High-Resolution Coherency Functionals for Improving the Velocity Analysis of Ground-Penetrating Radar Data
Round 1
Reviewer 1 Report
This paper describes the use of high-resolution coherency functionals for improving GPR velocity analysis. My main remarks are the following:
(1) My main concern is whether the methods and results described are innovative and significant enough by themselves to justify a paper. All the methods used have been developed and described elsewhere (references [8, 11, 12]); the only new thing is that here it is applied to a GPR data set. The significance could be increased by discussing some other published methods for hyperbola detection and velocity analysis of common-offset GPR data (e.g. Mertens et al. 2016 in IEEE TGRS; Maas & Schmalz 2013 in Computers & Geosciences; Ristic et al. 2009 in Computers & Geosciences, to give just a few examples, there are other publications dealing with these problems). Applying these approaches to the data presented in the manuscript, and comparing the results, could be informative, for example since the abovementioned methods could mitigate the problem of the computational cost (see e.g. lines 288-289 and the last paragraph of the conclusion).
(2) The abovementioned papers also signal the problem of the radius of the buried object, which is unknown in real data. Although in the current manuscript this problem is discussed in the section on the synthetic data (lines 225-228, 233-241), it is not elaborated sufficiently when dealing with the real data. It should be discussed in more detail how the proposed methods can estimate the radius of the object in real data, and how these methods avoid selecting the wrong velocity by including objects with a larger radius in the velocity analysis. Lines 397-399 seem not sufficient as an explanation of how to solve this problem.
(3) The line spacing of 50 cm (line 100 of the paper) is larger than what has been shown to be acceptable (see e.g. reference [19]), and what is recommended for archaeological sites (e.g. in the EAC guidelines for the use of geophysics in archaeology). How can the authors know that small features were not missed if such a large line spacing was used?
(4) Lines 204-206: could these problems with modelling based on ray-tracing not be avoided by using FDTD modelling (e.g. gprMax)? Several problems with ray tracing are described e.g. in reference [3].
(5) The methods presented in the paper allow to generate accurate velocity models, also varying laterally and in depth (Figure 5), allowing better imaging of features in profiles and slices. The question is, however, how they compare in speed and accuracy with simple methods such as hyperbola fitting or migration velocity analysis (also these allow generating varying velocity models). This should be further elaborated in the paper, by applying these methods to the presented data and comparing the results.
(6) Line 368: ‘consistent with the archaeological findings’: this is not the case everywhere (e.g. the wall running in southern direction (from the large square structure central in the trench) is not visible in the GPR data. Please discuss the correspondence (or not) of GPR data and excavated data in some more detail, and give possible explanations why some features are absent in the GPR data.
Other remarks:
- line 70: ‘small reflection on top’: please explain
- line 76: ‘coherency’: please give a definition here
- line 78, 153: ‘CDP’: the abbreviation for common midpoint gather is CMP
- line 79: ‘higher resolution’: why is this so?
- line 203: ‘a 170° angle’: please clarify.
- line 276-277: ‘range [120–500] MHz’: the upper frequency limit is lower than the centre frequency of the antenna ?
- line 317-318: ‘without imposing limits on the dip angle and on the available frequencies’: please clarify.
- line 319-320: ‘fairly collapsed’: this seems less the case for position E in Figure 8a. Please explain why this is.
- line 325: ‘multi-channel filtering process’: please explain what this is.
- line 352: ’25.9-29.8 ns’: this does not correspond with Figure 10, which shows slices until 36 ns.
- line 375: what are ‘interlocked decimetric boulders’ ?
- line 376-377: ‘top of these structures corresponds to a flat reflection’: is this visible in the data presented in Figure 6? If so, please indicate on the Figure.
Remarks regarding the language:
- line 49, 219, 291: impose instead of ‘over-impose’
- line 88: ‘algorithm’ (singular)
- line 94: Badia Pozzeveri
- line 241: ‘not possible / impossible’
- line 345: datasets
- line 360: please improve the construction of this sentence.
- line 377: ‘a flat reflection’
- line 400: ‘better than’
- line 408: ‘better imaged’
Please check reference [6] (spelling)
Author Response
Thank you very much for your insightful comments on the paper. We replied to your comments in the attached PDF file.
Best regards
Author Response File: 
Author Response.pdf
Reviewer 2 Report
A few notes authors might want to consider:
Line 40/41 – sentence seems fragments or parts do sync well
Line 94 – is a space missing in name of site? Or added to name in line 87?
Line 106 – allowed to discover is awkward phrase
Line 157 - should be “comment on them”
Line 242 – allows to estimate is awkward wording
Line 311 – d) Location H Ccmcm pick at about 32 ns seems inconsistent with other picking strategies employed in picking the velocity. Maybe do to the same and that the red dot obscures a high value spot? And why wasn’t a spot picked at 10 ns?
Line 354 – allows to better image is an awkward wording.
Line 377 – corresponds to flat a reflection sound odd. Maybe to a plane reflector, while the boulders to the arms of a hyperbolic reflector.
Line 400 – should be “perform better than in the case”.
Line 407 – allows to obtain is awkward wording
Line 423 – should be “cases”
Line 424 - should be “image”
Author Response
Thank you very much for your insightful comments on the paper. We replied to your comments in the attached PDF file.
Best regards
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper provides an interesting and well-presented comparison of three functions for estimating coherency to hyperbola arms. A previous article by two of the authors, reference [14], has a similar comparison of coherency functionals. Still, this paper has details for the comparison, particularly for the field of archaeology GPR with adjustments required for hyperbolas created from finite-sized targets and with the velocity estimates used to create a spatially varying velocity field used in migration. This is my understanding of the novelty of the paper.
I ask that the authors clearly and succinctly state their view of the innovation of the current paper in the abstract or introduction.
My only technical requests are for the authors to clarify figure 10. Firstly the axes are hard to read without zooming in, but they also appear to be incorrect, with the area being listed as being 20 cm x 40 cm; I think this should be meters. Secondly, by modifying line 352 – I think the time-slices are 28, 31, and 34 ns, but the text on the images implies perhaps that a range of time values are averaged?
Some of the highlights on the figures (e.g., red circles) are a bit hard to spot without zooming in to them, but they are acceptable in their current form.
Author Response
Thank you very much for your insightful comments on the paper. We replied to your comments in the attached PDF file.
Best regards
Author Response File: Author Response.pdf
Reviewer 4 Report
The paper is interesting and includes real and synthetic data. I suggest to improve the presentation including all the main results and the comparison between unmigrated data (field and synthetic), migrated data with a constant velocity (field and synthetic) and migrated data with variable velocity (field and synthetic).
Other comments are:
- In the site description and GPR survey section, the authors declare that the distance between radar lines is 50 cm. I suppose that the time slices are obtained using interpolation. It could be useful to know what type of interpolation.
- In Figure 1, the line numbers are over the map. Perhaps it is only in the version that I have for revision. However, be sure that it is correctly placed.
- In Figure 6 the authors declare that the radargrams aare sections of radar lines L74 and L92. It could be useful to indicate, over the radar lines in figure 1, the sections selected and analysed. Indicate also location F, E, G and H.
- In line 364, “This is an effect of the non-optimal 364 velocity used in the migration” The images demonstrate that the velocity was not defined by means of the hyperbolas. The authors must discuss what happens in the case of a velocity constant obtained as an average value for all the B-scan.
- The field data allows to obtain slices. I suggest, in order to compare better the results with the synthetic data, to simulate 3D data and determine also slices.
- In Figures 8 and 9, it is not clear what are the anomalies named G, H, E and F. What happens with the other anomalies? Also, arrows for G and H I suppose that are slightly moved with respect the radargram
- In Figure 9, put the same arrows in the two images, in order to define better the compared anomalies
- The authors must explain widely the way to obtain the different velocities in the B-scans. Is an experimental field of velocities obtained of only are considered two or fields of velocities corresponding to the most relevant anomalies? I suggest to include a most general field, not only focused in the location of the selected anomalies.
- Another point that can be improved is the state of the art. Some references about migration are missing. For example:
Moran, M. L., Greenfield, R. J., Arcone, S. A., & Delaney, A. J. (2000). Multidimensional GPR array processing using Kirchhoff migration. Journal of applied Geophysics, 43(2-4), 281-295.
Leckebusch, J., & Peikert, R. (2001). Investigating the true resolution and three‐dimensional capabilities of ground‐penetrating radar data in archaeological surveys: measurements in a sand box. Archaeological Prospection, 8(1), 29-40.
Zhao, W., Forte, E., Pipan, M., & Tian, G. (2013). Ground penetrating radar (GPR) attribute analysis for archaeological prospection. Journal of Applied Geophysics, 97, 107-117.
Allroggen, N., Tronicke, J., Delock, M., & Böniger, U. (2015). Topographic migration of 2D and 3D ground‐penetrating radar data considering variable velocities. Near Surface Geophysics, 13(3), 253-259.
And more other references based in this subject. I suggest to improve the state of the art because this part could be improved.
9. Finally, it could be interesting a discussion in
Author Response
Thank you very much for your insightful comments on the paper. We replied to your comments in the attached PDF file.
Best regards
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
A number of remarks signalled in my review of the original manuscript have been addressed by the authors. A few other problems remain:
Regarding the problem of the radius of the buried object (my remark No. 2 to the original manuscript):
I realize that in real GPR data there are few objects with a perfect cylindrical shape. What I meant is that the fact that the objects have finite dimensions (unlike point diffractors) results in considerable uncertainty when conducting the velocity analysis in common-offset GPR data. This has been shown in several papers (e.g. reference [8], or in Jacob and Urban, Archaeometry 58, p. 987-1002, to name just a few). This uncertainty can also result from
dipping interfaces that generate diffraction-like patterns. In the case of diffractors with finite dimensions, the authors propose to select only the hyperbola arms, and to avoid the top planar part (lines 389). Here, it should be discussed more in detail how to do this (e.g. how can the transition between the top planar part and the hyperbola arms be determined? Why can this improve the quality of the velocity analysis? Can this be turned into a general method useful for all GPR users?). Moreover, it should be clarified whether this entirely solves the problem of the uncertainty of velocity analysis (i.e. can the velocity be determined precisely, if nothing is known
about the character and dimensions of the object causing the hyperbola?), as this would be a considerable improvement, see e.g. the papers referred to
above. In my view it does not completely remove uncertainty (in common-offset data).
Regarding the bandpass filter (line 257), and looking at the profiles in the response letter: I am not sure if the noise between 5-10 ns is only caused by high-frequency noise that should be suppressed by a band-pass filter with a very low upper frequency limit. It may be useful to analyse the traces affected by this noise to see what else is going on.
Line 301: 'fairly collapsed': I do not understand why, if the right arm of event E is similar to the regular arm of a hyperbola (line 263), this diffraction is called 'fairly collapsed' (in my view also the right arm is not well collapsed).
Line 375: 'interlocked decimetric boulders': please insert the clarification in the response letter also in the paper. This is unclear for most readers.
Language:
Line 54: 'hyperpola detection'
Line 71, 262: 'misshapen hyperbola'
Line 298: 'on the one hand'
Author Response
Many thanks for the comments, we reply to these in the attached file.
Author Response File: Author Response.pdf
Reviewer 4 Report
Thank you for the answers to my comments.
Author Response
Many thanks to the reviewer for the time dedicated to our paper.
