Seismic Imaging of the Arctic Subsea Permafrost Using a Least-Squares Reverse Time Migration Method
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper is a case study of the application of the least-squares RTM technique, which is well known for its seismic data processing performance, to Arctic seismic data. Although various processing techniques based on seismic data have been developed and applied to real data and have gained reliability, I believe that there should be more examples. Therefore, I think articles like this are still highly valuable.
To make the paper more productive and meaningful, I would like to make the following suggestions.
About Figure 1.
- Criteria for LSRTM iteration end is missing. Please add it to the figure and text.
About synthetic examples
- Since the synthetic examples performed to evaluate the performance of LSRTM know the ture velocity model, it seems reasonable to present the model error rather than the residual-based misfit curve.
- In addition, misfit curves like the one shown in Figure 4 should be added for the real data applications.
- This paper is a case study of applying LSRTM to real data, and real data is contaminated with various forms of noise.
- We believe that testing and adding the effects of noise would increase the value of the article. This suggestion is optional.
About Figure 10
- Laplace-domain FWI is known to be good at providing reasonable long-wavelength velocity models. However, the permafrost in the paper does not appear to have a long-wavelength structure, so it is difficult to determine if the velocity model applied is appropriate. Is there an advantage to applying the conventional velocity analysis results (stack or interval velocities)?
About Figure 11
- Are the repetitive horizontal events evident in Figure 11b real structures or not? Please add an explanation.
Comments on the Quality of English Language
The English is adequate throughout. However, if you can afford it, I recommend that you have it proofread by a native speaker.
Author Response
Please see the attachment
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsDear Authors:
In the manuscript titled “Seismic imaging of the Arctic subsea permafrost using a least-squares reverse time migration method”, you proposed an application for LSRTM on the streamer data acquired in shallow water in the Canadian Beaufort Sea. The goal of the study was to leverage the potential of a high-resolution imaging method to image the Arctic subsea permafrost layer.
The manuscript is well written linguistically and conceptually. You review effectively the methodologies that you employed and discuss the details of the results appropriately. I have some minor comments, and I also offer you some suggestions to improve the field data results that you can find at the end.
My comments are as follows:
· All the equations need number labels.
· Line 20: I strongly recommend replacing the “simulated data” by “predicted data” in the whole manuscript. Since you also provided some synthetic experiences, and traditionally, “simulated data” refers to synthetic data more than the data that is simulated using first-order approximation modeling (like Born) and the recovered images. The latter mostly is called “predicted data”.
· Line 34-35: The statement “the down-going source and up-going receiver wavefields” is not generally correct. Generally, in RTM methods, the source wavefield includes both up-going and down-going waves because this wavefield is generated by solving the two-way wave equation; the same is true for receiver wavefield. Therefore, this statement should be change to “the source and receiver wavefields”. I understand that maybe authors can refer some papers to proof this statement, but mostly in those works rather downward continuation is used or the wavefield separation methods is applied before migration.
· Line 51: To describe the situation more precisely:
… shelf in shallow water at depths of … -> … shelf where shallow water has the depth of ...
· Line 67: For consistency, it is better to keep using “the single scattering forward modeling operator” instead of “forward Born modeling operator” or add citation for Born modeling.
· Line 75: LSM achieves a high-resolution image by iteratively converge to the solution of the inverse problem or by approximating the Hessian operator; therefor, the statement “LSM achieves this by attenuating the migration artifacts and balancing reflectivity amplitude” can be confusing. I recommend changing it to something like:
Attenuating the migration artifacts and reflectivity amplitude recovery are also the other LSM achievements.
· Line 78: … theory. These include one-way … -> … theory, for instance, one-way migration …
· Line 115: It would be better if you added a short explanation about why you prefer Kirchhoff modeling over Born modeling.
· Line 116: Regardless of the approximation used, … -> Regardless of which approximation is used for simulating predicted data, …
· Line 118: … simulated and observed data … -> … predicted and observed data …
· Line 124, 125: … simulated data. -> … predicted data (Lm).
· Line 125: Add a short explanation about the background velocity model, for instance, bare of any high wave-number perturbation or reflectors.
· Line 127: … wavefield extrapolation … -> … wavefield modeling …
· Line 124, 125: … the simulated data … -> … the predicted data …
· Line 137: It is written, “The Kirchhoff modeling operator can be expressed as follows”, however, following there is an equation which the Kirchhoff operator is its solution. Regarding please rewrite the sentence.
· Line 142: … reflectivity along … -> … reflectivity model along …
· Line 142: … reflectivity data … -> … reflection coefficients …
· Figure 1: simulated data -> predicted data ,
o Final reflectivity model -> Final reflectivity image
· Figure 1, in the caption: … least-square -> least-squares
· Line 153: … to the above inverse problem … -> … to the inverse problem in equation (1) …
· Line 157: where mmig represents … -> where mtrue represents …
· Line 158: … Hessian operator bold cap L to the cap T, bold cap L acts … -> … Hessian operator, (LTL), acts …
· Line 162: The challenge for computing the inverse of Hessian is not limited to the intensive computation demanding, the worse obstacle is that usually the Hessian matrix is ill-conditioned and doesn’t have an inverse. Please include this in your manuscript. (Refer to Schuster, G., 2017. Seismic inversions, SEG.)
· Line 167: The optimal solution for the equation can be … -> The optimal solution for equation (1) can be
· Line 167, 168: … updating the previous reflectivity model with new vectors, … -> …updating the reflectivity model iteratively, …
· Line 173: … the preconditioning operator … -> … the preconditioning operator (approximation of the inverse of Hessian)
· Line 181: delta d(xr,t;xs) -> delta d(xr,T-t;xs) where T is maximum recording time
· Line 203: Please add reference for the CPML method.
· Line 205: Before in lines 194, 202, and 203, you mentioned that the observed synthetic data is generated based on finite difference modeling of the wave equation, which is exactly what it must be. However, in line 205, you wrote: “the observed dataset for LSRTM examples is generated by demigration with the true reflectivity and background velocity models”. I understand that you used linearized modeling to prevent multiples, but you should pay attention that using linearized modeling misses simulation of prismatic, diving, and refracting waves in addition to internal multiples. The demigration operator must be only used to simulate the predicted data in LSRTM, while using the demigration operator for synthetic observed data will bias the results and is called imaging crime. So, please discuss about you choice or mention to these issues for your readers.
· For consistency, in Figures 2, 5, 12 in captions and line 259-260-338-350: change migration velocity to background velocity.
· Line 258: You mentioned the shots extent from 1.75 km to 30.16 km while your model offset is 14 km, please correct it.
· Line 312: Because free surface multiples are related to the water environment and internal multiple reflections are related to high-velocity structures arising from subsea permafrost, it is better to apply the following change:
… suffers from internal multiple reflections and free surface multiples. -> … suffers from free surface multiples and internal multiple reflections.
· Line 359: These reflections exhibit … -> These reflectors exhibit …
· Line 362: You mentioned here “Furthermore, despite using a short-offset streamer, LSRTM successfully images reflectors in the lower part of the subsea permafrost.”
It is correct that streamers data can not participate in imaging the events deeper than the offset, but in your example the maximum depth is 1 km and the offset is 1.5 km. Therefore, I believe the longer offset only help for better fold and so better signal to noise ratio and improve the lateral continuity of the final image.
· Figure 11: In both results, a repetitive hachure artifacts are visible. These artifacts may related to the source interval, however, I believe they related to aliasing. To suppressed them you should set lower frequency for the wavelet that you convolve with real data and also filter higher frequency or considering the CFL condition of the hired finite difference method decrease the spatial grid interval.
Sincerely yours,
Author Response
Please see the attachment
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper "Seismic imaging of the Arctic subsea permafrost using a least squares reverse time migration method" applies the least squares reverse time migration (LSRTM) method to 24 seismic datasets obtained from the Canadian Beaufort Sea (CBS) and generates a seismic image depicting 25 subsea permafrost structures in the Arctic region. The research results are of significant practical value, and I suggest the following modifications:
1. Line 224: The description of the LSRTM could benefit from a more detailed explanation of how the technique balances amplitude and reduces low-wavenumber artifacts, as well as other potential advantages of LSRTM. For example, in addition to basic iterative enhancements, the introduction of Laplace image filtering can also effectively balance amplitude and suppress strong low-wavenumber artifacts.
2. Figures: All figures need to be resized and compactly arranged. For instance, Figures 2, 3, and 4 are too small.
3. Figure 4: It is suggested to provide the value of the normalized misfit after the 10th iteration in detail.
4. Line 284: The author is advised to provide relevant background information about the Canadian Beaufort Sea (CBS), including the significance of the research and previous studies in the area.
5. Figure 9: It is recommended to add clear annotations in the key areas of the figure.
6. Figure 11: It is suggested to add clear annotations in Figure 11 to indicate the areas where LSRTM excels in balancing amplitude and reducing low-wavenumber artifacts.
7. Line 318: The Omega2 seismic data processing software should be referenced.
8. Line 324: It is recommended to explain why a 40 Hz Ricker wavelet was chosen and to describe the specific impact of this choice on data processing.
9. Line 343: The number of iterations is set to 30 to ensure convergence. It is recommended to provide quantitative charts to describe this.
10. Line 362: Does the "short-offset towed streamer" have any impact on imaging? This needs a clear explanation.
11. Line 350: Figure 12 was obtained by "overlaying" the LSRTM results with the migration velocity model. The specific "overlay" method used should be clarified.
12. Line 357: There is a reflection representing the upper boundary of the subsea permafrost approximately 6-70 m below the seafloor, but this is not clearly observed in Figure 12. A better legend is needed.
Author Response
Please see the attachment.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authers,
I am pleased to see the author's response.
It is very impressive and I believe you have done an excellent job of addressing the revision request.
