High-Dimensional Seismic Data Reconstruction Based on Linear Radon Transform–Constrained Tensor CANDECOM/PARAFAC Decomposition

Round 1

Reviewer 1 Report

 

1.     Since Linear Radon Transform is simply a mathematical transformation for a time-space signal which may has widely meaning in different domain, the radon transform should not be directly applied as a constraint condition. The expression: “linear transform constrained “used in the title is not very appropriate.

2.     It will be more reasonable to change the word “Review” in line 110 ( section 2.2…) by principle. Generally speaking, people will that the review should contain analysis and comments.

3.     The linear Radon transform is not firstly introduced in seismic exploration by professor Claerbout. The authors should refer to more relevant papers.

4.     The test processing for the proposed method gives very good reconstruction results, but there only two emphasized mark in the paper by ovals. It is suggested that all improved results should be marked to illustrate the effectiveness of the new method.

5.     Be careful of grammar, such as “The linear Radon transform is proposed by Radon…”.

Author Response

Thanks for your comments. Here is my reply in the uploaded file.

Author Response File: Author Response.docx

Reviewer 2 Report

The random noise and missing traces in the acquired seismic data will seriously affect the quality of subsequent inversion imaging. In order to solve the problem of noise and seismic data missing, this paper combines the linear Radon transform with the CANDECOM/PARAFAC decomposition method, and proposed the linear Radon transform constrained tensor CANDECOM / PARAFAC decomposition method (RCPD). Both synthetic data and field data in numerical experiments verify the effectiveness of the method. The structure of the article is clear, the content is highly readable, the numerical experiments are sufficient and convincing, the diagrams are clear, and the format is standardized, which can be published in remote sensing.

Here are some suggestions for articles:

1 In order to make it easier for readers to understand the difference between RCPD and CPD, the author should give the meaning of R in RCPD.

 2 Figures 5 and 7 show the 3D data results of de-noising and reconstruction of by different methods. In order to facilitate readers to clearly see the difference between RCPD and CPD, it is recommended that the author give a two-dimensional data or even one-dimensional data among the three-dimensional data for comparison.

 3 Figures 9 and 10 show the 5D field data results of reconstruction of by different methods. It is recommended that the author give a one-dimensional data among the 5D field data for comparison.

 4 The following article can be added as a reference for the application of the curvelet transform to denoising and data reconstruction

 

Guoxin Chen, Shengcheng Chen, Hanchuang Wang, Bo Zhang. Geophysical data sparse reconstruction based on L0-norm minimization. Applied geophysics, 2013, 10(2):181-190.

Author Response

Thanks for your comments. Here is my reply in the uploaded file.

Author Response File: Author Response.docx

Reviewer 3 Report

In this paper, a linear Radon transform constrained tensor CANDECOM / PARAFAC decomposition method (RCPD) is proposed, and the alternating direction multiplier method (ADMM) is used for High-dimensional seismic data reconstruction. It is an interesting research. I think it needs some revisions:

(1) In the section of Abstract: I think you should rewrite the Abstract because you spend too much words introducing the background and problems of the existing methods and 1~2 sentences describing your method. In addition, you should highlight your innovation point and describe your example results of your method to show the advantage over the conventional method. In summary, readers should know your work from the abstract. What does the proposed method in this paper do to solve these problems? Compared with the traditional method, what improvements can be made by applying the proposed method? These questions should be answered  in the abstract, which introduces too many facts that everyone knows.

(2) In the section of Introduction: You only cited two related papers of your own group in the last three years. Are there no related researches in the last three years?

In 3D CMP, the seismic signal can be regarded as the superposition of the near-surface envets in conical shape and the reflected envets in hyperboloid shape. The 3D conical Radon transform can also be used for reconstruction. I suggest that authors quote the the a 3D conical Randon transform research to the introduction part to enrich the article so that readers can better understand your work.

Page 2, Line 59-60: Zhang et al. [18] proposed constraint CPD with Vandermonde structure (VCPD) to fit the exponential characteristics of frequency domain data. What is the problem or disadvantage of the Zhang et al.’s method; What does this paper give you? I suggest you give some comment instead of just giving a statement.

(3) The fidelity of the two methods should be analyzed, that is, the two methods are used to reconstruct the CMP respectively, in order to compare the performance of the two methods to retain the AVO of reflected signal.

(4) Some minor suggestions.

The third sentence of the abstract uses too much "regarded as". In addition, the text also uses too many "regarded as".

The font is too small in Figures 9 and 10.

 

 

Author Response

Thanks for your comments. Here is my reply in the uploaded file.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

General comments

  I find it interesting to implement CPD in frame of the linear Radon transform and Figure 11 also show its effect of eliminating missing traces. However, some problems still exist in the manuscript and I will elaborate them as follows:

1. Many mistakes about specified letters need to be address and I conclude them according to their types. The author should recheck the whole manuscript and modify them.

First, all specified letters should have similar sizes. For example, on line 140 of page 4,  is too small; on line 153 of page 5, x is too small; on line 204 of page 7, M is too big.

Second, there should be a space before and after the special letters. For example, on line 142 of page 4, p is too close to other words.

Third, special letters should be single one. The author should not use two special letters to represent one meaning, which would cause confusing meaning. For example, on lines 151-152 of page 4, the author should not use np and he should use a subscript such as  to replace it.

Fourth, special letters should be italicized. For example, on lines 256-257 of page 10, x and y should be italicized.

2. On line 209 of page 7, I think these sudden updates of many formulas seem abrupt. Before giving so many updates, the author should give the necessary narrative to connect. Also, in what order were the updates made, were they made at the same time or in a specific order? I think the author should describe this part more instead of just giving many complicated formulas, because this is an important part of the algorithm.

3. Figure 8d is close to Figure 8f. I think the minor difference cannot show advantages of RCPD. This is why I hope the author should use complex model to further show the merit of RCPD, which also can convince readers more.

4. The author only consider the linear Radon transform but Radon transform also includes hyperbolic and parabolic Radon transforms. I think the author should discuss them in the manuscript. Why do you use linear Radon transform to constrain CPD instead of other Radon transforms? I think the author should both explain the advantages and disadvantages of linear Radon transform compared with other Radon transforms.

 

Specified comments

1. The pixel of the figures 1, 2, 3 is too low, the author should change them to higher pixel figures.

2. On line 99 of page 3, generally, 3D is familiar to readers but 5D is not familiar to most of readers. I think that the author should give necessary explanation before using the expression of 5D.

3. On line 142 of page 4, the presence of “where is the time intercept, and is the slope of the integral path” is strange and confusing to readers. I think the author should reconsider the sentence.

4. On lines 199-200 of page 7, “  which is the corresponding Radon spectrum after the transformation” is confusing. The author should rewrite it.

5. On lines 243-244 of page 10, “The reconstruction iterative formula” should be modified as“The iterative reconstruction formula”.

Author Response

Thank you for your review, the specific information in the annex.

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

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.