Pseudo-3D Receiver Deghosting of Seismic Streamer Data Based on l₁ Norm Sparse Inversion

Round 1

Reviewer 1 Report

 

Dear Author:

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Author Response

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Reviewer 2 Report

The article ''Pseudo-3D Receiver Deghosting of Seismic Streamer Data based L1 norm sparse inversion” presents a methodology of geophysical data inversion regularized by L1-norm to attenuate the ghost effects caused by the iteration of the seismic wave with the free-surface (sea-surface). The topic is of interest to geophysicists who work with waveforms analysis. The presented methodology is interesting, applicable, and very useful for the academic and industrial communities. Although the article deals with an interesting subject, it still needs to be improved. In fact, the presentation is sometimes confusing, with missing or poorly motivated definitions, in addition to a (possibly) useless example. Please see comments below. 

 

(1) Lines 76-77: The authors state that "(...) we introduce a L1-norm sparse inversion in pseudo-3D Radon domain to avoid the local minimum." (see also line 66)

 

     Authors should be careful with this statement. I suggest that authors make it clear in the present manuscript (not necessarily in the Introduction section) that they are dealing with an inverse problem, and therefore need to make it clear what is the forward problem (mechanism for obtaining the modeled data) and what is the inverse problem (obtaining model parameters by optimizing an objective function that compares modeled data with observed data). It is worth remembering that inverse geophysical problems are intrinsically ill-posed, and therefore the global minimum (exact representative model) is just a utopia. 

     In this context, the local minimum is not avoided, but rather, an "informative local minimum" is sought (good resulting model).

 

(2) I understand that p is the slowness, but what does the index p mean? Please make it clear in the text after eq. 1.

 

(3) Is eq. 1 only valid for streamer data? If not, remove the word “streamer”, or replace it by “seismic”.

 

(4) Figure 1 is not very informative, and it is in low resolution. Since the main goal of the present work is proposes an approach for deghosting seismic data acquired by streamer surveys, illustrating only the seismic acquisition is insufficient. Authors should construct a schematic figure of the acquisition geometry that illustrates the z and v parameters of eq. 3, the wavepaths of primaries and their ghosts. This will help the reader to understand the process that led to the generation of ghost and its relationship with the existing equations in the article.

 

(5) Regarding the abbreviations, they must be inserted in parentheses right after the written-out means, when defined for the first time. This one should be made at its first appearance in the abstract, in the first figure (or table), and in the main text (please see the "Instructions for Authors" in https://www.mdpi.com/journal/applsci/instructions for more details). I suggest that the authors review the abbreviations entered in the manuscript. For example, define the abbreviations CSGs and COG on line 108.

 

(6) Lines 129-130: The authors state that "Because the signal becomes sparse, it is not easy to fall into the local minimum during inversion”. Is the motivation for trapped in a non-informative minimum due to signal sparseness? And is not seismic illumination a determining factor? Please clarify this one in the new version of the manuscript.

 

(7) Lines 133-149: The work is based on the L1 norm as a model constraint, why was the example given using the L0 norm? What do the authors want to show with this example using the L0 norm that would not be possible to do with the L1 norm? 

 

(8) Section 3. Results: How was the "observed" data from the synthetic example generated? That is, what mechanism is used in forward modeling? Wave equation? Convolutional model? eq. 5? Please clarify it. 

 

(9) Section 3. Results: Is the saltdome model, acoustic? Elastic? Please, clarify it.

 

(10) The manuscript contains some typos and grammar errors that should be corrected, such as "mul-shot gathers" instead "multi-shot gathers" in line 76 and various other parts of the manuscript, among others. For instance, please replace “Synthetic” with  “synthetic” in line 77, “kronecker” with “Kronecker” in line 165 (the same for Randon in line 200), and so on. Also, authors should write the notations of mathematical sets properly. Please rewrite the definitions on line 134 (and the others following) accordingly with standard mathematics. 

 

(11) Finally, it is worth emphasizing that the ideas addressed in the present manuscript can be applied beyond this problem. Thus, since the Applied Sciences is an interdisciplinary journal, I believe it is worth including in the introduction (or in the conclusion) a sentence indicating that the present proposal is a potential methodology for applications in several other fields of science and engineering (please search for some applications that use objective functions regularized using the L1 norm).

 

In my opinion, the article should address the above points in order for the work to be interesting for several readers. The above points must be addressed before the manuscript can be considered for publication.

Author Response

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Reviewer 3 Report

-Fig3 should move to another place since it appear before the text.

-Software used for this study should be explained.

-Fig5, please edit scale bar with finer scale and label.

-Fig6,7,8 should move another place since they appear before the text.

-Fig6,7,8 as well as 9, 10, 11. More details on figure caption should be added.

-In section4, discussion and conclusion. This section seem to have only conclusion, thus more discussion should be added or move to section 3 as results and discussion.

Author Response

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Round 2

Reviewer 2 Report

The authors adequately answered all the points raised by this reviewer. I recommend this article for publication.