Tomographic Joint Inversion of Direct Arrivals, Primaries and Multiples for Monochannel Marine Surveys
Round 1
Reviewer 1 Report
The manuscript introduced a joint traveltime inversion of direct arrivals, primaries, and multiples for monochannel marine surveys. The current version lacks coherence and requires major clarification, especially on the results. Below I provide some comments and suggestions which may help further improve the manuscript.
- It seems that the proposed joint inversion scheme has not been applied to the field data example. Since from both the text and figures 9 and 10, I did not find the corresponding results of the inversion. The authors only mentioned Dix formula around Figure 9. What the motivation of showing Figure 8 with clear picked horizons (but Dix formula only involves traveltime of primary ABC and zero-offset traveltime). Why not compare the two methods like in synthetic data example?
- In Figures 3 to 6, what do the red circles denote? Tomography + Dix or only Dix (the text says based on formula 7 only) ?
- Please explain that why the results of Dix (red circles) in Figure 3 are located at the left-bottom area (“systematically lower than the true ones”), while the (most) Tomography results are opposite (see (b)and (c) and this is quite obvious).
- In Line 295, the authors concluded “the late arrivals from multiples are prone to larger errors than the early ones.” This looks quite natural but from the field data (Figure 8) we may find high-quality late arrivals. The proposed method includes late arrivals compared with Dix formula, if the late arrivals are prone to larger errors, then what is the advantage of the proposed method? You may just check this with the synthetic example by adding larger error to the late multiples.
- Other minor issues:
Figure 2, how the 50 traces are arranged since the trace number in the figure is about 500, please clarify it in the text and the figure.
Line 110, the ray bending in negligible, in to is.
Line 204, Jut to Just.
Exchange the position of Figure 8 and 9.
Figure 8, I spot the pink as purple/violet, and brown as red, please check.
Author Response
The manuscript introduced a joint traveltime inversion of direct arrivals, primaries, and multiples for monochannel marine surveys. The current version lacks coherence and requires major clarification, especially on the results.
We added a new paragraph explaining how the object function is built and then used for the joint traveltime inversion of primaries and multiples. This new part explains that we cannot expect the usual benefit of joint inversion (e.g., for direct, reflected and refracted waves) because each added multiple is adding a new unknown too, so that the Null Space is not reduced.
Also, we validated further the joint inversion by adding a second inversion kernel based on the parametrization of the incidence angles of the raypaths, which is slightly more stable than the direct joint inversion in the time domain. The reason for this difference is that the solution space dimension is 4 in the time domain, and 2+2 in the angle domain – (the water velocity and depth are solved first, independently, and the layer velocity and thickness are solved later, in a layer-stripping approach). These minor differences are visible in the new version of Figures 3 to 6, and are mentioned in the Conclusions.
It seems that the proposed joint inversion scheme has not been applied to the field data example. Since from both the text and figures 9 and 10, I did not find the corresponding results of the inversion. The authors only mentioned Dix formula around Figure 9.
We totally reprocessed the presented data by expanding the sub-section and taking into account variations of the offset during the acquisition, due to variable tension and feathering of the cable. We found out that this factor is more relevant than what we believed in the original submission, so we included in the revised manuscript and in the Figure 10. In the revised Figure 9 and 10, the tomography result is included with the Dix post-processing added. The latter one provides unreliable absolute values, but the trend is consistent with that one of the tomographic inversion.
What the motivation of showing Figure 8 with clear picked horizons (but Dix formula only involves traveltime of primary ABC and zero-offset traveltime).
Recognizing the multiples in Figure 8 only, without the interpretation based on Figure 7, might be quite questionable. For this reason, we prefer showing these two figures in sequence. Figure 8 is a zoom that allows appreciating the waveforms better than in the compressed scale of Figure 7, so adding information to the reader.
Note that the zero-offset traveltime is NOT measured directly – (as we have only a single non-zero offset trace available) – but estimated from the multiple inversion. So, in our specific case, we must pick both primaries and multiples. We remarked this point in the Discussion.
Why not compare the two methods like in synthetic data example?
We did so, as suggested.
In Figures 3 to 6, what do the red circles denote? Tomography + Dix or only Dix (the text says based on formula 7 only)?
We clarified that the red circles denote the solutions in the angle domain, followed by a post-processing using the Dix formula.
Please explain that why the results of Dix (red circles) in Figure 3 are located at the left-bottom area (“systematically lower than the true ones”), while the (most) Tomography results are opposite (see (b) and (c) and this is quite obvious).
We introduced a new paragraph in the Discussion trying to explain the differences in the estimation.
In Line 295, the authors concluded “the late arrivals from multiples are prone to larger errors than the early ones.” This looks quite natural but from the field data (Figure 8) we may find high-quality late arrivals. The proposed method includes late arrivals compared with Dix formula, if the late arrivals are prone to larger errors, then what is the advantage of the proposed method?
If we do not use late arrivals, simply we do not have enough data to constrain our equations. The key point of the proposed method is using a multiple to replace a (missing) zero-offset trace in a Boomer survey with a single offset trace available. Thus, the advantage is reducing the acquisition cost and complexity (by adopting a monochannel Boomer system) while still getting semi-quantitative information about the thickness and velocity of a shallow layer.
You may just check this with the synthetic example by adding larger error to the late multiples.
We agree definitely with the point, and indeed we recently carried out tests with different error levels in a paper published two months ago (Vesnaver and Baradello 2022). To avoid extending too much the paper length and widening too much its scope, we prefer sending the reader to that paper for further details.
Other minor issues:
Figure 2, how the 50 traces are arranged since the trace number in the figure is about 500, please clarify it in the text and the figure.
We did so both in the caption and in the main body.
Line 110, the ray bending in negligible, in to is.
Corrected.
Line 204, Jut to Just.
Corrected.
Exchange the position of Figure 8 and 9.
Sorry, we do not understand the reason for this request. Figure 8 shows the picked traveltimes used for the inversion, i.e., the Input, while Figure 9 shows the inversion result, i.e., the Output. Normally, the Input precedes the Output … We believe that inverting the order of these figures might reduce the presentation clarity.
Figure 8, I spot the pink as purple/violet, and brown as red, please check.
Corrected both in the caption and in the main body.
Reviewer 2 Report
The manuscript under review presents a tomographic approach that exploits 13 multiple reflections, in addition to primaries and direct arrivals, which works for monochannel surveys with a short offset. The manuscript is well organized and the math sounds good. Real data has been applied to the proposed method and the results are good.
I'd suggest accepting the manuscript as is.
Author Response
We thank the Reviewer for his/her appreciation.
Round 2
Reviewer 1 Report
Thank you for the authors' revision and response. My issues are well addressed and I would like to suggest the revised version for publication.
I am pleased to see the better results for the alternative inversion kernel by perturbing the angles. I may suggest also remarking this inversion kernel in the Abstract.
Figure 5 lacks the title of the y-axis, though more minor issues will be addressed during the proofreading process.
