Elastic Correlative Least-Squares Reverse Time Migration Based on Wave Mode Decomposition
Round 1
Reviewer 1 Report
Good and valuable paper ready for publication after small corrections that authors have to accomplish.
- For equations there should be a space before and after equation and also between equations in order to obtain an optimal visibility.
- The equations font must also be adjusted because some indexes are written in too small font, also some terms are written in bold text other not. Please see the author guides for paper.
- All equations are followed by comma. The punctuation signs after each equation should be avoided.
- On page 6 are two equations with the same numbering: 14C. Although in the text there is a reference to equation 14 d. Please remedy this issue.
- A chapter title is placed at the bottom of page 7. It should be moved to the next page for a better aspect of the paper.
- Please check the spaces across the paper because there are many situations of useless spaces (lines 177, 182, etc.)
- There are also situations in which spaces are need to be added, for example between names and cross references (i.e., line 184).
- Regarding the figures placement is recommended if possibly center placed of all figures and their caption, for a better page aspect. Please see the editing rules for figures and caption.
- Figures also appear too large and therefore exceed the space of a single page for a figure, for example figures 11 and 13. It may be more appropriate to resize some of the figures for better page placement.
Comments for author File: 
Comments.pdf
Author Response
We would like to express our sincere thanks to you for the constructive and positive comments.
Point 1: For equations there should be a space before and after equation and also between equations in order to obtain an optimal visibility.
Response 1: Much appreciates for your detail suggestions, and we have found many such mistakes throughout the manuscript. We have corrected these mistakes in the revised manuscript.
Point 2: The equations font must also be adjusted because some indexes are written in too small font, also some terms are written in bold text other not. Please see the author guides for paper.
Response 2: Thank you for your constructions! The equations font have been checked throughout the manuscriptare. Some terms are written in bold text because they are vectors, while those normal are scalars.
Point 3: All equations are followed by comma. The punctuation signs after each equation should be avoided.
Response 3: Thank you for your suggestions! Commas follwing all equations is the requirement or format of the journal. We have checked the comma or dot after the quations. Yes, it should be a comma in the paragraph, while it should be dot at the end of the paragraph.
Point 4: On page 6 are two equations with the same numbering: 14C. Although in the text there is a reference to equation 14d. Please remedy this issue.
Response 4: Thank you for your careful observations! We have corrected all similar mistakes thourghout the manuscript. Thanks a lot!
Point 5: A chapter title is placed at the bottom of page 7. It should be moved to the next page for a better aspect of the paper.
Response 5: Thank you for your good suggestions. We have corrected it according to your suggestion.
Point 6: Please check the spaces across the paper because there are many situations of useless spaces (lines 177, 182, etc.)
Response 6: Thanks a lot! We have deleted all useless spaces.
Point 7: There are also situations in which spaces are need to be added, for example between names and cross references (i.e., line 184).
Response 7: Thank you for your constructive comments. We agree with you and apologize for such errors. We have added spaces between names and cross references.
Point 8: Regarding the figures placement is recommended if possibly center placed of all figures and their caption, for a better page aspect. Please see the editing rules for figures and caption.
Response 8: Thanks a lot! Figures have been center placed for a better page aspect. We prefer to display figures in longitudinal aspect.
Point 9: Figures also appear too large and therefore exceed the space of a single page for a figure, for example figures 11 and 13. It may be more appropriate to resize some of the figures for better page placement.
Response 9: Thank you for your good suggestions! We have resized all figures for better page placement.
Author Response File: Author Response.pdf
Reviewer 2 Report
Reviewed article concerns elastic correlative least-squares reverse time migration based on wave mode decomposition and is write in accordance with generally accepted standards of the scientific works. After careful reading of the submitted text there are some substantive remarks that should be taken into consideration by the Authors to improve reviewed text.
- The abstract should include information about new methods, results, concepts, and conclusions – in its current form, the abstract needs to be rewritten to include more information on achievements described in the manuscript.
- The Authors should clearly indicate what is the aim and the novelty in presented investigation.
- Presented study widely covers defined scientific problem and provides proper background for given conclusions, however deeper scientific consideration of obtained results referred to the basic phenomena in analyzing processes should be given.
- In the discussion section should be provide more references to already known results from literature.
- The strengths and limitations of the obtained results and applied methods should be clearly described.
- I suggest providing the main conclusions as numbered sentences and refer to specific values (results of analysis) as well as basic phenomena that cause described results.
- The conclusions should highlight the novelty and contribution to the state of the knowledge in given area.
Author Response
Please see the attached.
Author Response File: Author Response.pdf
Reviewer 3 Report
Authors developed a new inversion scheme for elastic LSRTM method. The title is clear, accurate and unambiguous. The abstract includes a clear overview of the study and the research problem. The introduction provides sufficient background and include all relevant information. The research design, methodology and framework are appropriate for this type of analysis. The results, charts and tables are clearly presented. Discussion and conclusion sections are also well written; however, some aspects should be improved.
1) Authors should add an additional paragraph and discuss why their approach is better to similar techniques already applied in geophysics. It would be good to quantify it performance.
2) please provide explanation/ justification of using 361x241 grid cells in 3.1 subsection vs. 1290x300 grid cells in subsection 3.2. Additionally, why you used such numbers? What do you think about detailed values for initial steps?
3) please include units for amplitude in Fig. 6, 7, 8, 14, 15.
After minor revision, I think manuscript will be ready for publication.
Author Response
We would like to express sincere thanks to you for the constructive and positive comments.
Point 1: Authors should add an additional paragraph and discuss why their approach is better to similar techniques already applied in geophysics. It would be good to quantify it performance.
Response 1: Thank you for your constructive suggestions! We have added an additional paragraph to discuss why the proposed method is well behaved compared to other techniques, and limitations. Then we set up another paragraph to provide main conclusions. The discussion section are attached below.
In contrast with inversion schemes of impedance, P- and S-wave velocity and other forms of elastic parameters, we chose to invert for the reflectivity images which represents physical meanings in geological interpretation. In numerical tests of images and shot records, we can find that the proposed method can balance the amplitude and compensate the illumination for deep structures, and improve the image quality, especially for the faults beneath the salt dome in SEG/SALT example. Besides, we have deduced the demigration operator which needs no extra decomposition in seismic records in comparison with works of ELSRTM of multicomponent seismic data, and thus reduce the cost of computation and free from an accurate velocity model required by separation of seismic records. In both the layered model and the SEG/SALT model, we have tested the efficiency of L-BFGS method against CG. Numerical tests have verified that the L-BFGS method converges rapidly that it derives the value of the objective function value to the minimum, which proves that it is more efficient.
As shown by Zhang et al. (2015) and Liu et al. (2016), the CLSRTM is expected to be practical and robust than the amplitude-matching based LSRTM.It relaxes the amplitude matchingand uses phase information to measure the closeness between simulatedand observed seismic data. However, it shares the commonshortcommings of the LSRTM, i.e. the accuracy of the migration velocity model, when compared to the ray theory based LSM, such as the Kirchhoff least-squares migration. We will further test its potential to real data.
Point 2: please provide explanation/ justification of using 361x241 grid cells in 3.1 subsection vs. 1290x300 grid cells in subsection 3.2. Additionally, why you used such numbers? What do you think about detailed values for initial steps?
Response 2: Thanks a lot! In migration community, the standard industry models are adopted to verify its effectiveness. In subsection 3.1, we design a model with 361×241 to verify the effectiveness of our method. There is not any specific consideration except for computing costs. In subsection 3.2, we adopt the original grid cells of the standard industry SEG/SALT model with grid cells of 1290×300. Thus, we obtain a modified SEG/SALT model with 1290×300 grid cells.
As for the detailed values for initial steps, we do not quite sure what is the meaning of your concerns. In section 2.7, we proposed a ECLSRTM scheme, the first step is to compute initial image and . The initial image are calculated through reverse time migration (RTM) based on observed data. This method can be summarized as: forward propagating the source wavefield and backward propagating the receiver wavefield (adjoint wavefield) in the meantime, then apply the cross-correlation imaging condition. Thus we can get the initial image of PP, PS, SP and SS.
Point 3: please include units for amplitude in Fig. 6, 7, 8, 14, 15.
Response 3: Thank you for your careful observations! The units for amplitude has been added in Fig. 8, 9, 10, 18, 19, 20.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have not taken into account comment 6 from the previous version of the review. Therefore, I ask again to provide the main conclusions as numbered sentences and refer to specific values (results of analysis) as well as basic phenomena that cause described results.
Author Response
We appreciate your suggestions and comments greatly. Actually, in the previous version of response, we have responsed your this comment and suggestion. We appolagized for the unclear clarification. Unlike experiment-based study, our study is a algorithm to process seismic data to obtain physical-meaningful images. It does not involve in any observations, or any basic phenomena such as those experimental driven study. This algorithm is based on some laws of physics (wave progragation theory of seismic waves) and numerical experiments, i.e. seismic equations and some industrial standard model. Due to many numerical experiments, specific values (results of analysis) will be tediously long so that they can not be listed in numbered sentences. Therefore, we summary their common characteristics or advantages in conclusions rather than listed specific values. We would say many thanks to you for your constructive suggestions. However, we think that our conclusions can be well represented in the current form instead of numbered sentences to list specific values. Certainly, this algorithm is expected to be robust and pratical in real data application. We will further study its effect in real data. As a result, some real observations will be obtained. In summary, we have adopted acorrelative objective function, which relaxes the amplitude matching and emphases the phase constraint. Therefore, we compared the phase information of synthetic shot, initial record and inverted record using the ECLSRTM in numerical tests. Besides, we also have analyzed the convergence rate of the CG and L-BFGS methods, numerical results have proved that the L-BFGS method has a faster comvergence rate than the CG method thus verifying the effectiveness of the L-BFGS method. In addition, The presented ECLSRTM improves the resolution of the results and generates balanced the amplitude. Compared with conventional methods, it frees from an accurate velocity model that unavailable in real data needed by separation of seismic records, and it also significantly improve computational efficiency. Nevertheless, we really appreciate your advice.
Author Response File: 
Author Response.docx
Reviewer 3 Report
Thank you for improving the manuscript.
Author Response
Thank you for your support and encouragement. We really appreciate your suggestions and comments greatly.
Author Response File: Author Response.docx
