the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Analysis of phase lead "anomalies" in the tidal response of groundwater levels
Abstract. The tidal response to the groundwater level refers to an aquifer under the influence of tidal forces, the pressure head (pore pressure) within the aquifer produces changes that drive the alternating transportation of water between wellaquifers, causing the rise and fall of the water level in the wells. Considering the driving process of force and seepage of water, the groundwater level response should only have a phase lag compared to the Earth's solid tides. However, the actual observation data show that the phase of the groundwater level tidal response exceeded that of the theoretical gravity tides, which is not in accordance with the commonly occurring mechanical process of the phenomenon. Using the theory of transcurrent recharge, the seepage of aquifer water was decomposed into lateral and vertical transport, and the two kinds of "lagging" transport processes were superimposed to obtain the final groundwater level tidal response, which may appear as an anomalous phenomenon in which the phase is over the front after superposition. Taking the Lugu Lake well as an example, before the Wenchuan earthquake, the phase of groundwater level was ahead of the theoretical solid tide, indicating the existence of a transgressive aquifer, whereas the groundwater level tidal factor declined from 0.28 mm/uGal before the earthquake to 0.23 mm/uGal after the earthquake. The phase, from 15 min ahead in preearthquake to 15 min lagged after the earthquake, combined with the theoretical analysis it can be seen that the Wenchuan earthquake led to develop the new fissure in the Lugu Lake well, thus permanently altering its aquifer response and changing the permeability of the aquifer. However, the subsequent earthquakes did not produce new fissures; only the seismic waves caused by the stress redistribution process were observed. This coseismic response of the groundwater level shows a stepdown phenomenon, phase analysis of the groundwater level has scientific significance for the study of wellaquifer conditions and wellborehole seismic capacity.
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RC1: 'Comment on egusphere20232816', Anonymous Referee #1, 22 Jan 2024
This manuscript documented a phase lead phenomenon of groundwater level in response ti earth tide and try to explain what the phase advance occur.
To be honest, I do not think the phase advance is new and unexplainable, and there are several published papers have dealt the issue (pelease refer to Barbour et al., 2019; Gao et al., 2020; Valois et al. 2023 .Wang et al. 2018 ....). In these papers, they discussed the changes of Taqu, Tcon, Saqu, Scon would have signficant impact on the phase shift. Such findings provide a basic physical mechanism of the phase shift. The discussion of your comniation of two siganls (x1, x2) only provide a exterior discussion on the changes of tidal wave, and ignored the physical nature of such phase advance phenomenon. Furthermore, your synthetic wave could not fit the theories M2 wave in Fig.7 and Fig.8, which means the fixed phase shift of leaky aquifer or fixed amplitude may not able to explain your observations.
Second, the tidal phase shift results showed in this manuscript is opposite with other published studies (Lai et al., 2014; Lai et al., 2016) , the phase shift of Lugu Lake(LGH in their paper) is around 10° before the Wenchuan earthquake, and increased to 10° after the earthquake. And it is unclear how you set the parameters in the tidal analysis, I am also not quite sure about the result from T_tide. The widely used tidal analysis programs are Baytap08, HALS method etc, I think you should rechecked your setting and the results.
Minor comments:
1. I cannot understand many terminology in your manuscript and I think you should pay much more attention about them. i.e. transcurrent recharge, transgressive aquifer, semi[pressurized aquifer and so on.....
2. I would strongly ask you to seek help from a native speaker to help you improve the language of this manuscript.
3. A borehole lithology is required to show the aquifer type of this well, where does the semiconfined layer exists? And also the hydrogeological setting of the study area should be presented.
4. Line 4344, borehole has no unconfined or confiend characteristics, here should be confined aquifer, and not unconfined aquifer, it is very difficut for the unconfined aquifer to record tidal signal.
5.Line 5354 groundwater level could record the tidal signal, but it also contains many other frequency comppoents of other signals.
6.Line 7576, there are already many studies discussed the phase lead.
7.Line 8085, there are papers that modeling the tidal response with real world data. (Zhang et al., 2023; Bastias Espejo et al., 2022)
positive fracture?
8.Figure 3, I would suggest to use the cpd in Xaxis.
9.Line 213, onedimensional wellaquifer structure, could you provide a figures to show this structure?
10.The conclusion section is too long and not clear, please reworded.
11.The innovation of the study should be reworded.
References:
Wang, C. Y., & Manga, M. (2023). Changes in Tidal and Barometric Response of Groundwater during Earthquakes—A Review with Recommendations for Better Management of Groundwater Resources. Water, 15(7), 1327.
Bastias Espejo, J. M., Rau, G. C., & Blum, P. (2022). Groundwater responses to Earth tides: Evaluation of analytical solutions using numerical simulation. Journal of Geophysical Research: Solid Earth, 127(10), e2022JB024771.
Valois, R., Rau, G. C., Vouillamoz, J. M., & Derode, B. (2022). Estimating hydraulic properties of the shallow subsurface using the groundwater response to Earth and atmospheric tides: A comparison with pumping tests. Water Resources Research, 58(5), e2021WR031666.
Gao, X., Sato, K., & Horne, R. N. (2020). General solution for tidal behavior in confined and semiconfined aquifers considering skin and wellbore storage effects. Water Resources Research, 56(6), e2020WR027195.
Lai, G., Ge, H., Xue, L., Brodsky, E. E., Huang, F., & Wang, W. (2014). Tidal response variation and recovery following the Wenchuan earthquake from water level data of multiple wells in the nearfield. Tectonophysics, 619, 115122.
Lai, G., Jiang, C., Han, L., Sheng, S., & Ma, Y. (2016). Coseismic water level changes in response to multiple large earthquakes at the LGH well in Sichuan, China. Tectonophysics, 679, 211217.
Zhang, J., Liang, X., & Wang, C. Y. (2023). Capillary Impact on Tidal Response of Groundwater in Unconfined Aquifers With Finite Thickness, Anisotropy and Wellbore Storage—An Analytical Model. Water Resources Research, 59(3), e2022WR033578.
Citation: https://doi.org/10.5194/egusphere20232816RC1 
AC1: 'Reply on RC1', Anhua He, 17 Feb 2024
Thank you very much for the comments from this anonymous reviewer. The public discussion has ended, and we will immediately revise the manuscript item by item based on these commetnss and respond accordingly. Thank you again.
Citation: https://doi.org/10.5194/egusphere20232816AC1 
AC2: 'Reply on RC1', Anhua He, 25 Feb 2024
We have made the modifications according to the comments and are currently inviting a professional translation company to make language improvements. Maybe need more 4 days.
Citation: https://doi.org/10.5194/egusphere20232816AC2 
AC3: 'We have reviesed the manusciprt and responed the comments', Anhua He, 28 Feb 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere20232816/egusphere20232816AC3supplement.pdf

AC1: 'Reply on RC1', Anhua He, 17 Feb 2024

RC2: 'Comment on egusphere20232816', Anonymous Referee #2, 12 Mar 2024
Review of: Analysis of phase lead "anomalies" in the tidal response of groundwater levels, Anhua He et al.
I  general comments
The manuscript “Analysis of phase lead "anomalies" in the tidal response of groundwater levels” analyses borehole piezometric level responses to solid earth tide and its evolution over time under the influence of earthquakes. The geological context is briefly presented (yet a borehole cross section would be welcome). The input data seem promising, and the signal analysis seems to be correctly carried out, yet the phase and amplitude evolutions are poorly presented, and some technical details of this analysis are omitted. Sadly, the subsequent analysis of the phase and amplitude with a physical model is absent and the remaining of the paper is misleading or at least does not bring the necessary arguments to justify the claims of the authors which could be interesting (about permeability evolution in particular).
The authors do not bring new modelling concepts or ideas and repeatedly designate positive phase lag observations as anomalies while they are today well modelled in different aquifer/aquitard geometries, see namely (Wang et al. 2018) (which is listed in the references but does not appear in the text). The fact that a positive phase lag is counterintuitive does not make it an “anomaly”; the authors should consider the scientific literature on the topic, (which is partly cited in the paper).
No physical model is given, except in equation 2, (yet it is not used), and the theoretical analysis (equation 5 and following) does not make sense to me and is disconnected from any physical process, which would be the necessary step here (in particular to justify the new fractures in the aquifer). The expectations of the readers (i.e. an explanation of the observed positive phase lags) are not met. In particular, the terms x1 & x2 (eq. 5) are not well defined and their association in eq 6 is unjustified. In the following, the meaning of parameters i & j are obscure and seem completely arbitrary. Therefore the interpretation of figure 7 and 8 are impossible.
Finally, the overall presentation of the paper and its organization are poor. The English language is frequently misused, some terms are not defined and their units omitted, the figures are too small and should present the data more appropriately and most importantly the “results” and “discussion” section should be re organized completely to only include results and discussion.
All of these comments are similar to the ones given by Anonymous Referee #1, and do not seem to have been answered to in the available manuscript.
II  specific comments
 line 50 the reference to Cooper model is not adapted here as the model was not designed for the response to tides initially.
 line 7075: I do not have access to the cited articles (Zhang et al., 1991; Zhou et al., 1993), which references are incomplete, so I cannot check the initial argument, yet the claim that the inelastic response of the aquifer system leads to a phase difference is wrong.
 Figure 4 presents input data, not results, it should be presented earlier in the paper.
 Equation 2 corresponds to a model and should not be presented in the discussion section but rather a methodology one. It is also wrong as the tidal source term is incorrect.
 aquitard should be used instead of “transgressive aquifer”
III  technical corrections
 some references in the reference section are not cited in the text, e.g.: Wang et al 2018, Wood et al 1973
 The authors may consider replacing the term “seepage”, used 4 times in the manuscript, by “flow”, as seepage is ambiguous given its usage in geotechnics. It should probably be kept to refer to unsaturated flow, and can here lead to reader confusion, especially in the abstract.
 line 22 “the theory of transcurrent recharge” is unclear
 line 3031 the phase should be expressed in degrees ° or radians rather than in minutes as minutes are ambiguous when no frequency is given.
 line 99 “the permeability coefficient“ expressed in “m/d” is unclear, is it a hydraulic conductivity in meters /day?
 line 115: 0.5 cpd (cycles per day) is clearer than 48h1
 Figure 3 : The figure should be enlarged, frequency units changed to cycles per day instead of cycles per hour, “greenwhich phase” is not defined: phase lags should be plotted instead of absolute phases of both signals.
 Table 2 is useless in the present form, only the main frequencies (significant ones) should be presented
Citation: https://doi.org/10.5194/egusphere20232816RC2 
AC4: 'Reply on RC2', Anhua He, 18 Mar 2024
Reviewer 2#
Review of: Analysis of phase lead "anomalies" in the tidal response of groundwater levels, Anhua He et al.
I  general comments
The manuscript “Analysis of phase lead "anomalies" in the tidal response of groundwater levels” analyses borehole piezometric level responses to solid earth tide and its evolution over time under the influence of earthquakes. The geological context is briefly presented (yet a borehole cross section would be welcome). The input data seem promising, and the signal analysis seems to be correctly carried out, yet the phase and amplitude evolutions are poorly presented, and some technical details of this analysis are omitted. Sadly, the subsequent analysis of the phase and amplitude with a physical model is absent and the remaining of the paper is misleading or at least does not bring the necessary arguments to justify the claims of the authors which could be interesting (about permeability evolution in particular).
Authors: Many thanks to the Referee for sparing valuable time in reading our manuscript. We appreciate constructive comments/suggestions of the Referee. We do agree with the comments of the Referee about the geological context, at the same time we do appreciate the positive comments of the Referee. Now we have revised the manuscript in the light of comments/suggestions of the Referee so that the our claims stated in the manuscript is clearly conveyed to the learned Referee and to the readers. We have taken care of the evolution of the permeability as pointed out by the learned Referee in particular. We hope that the learned Referee will be satisfied by our revised manuscript and our manuscript will be acceptable.
The authors do not bring new modelling concepts or ideas and repeatedly designate positive phase lag observations as anomalies while they are today well modelled in different aquifer/aquitard geometries, see namely (Wang et al. 2018) (which is listed in the references but does not appear in the text). The fact that a positive phase lag is counterintuitive does not make it an “anomaly”; the authors should consider the scientific literature on the topic, (which is partly cited in the paper).
No physical model is given, except in equation 2, (yet it is not used), and the theoretical analysis (equation 5 and following) does not make sense to me and is disconnected from any physical process, which would be the necessary step here (in particular to justify the new fractures in the aquifer). The expectations of the readers (i.e. an explanation of the observed positive phase lags) are not met. In particular, the terms x1 & x2 (eq. 5) are not well defined and their association in eq 6 is unjustified. In the following, the meaning of parameters i & j are obscure and seem completely arbitrary. Therefore the interpretation of figure 7 and 8 are impossible.
Finally, the overall presentation of the paper and its organization are poor. The English language is frequently misused, some terms are not defined and their units omitted, the figures are too small and should present the data more appropriately and most importantly the “results” and “discussion” section should be re organized completely to only include results and discussion.
All of these comments are similar to the ones given by Anonymous Referee #1, and do not seem to have been answered to in the available manuscript.
Authors: We have similar comments by the Referee #1, we do agree that our original manuscript was not very clear to the Referee, now we have provided a detailed borehole cross section, changed the calculating method from T_tide to FFT, added analysis of the phase and amplitude with a simple onedimensional wellaquifer model, and rewritten the conclusion section. We do agree that due to our limitations with the English language, our communication in original manuscript created some confusion. Now we have taken care of the English language and also taken help from a professional English translation company to improve the language. As pointed out by the Referee, we do agree that the phase advancement of water level to earth tide is not a completely new topic; many related papers have been published. We have read these papers carefully during the revision process and included these papers in the revised manuscript. In the Discussion section of the revised manuscript, we have analyzed the mechanism of phase lead through a simple onedimensional wellaquifer model. Restricted by current observational data and basic information, it is hard to provide a scientific answer to the question of quantifying the proportion of leaky aquifers and skin effects. We will submit our response at first. We are currently improving the English language by a professional English translation company and will be completed within one week.
II  specific comments
line 50 the reference to Cooper model is not adapted here as the model was not designed for the response to tides initially.
Authors: Many thanks to the Referee for the insightful suggestions. We supported the idea that “Cooper model was not designed for the response to tides initially”. However, we considered that Cooper model is a fundamental model for studying the relationship between groundwater activity and earthquakes, and kept this sentence mainly to introduce the following content.
line 7075: I do not have access to the cited articles (Zhang et al., 1991; Zhou et al., 1993), which references are incomplete, so I cannot check the initial argument, yet the claim that the inelastic response of the aquifer system leads to a phase difference is wrong.
Authors: This is an error in our expression. In the original manuscript, we discussed Chinese and international situations separately. Although many international studies have discussed the phase lead regarding this question, an ideal answer to this question has not been reported in China. In the revised manuscript, we have made modifications to this statement by deleting the research situation in China.
Figure 4 presents input data, not results, it should be presented earlier in the paper.
Authors: Many thanks to the learned Referee for good suggestion. We have moved Figure 4 and the corresponding context to the introduction section.
Equation 2 corresponds to a model and should not be presented in the discussion section but rather a methodology one. It is also wrong as the tidal source term is incorrect.
Authors: Very good suggestion. We have moved Equation 2 and the context to the methodology section. Regarding the tidal source term, Equation 2 uses the solid tidal body strain. We have included references as suggested by the Referee. This reference is a Chinese manuscript which hardly to access, so we have submitted it as attachment.
Zhang Z. D., Zheng J. H., Zhang G. C. (1995). Response function of well aquifer system to tide (in Chinese), Northwestern Seismological Journal, 17(3): 6671.
aquitard should be used instead of “transgressive aquifer”
Authors: This is indeed an error in the original manuscript. We have changed "transitional acquirer" to "leaky acquirer" by referring to relevant papers.
III  technical corrections
some references in the reference section are not cited in the text, e.g.: Wang et al 2018, Wood et al 1973
Authors: Many thanks for your suggestions, now we have included these references in the revised manuscript. We have checked each reference one by one.
The authors may consider replacing the term “seepage”, used 4 times in the manuscript, by “flow”, as seepage is ambiguous given its usage in geotechnics. It should probably be kept to refer to unsaturated flow, and can here lead to reader confusion, especially in the abstract.
Authors: The revised manuscript has been carefully checked, and we have taken help from a professional English translation company. We have deleted the term “seepage” in revised manuscript as suggested by the learned Referee.
line 22 “the theory of transcurrent recharge” is unclear
We have reworded following sentences as suggested by the learned Referee.
From:
Using the theory of transcurrent recharge, the seepage of aquifer water was decomposed into lateral and vertical transport, and the two kinds of "lagging" transport processes were superimposed to obtain the final groundwater level tidal response, which may appear as an anomalous phenomenon in which the phase is over the front after superposition.
To:
Using the theory of leakage recharge, the transfer of aquifer water was decomposed into horizontal and vertical transport and two kinds of "lagging" transport processes were superimposed to obtain the final groundwater level tidal response, which may resemble an anomalous phenomenon in which a phase lead occurs after superposition.
line 3031 the phase should be expressed in degrees ° or radians rather than in minutes as minutes are ambiguous when no frequency is given.
Authors: We have adopted radians in the revised manuscript as suggested by the Referee.
line 99 “the permeability coefficient“ expressed in “m/d” is unclear, is it a hydraulic conductivity in meters /day?
Authors: We have changed the “permeability coefficient” to “hydraulic conductivity” as suggested by the learned Referee
line 115: 0.5 cpd (cycles per day) is clearer than 48h1
Authors: Very good suggestion, 48h^{1} has been changed to 0.5 cpd.
Figure 3 : The figure should be enlarged, frequency units changed to cycles per day instead of cycles per hour, “greenwhich phase” is not defined: phase lags should be plotted instead of absolute phases of both signals.
Authors: Through our comparison of several methods (T_tide, Baytap08, HALS method, etc.), the results obtained by different calculation methods are almost identical except minor differences. According to the statement "Fourier analysis provides a robust means of estimating equilibrium conclusion status" (Turnadge et al., 2019), Fourier analysis has been directly used to calculate the tidal response parameters. Combining with the comments of Reviewer1, our calculation method was directly changed to FFT, so the original calculation process using the TTide tool has been deleted.
Table 2 is useless in the present form, only the main frequencies (significant ones) should be presented
Authors: Through our comparison of several methods (T_tide, Baytap08, HALS method, etc.), the results obtained by different calculation methods are almost identical except for minor differences. According to the statement "Fourier analysis provides a robust means of estimating equilibrium conclusion status" (Turnadge et al., 2019), Fourier analysis has been directly used to calculate the tidal response parameters. Combining the comments of Referees 1 and 2, our calculation method was directly changed to FFT, so the original calculation process using the TTide tool has been deleted.
We hope that the learned Referee will appreciate our efforts in revising the manuscript in the light of comments/suggestions of the Referee. We hope that the revised manuscript will be acceptable to the learned Referees.
Status: closed

RC1: 'Comment on egusphere20232816', Anonymous Referee #1, 22 Jan 2024
This manuscript documented a phase lead phenomenon of groundwater level in response ti earth tide and try to explain what the phase advance occur.
To be honest, I do not think the phase advance is new and unexplainable, and there are several published papers have dealt the issue (pelease refer to Barbour et al., 2019; Gao et al., 2020; Valois et al. 2023 .Wang et al. 2018 ....). In these papers, they discussed the changes of Taqu, Tcon, Saqu, Scon would have signficant impact on the phase shift. Such findings provide a basic physical mechanism of the phase shift. The discussion of your comniation of two siganls (x1, x2) only provide a exterior discussion on the changes of tidal wave, and ignored the physical nature of such phase advance phenomenon. Furthermore, your synthetic wave could not fit the theories M2 wave in Fig.7 and Fig.8, which means the fixed phase shift of leaky aquifer or fixed amplitude may not able to explain your observations.
Second, the tidal phase shift results showed in this manuscript is opposite with other published studies (Lai et al., 2014; Lai et al., 2016) , the phase shift of Lugu Lake(LGH in their paper) is around 10° before the Wenchuan earthquake, and increased to 10° after the earthquake. And it is unclear how you set the parameters in the tidal analysis, I am also not quite sure about the result from T_tide. The widely used tidal analysis programs are Baytap08, HALS method etc, I think you should rechecked your setting and the results.
Minor comments:
1. I cannot understand many terminology in your manuscript and I think you should pay much more attention about them. i.e. transcurrent recharge, transgressive aquifer, semi[pressurized aquifer and so on.....
2. I would strongly ask you to seek help from a native speaker to help you improve the language of this manuscript.
3. A borehole lithology is required to show the aquifer type of this well, where does the semiconfined layer exists? And also the hydrogeological setting of the study area should be presented.
4. Line 4344, borehole has no unconfined or confiend characteristics, here should be confined aquifer, and not unconfined aquifer, it is very difficut for the unconfined aquifer to record tidal signal.
5.Line 5354 groundwater level could record the tidal signal, but it also contains many other frequency comppoents of other signals.
6.Line 7576, there are already many studies discussed the phase lead.
7.Line 8085, there are papers that modeling the tidal response with real world data. (Zhang et al., 2023; Bastias Espejo et al., 2022)
positive fracture?
8.Figure 3, I would suggest to use the cpd in Xaxis.
9.Line 213, onedimensional wellaquifer structure, could you provide a figures to show this structure?
10.The conclusion section is too long and not clear, please reworded.
11.The innovation of the study should be reworded.
References:
Wang, C. Y., & Manga, M. (2023). Changes in Tidal and Barometric Response of Groundwater during Earthquakes—A Review with Recommendations for Better Management of Groundwater Resources. Water, 15(7), 1327.
Bastias Espejo, J. M., Rau, G. C., & Blum, P. (2022). Groundwater responses to Earth tides: Evaluation of analytical solutions using numerical simulation. Journal of Geophysical Research: Solid Earth, 127(10), e2022JB024771.
Valois, R., Rau, G. C., Vouillamoz, J. M., & Derode, B. (2022). Estimating hydraulic properties of the shallow subsurface using the groundwater response to Earth and atmospheric tides: A comparison with pumping tests. Water Resources Research, 58(5), e2021WR031666.
Gao, X., Sato, K., & Horne, R. N. (2020). General solution for tidal behavior in confined and semiconfined aquifers considering skin and wellbore storage effects. Water Resources Research, 56(6), e2020WR027195.
Lai, G., Ge, H., Xue, L., Brodsky, E. E., Huang, F., & Wang, W. (2014). Tidal response variation and recovery following the Wenchuan earthquake from water level data of multiple wells in the nearfield. Tectonophysics, 619, 115122.
Lai, G., Jiang, C., Han, L., Sheng, S., & Ma, Y. (2016). Coseismic water level changes in response to multiple large earthquakes at the LGH well in Sichuan, China. Tectonophysics, 679, 211217.
Zhang, J., Liang, X., & Wang, C. Y. (2023). Capillary Impact on Tidal Response of Groundwater in Unconfined Aquifers With Finite Thickness, Anisotropy and Wellbore Storage—An Analytical Model. Water Resources Research, 59(3), e2022WR033578.
Citation: https://doi.org/10.5194/egusphere20232816RC1 
AC1: 'Reply on RC1', Anhua He, 17 Feb 2024
Thank you very much for the comments from this anonymous reviewer. The public discussion has ended, and we will immediately revise the manuscript item by item based on these commetnss and respond accordingly. Thank you again.
Citation: https://doi.org/10.5194/egusphere20232816AC1 
AC2: 'Reply on RC1', Anhua He, 25 Feb 2024
We have made the modifications according to the comments and are currently inviting a professional translation company to make language improvements. Maybe need more 4 days.
Citation: https://doi.org/10.5194/egusphere20232816AC2 
AC3: 'We have reviesed the manusciprt and responed the comments', Anhua He, 28 Feb 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere20232816/egusphere20232816AC3supplement.pdf

AC1: 'Reply on RC1', Anhua He, 17 Feb 2024

RC2: 'Comment on egusphere20232816', Anonymous Referee #2, 12 Mar 2024
Review of: Analysis of phase lead "anomalies" in the tidal response of groundwater levels, Anhua He et al.
I  general comments
The manuscript “Analysis of phase lead "anomalies" in the tidal response of groundwater levels” analyses borehole piezometric level responses to solid earth tide and its evolution over time under the influence of earthquakes. The geological context is briefly presented (yet a borehole cross section would be welcome). The input data seem promising, and the signal analysis seems to be correctly carried out, yet the phase and amplitude evolutions are poorly presented, and some technical details of this analysis are omitted. Sadly, the subsequent analysis of the phase and amplitude with a physical model is absent and the remaining of the paper is misleading or at least does not bring the necessary arguments to justify the claims of the authors which could be interesting (about permeability evolution in particular).
The authors do not bring new modelling concepts or ideas and repeatedly designate positive phase lag observations as anomalies while they are today well modelled in different aquifer/aquitard geometries, see namely (Wang et al. 2018) (which is listed in the references but does not appear in the text). The fact that a positive phase lag is counterintuitive does not make it an “anomaly”; the authors should consider the scientific literature on the topic, (which is partly cited in the paper).
No physical model is given, except in equation 2, (yet it is not used), and the theoretical analysis (equation 5 and following) does not make sense to me and is disconnected from any physical process, which would be the necessary step here (in particular to justify the new fractures in the aquifer). The expectations of the readers (i.e. an explanation of the observed positive phase lags) are not met. In particular, the terms x1 & x2 (eq. 5) are not well defined and their association in eq 6 is unjustified. In the following, the meaning of parameters i & j are obscure and seem completely arbitrary. Therefore the interpretation of figure 7 and 8 are impossible.
Finally, the overall presentation of the paper and its organization are poor. The English language is frequently misused, some terms are not defined and their units omitted, the figures are too small and should present the data more appropriately and most importantly the “results” and “discussion” section should be re organized completely to only include results and discussion.
All of these comments are similar to the ones given by Anonymous Referee #1, and do not seem to have been answered to in the available manuscript.
II  specific comments
 line 50 the reference to Cooper model is not adapted here as the model was not designed for the response to tides initially.
 line 7075: I do not have access to the cited articles (Zhang et al., 1991; Zhou et al., 1993), which references are incomplete, so I cannot check the initial argument, yet the claim that the inelastic response of the aquifer system leads to a phase difference is wrong.
 Figure 4 presents input data, not results, it should be presented earlier in the paper.
 Equation 2 corresponds to a model and should not be presented in the discussion section but rather a methodology one. It is also wrong as the tidal source term is incorrect.
 aquitard should be used instead of “transgressive aquifer”
III  technical corrections
 some references in the reference section are not cited in the text, e.g.: Wang et al 2018, Wood et al 1973
 The authors may consider replacing the term “seepage”, used 4 times in the manuscript, by “flow”, as seepage is ambiguous given its usage in geotechnics. It should probably be kept to refer to unsaturated flow, and can here lead to reader confusion, especially in the abstract.
 line 22 “the theory of transcurrent recharge” is unclear
 line 3031 the phase should be expressed in degrees ° or radians rather than in minutes as minutes are ambiguous when no frequency is given.
 line 99 “the permeability coefficient“ expressed in “m/d” is unclear, is it a hydraulic conductivity in meters /day?
 line 115: 0.5 cpd (cycles per day) is clearer than 48h1
 Figure 3 : The figure should be enlarged, frequency units changed to cycles per day instead of cycles per hour, “greenwhich phase” is not defined: phase lags should be plotted instead of absolute phases of both signals.
 Table 2 is useless in the present form, only the main frequencies (significant ones) should be presented
Citation: https://doi.org/10.5194/egusphere20232816RC2 
AC4: 'Reply on RC2', Anhua He, 18 Mar 2024
Reviewer 2#
Review of: Analysis of phase lead "anomalies" in the tidal response of groundwater levels, Anhua He et al.
I  general comments
The manuscript “Analysis of phase lead "anomalies" in the tidal response of groundwater levels” analyses borehole piezometric level responses to solid earth tide and its evolution over time under the influence of earthquakes. The geological context is briefly presented (yet a borehole cross section would be welcome). The input data seem promising, and the signal analysis seems to be correctly carried out, yet the phase and amplitude evolutions are poorly presented, and some technical details of this analysis are omitted. Sadly, the subsequent analysis of the phase and amplitude with a physical model is absent and the remaining of the paper is misleading or at least does not bring the necessary arguments to justify the claims of the authors which could be interesting (about permeability evolution in particular).
Authors: Many thanks to the Referee for sparing valuable time in reading our manuscript. We appreciate constructive comments/suggestions of the Referee. We do agree with the comments of the Referee about the geological context, at the same time we do appreciate the positive comments of the Referee. Now we have revised the manuscript in the light of comments/suggestions of the Referee so that the our claims stated in the manuscript is clearly conveyed to the learned Referee and to the readers. We have taken care of the evolution of the permeability as pointed out by the learned Referee in particular. We hope that the learned Referee will be satisfied by our revised manuscript and our manuscript will be acceptable.
The authors do not bring new modelling concepts or ideas and repeatedly designate positive phase lag observations as anomalies while they are today well modelled in different aquifer/aquitard geometries, see namely (Wang et al. 2018) (which is listed in the references but does not appear in the text). The fact that a positive phase lag is counterintuitive does not make it an “anomaly”; the authors should consider the scientific literature on the topic, (which is partly cited in the paper).
No physical model is given, except in equation 2, (yet it is not used), and the theoretical analysis (equation 5 and following) does not make sense to me and is disconnected from any physical process, which would be the necessary step here (in particular to justify the new fractures in the aquifer). The expectations of the readers (i.e. an explanation of the observed positive phase lags) are not met. In particular, the terms x1 & x2 (eq. 5) are not well defined and their association in eq 6 is unjustified. In the following, the meaning of parameters i & j are obscure and seem completely arbitrary. Therefore the interpretation of figure 7 and 8 are impossible.
Finally, the overall presentation of the paper and its organization are poor. The English language is frequently misused, some terms are not defined and their units omitted, the figures are too small and should present the data more appropriately and most importantly the “results” and “discussion” section should be re organized completely to only include results and discussion.
All of these comments are similar to the ones given by Anonymous Referee #1, and do not seem to have been answered to in the available manuscript.
Authors: We have similar comments by the Referee #1, we do agree that our original manuscript was not very clear to the Referee, now we have provided a detailed borehole cross section, changed the calculating method from T_tide to FFT, added analysis of the phase and amplitude with a simple onedimensional wellaquifer model, and rewritten the conclusion section. We do agree that due to our limitations with the English language, our communication in original manuscript created some confusion. Now we have taken care of the English language and also taken help from a professional English translation company to improve the language. As pointed out by the Referee, we do agree that the phase advancement of water level to earth tide is not a completely new topic; many related papers have been published. We have read these papers carefully during the revision process and included these papers in the revised manuscript. In the Discussion section of the revised manuscript, we have analyzed the mechanism of phase lead through a simple onedimensional wellaquifer model. Restricted by current observational data and basic information, it is hard to provide a scientific answer to the question of quantifying the proportion of leaky aquifers and skin effects. We will submit our response at first. We are currently improving the English language by a professional English translation company and will be completed within one week.
II  specific comments
line 50 the reference to Cooper model is not adapted here as the model was not designed for the response to tides initially.
Authors: Many thanks to the Referee for the insightful suggestions. We supported the idea that “Cooper model was not designed for the response to tides initially”. However, we considered that Cooper model is a fundamental model for studying the relationship between groundwater activity and earthquakes, and kept this sentence mainly to introduce the following content.
line 7075: I do not have access to the cited articles (Zhang et al., 1991; Zhou et al., 1993), which references are incomplete, so I cannot check the initial argument, yet the claim that the inelastic response of the aquifer system leads to a phase difference is wrong.
Authors: This is an error in our expression. In the original manuscript, we discussed Chinese and international situations separately. Although many international studies have discussed the phase lead regarding this question, an ideal answer to this question has not been reported in China. In the revised manuscript, we have made modifications to this statement by deleting the research situation in China.
Figure 4 presents input data, not results, it should be presented earlier in the paper.
Authors: Many thanks to the learned Referee for good suggestion. We have moved Figure 4 and the corresponding context to the introduction section.
Equation 2 corresponds to a model and should not be presented in the discussion section but rather a methodology one. It is also wrong as the tidal source term is incorrect.
Authors: Very good suggestion. We have moved Equation 2 and the context to the methodology section. Regarding the tidal source term, Equation 2 uses the solid tidal body strain. We have included references as suggested by the Referee. This reference is a Chinese manuscript which hardly to access, so we have submitted it as attachment.
Zhang Z. D., Zheng J. H., Zhang G. C. (1995). Response function of well aquifer system to tide (in Chinese), Northwestern Seismological Journal, 17(3): 6671.
aquitard should be used instead of “transgressive aquifer”
Authors: This is indeed an error in the original manuscript. We have changed "transitional acquirer" to "leaky acquirer" by referring to relevant papers.
III  technical corrections
some references in the reference section are not cited in the text, e.g.: Wang et al 2018, Wood et al 1973
Authors: Many thanks for your suggestions, now we have included these references in the revised manuscript. We have checked each reference one by one.
The authors may consider replacing the term “seepage”, used 4 times in the manuscript, by “flow”, as seepage is ambiguous given its usage in geotechnics. It should probably be kept to refer to unsaturated flow, and can here lead to reader confusion, especially in the abstract.
Authors: The revised manuscript has been carefully checked, and we have taken help from a professional English translation company. We have deleted the term “seepage” in revised manuscript as suggested by the learned Referee.
line 22 “the theory of transcurrent recharge” is unclear
We have reworded following sentences as suggested by the learned Referee.
From:
Using the theory of transcurrent recharge, the seepage of aquifer water was decomposed into lateral and vertical transport, and the two kinds of "lagging" transport processes were superimposed to obtain the final groundwater level tidal response, which may appear as an anomalous phenomenon in which the phase is over the front after superposition.
To:
Using the theory of leakage recharge, the transfer of aquifer water was decomposed into horizontal and vertical transport and two kinds of "lagging" transport processes were superimposed to obtain the final groundwater level tidal response, which may resemble an anomalous phenomenon in which a phase lead occurs after superposition.
line 3031 the phase should be expressed in degrees ° or radians rather than in minutes as minutes are ambiguous when no frequency is given.
Authors: We have adopted radians in the revised manuscript as suggested by the Referee.
line 99 “the permeability coefficient“ expressed in “m/d” is unclear, is it a hydraulic conductivity in meters /day?
Authors: We have changed the “permeability coefficient” to “hydraulic conductivity” as suggested by the learned Referee
line 115: 0.5 cpd (cycles per day) is clearer than 48h1
Authors: Very good suggestion, 48h^{1} has been changed to 0.5 cpd.
Figure 3 : The figure should be enlarged, frequency units changed to cycles per day instead of cycles per hour, “greenwhich phase” is not defined: phase lags should be plotted instead of absolute phases of both signals.
Authors: Through our comparison of several methods (T_tide, Baytap08, HALS method, etc.), the results obtained by different calculation methods are almost identical except minor differences. According to the statement "Fourier analysis provides a robust means of estimating equilibrium conclusion status" (Turnadge et al., 2019), Fourier analysis has been directly used to calculate the tidal response parameters. Combining with the comments of Reviewer1, our calculation method was directly changed to FFT, so the original calculation process using the TTide tool has been deleted.
Table 2 is useless in the present form, only the main frequencies (significant ones) should be presented
Authors: Through our comparison of several methods (T_tide, Baytap08, HALS method, etc.), the results obtained by different calculation methods are almost identical except for minor differences. According to the statement "Fourier analysis provides a robust means of estimating equilibrium conclusion status" (Turnadge et al., 2019), Fourier analysis has been directly used to calculate the tidal response parameters. Combining the comments of Referees 1 and 2, our calculation method was directly changed to FFT, so the original calculation process using the TTide tool has been deleted.
We hope that the learned Referee will appreciate our efforts in revising the manuscript in the light of comments/suggestions of the Referee. We hope that the revised manuscript will be acceptable to the learned Referees.
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