Improving the quality of empirical Green's functions, obtained by cross-correlation of high-frequency ambient seismic noise

Afonin, Nikita; Kozlovskaya, Elena; Nevalainen, Jouni; Narkilahti, Janne

doi:https://doi.org/10.5194/se-10-1621-2019

Articles | Volume 10, issue 5

https://doi.org/10.5194/se-10-1621-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Special issue:

Advances in seismic imaging across the scales

https://doi.org/10.5194/se-10-1621-2019

© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 10, issue 5

Research article

|

02 Oct 2019

Research article |

| 02 Oct 2019

Improving the quality of empirical Green's functions, obtained by cross-correlation of high-frequency ambient seismic noise

Nikita Afonin, Elena Kozlovskaya, Jouni Nevalainen, and Janne Narkilahti

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Final revised paper (published on 02 Oct 2019)
Preprint (discussion started on 11 Feb 2019)

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AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'Review of: Improving quality of empirical Greens functions, obtained by cross-correlation of high-frequency ambient seismic noise', Anonymous Referee #1, 05 Mar 2019
- AC1: 'Replies to review Anonymous Referee #1', Nikita Afonin, 01 May 2019
SC1: 'S/N ratio stacking vs coherency', Michał Chamarczuk, 02 Apr 2019
- AC2: 'Replies to review of Michał Chamarczuk', Nikita Afonin, 01 May 2019
RC2: 'Review of Improving quality of empirical Greens functions, obtained by cross-correlation of high-frequency ambient seismic noise', Anonymous Referee #2, 02 Apr 2019
- AC3: 'Replies to review of Anonymous Referee #2', Nikita Afonin, 01 May 2019

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Nikita Afonin on behalf of the Authors (28 May 2019)

ED: Referee Nomination & Report Request started (08 Jul 2019) by Nicholas Rawlinson

RR by Anonymous Referee #1 (10 Jul 2019)

RR by Anonymous Referee #2 (04 Aug 2019)

Suggestions for revision or reasons for rejection

Thanks for the last corrections and additions. The manuscript and the English usage has improved a bit; however, there is still much room for improvements and main issues have not been solved. In particular, the introduction has to improve a lot to allow the reader to put your method in context and to clearly know the similarities and the differences with existing alternative methods. In addition to field data examples, synthetic examples and comparisons with conventionally used methods are often essential to illustrate the key contributions.

MAIN COMMENTS

The third paragraph of the introduction (Pg. 2, lines 9-27) has several errors and some parts are misleading.

• Line 16: The time-frequency phase weighted stack (tf-PWS) was introduced by Baig et al. (2009) and Schimmel et al. (2011). Li et al. (2017) study the errors that some inverse S-transforms may introduce on subsequent phase-velocity measurements.

• I have to insist Li et al. (2017) should be Li et al. (2018), doi: 10.1093/gji/ggx448 . Although Advance Access publication dates from October 2017, the official publication date is from February 2018. I will use Li et al. (2017) below to avoid confusion.

• As its name indicates, the time-frequency phase weighted stack studied by Li et al. (2017) is using stacking in the time-frequency domain not the frequency domain.

• Line 17: The time-scale phase weighted stacking from Ventosa et al. (2017) is not using stacking in the domain. It works on the time-frequency domain, as the tf-PWS, using the wavelet transform instead of the S-transform.

• Line 17-19: This sentence has not much sense. Coherence can be written as a function signal-to-noise ratio (SNR). In order to improve SNR, the tf-PWS methods focus on weighting the components of the cross-correlation function (in seismic ambient noise applications) represented on the time-frequency domain in function of their coherence. I agree on that all cross-correlation are weighted equally. However, in conventional processing flows, anomalous cross-correlation are discarded in advance or in a second iteration. For example, Boué et al. (2015) classify day-long cross-correlation in high- and low-coherence days according to its coherence with the stack of one year of day-long cross-correlations and then stack them linearly. In addition, 1-bit amplitude normalization followed by cross-correlation, normalized cross-correlation or phase cross-correlation (PCC) methods contributed to severely improve the quality of the resulting EGFs by weighting signals instantaneously (1-bit & PCC) or per pair (normalized cross-correlation). Consequently, (1) it is not correct saying that these methods do not analyze SNR, and (2) it is not important that "ALL non-suitable cross-correlation functions are excluded from the final stack" as long as there are a subset of cross-correlation functions that contributes to the "final stack" with enough energy to be able to detect the signals under study.

• Line 19-21: In teleseismic coda-wave interferometry the source is known indeed. Conventionally, only a few hours of data are cross-correlated at once. As the source is an earthquake using the term "distribution of noise sources" is at least misleading. You may check Pham et al. (2018) for recent work on this topic.

• Line 23: We cannot control or change the distribution of sources; at most, what we can pursue is improving the balance of sources.

• Line 25: It is not correct citing Li et al. (2017) here, see comment from line 16 and lines 17-19 above.

• Line 24-26: Methods weighting or selecting correlations according to its coherence (e.g., Boué et al 2015 or yours), SNR (e.g., Cheng et al., 2015 and Nakata et al., 2015), or even rms (e.g., Shirzad et al., 2014) are close related. They all seek an improvement on the quality of the signals observed in stacked interstation correlations. They only differ on the strategies used to evaluate the contribution of each correlation to build up signals in the final stack and how they are weighted. In my opinion, it is key that you explain these ideas very clearly to allow the reader judge the contribution of your method in comparison to existing alternatives and to evaluate its potential contribution in their applications.

Pg. 3, eq. (1): Your SNR estimator evaluates the signal level assuming that the signal arrives from -t_{ds} to t_{ds} and considers everything as noise outside this range in order to evaluate the noise level. Two things have to be discussed to justify that this estimator is sufficient for your application: what happens when strong signals (not noise) are present from t_{ds} to t_{m} or from -t_{m} to -t_{ds}, and when signals are too weak to be observed in a cross-correlation function but arise after stacking.

Pg. 9 lines 18-20: Standard array methods such as beamforming allow us to measure backazimuth and apparent slowness of signals generated by punctual noise sources and then estimate the direction of arrival of surface waves or the location of body waves (e.g., through backprojection). To first order, the aperture of the array determines the resolution of these measurements. Can you be more specific on how you can relate directly the aperture of the arrays with the location of noise sources.

Pg. 10 lines 3-8: The figure of using from about 8 to 35% of the number of correlations available in the final stack is important for the reader, could you add this information to the manuscript.

Finally, the English usage has to further improved. For example, in pg. 3 lines 23 and 24 and in pg. 4 lines 3 and 6, using "Let it is" or "Let they are" is not correct. You may use "It is / They are" or "Let it be".

REFERENCES

Phạm, T.‐S., Tkalčić, H., Sambridge, M., & Kennett, B.L.N. (2018). Earth's correlation wavefield: Late coda correlation. Geophysical Research Letters, 45, 3035–3042. doi:10.1002/2018GL077244

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ED: Publish subject to minor revisions (review by editor) (06 Aug 2019) by Nicholas Rawlinson

AR by Nikita Afonin on behalf of the Authors (13 Aug 2019) Author's response Manuscript

ED: Publish as is (15 Aug 2019) by Nicholas Rawlinson

ED: Publish as is (03 Sep 2019) by CharLotte Krawczyk (Executive editor)

AR by Nikita Afonin on behalf of the Authors (03 Sep 2019)