Modeling and Imaging of Multiscale Geological Media: Exploding Reflection Revisited

Round  1

Reviewer 1 Report

The paper presents an interesting study about modeling and imaging of geological media, developing a mathematical simulation that supplements the use of finite-difference methods on adaptive grids with the concept of exploding reflectors. This methodology not only offers good results but also reduce the computer resources.

I  recommend minor revision.  Please, consider the points hereinafter.

1.    Is affiliation 1 incomplete?

2.    Line 49: “of 0.1 - 0.2” show the units, please

3.    In line 94 you say “…and consider possible ways for further development”. However, I do not find in the text any comment about further development. Please, consider to include it.

4.    Line 116: Explain the meaning of each parameter, please.

5.    Line 120: please add that they are the Lamé parameters.

6.    Line 139: PU (Processor Unit)? You must explain the meaning of an acronym the first time that it appears.

7.    Line 147: Do you mean Figure 2? The Figure 2 is not cited in the text.

8. Line 166: " As we already mentioned (see section 2.2) told above…” I would suggest “As we already mentioned (see section 2.2) above…”

    9.    Line 178: “MPI” explain the acronym, please.

  10. Although the “Discussion” is very complete and interesting, I would suggest to increase the “Conclusions” part, underlining the methodology and results. Perhaps you could include here the comments on further development.

11. Line 383: Please complete the Acknowledgments section.

I apologize if I overlooked and/or misunderstood something. I hope that my comments may help you to improve the paper.

Author Response

1) All affiliations are complete now.

2) 0.1 - 0.2 of a dominant wavelength - it depends on velocity and dominant frequency.

3) Than you. We added our future efforts in the conclusion now.

4) Done.

5) Done

6) Thank you, done.

7) Thank you, it is really Figure 2.

8) Yes, Thank You, it is done.

9) Done

10) Done

11) Done

Reviewer 2 Report

Dear Authors,

Thank you very much for the research. I enjoyed reading the paper and, in my opinion, it is worth publishing. The paper is about a new and an efficient method to model zero-offset sections from an overburden with a target area – the reservoir - in which the former has a sparse discretization and the latter has a finer discretization to account for small-scale heterogeneities producing diffractions. The paper is well written but would benefit from clarifications, certain reformulations and changes in main points or ``story’’, how to address which, in my opinion, I formulate below. I recommend the paper for a moderate revision.

1.<span style="font-stretch: normal; ; ; ;Times New Roman";">     While reading the paper I was struggling to find the main point. On page 1 you start with ``diffraction imaging’’, which, in my opinion, is an interesting part of the paper, but putting it as the first point in the introduction distracted me from the main method described in the paper. May be put diffraction imaging in a separate section called application to diffraction imaging. The paper is not about ``carbonate environment’’ either. Also talking about multiples on page 9 and line 218 distracts from the main point of the paper.

2.     You indeed describe what contributions which author made to the paper. I think that explicitly describing the novelty of the methods would benefit the paper, e.g. directly stating that no one has ever applied the approach developed by Lisitsa et al., 2012 [2] to exploding reflectors.

3.     If I correctly understand formulas on page 11 are novel. Are they or they were derived in [2]? Please at least say that ``we derive’’, ``we propose novel formulas’’. While reading it I was convinced this is a conventional Born-modeling. Please revise the paper in this light so that the novelty stands out.

4.     I would mention finite-elements in the second paragraph on the second page and other possible schemes for adaptive grid or mesh refinement. What advantages does the method described in [2] have over other methods? Why your approach is advantageous? This would be really interesting to read about. Also why not first run downward continuation and then model the diffraction response?

5.     Second and third paragraphs on page 2 are in conflict – first, you claim that for proper discontinuity response modeling, excessive sampling is necessary. But then propose a way for adaptive gridding, which tackles the problem. I would first mention your proposed solution using the approach described in [2] but then still claim that indeed it should be more computationally efficient to model zero-offset sections. Indeed, after that, you can smoothly transition to the point that although reflections or in particular reflection-based velocity analysis becomes degenerate in the zero offset case, diffractions retain much more information about the subsurface and this is why the modeling approach presented in the paper is important for diffraction imaging.

6.     I would remove bullet points on the page 11. First I thought that you separately model the incident wave field and the reflected/diffracted/scattered. Is this the case? Is this what you do? What is the workflow? I think the paper would benefit from the clarification of a sequence of procedures?

7.     I also suggest condensing numerical section 2.4 – it also distracts from the main message of the paper. Figures look really nice though.

8.     Please mention how much faster is your approach than a conventional one (you refer to it as full model or full finite difference simulation). I would also describe what do you mean by full simulation – very fine sampling for the whole model?

9.     Could you please let me know why the reservoir has somewhat ``blocky’’ compartmentalization? Is this deliberate? I like the edges prominent in the Figure 11 c.

10. Starting from here are minor edits: page 1 line 18 ``rather than the shot-by-shot’’ -> ``rather than by shot-by-shot’’

11. Page 11 line 244 should be ``4.2’’ instead of ``3.2’’.

12. In the abstract. I don’t quite understand the sentence ``To be able to simulate realistic models…’’ -> may be just write you have also developed software, which efficiently implements the method.

13. Page 1 line 35 I would add some references to diffraction imaging.

14. Page 2 lines 49-55 I would put a condensed summary of these statements into the abstract to make potential connection with diffraction imaging clearer.

15. Page 3 line 84 ``depends’’ -> ``depend’’.

16. Page 3 line 87 may be talk more about zero offset diffraction imaging. Something like as at the end of my comment 5.

17. Page 3 line 96 ``Statement of the problem’’ -> ``Problem Statement’’

18. Page 4 line 135 ``Reservoir binding is doing by the coordinates of the opposite ends’’? Sentence is unclear to me.

19. Page 6 line 166 ``told above’’ -> ``mentioned above’’

20. I guess Equation 3 should have a hat over L

21. Page 2 line 80 conception -> concept

22. Figure 1: Both grids representing fine and coarse sampling look the same. Could you please make them different?

23. I do not quite understand what is going on in the Figure 2. Could you please elaborate? Figure 3 looks very clear. Is Figure 2 actually needed?

24. Please number equations in the appendix and finalize acknowledgements.

Author Response

1. See Introduction, Line 84:

The joint use of the exploding reflectors concepts and multiscale finite-difference simulation on the base of locally refined grids for the first time opens up the possibility to simulate realistic 3D scattered/diffracted data. We use this data to validate diffraction imaging approach to detect and delineate small-scale subsurface heterogeneities.

2. line 83: It is worth mentioning that joint use of the exploding reflectors concepts and multiscale finite-difference simulation on the base of locally refined grids for the first time opens up the possibility to simulate realistic 3D scattered/diffracted data.

3. line 249: Here we derive new formulas to reformulate statement with a point source to the exploding reflectors.

It is based on Born's like linearization, but there are additional considerations connected with asymptotic representation of the P-wave in smooth media (see Appendix B).

4. There are few advantages in comparison with finite elements:

a) we avoid one of the most difficult problem of the modern FE - mesh generation for complicated 3D geometry;

b) time-domain finite-difference at the moment is the most effective computational tool for simulation of wave propagation;

c) the main advantage is the possibility to apply effective time-stepping procedure.

When using adaptive finite elements there is necessary to adapt time step as well, which is not easy to implement.

Another advantage is that we do not need to fit grid with microheterogeneities - when grid cells are small enough the approximation should be satisfactory.

See the text from line 374 in the section "Discussion".

5. I cannot agree with you, because we say that simulation of the scattering/diffraction needs locally refined grids, but this is not enough and propose to be restricted to zero offset data.

6. You are right. For the beginning we decompose the model onto two constituent - the smooth macrovelocity/background and sharp perturbations for reflections/scattering/diffractions. We compute u_0 from by "inversion" of L_0 for the smooth constituent and continue with computation of u_1 by resolution of (2). Then we use ray method to represent the "incident" wave. As we deal with zero offset, we avoid (almost) singular points.

I cancelled bullets.

7. I would like to save this point - it is informative and as explains how we organize parallel computations and interactions between coarse and fine grids.

8. Please mention how much faster is your approach than a conventional one (you refer to it as full model or full finite difference simulation). I would also describe what do you mean by full simulation – very fine sampling for the whole model? 

As full simulation we mean very fine sampling, the same in overburden and in reservoir. Hence, I can not say how much faster is our approach - the same fine sampling in reservoir and overburden is unrealistic, while comparison for the coarse sampling is meaningless.

9.  "Could you please let me know why the reservoir has somewhat ``blocky’’ compartmentalization? Is this deliberate? I like the edges prominent in the Figure 11 c." Sorry, I do not know, the model is prepared by our colleagues from geological department. But what do you call 'blocky" is not reservoir. It corresponds to some layers under paleochannel, compare with Figure 5.

10. Done

11. Yes, thank you!

12. Thank you, see Line 22.

13. Done

14. Done

15. Done

16. I am not sure it would be reasonable. It is the different subject. The paper mainly is about how to compute zero offset.

17. Done

18. Now it is as:

The coordinates of the opposite ends of its principal diagonal determine reservoir position.

19. Done

20. Yes, thank you!

21. Done

22. ‍ Sorry, but these are not grids, but groups of Processor Units, which must be the same, they are from the same cluster.

23. I canceled it, now both refinement are on the same Figure 2.

24. Done‍