 and 156: What does Nx and Nx mean? Nx=Ns= time samples?
(20) Equations 7 and 8 seem to represent Pearson's coefficients, meaning that the two variables have means equal to zero. Could the authors clarify?
(21) Were the parameters summarized in Table 1 determined by the authors or did they come from some seismic catalog? This needs to be written in the manuscript.
(22) Do the blue lines in figures 5 and 6 represent the automatically calculated picking? Were they calculated only at the receivers' position or neighboring positions?
(23) Although I found the article interesting in principle, a more systematic evaluation of the method, say on a variety of synthetic scenarios, would be desirable. Indeed, a validation of the approach by means of synthetic examples need to be documented, because in controlled environments it is possible to verify the errors and the accuracy of the proposed methodology.
Author Response
Response to Reviewer 2 Comments
Point 1: The word "Earth" is sometimes capitalized, but not in others. Both styles are acceptable, but using just one style throughout the manuscript is most suitable. See line 32, for instance.
Response 1: Thank you for your comment. All capitalized initials have been rewritten.
Point 2: In lines 32-33, what does "three elements of an earthquake" mean? Do the authors refer to the strike, dip, and rake parameters to describe a focal mechanism? Please clarify it.
Response 2: This suggestion is appreciated. Added in the introduction. The three elements of an earthquake are the time of occurrence, the epicenter, and the magnitude of the earthquake. Please check at line 34.
Point 3: Regarding the abbreviations, they must be inserted in parentheses right after the written-out means when defined for the first time. This one should be made at its first appearance in the main text. I suggest that the authors review the abbreviations entered in the manuscript. For example, please replace "AIC" with "Akaike Information Criterion (AIC)" in line 65. In line 75, what does "MCCC" mean? Please double-check the abbreviations.
Response 3: We thank you for this suggestion. Modified, multi-channel cross-correlation technique. Please check at line 75.
Point 4: The authors did not mention the most popular method for seismic phase picking, namely the short-term average/long-term average (STA/LTA) technique proposed by Allen R. V. (1978) Automatic earthquake recognition and timing from single traces. Bulletin of the Seismological Society of America, 68(5): 1521-1 533. I suggest two works to be referenced in which the STA/LTA technique is used to perform automatic picking: (i) da Silva, S.L.E.F. ; Corso, G. (2022) Microseismic event detection in noisy environments with instantaneous spectral Shannon entropy. Physical Review E, 106, 014133; and (ii) Wu, H.; Xiao, W.; Ren, H. (2022) Automatic Time Picking for Weak Seismic Phase in the Strong Noise and Interference Environment: An Hybrid Method Based on Array Similarity. Sensors, 22, 9924. In addition, authors should also mention works involving automatic picking through techniques based on Machine Learning; follow the suggestions: (i) Dimililer, K.; Dindar, H.; Al-Turjman, F. (2021) Deep learning, machine learning and internet of things in geophysical engineering applications: An overview. Microprocessors and Microsystems, 80, 103613; and (ii) Wang, J.; Xiao,Z.; Liu, C.; Zhao, D.; Yao, Z. (2019) Deep Learning for Picking Seismic Arrival Times. Journal of Geophysical Research: Solid Earth. 124(7), 6612.
Response 4: We thank you for this suggestion. These references(21-26) have been added. Please check at line 64 to 71.
Point 5: Lines 79-85: In the last paragraph of the introduction, the authors must inform which methods they used in this work and if they are applying existing methods or proposing new strategies. Detail this paragraph more to guide readers better.
Response 5: Thank you very much for your valuable suggestion. The last paragraph of the introduction has been revised.
Point 6: Figure 1 represents the Earth model used in this work. However, this figure is not mentioned in the body of the text. Authors should further develop the first paragraph of Section 2, providing more details of the IASP91 model illustrated in Figure 1.
Response 6: Thank you for the suggestion. A new Table 1 has been added.
Point 7: After Equation (1), the spatial dependence of τ and v must be explained. Also, it is essential to clarify that travel time τ refers to the first arrival.
Response 7: Thank you for your comment. τ is the travel time of the seismic wave propagating from the source S to any point (x, y, z) in space. v is the velocity of the medium at any point in space.
Point 8: In lines 99 and 103, are x, y, z angles or spatial coordinates? This seems ambiguous.
Response 8: Thank you for the suggestion. It refers to the Cartesian coordinate system, spatial coordinates.
Point 9: Please provide more details on how the authors obtained Equation 3.
Response 9: This suggestion is appreciated. The derivation process has been added. Please check at line 108 to 148.
Point 10: In this case, the authors must clarify that the 2D model is composed of concentric circles similar to the one illustrated on the right side of Figure 1 (or Figure 2). Are the earthquakes analyzed in Section 4 contained in an x-z plane?
Response 10: We thank you for this suggestion. It has been clarified in the last paragraph of Section 2 that the earthquakes analyzed in Section 4 are contained in the x-z plane.
Point 11: In line 117, vx and vz are only valid for P-waves? S-waves? All seismic phases?
Response 11: Thank you very much for your valuable suggestion. All seismic phases.
Point 12: Figure 2 is in low resolution. Please provide a higher-resolution figure.
Response 12: Thank you for the suggestion. Modified.
Point 13: The paragraph in lines 125-129 should be transferred to line 110.
Response 13: Thank you for the suggestion. Modified.
Point 14: Consider removing—repeated information—the expression "The Earth model used in this paper is the IASP91 velocity model." in line 125.
Response 14: Thank you for the suggestion. Deleted.
Point 15: The term "the corresponding" in line 135 seems to be incorrect.
Response 15: Thank you for the suggestion. Deleted.
Point 16: Please explain what v0 means in Equation 5.
Response 16: We are grateful to you for your effort reviewing our paper. It has been explained that v0 denotes the velocity of the ray at the epicenter S. Please check at line 182.
Point 17: In the last paragraph of Section 2, please explain in detail the numerical methodology used; several computational techniques exist in the literature. What methodology was used by the authors? Please justify the methodological choice.
Response 17: Thank you very much for your valuable suggestion. Modified the last paragraph of section 2. Please check at line 184 to 191.
Point 18: Line 155: What does the index j mean in xij? The time? Please clarify.
Response 18: Thank you for your comment. It refers to stations other than the reference station.
Point 19: Lines 155 and 156: What does Nx and Nx mean? Nx=Ns= time samples?
Response 19: We thank you for this suggestion. Nx is a station different from N, and NS is a station different from Nx and N.
Point 20: Equations 7 and 8 seem to represent Pearson's coefficients, meaning that the two variables have means equal to zero. Could the authors clarify?
Response 20: Thank you for the suggestion.This is the correlation coefficient and Equation 8 is the discrete form of Equation 7. Ri takes values in the range 0 to 1.
Point 21: Were the parameters summarized in Table 1 determined by the authors or did they come from some seismic catalog? This needs to be written in the manuscript.
Response 21: We thank you for this suggestion. From USGS, added to the table name.
Point 22: Do the blue lines in figures 5 and 6 represent the automatically calculated picking? Were they calculated only at the receivers' position or neighboring positions?
Response 22: Thank you for the suggestion. The blue lines in Figures 5 and 6 are the theoretical arrival times calculated automatically according to the theoretical method in Section 2. It can be calculated at any receiving station location.
Point 23: Although I found the article interesting in principle, a more systematic evaluation of the method, say on a variety of synthetic scenarios, would be desirable. Indeed, a validation of the approach by means of synthetic examples need to be documented, because in controlled environments it is possible to verify the errors and the accuracy of the proposed methodology.
Response 23: We are grateful to you for your effort reviewing our paper. Our method has been continuously improved during the 5 years of data experiments and good results have been achieved. The examples in this paper are the theoretically calculated and measured arrival times of two common first-to-earth phases in the 5-year data, and their relative arrival time differences.
Special thanks to you for your good comments.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
Dear Authors and Editor,
I have two comments on the paper. Hope these will help the authors improve this manuscript.
1. Cited papers are mostly 15~20 years ago, I do not think the authors have done enough literature review on the recent progress and publications. I believe there are more new method on traveltime picking, say mechine learning method.
2. Meanwhile, traveltime calculation of 1-D velocity model is already well established domain. The authors did not mention whether they write their own code to implement all these equations, or use some open softwares. For instance, SAC has its own traveltime calculation functions, while taup can also compute the theoretical traveltime. If you all write your own code, have you done a benchmark test with the results from SAC, taup, or any other packages.
Author Response
Response to Reviewer 3 Comments
Point 1: Cited papers are mostly 15~20 years ago, I do not think the authors have done enough literature review on the recent progress and publications. I believe there are more new method on traveltime picking, say mechine learning method.
Response 1: We are grateful to you for your effort reviewing our paper. These references(21-26) have been added. Please check at line 64 to 71.
Point 2: Meanwhile, traveltime calculation of 1-D velocity model is already well established domain. The authors did not mention whether they write their own code to implement all these equations, or use some open softwares. For instance, SAC has its own traveltime calculation functions, while taup can also compute the theoretical traveltime. If you all write your own code, have you done a benchmark test with the results from SAC, taup, or any other packages.
Response 2: This suggestion is appreciated.
We have written our own code to implement all these equations. We have created an executable .exe file that can be installed directly into Windows using a password, no programming skills are required to use the functions of the software and no additional files need to be copied. The names of the functions are simple and can be easily found and used by the user.
Our simulated results for calculating the orthogonal walk time of each seismic phase can match well with the seismic wave travel schedule of the corresponding phase calculated by Kennett [4], and the computational speed can be guaranteed. A comparison with SAC has also been done and the error time is within the range of 0.001s.
Special thanks to you for your good comments.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors addressed all questions asked in the first review round.
Reviewer 3 Report
Dear Authors,
Thanks for your timely effort on improving this manuscript. I have seen the content being more complete, and you have answered my comments well enough. I think it is ready for publish. Please double check if there is any small typo/grammar issue.
