Multi-Scale Acoustic Velocity Inversion Based on a Convolutional Neural Network

Round 1

Reviewer 1 Report (Previous Reviewer 4)

Comments and Suggestions for Authors

Dear Authors,

Thank you for revising the points and answering the questions from the previous review. Now, your method is more clear to understand. However, I could not find the red text of the answer to my first question about the convergence criteria reflected in the text. Maybe you forgot to include this? Besides, I suggest you include in the paper the images you have shown in the answer comparing angle RTM and the normal RTM; this would increase the understanding of the reader.

Correcting these issues, I recommend the manuscript for publication

Best Regards

 

Author Response

Dear reviewer

Thank you for your valuable comments on several reviews of the manuscript. Your concerns have been addressed.

Best wishes

Wenda

Reviewer 2 Report (Previous Reviewer 5)

Comments and Suggestions for Authors

In this paper, Using the Ms-CNNVI method, a multi-scale strategy is integrated into the CNN-based velocity inversion algorithm to improve the accuracy by combining the smoothing strategy and the multi-scale inversion process.

After carefully reading this paper, I suggest a major revision.

General comments

1. The numerical examples section: more details should be stated, e.g. how many training sets, how to select training sets, etc.

2. The exact form of the attention U-Net network used in this paper should be explained.

3. Figure 6 is not labelled a and b, but figures 6a and 6b appear in the paper, and the second figure of figure 6 is not clearly visible, so it is suggested that a paragraph be enlarged for easier reading.

4. Is there a difference between angular domain RTM and conventional RTM results? It is not described in the paper.

5. Do the two graphs in Figure 12 represent the results of the two models in Figure 8? Please explain in the paper. And please also label the inversion method represented by the scatter in Figure 12.

6. Since both smoothing and multiscale can improve the inversion accuracy, why does this paper not directly combine the two to form a multiscale smoothing inversion.

7. In the section of introduction, “The aim of these techniques is to produce high-resolution velocity models that can provide valuable insight into subsurface geological structures and enable accurate seismic imaging and interpretation”. You can cite “Research progress on seismic imaging technology, Petroleum Science”; “The same multi-scale algorithm also can be combined with AI inversion to enhance the inversion effect”. An interesting and related researches: Multiscale Fusion Network With SR-Attention for Seismic Velocity Model Building: IEEE Transactions on Geoscience and Remote Sensing

8. You should compare the computational efficiency of all numerical examples.

9. You can discuss the application prospects in QFWI: Q-compensated full waveform inversion for velocity and density, Exploration Geophysics.

10. In the conclusion section, you should describe the shortcomings and limitations of the methodology.

11. Some of the references have incorrect formatting, please correct them.

12. Some minor comments:

(1) It is recommended that the reference citation markup be changed to a superscript format.

(2) The velocity axis in Figure 8 is too far up and it is recommended that it be moved down.

(3) In Figure 13, a,b,c,d,e duplicate labels and it is recommended that the bottom label be deleted and only the top left be retained.

(4) Figure 16 is not labelled a and b, but figures 16a and 16b appear in the paper, please label them.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Dear reviewers

We deeply appreciate your valuable feedback in the form of helpful suggestions. Each and every one of your comments and suggestions has been carefully considered, and as a result, we have made major revisions to this revised manuscript. We are sincerely grateful for your assistance in enhancing our work.

Please find the file named "Points to Points" in the following attachment.

Wenda

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report (Previous Reviewer 5)

Comments and Suggestions for Authors

I would like to congratulate the authors for this interesting piece of work. Thanks for addressing all of my comments. It is clear that the authors have tried the effort to address the comments and critiques. And overall, I’m satisfied with the replies. I feel the manuscript has been greatly improved. I would to recommend it to be accepted after some minor revision:

(1) Please increase the font size of some coordinate axes as they are too small to read easily, such as Figure 6 and Figure 10.

(2) There are errors in the units following some formulas, such as formulas 1, 2, 5, 6, 7, 8, and 10. The "." should be changed to ",", and also, the first letter of "Where" in the next line should be lowercase and without the double-space indentation.

 

(3) I suggest you give some description of your method on the field data set.

Please increase the font size of some coordinate axes as they are too small to read easily.

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Dear reviewer,

Thank you for your twice detailed review comments. The article has become better with your comments. Below are the specific responses:

We have changed the coordinate axis fonts and legends, etc., and corrected the errors in the formatting of the formulas that you suggested.

The method is crucial for real data applications. The method proposed in this paper is similar to the iterative updating process of full waveform inversion, so it is consistent with the problems faced by FWI for real data. In addition, the method in this paper has a good generalization ability, and the inversion work can be realized for different underground media.

For the real data, the current FWI needs a good initial modeling, that is, tomography and other methods to get an initial background velocity field, and then further realize the FWI through the background velocity field. FWI in the absence of a good initial model can lead to a direct failure of the model to continue updating and unable to find the direction of descent of the gradient. The method in this paper needs a good initial model because of the need to provide a good initial condition to the model parcellation method. In addition, as in the case of the FWI method, the level of super noise in the real data also restricts the method to some extent. To summarize the potential of real data in this paper is consistent with FWI and requires a better background velocity field and seismic data with good signal-to-noise ratio.

In, summary , the method in this paper is consistent with the FWI, which also needs a good background velocity field, and can realize more refined real data modeling with an initial background velocity.

 

Wenda

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposed a multi-scale network-based acoustic velocity inversion method. The paper is well organized and the ideas are clearly illustrated. Numerical tests support the conclusions. The following are some suggestions to further improve the manuscript:

1. The Ms-CNNVI includes training and prediction stages. As shown in Figure 1, each iteration in the training process involves generating multiple perturbed velocity models using the model parcellation method, as well as calculating observed seismic data and RTM images using forwarding modeling and RTM. It is necessary to list the training time of Ms-CNNVI and the computational time of conventional FWI when comparing these methods.

2. For Ms-CNNVI, network architecture plays an important role in obtaining an accurate velocity model. Please provide a detailed description of network architecture and parameters in section 2.3.1.

3. For the generalization ability of Ms-CNNVI, the inversion frequency may be an important factor. Please discuss the impact of inversion frequency on prediction results.

4. Could the authors comment on the potential application of the proposed method on real field data?

5. In the conclusion section, the author mentioned “Furthermore, compared to other AI inversion methods, our approach exhibits strong generalization performance”. Please add related comparisons in the manuscript.

 

Author Response

Dear reviewer;

First of all, thank you for your helpful comments. Your comments will help a lot to improve the quality of the manuscript. We have improved the writing and details of the article based on your comments.

Please find attached my point-by-point response to your comments.

Wenda

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper introduces the theory of multi-scale full waveform inversion using deep learning, starting with low-frequency signals to construct a preliminary background field and then using high-frequency signals to build model details. This approach appears promising, but the paper should provide more detailed explanations and justifications for this methodology, including any limitations or conditions under which it is most effective.

Use of Abbreviations and Terminology:

Comment: It's crucial for readability and clarity that all abbreviations are introduced at their first occurrence in the text. The paper should be revised to adhere to standard practices in academic writing regarding the use of abbreviations.

a)       The term 'CNN' is used in the abstract without prior introduction.

 

b)       Similarly, 'multi-scale (MS)' appears in the introduction without being defined at its first use. 

Issues with Figures:

Comment:

a)       The font size of the axes in the figures is too small and needs to be enlarged for better readability.

b)       In Figure 1, the use of different colored arrows to represent training and prediction processes is confusing and inconsistent with the actual processes depicted. A revision with more accurate symbols and clearer distinctions is required.

 

c)        For Figure 9, it is unclear why the multi-scale FWI results are inferior to the FWI results, which is counterintuitive. An explanation for this observation should be provided.

Technical Clarifications and Additional Information:

Comment:

a)       Are the two types of CNN described in this article, 'well pre trained CNN' and 'CNN', sharing the same network parameter? If there are differences, please introduce any differences between them.

b)       The paper should clarify whether the ‘well-trained CNN’ requires further training or parameter updates post-initial training.

c)        Questions about input sizes, transformations for different dimensions, and the network's effectiveness on varying input sizes need addressing.

d)       Additionally, the paper should elaborate on the down-sampling process, its impact on frequency, and whether high-frequency information is lost.

 

e)       Finally, details about the training cost and loss function should be included for a comprehensive understanding of the model's performance.

Comments on the Quality of English Language

Language, Textual, and Formatting Corrections:

Comment: The language and formatting need improvement for clarity and grammatical correctness.

a)       In the third paragraph of the Introduction, 'The second is' should be revised to 'The second method/algorithm is'.

b)       Also, the reference formatting needs to be consistent and correct

 

c)        There should be a clear subject before verbs like 'proposed' and 'developed'. 

Author Response

Dear reviewer;

First of all, thank you for your helpful comments. Your comments will help a lot to improve the quality of the manuscript. We have improved the writing and details of the article based on your comments.

Please find attached my point-by-point response to your comments.

Wenda

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors,

 

Thank you very much for your paper. I have a few comments you can find below:

 

The first comments refer to section 2.
1. In my opinion, the presentation in section 2 is not clear needs some clarifications. Here are some suggestions:

·         Although this training loop is straightforward for an expert, it is not the case for the general reader. I encourage you to revise this part as it fundamental part of the method and will give better understanding to the reader.

·         The loop in Figure 1 needs to be better explained. The workflow should be better illustrated. Also, figure caption is missing.

·         How convergence is achieved? What is the criterion? Please comment

·         Please explain what a "well-trained CNN" is and how to achieve its parameters.

·         The authors using the "parcellation method" to create new slices. Although a reference is given, the method should be explained in more detail as it is a fundamental part of the network.

·         The authors cite that "If it does not converge, new model parcellation will be performed on the new prediction velocity model to create the training dataset for the next iteration". How it is done? Using a new velocity model or with the same model only applying the parcellation method again.

 

2. The authors use the angle domain RTM to create the RTM images. It should explain why this method "convergence rate and enhancing the inversion". How many angels are you using? What is the criterion? These should well explained for the general reader.

3. Eq. 7 is written in the time domain, while the authors refer to a single free RTM. Please comment

4. Why does angle domain RTM "can accelerate the convergence speed of CNNVI"? Isn't it only help accelerate the RTM?

 

I also have concerns regarding the ability of the method to generalize to different models. To my understanding, the training data is limited to perturbations of the original velocity model. The authors also base the method on the first Born series. Also, the numerical examples show test with similar structures.  In my opinion, the network would not be able to generalize to velocities with different geological structures (subsalt etc.). Can you comment?

 

Finally, a better comparison between the proposed and conventional FWI methods should be given. Especially what degree of acceleration one obtains with the proposed method, what is the computational complexity of the method?

 

I hope you'll find these comments helpful

Thank you

 

 

Comments on the Quality of English Language

NA

Author Response

Dear reviewer;

First of all, thank you for your helpful comments. Your comments will help a lot to improve the quality of the manuscript. We have improved the writing and details of the article based on your comments.

Please find attached my point-by-point response to your comments.

Wenda

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors and Editor,

Thank you for the opportunity to evaluate this manuscript. The authors proposed a method which uses deep learning tools to obtain accurate velocity models from seismic data and compared this method with conventional FWI inversion. The topic is relevant, and the research is interesting, but to be considered for publication, the manuscript needs a major revision to answer some critical questions.

In summary, many aspects of the methodology need to be included/clarified from the perspective of geophysics as from the deep learning perspective. After understanding these aspects, I could evaluate the manuscript's relevance for publication.

I have annotated many points in the attached manuscript, but the main considerations and critical aspects to me are listed below:

1) How do you train the neural network? Is the method a supervised learning approach? In the positive case, which loss function have you used?

2) What is the size of the training set? Have you cared about overfitting? How about validation and test set?

3) If I understand correctly, the parcellation method generates models similar to the true/goal model. How do you expect to conduct this for real applications without knowing the true model?

4) How have you generated the training data? Please provide details about the wavelet, acquisition geometry, etc. Even the generation of the velocity models for trainning lacks details. Do they need to be similar to the goal model?

5) If I understand correctly, the parcellation generates new training data and the corresponding geophysical data at each iteration. How about the computational cost of this process? You have mentioned, at some point, 800 epochs. Is it necessary 800*24 modelling + migration process until convergence?

6) When you discussed generalisation, you showed the result for a different model. Was the neural network retrained to work for this model? Or was the training process conducted once for all the results presented in the paper? If you trained once, you must show details about the training set. If you need to retrain for each case, there is a generalisation issue on the method.

7)I was not clear to me how you use the angle gathered from RTM. You mentioned once that you have two channels as input for the neural network. How about the angles?

8) In Figure 9 d) and h), if I understood right, you got the worst results when you used original models closer to the solution. Could you explain this result better?

9) In Figure 12, what is the difference between the two figures? Which measure do the lines represent? 

10) The discussion section needs to be longer and reflect and clarify the main aspects of the work. Please rewrite this.

 

Best Regards

Comments for author File: Comments.pdf

Author Response

Dear reviewer;

First of all, thank you for your helpful comments. Your comments will help a lot to improve the quality of the manuscript. We have improved the writing and details of the article based on your comments.

Please find attached my point-by-point response to your comments. I responded to all the annotations you made in the PDF as well.

Wenda

Author Response File: Author Response.docx

Reviewer 5 Report

Comments and Suggestions for Authors

Title “Multi-scale acoustic velocity inversion based on a convolutional neural network”

This paper proposed method is a multi-scale convolutional neural network velocity inversion that incorporates a multi-scale strategy into the CNN-based velocity inversion algorithm for the first time.

After carefully reading this paper, I suggest a major revision.

major comments:

1. In line 2 of page 6, ”Angle domain RTM based on the Poything vector method does not increase the computational effort, but it can accelerate the convergence speed of CNNVI.”. Does Angle domain RTM based on the Poything vector method not increase the computational effort?

2. It is best to add a table in Section 3.1 of the Numerical Simulation section to compare the computation times of Ms-CNNVI, CNNVI, and smooth strategy.

minor comments:

1.For the two iterative processes shown in Figure 7, is the angular domain RTM convergence exceeded by RTM after the eighth iteration, or does the iteration stop? It is best to show the process of subsequent iterations, or to indicate the number of iterations terminated.

2. “Figure 9. (a) and (b) are the original model. (b) and (f) are the Ms-CNNVI results.” Please clarify whether Figure 9. (b) is the original model or Ms-CNNVI results.

 

 

Comments on the Quality of English Language

Minor editing of English language required

Author Response

Dear reviewer;

First of all, thank you for your helpful comments. Your comments will help a lot to improve the quality of the manuscript. We have improved the writing and details of the article based on your comments.

Please find attached my point-by-point response to your comments.

Wenda

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

 

Thank you for the revised version of the paper. I have a minor and major comments

1. Minor - Regarding the convergence of the network, Thanks for the wide discussion over the cover letter. I recommend that you add it to the newspaper since some of the achievements in the coverage should be "clear" to the reader. A quantitative measure could help

 

2. Major - I am still having difficulty discerning the approach's benefits. The experiments mentioned in the paper do not indicate whether the results in Figure 14 are presented using the network trained in section 3.1 or whether a new network must be retrained.

 

To the best of my understanding, it seems that the network underwent retraining to produce the results in Figure 14. If this is the case, it may not illustrate the method's capability to generalize to models beyond the training set. Please clarify the method's limitations concerning its ability to generalize across various sections.

 

 

Additionally, a more comprehensive discussion on the advantages of the method compared to conventional Full Waveform Inversion (FWI) is needed. While different FWI methods may yield superior results, it's crucial to consider the computational cost as a significant factor.

 

Hope these comments help

Reviewer 4 Report

Comments and Suggestions for Authors

Dear Authors,

Thank you for the revised manuscript and the detailed answers you provided. Now, I can better understand and see the novelty of the method proposed. However, I still have many questions and suggestions to improve the accuracy of the methods described and the understanding of the technique.

I have attached a revised file with minor points, which I ask you to carefull revise. But the main questions are detailed below.

 1) When you say, "Network prediction at the end, determine whether the inversion converges or not. If converged, the whole CNNVI process is ended",  I am still not able to understand which criteria you use to determine if the inversion has converged or not for real cases where you do not have the true model. Please clarify how you intend to evaluate the predicted model when you do not know the true model.

 

 2) Many times in the text, you used the generalization term. I do not agree with this use. By generalization in the AI field, we understand that once a neural network is trained with a training set, it is able to perform well over unseen data. Since the proposed method has a training process dedicated to the specific model you are trying to invert, to my understanding, generalization is a term that is unsuitable in this context and can lead to misunderstandings of the method proposed. I understand that to be able to predict the right model for many geological configurations is important and desired, but in your case, with the dedicated training for each model, this propriety can not be named as a generalization.

 

 3) On page 6, you said that "Angle domain RTM based on the Poything vector method does not increase the computational effort, but it can accelerate the convergence speed of CNNVI." it is unclear why this angle domain RTM can improve the method. In the separate file you sent, you said, "It can effectively suppress wavefield noise and improve RTM imaging quality."  The advantages of angle domain must be better discussed in the manuscript.

 

 4) Still on page 6, I believe some FWI concepts are misunderstood. It was said that high-frequency components can introduce errors and redundancy in the inversion process. Redundancy on the inversion problem, when well-modelled and represented, is not a problem; on the contrary, redundancy reduces the null space.

 

But the most critical point in the paragraph, which I have questioned in the previous review, is the statement:  MS inversion process is more consistent/ aligns more closely with the laws of physics.

First, the laws of physics used for modelling/ inverting are not affected by the frequency content used. There is no expectation of better modelling the data by changing its frequency content.

Second, the decision to invert low frequencies first in FWI is not dictated by a specific law of physics, but rather, it is a strategy developed to deal with the nonlinearity of the problem and to ensure the robustness of the inversion process. FWI inversion suffers from the  “cycle skipping” problem,  where the predicted and observed data are out of phase, leading to incorrect updates of the model parameters. Low-frequency components of the seismic data are less sensitive to errors in the initial model and are less likely to cause cycle skipping. Therefore, starting the inversion with low-frequency data can help ensure the inversion converges to the global minimum of the objective function. Thus, MS is not related to the physics laws involved in the problem but to the design of the inversion problem. I strongly recommend revising this discussion to align better with the current understanding of MS in FWI.

 

 5) Concerning the acquisition geometry, it still lacks the receiver distribution. Is it a fixed spread geometry?

 

 6) On page 10, final paragraphs, both FWI and RTM require the backpropagation of the source and adjoint sources or receivers fields. This forward term here does not make sense. The most suitable term in this case would be wavefield propagation.

 

7)"Salt dunes". The accurate geological nomenclature is salt domes.

 Best Regards

 

Comments for author File: Comments.pdf