An Envelope Travel-Time Objective Function for Reducing Source–Velocity Trade-Offs in Wave-Equation Tomography
Round 1
Reviewer 1 Report
In this paper, authors propose a new methods related to the tomography problem. The effectiveness and advantages of the method are verified by the use of experimental data in order to retrieve the near-surface velocity structures. Both synthetic inversion experiments and practical field data application are used.
In general the paper is well presented and articulated. However, I have to admit it is a little bit heavy in the mathematical part, making the paper not to be easily readable for people outside this research domain. Nevertheless, it is submitted to a specific scientifici journal which has the goal to reach also scientists in this field.
I'm general, figures are appropriate and we'll structured and designed.
I do suggest that authors enlarge the discussion and conclusions parts that at the moment are to skinny.
Author Response
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Author Response.pdf
Reviewer 2 Report
This study proposes a new method to reduce Source-Velocity Trade-Offs, using the Envelope Traveltime function. In addition to the theoretical formulation, numerical experiments have been performed to demonstrate its validity under the given conditions.
This method seems to work to some extent under the condition that the Envelope Traveltime function is not influenced by very local subsurface velocity structures. On the other hand, if there are three-dimensionally inhomogeneous and high-contrast inhomogeneities in the vicinity of the surface layer, the Envelope Traveltime function will be greatly affected, and there is concern that the accuracy will decrease.
Therefore, it seems necessary to show cases where the proposed method does not necessarily work effectively, and to limit the range in which this method is effective.
If the above considerations are taken into consideration, this paper will be worthy of publication.
Author Response
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Reviewer 3 Report
This paper slightly update a tool that has been used for a long time in seismic data processing, i.e., using the envelope for a first pass in picking traveltime, for their inversion.
The authors seem ignoring a basic concept, i.e., that phase rotations of a wavelet does not change its envelope. I suggest them so to read the key paper by Taner, Koehler and Sheriff about complex attributes - (which indeed is not even cited in their paper). Knowing this, all what they present is an obvious consequence, or so.
Nevertheless, I think that the paper is a clear example for this well-known approach, and for this reason I think it might be published, as a kind of tutorial for interested readers. As this is, in my opinion, its main value, I strongly suggest moving the paragraph 2.1 into an Appendix, for two reasons:
1. It is almost irrelevant for the key message of the paper, i.e., the use of envelope to compensate for unknown phase rotations of the source.
2. It seems written just to scare the reader, as its mathematics is involute and presented in an incomplete way.
The claim of the paper is definitely overstated: the authors study ONLY phase rotations of the source, and NOT arbitrary errors (e.g., due to noise or source failures). This must be clarified both in the abstract and in the conclusions. Indeed, in a more general case, the results are expected to be extremely different, and the related conclusions too.
I attach an annotated PDF file with further detailed recommendations.
Comments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Reviewer 4 Report
remotesensing-1928191 Review.
This paper shows that for WET (wave equation tomography), the ET approach (correlating the envelopes of observed and synthetic traces) that the authors introduce gives more accurate inversions than the traditional CC approach (correlating the observed and synthetic traces themselves) when a wrong wavelet estimate is used. I think this is worth publishing after perhaps some minor revisions. I have only some minor comments:
[1] Page 3: For (2), (3), etc., perhaps the authors should state that the summation convention is being used, i.e., a sum is performed over terms with a doubly repeated subscript (and also point out where a doubly repeated subscript does not indicate a sum), for clarity.
[2] Page 3: In (7) perhaps, for clarity, use brackets on the right side to indicate if this is the derivative of u_iu_i or just the derivative of u_i multiplied by u_i. Perhaps the other equations in the paper should also be looked at for this, with clarity in mind.
[3] Page 5: Is the sentence immediately above Figure 1 a general statement, i.e., is it true for all cases, or does it apply only in this specific case?
[4] Page 6, eq. (14)-(25): The authors introduce a new envelope traveltime objective function and a new adjoint source in the theory section and use them to demonstrate the improvement. But how new are these results? What is different about their new envelope function when compared to those used in previous work? The differences between the envelopes of observed and synthetic traces have been used by others in previous work, according to the authors. In fact, the authors point this out and cite several references. Or has the envelope method never been used before to reduce waveform distortions? Is that what is new here? Some further clarification on how different their work is from previous work might be useful.
[5] Page 9, Figures 4-8: If I understand correctly, it seems to me that it is predictable that correlating the envelopes of the observed and synthetic traces gives better results than correlating the observed and synthetic traces themselves, because the envelopes of the traces resemble each other more than the traces themselves resemble each other. Is this correct?
[6] Pages 12-14: If I understand correctly, in the Vibroseis field data, it is possible to directly calculate the correct (Klauder) wavelet. Therefore, the ET approach is not needed. Figures 12a and 13a give the best possible results. Is this correct? Are the authors then suggesting that the ET approach be used only for other non-Vibroseis data? Would the ET method work just as well for other data?
[7] Pages 18-19, Discussion and Conclusions: As the envelopes of the wavelets can be thought of as “smoothed” or “averaged” versions of the wavelets, it seems almost counter-intuitive that the ET method should give better results by smoothing out waveform distortions (because of the loss of information produced by smoothing). Are there cases where the ET method would not work as well? Do the authors see any disadvantage to the ET method because of this “smoothing”?
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The manuscript is properly revised. This study is judged to be publishable as it is.
Reviewer 3 Report
The authors took fully into account my remarks, so I recommend the publication of this paper. Definitely, it is now much more solid in terms of theoretical consistency and practical use.
