Wavefield Reconstruction Inversion Based on the Multi-Scale Cumulative Frequency Strategy for Ground-Penetrating Radar Data: Application to Urban Underground Pipeline

Round 1

Reviewer 1 Report

This paper is difficult to read because of long sentences. Nevertheless, this is an interesting paper. It proposes a method for the detection of underground pipelines based on wavefield reconstruction inversion strategy. It compares several strategies using numerical simulation. An application on a test site is also presented.

The context and issues are presented in (a long) introduction, the content of the paper is detailled and the objectives to valorize the methods appear clearly.

The algorithm, the numerical study and the experimental application are well detailled, especially the use of the addition of more frequency components at each frequency sub-sequence, designed as "strategy". The fact to increase the number of additionnal frequency shorten the number of iteration but it results in an increase of errors. At this point, man can obviously assumes that a compromise between the precision of results and the number of iteration should be found to enhance the method. This can perhaps be mentionned in the discussion part.

Some sentences in this paper extends up to 5 lines (or more !), which is too long and can saturate readers. Consider cutting these long sentences into 2 or 3 shorter ones.

Some remarks are included in the pdf file. I add some sentences rewritting propositions hereafter :

*introduction : consider sentence length reduction (example : lines 95 to 107 and lines 110 to 118 : replace semi-column ( by a point (.)

*Lines 240 & 319 : smallER and largeR ?

*Line 264 : can be FOUND

*Lines 275 & 283 : the strategy B1 appears with the smallest...

*Figure 8 : in the third group of circular anomaly (upper right), the circle on the left shoud be brown in the figures 8a and 8b

*Lines 354 & 355 : Wouldn't it be better to write "while the end number of iteration of  B2 > B5 > B3 > B4" ?

*Lines 351 to 357 : Long sentence, consider replacing semi-column ( by a point (.). Same for lines 357 to 364.

*Line 358 : the strategies B1 and B2 APPEAR WITH the smaller final error.

*Lines 360 to 361 : "the end errorS of B3, B4, and B5 increaseS slightly" : is "error" singular (so it increases), or plural (errors (...) increase) ?

*Lines 361 to 362 : the reconstruction ERROR of strategy S begins TO decline.

*Lines 382 to 383 : The left one is an empty pipe with a diameter of 0.12 m, and the right one is a pipe with a diameter of 0.08 m filled with soil (...)

*Lines 416 to 418 : (...) each inversion sub-sequence is equivalent to providE a better initial model for the next sub-sequence. Thus, the PERFORMED inversion is more accurate and stable than (...)

*Lines 439 to 440 : that is an appropriate regularization ABLE TO eliminate some inaccurate inversion trends  (...)

*Line 452 to 453 : the frequency inversion method was COMBINING (...)

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

General comments:

This paper presents an EM reconstruction inversion strategy, using in the frequency domain GPR data for the detection/location of urban pipelines. Through a numerical study, the authors shows that a frequency weighting strategy can avoid the high-frequency component data domination, optimize the process and enhance the stability of inversion.

The article is interesting but a lot of information are missing, mainly on the inversion process itself, requiring detailed justifications. That is why, my global comments lead to recommend a “Major revision”.

 Details and questions:

• L32: the reader expects a reference dedicated to management of utilities and standards – or guidelines, and not on the use of GPR.
• L73: please, replace “Ref. [15]” by “Watson”
• L77: idem, replace “ref [14]”, by “Bunks et al.”
• L96: replace “ref [26]”
• L98: replace “ref [27]”. Same presentation to be modified in L101, 103, 105, 107, 176
• L231: the green colour of the conductivity of the background medium suggest a value of 0.005. Please, specify the diameter and the depth cover of the utilities
• L234: similarly, there are several differences between the conductivity values in the text and those in Fig. 1b;
• L243: The text does not specify what are the strategies Bi, please add information (idem for strategy S, for which we do not know how many sub-sequences were fixed). This lack of information does not allow to understand with strategy is better and why, considering that all, but strategy S, give roughly similar results.
• The reader understand that the parametric study is focused on the choice and the weight of the chosen frequencies to be inverted. It must be noted that the greater influence of the high frequencies could be due to the definition of k² with e and s as constants. This last hypothesis is not correct. As consequence, as the EM attenuation is proportional to sigma/w, this induces a contribution stronger than reality for high frequencies. Please comment this point.
• Section 3.3: How is estimated the permittivities and conductivities of the quartz sand and the sand in the pipe ? and does that correspond to the inverted estimations ?

References

• Some references on GPR applied for the detection/mapping of utilities should be added

Author Response

Please see the attachment.

Author Response File: Author Response.docx

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.