the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Nov 2023
Firn Seismic Anisotropy in the North East Greenland Ice Stream from Ambient Noise Surface Waves
Abstract. We analyse ambient noise seismic data from 23 three-component seismic nodes to study firn velocity structure and seismic anisotropy near the EastGRIP camp along the Northeast Greenland Ice Stream (NEGIS). Using 9-component correlation tensors, we derive dispersion curves of Rayleigh and Love wave group velocities from 3 Hz to 40 Hz. These velocity distributions exhibit anisotropy along and across the flow. To assess these variations, we invert dispersion curves for shear wave velocities (Vsh and Vsv) in the top 150 m of NEGIS using a Markov Chain Monte Carlo approach. The reconstructed1-D shear velocity model reveals radial anisotropy in the firn, with Vsh 12 %–15 % greater than Vsv, peaking at the critical density (550 kg m–3). We combine density data from firn cores drilled in 2016 and 2018 to create a new density parameterisation for NEGIS, serving as a reference for our results. We link seismic anisotropy in the NEGIS to effective and intrinsic causes. Seasonal densification, wind crusts, and melt layers induce effective anisotropy, leading to faster Vsh waves. Changes in firn recrystalisation cause intrinsic anisotropy, altering the Vsv to Vsh ratio. We observe a shallower firn-ice transition across flow (≈ 50 m) compared to along flow (≈ 60 m), suggesting increased firn compaction due to the predominant wind direction and increased deformation towards the shear margin. We demonstrate that short-duration (nine-day minimum), passive, seismic deployments, and noise-based analysis can determine seismic anisotropy in firn, and reveal 2-D firn structure and variability.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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CC1: 'Comment on egusphere-2023-2192', Hanbing Ai, 03 Dec 2023
This paper is interesting and well-written. The authors analyzed ambient noise seismic data and picked the Rayleigh and Love wave group velocities in order to obtain the Vsv and Vsh structures. More interestingly, they obtained the radial anisotropy and analyzed the possible causes of the specific feature. I thus recommend publishing this work after the authors address some issues further:
Comment 1: Please check Line 40; the reference by Pearce et al. (2023) seems to have nothing to do with refraction data.
Comment 2: The core of this paper is the inversion of the picked Rayleigh and Love wave group velocities. As for the MCMC method, have you ever considered using the transdimensional MCMC method to solve the problem of priorly defining the layers? I mean, how to minimize the difference generated by models containing different layers?
Comment 3: The authors did not clearly explain the Vp and density models used for inverison, which makes it hard for readers to validate the results obtained. Table 1 only contains layer thicknesses, numbers, and Vs velocities.
Comment 4: How to convince readers that the retrieved difference between Vsv and Vsh is not caused by inversion uncertainty. I mean, if we perform the MCMC method multiple times, is the difference between Vsv and Vsh still the same or similar?
Comment 5: Please explain why the second-order information in Figures 5b and 5d ill-fitted the picked ones.
Comment 6: I suggest the authors perturb the velocity of Vsh and Vsv within 0~20 and 60~140, like 10%, to see whether the sensitivity exists or not (comparing the calculated group velocities).
Comment 7: I recommend the author calculate the Vp/Vs ratio to gain more insights (if possible).
Thank you.
Citation: https://doi.org/10.5194/egusphere-2023-2192-CC1 -
AC1: 'Reply on CC1', Emma Pearce, 08 Mar 2024
My co-authors and I thank Hanbing Ai for their review and community comments of our manuscript. In the following, we address point-by-point your concerns and outline the corrections we will make to our paper. We hope our replies and modifications are clear and satisfactory.
Comment 1: Please check Line 40; the reference by Pearce et al. (2023) seems to have nothing to do with refraction data.
- The paper referenced uses refraction data to image Firn.
Comment 2: The core of this paper is the inversion of the picked Rayleigh and Love wave group velocities. As for the MCMC method, have you ever considered using the transdimensional MCMC method to solve the problem of priorly defining the layers? I mean, how to minimize the difference generated by models containing different layers?
- This was not something we considered in this study, but will consider in future.
Comment 3: The authors did not clearly explain the Vp and density models used for inverison, which makes it hard for readers to validate the results obtained. Table 1 only contains layer thicknesses, numbers, and Vs velocities.
- VP and density are not used for the inversion, but rather are outputs of the MCMC inversion. We now explain clearer in the text how these models are obtained, and why we do not interpret them, as the Rayleigh and Love waves used for the inversion have poor sensitivity to Vp and density.
Comment 4: How to convince readers that the retrieved difference between Vsv and Vsh is not caused by inversion uncertainty. I mean, if we perform the MCMC method multiple times, is the difference between Vsv and Vsh still the same or similar?
- This is always something which might be possible, no matter if at 10, 1 or 0.1% confidence level. However, as we discussed the uncertainties we come to the conclusions as pointed out in the paper. In the revision, by incorporating the reviewers’ comments, we hope to be able to make this more clear.
Comment 5: Please explain why the second-order information in Figures 5b and 5d ill-fitted the picked ones.
- This will now be explained in the text.
Comment 6: I suggest the authors perturb the velocity of Vsh and Vsv within 0~20 and 60~140, like 10%, to see whether the sensitivity exists or not (comparing the calculated group velocities).
A . Thank you for your suggestion. We allow the MCMC inversion to explore a range of velocities between 400 and 1800 m/s, and therefore this has been accounted for in the modelling.
Comment 7: I recommend the author calculate the Vp/Vs ratio to gain more insights (if possible).
A. This is not possible since the Vp we obtain from the model is not reliable. This is now better explained in the text that we are not sensitive to Vp.
Citation: https://doi.org/10.5194/egusphere-2023-2192-AC1
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AC1: 'Reply on CC1', Emma Pearce, 08 Mar 2024
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RC1: 'Comment on egusphere-2023-2192', Anonymous Referee #1, 04 Dec 2023
Using ambient noise recording, the authors show seismic radial anisotropy of the firn layer in the North East Greenland Ice Stream. They pick the dispersion curves of Rayleigh and Love waves from the computed cross-correlations of ambient noise data and conduct 1D inversions. The difference between inverted Vsv and Vsh indicates the radial anisotropy of the target area. The results are similar to what we found in western Antarctica, although we used different inversion methods and focused on different areas. After reading the manuscript, I have the following concerns:
- The source of ambient noise. As you mentioned, the EastGRIP camp may provide the primary source for ambient noise recording. From Fig. 1c, it seems the incident noise are more parallel to Line 1 other than Line 5. Did you observe the difference between the computed crosscorrelations for Lines 1 and 5?
- Following the first question, the crosscorrelations shown in Fig3 have strong energies at zero lag. You mentioned the possibility of wind. I would like to know whether wind could cause such strong energy and whether this could affect the calculated Rayleigh or Love waves.
- In the inversion, you use group velocity dispersion curves. How about the phase velocity? The picking shown in Fig 5 is misleading as nondispersive body S waves have been picked at high freqs.
- The radial anisotropy below 60m shown in Fig 7 is reaching zero. Is this caused by the reduced sensitivity of surface waves?
- Fig 9 could be moved to the data processing section.
- A typo of 'fig. AA1' in line 225.
- Line 210, 'an averaged 2D velocity' I'm confused since I only saw 1D profiles.
Citation: https://doi.org/10.5194/egusphere-2023-2192-RC1 -
AC2: 'Reply on RC1', Emma Pearce, 08 Mar 2024
My co-authors and I thank the anonymous reviewers and editor for careful analysis of our manuscript. In the following, we address point-by-point the concerns and outline the corrections we will make to our paper. We hope our replies and modifications are clear and satisfactory and we will get approval to go ahead with the revision.
Regards, Emma Pearce on behalf of all co-authors
- The source of ambient noise. As you mentioned, the EastGRIP camp may provide the primary source for ambient noise recording. From Fig. 1c, it seems the incident noise are more parallel to Line 1 other than Line 5. Did you observe the difference between the computed cross correlations for Lines 1 and 5?
The camp is not more parallel to line 1, only the runway has a direction and orientation which is orientated approximately 45 degrees between the two lines. Planes did not land when the ambient noise data were being recorded, we therefore assume that the camps orientation has no impact on the cross correlations. We did observe a difference between the computed cross correlations for line 1 and 5, but this is attributed to the variations in the ice stream. We will make this clearer in the new version of the manuscript.
- Following the first question, the crosscorrelations shown in Fig3 have strong energies at zero lag. You mentioned the possibility of wind. I would like to know whether wind could cause such strong energy and whether this could affect the calculated Rayleigh or Love waves.
The Zero lag cross correlations are attributed to wind since the previous season in 2019, seismometers were deployed without the use of bamboo and this feature is not seen. In the 2022 season, bamboos were placed less than 3 m from the same seismometers for relocation purposes and this feature appeared. Nothing else in the deployment was changed. The energy at zero lag is not used in the calculations of the cross correlations, a taper is applied to the data to remove the impact of this feature. Hence, no effect on the calculated love or Rayleigh waves is observed. In addition, this zero-lag feature has a frequency different from the one use to analyse the surfaces waves. - In the inversion, you use group velocity dispersion curves. How about the phase velocity? The picking shown in Fig 5 is misleading as nondispersive body S waves have been picked at high freqs.
We used group velocity to avoid dealing with 2 Pi jumps in the phase velocity estimations that are sometimes annoying to correct on noise cross correlations. The nondispersive S waves are indeed present in Fig. 5 and we agree with the reviewer that our figure is misleading here. We will correct that in the revised version.
- The radial anisotropy below 60m shown in Fig 7 is reaching zero. Is this caused by the reduced sensitivity of surface waves?
In general, the sensitivity below 60 to 70m starts to decrease fast. We present the sensitivity diagram for Love and Rayleigh in appendix figure 1A and they show that for our available frequencies, we have sensitivity from our data to depths of 80-100 m. Based on those diagrams and even if the sensitivity starts to decrease at 60m depth, it seems clear that the radial anisotropy is low after crossing the firn/ice transition. - Fig 9 could be moved to the data processing section.
we thank the reviewer for their suggestion, but opt to keep figure 9 in the same location since it is independent of the noise correlation data processing.
- A typo of 'fig. AA1' in line 225.
We will alter this typo in the reviewed document. - Line 210, 'an averaged 2D velocity' I'm confused since I only saw 1D profiles.
You are correct, the text will be changed to 1-D.
Citation: https://doi.org/10.5194/egusphere-2023-2192-AC2 - The source of ambient noise. As you mentioned, the EastGRIP camp may provide the primary source for ambient noise recording. From Fig. 1c, it seems the incident noise are more parallel to Line 1 other than Line 5. Did you observe the difference between the computed cross correlations for Lines 1 and 5?
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RC2: 'Comment on egusphere-2023-2192', Stefano Picotti, 21 Dec 2023
Enclosed please find my review.
Regards, SP
-
AC3: 'Reply on RC2', Emma Pearce, 08 Mar 2024
My co-authors and I thank Stefano Picotti for their careful analysis of our manuscript. In the following, we address point-by-point the concerns and outline the corrections we will make to our paper. We hope our replies and modifications are clear and satisfactory and we will get approval to go ahead with the revision.
Regards, Emma Pearce, on behalf of all co-authors.
Major concerns:
1- Lines 125-129 : This is an interesting hypothesis, but not enough supported. Could you please add some references?
A. We will add references related to this.2- Lines 160-161 : “To avoid anomalous measurements, we further remove the frequencies for which the dispersion measurements look anomalous. The remaining values selected for the inversion are presented as orange curves”. Could you please better explain the removal criteria?
A. This will be changed, and will read “To avoid non representative dispersion measurements, we do not include modes higher than mode 3, since our dispersion curves at this point are not distinctive enough to establish which mode they represent. The criteria used to select the modes used were based on the gradient of the mode always decreasing.3- The orange curves in Figures 4 and 5 represent the smoothed values used as the input for MCMC inversion. I noticed that in some cases these curves are quite different than the original picking of the maximum group velocities. Why? How much does this difference affect the final results? I have the impression that this mismatch is important.
A. We thank the reviewer for pointing this. We propose to address this point in the resubmission by presenting better the sensitivity of the output models to the used dispersions. In the current version we used a smoothed average dispersion for simplicity, but this choice can be better explained which we will do in a new version of the manuscript.
4. Could you please explain why you used group velocities instead phase velocities (Figures 4 and 5)?
A. We used group velocity to avoid dealing with 2 Pi jumps in the phase velocity estimations that are sometimes annoying to correct on noise cross correlations.5. To my opinion data parametrization for MCTC could be better explained. Table 1 shows 6 layers and S-wave velocities ranging between 0.1 and 1.9 km/s for all layers. However, the authors do not justify these choices. In particular, why so wide ranges for the Vs at all depths? Have the authors considered to better constrain the S-wave velocities versus depth? For example, by using the density profile and the empirical relationship from Diez et al. (2016). Then, it is unclear whether the densities (Figure 6) were actually used in the inversion procedure. If density effects were ignored, how much this approximation affects the final uncertainties?
A. The choice of velocity range for the inversion is based on the range of possible velocities that exist for snow and ice. The wide range is kept to avoid prior constraints on the inversion. Since the transition of firn to ice is a relatively fast process with a large velocity gradient, it is important to allow all possible velocities for depths in order to not pre condition the inversion. Densities were not used during the inversion since it is not possible to obtain them independently prior to the inversion. If Vp were recorded from refraction seismic, then this could be used to pre condition the density measurements, but in this instance, that was not the case.
6- P waves were never mentioned in the article, which suggests that the contribution of P waves was likely ignored in the inversion. Again, how much this approximation affects the final uncertainties? Although Rayleigh waves weakly depend on P waves, I think that the authors should relate uncertainties of the inverted Vsv wave velocities also to the P to S wave velocity ratio. However, P waves can be easily modeled by using, for example, the density profile and the empirical relationship from Kohnen (1972), and can be included in the inversion.
A. As state by the reviewer, the sensitivity of surface waves to P wave is low. As a result, constraining P wave velocity with our dataset is difficult. However, we now will include a sentence explaining why P waves are not used in this inversion, and mention the uncertainties that this will cause.
7- The computed differences between Vsv and Vsh are small if compared to uncertainties. In the along flow direction, this difference is below the experimental error, with the error bars overlapping, i.e., the two curves are almost identical. Have the above approximations (i.e., ignoring density and P-wave effects) already considered in the estimation of uncertainties? The estimated weak anisotropy is already at the limit of detection threshold. My main concern is that even larger uncertainties may lead to indistinguishable Vsv and Vsh curves, and to a negligible anisotropy.
A. The current uncertainty and inversion is independent to the effects of density and p-wave velocity. Even if incorporating P-wave velocity of density information in the inversions can reduce our final error bars, with don’t have such information available. We therefore decided to use only what is provided by the data. As such, although the current uncertainty is at the limit of detection, we are confident in our interpretation that the variation is due to radial anisotropy and not uncertainty. Note also that the level of firn of anisotropy that we report here is typical for ice sheet/stream as stated in our paper and confirmed by both reviewers.
8- The error bars are larger between 20 and 60 m, and thinner above and below this depth interval. Moreover, errors are similar at surface and at the firn bottom. Since the deeper parts of the firn column are excited by the lowest frequencies, which have the largest uncertainties (the gray bands in Figures 4 and 5 are very wide below 5 Hz), one expects errors increasing with depth. Could the authors comment on that?
A. The error bars are dependent on the number of measurements at each frequency and the consistency of those measurements. It is true that the error are relatively large for low frequencies, however, despite those large errors, most models converge toward the 1800 m/s S waves velocity because such velocities are needed to fit sharp increase of surface waves velocity at low frequencies. A s results, despite the errors, the variability of the proposed models for large depth is lower than for shallower depths.9- Following points 7 and 8, the sensitivities shown in Figure A1 looks quite different for Rayleigh and Love waves. Thus, the inversion reliability is different for the two wave types and changes vs. depth. Could you comment on this? The authors should be more specific about the depth interval in which the estimation of the anisotropy is actually reliable.
A. In a layered earth model, Rayleigh and Love wave phase velocities have different sensitivities in response to the change of S-wave velocity of the same layer. We will now comment on this in the text explaining why the sensitivities are different for the same frequency bands. In our discussion, we will highlight further where our sensitivity is good and bad, hence allowing the reliability of the results to be clearly identified.
10- Lines 207-208 : "The terms of that covariance matrix are adjusted along the inversion to stabilize the acceptance ratio around 25%". Could you please expand this sentence please?
A. This will now be further explained in the text.
Minor comments1 – Line 138: Signal-to-Noise ratio (SNR).
2 - Line 205 : (Herrmann, 2013) is redundant.
A- Both minor comments will be addressed in the corrected manuscript.Citation: https://doi.org/10.5194/egusphere-2023-2192-AC3
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AC3: 'Reply on RC2', Emma Pearce, 08 Mar 2024
Interactive discussion
Status: closed
-
CC1: 'Comment on egusphere-2023-2192', Hanbing Ai, 03 Dec 2023
This paper is interesting and well-written. The authors analyzed ambient noise seismic data and picked the Rayleigh and Love wave group velocities in order to obtain the Vsv and Vsh structures. More interestingly, they obtained the radial anisotropy and analyzed the possible causes of the specific feature. I thus recommend publishing this work after the authors address some issues further:
Comment 1: Please check Line 40; the reference by Pearce et al. (2023) seems to have nothing to do with refraction data.
Comment 2: The core of this paper is the inversion of the picked Rayleigh and Love wave group velocities. As for the MCMC method, have you ever considered using the transdimensional MCMC method to solve the problem of priorly defining the layers? I mean, how to minimize the difference generated by models containing different layers?
Comment 3: The authors did not clearly explain the Vp and density models used for inverison, which makes it hard for readers to validate the results obtained. Table 1 only contains layer thicknesses, numbers, and Vs velocities.
Comment 4: How to convince readers that the retrieved difference between Vsv and Vsh is not caused by inversion uncertainty. I mean, if we perform the MCMC method multiple times, is the difference between Vsv and Vsh still the same or similar?
Comment 5: Please explain why the second-order information in Figures 5b and 5d ill-fitted the picked ones.
Comment 6: I suggest the authors perturb the velocity of Vsh and Vsv within 0~20 and 60~140, like 10%, to see whether the sensitivity exists or not (comparing the calculated group velocities).
Comment 7: I recommend the author calculate the Vp/Vs ratio to gain more insights (if possible).
Thank you.
Citation: https://doi.org/10.5194/egusphere-2023-2192-CC1 -
AC1: 'Reply on CC1', Emma Pearce, 08 Mar 2024
My co-authors and I thank Hanbing Ai for their review and community comments of our manuscript. In the following, we address point-by-point your concerns and outline the corrections we will make to our paper. We hope our replies and modifications are clear and satisfactory.
Comment 1: Please check Line 40; the reference by Pearce et al. (2023) seems to have nothing to do with refraction data.
- The paper referenced uses refraction data to image Firn.
Comment 2: The core of this paper is the inversion of the picked Rayleigh and Love wave group velocities. As for the MCMC method, have you ever considered using the transdimensional MCMC method to solve the problem of priorly defining the layers? I mean, how to minimize the difference generated by models containing different layers?
- This was not something we considered in this study, but will consider in future.
Comment 3: The authors did not clearly explain the Vp and density models used for inverison, which makes it hard for readers to validate the results obtained. Table 1 only contains layer thicknesses, numbers, and Vs velocities.
- VP and density are not used for the inversion, but rather are outputs of the MCMC inversion. We now explain clearer in the text how these models are obtained, and why we do not interpret them, as the Rayleigh and Love waves used for the inversion have poor sensitivity to Vp and density.
Comment 4: How to convince readers that the retrieved difference between Vsv and Vsh is not caused by inversion uncertainty. I mean, if we perform the MCMC method multiple times, is the difference between Vsv and Vsh still the same or similar?
- This is always something which might be possible, no matter if at 10, 1 or 0.1% confidence level. However, as we discussed the uncertainties we come to the conclusions as pointed out in the paper. In the revision, by incorporating the reviewers’ comments, we hope to be able to make this more clear.
Comment 5: Please explain why the second-order information in Figures 5b and 5d ill-fitted the picked ones.
- This will now be explained in the text.
Comment 6: I suggest the authors perturb the velocity of Vsh and Vsv within 0~20 and 60~140, like 10%, to see whether the sensitivity exists or not (comparing the calculated group velocities).
A . Thank you for your suggestion. We allow the MCMC inversion to explore a range of velocities between 400 and 1800 m/s, and therefore this has been accounted for in the modelling.
Comment 7: I recommend the author calculate the Vp/Vs ratio to gain more insights (if possible).
A. This is not possible since the Vp we obtain from the model is not reliable. This is now better explained in the text that we are not sensitive to Vp.
Citation: https://doi.org/10.5194/egusphere-2023-2192-AC1
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AC1: 'Reply on CC1', Emma Pearce, 08 Mar 2024
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RC1: 'Comment on egusphere-2023-2192', Anonymous Referee #1, 04 Dec 2023
Using ambient noise recording, the authors show seismic radial anisotropy of the firn layer in the North East Greenland Ice Stream. They pick the dispersion curves of Rayleigh and Love waves from the computed cross-correlations of ambient noise data and conduct 1D inversions. The difference between inverted Vsv and Vsh indicates the radial anisotropy of the target area. The results are similar to what we found in western Antarctica, although we used different inversion methods and focused on different areas. After reading the manuscript, I have the following concerns:
- The source of ambient noise. As you mentioned, the EastGRIP camp may provide the primary source for ambient noise recording. From Fig. 1c, it seems the incident noise are more parallel to Line 1 other than Line 5. Did you observe the difference between the computed crosscorrelations for Lines 1 and 5?
- Following the first question, the crosscorrelations shown in Fig3 have strong energies at zero lag. You mentioned the possibility of wind. I would like to know whether wind could cause such strong energy and whether this could affect the calculated Rayleigh or Love waves.
- In the inversion, you use group velocity dispersion curves. How about the phase velocity? The picking shown in Fig 5 is misleading as nondispersive body S waves have been picked at high freqs.
- The radial anisotropy below 60m shown in Fig 7 is reaching zero. Is this caused by the reduced sensitivity of surface waves?
- Fig 9 could be moved to the data processing section.
- A typo of 'fig. AA1' in line 225.
- Line 210, 'an averaged 2D velocity' I'm confused since I only saw 1D profiles.
Citation: https://doi.org/10.5194/egusphere-2023-2192-RC1 -
AC2: 'Reply on RC1', Emma Pearce, 08 Mar 2024
My co-authors and I thank the anonymous reviewers and editor for careful analysis of our manuscript. In the following, we address point-by-point the concerns and outline the corrections we will make to our paper. We hope our replies and modifications are clear and satisfactory and we will get approval to go ahead with the revision.
Regards, Emma Pearce on behalf of all co-authors
- The source of ambient noise. As you mentioned, the EastGRIP camp may provide the primary source for ambient noise recording. From Fig. 1c, it seems the incident noise are more parallel to Line 1 other than Line 5. Did you observe the difference between the computed cross correlations for Lines 1 and 5?
The camp is not more parallel to line 1, only the runway has a direction and orientation which is orientated approximately 45 degrees between the two lines. Planes did not land when the ambient noise data were being recorded, we therefore assume that the camps orientation has no impact on the cross correlations. We did observe a difference between the computed cross correlations for line 1 and 5, but this is attributed to the variations in the ice stream. We will make this clearer in the new version of the manuscript.
- Following the first question, the crosscorrelations shown in Fig3 have strong energies at zero lag. You mentioned the possibility of wind. I would like to know whether wind could cause such strong energy and whether this could affect the calculated Rayleigh or Love waves.
The Zero lag cross correlations are attributed to wind since the previous season in 2019, seismometers were deployed without the use of bamboo and this feature is not seen. In the 2022 season, bamboos were placed less than 3 m from the same seismometers for relocation purposes and this feature appeared. Nothing else in the deployment was changed. The energy at zero lag is not used in the calculations of the cross correlations, a taper is applied to the data to remove the impact of this feature. Hence, no effect on the calculated love or Rayleigh waves is observed. In addition, this zero-lag feature has a frequency different from the one use to analyse the surfaces waves. - In the inversion, you use group velocity dispersion curves. How about the phase velocity? The picking shown in Fig 5 is misleading as nondispersive body S waves have been picked at high freqs.
We used group velocity to avoid dealing with 2 Pi jumps in the phase velocity estimations that are sometimes annoying to correct on noise cross correlations. The nondispersive S waves are indeed present in Fig. 5 and we agree with the reviewer that our figure is misleading here. We will correct that in the revised version.
- The radial anisotropy below 60m shown in Fig 7 is reaching zero. Is this caused by the reduced sensitivity of surface waves?
In general, the sensitivity below 60 to 70m starts to decrease fast. We present the sensitivity diagram for Love and Rayleigh in appendix figure 1A and they show that for our available frequencies, we have sensitivity from our data to depths of 80-100 m. Based on those diagrams and even if the sensitivity starts to decrease at 60m depth, it seems clear that the radial anisotropy is low after crossing the firn/ice transition. - Fig 9 could be moved to the data processing section.
we thank the reviewer for their suggestion, but opt to keep figure 9 in the same location since it is independent of the noise correlation data processing.
- A typo of 'fig. AA1' in line 225.
We will alter this typo in the reviewed document. - Line 210, 'an averaged 2D velocity' I'm confused since I only saw 1D profiles.
You are correct, the text will be changed to 1-D.
Citation: https://doi.org/10.5194/egusphere-2023-2192-AC2 - The source of ambient noise. As you mentioned, the EastGRIP camp may provide the primary source for ambient noise recording. From Fig. 1c, it seems the incident noise are more parallel to Line 1 other than Line 5. Did you observe the difference between the computed cross correlations for Lines 1 and 5?
-
RC2: 'Comment on egusphere-2023-2192', Stefano Picotti, 21 Dec 2023
Enclosed please find my review.
Regards, SP
-
AC3: 'Reply on RC2', Emma Pearce, 08 Mar 2024
My co-authors and I thank Stefano Picotti for their careful analysis of our manuscript. In the following, we address point-by-point the concerns and outline the corrections we will make to our paper. We hope our replies and modifications are clear and satisfactory and we will get approval to go ahead with the revision.
Regards, Emma Pearce, on behalf of all co-authors.
Major concerns:
1- Lines 125-129 : This is an interesting hypothesis, but not enough supported. Could you please add some references?
A. We will add references related to this.2- Lines 160-161 : “To avoid anomalous measurements, we further remove the frequencies for which the dispersion measurements look anomalous. The remaining values selected for the inversion are presented as orange curves”. Could you please better explain the removal criteria?
A. This will be changed, and will read “To avoid non representative dispersion measurements, we do not include modes higher than mode 3, since our dispersion curves at this point are not distinctive enough to establish which mode they represent. The criteria used to select the modes used were based on the gradient of the mode always decreasing.3- The orange curves in Figures 4 and 5 represent the smoothed values used as the input for MCMC inversion. I noticed that in some cases these curves are quite different than the original picking of the maximum group velocities. Why? How much does this difference affect the final results? I have the impression that this mismatch is important.
A. We thank the reviewer for pointing this. We propose to address this point in the resubmission by presenting better the sensitivity of the output models to the used dispersions. In the current version we used a smoothed average dispersion for simplicity, but this choice can be better explained which we will do in a new version of the manuscript.
4. Could you please explain why you used group velocities instead phase velocities (Figures 4 and 5)?
A. We used group velocity to avoid dealing with 2 Pi jumps in the phase velocity estimations that are sometimes annoying to correct on noise cross correlations.5. To my opinion data parametrization for MCTC could be better explained. Table 1 shows 6 layers and S-wave velocities ranging between 0.1 and 1.9 km/s for all layers. However, the authors do not justify these choices. In particular, why so wide ranges for the Vs at all depths? Have the authors considered to better constrain the S-wave velocities versus depth? For example, by using the density profile and the empirical relationship from Diez et al. (2016). Then, it is unclear whether the densities (Figure 6) were actually used in the inversion procedure. If density effects were ignored, how much this approximation affects the final uncertainties?
A. The choice of velocity range for the inversion is based on the range of possible velocities that exist for snow and ice. The wide range is kept to avoid prior constraints on the inversion. Since the transition of firn to ice is a relatively fast process with a large velocity gradient, it is important to allow all possible velocities for depths in order to not pre condition the inversion. Densities were not used during the inversion since it is not possible to obtain them independently prior to the inversion. If Vp were recorded from refraction seismic, then this could be used to pre condition the density measurements, but in this instance, that was not the case.
6- P waves were never mentioned in the article, which suggests that the contribution of P waves was likely ignored in the inversion. Again, how much this approximation affects the final uncertainties? Although Rayleigh waves weakly depend on P waves, I think that the authors should relate uncertainties of the inverted Vsv wave velocities also to the P to S wave velocity ratio. However, P waves can be easily modeled by using, for example, the density profile and the empirical relationship from Kohnen (1972), and can be included in the inversion.
A. As state by the reviewer, the sensitivity of surface waves to P wave is low. As a result, constraining P wave velocity with our dataset is difficult. However, we now will include a sentence explaining why P waves are not used in this inversion, and mention the uncertainties that this will cause.
7- The computed differences between Vsv and Vsh are small if compared to uncertainties. In the along flow direction, this difference is below the experimental error, with the error bars overlapping, i.e., the two curves are almost identical. Have the above approximations (i.e., ignoring density and P-wave effects) already considered in the estimation of uncertainties? The estimated weak anisotropy is already at the limit of detection threshold. My main concern is that even larger uncertainties may lead to indistinguishable Vsv and Vsh curves, and to a negligible anisotropy.
A. The current uncertainty and inversion is independent to the effects of density and p-wave velocity. Even if incorporating P-wave velocity of density information in the inversions can reduce our final error bars, with don’t have such information available. We therefore decided to use only what is provided by the data. As such, although the current uncertainty is at the limit of detection, we are confident in our interpretation that the variation is due to radial anisotropy and not uncertainty. Note also that the level of firn of anisotropy that we report here is typical for ice sheet/stream as stated in our paper and confirmed by both reviewers.
8- The error bars are larger between 20 and 60 m, and thinner above and below this depth interval. Moreover, errors are similar at surface and at the firn bottom. Since the deeper parts of the firn column are excited by the lowest frequencies, which have the largest uncertainties (the gray bands in Figures 4 and 5 are very wide below 5 Hz), one expects errors increasing with depth. Could the authors comment on that?
A. The error bars are dependent on the number of measurements at each frequency and the consistency of those measurements. It is true that the error are relatively large for low frequencies, however, despite those large errors, most models converge toward the 1800 m/s S waves velocity because such velocities are needed to fit sharp increase of surface waves velocity at low frequencies. A s results, despite the errors, the variability of the proposed models for large depth is lower than for shallower depths.9- Following points 7 and 8, the sensitivities shown in Figure A1 looks quite different for Rayleigh and Love waves. Thus, the inversion reliability is different for the two wave types and changes vs. depth. Could you comment on this? The authors should be more specific about the depth interval in which the estimation of the anisotropy is actually reliable.
A. In a layered earth model, Rayleigh and Love wave phase velocities have different sensitivities in response to the change of S-wave velocity of the same layer. We will now comment on this in the text explaining why the sensitivities are different for the same frequency bands. In our discussion, we will highlight further where our sensitivity is good and bad, hence allowing the reliability of the results to be clearly identified.
10- Lines 207-208 : "The terms of that covariance matrix are adjusted along the inversion to stabilize the acceptance ratio around 25%". Could you please expand this sentence please?
A. This will now be further explained in the text.
Minor comments1 – Line 138: Signal-to-Noise ratio (SNR).
2 - Line 205 : (Herrmann, 2013) is redundant.
A- Both minor comments will be addressed in the corrected manuscript.Citation: https://doi.org/10.5194/egusphere-2023-2192-AC3
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AC3: 'Reply on RC2', Emma Pearce, 08 Mar 2024
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Dimitri Zigone
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