Generalized Pattern Search Algorithm for Crustal Modeling

Round 1

Reviewer 1 Report

Please, see my report attached.

Comments for author File: Comments.pdf

Author Response

Additional several new lines of text (lines 293-299) and new references (lines 433-440) are added to address the issue described by reviewer 1. In light of recent investigations, we discussed the issue of a potential decrease in k value few weeks or few months before the occurrence of a main shock.

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript shows an implementation of Generalized Pattern Search algorithm to H-k stacking on receiver functions. Overall, the authors presented the method and result clearly. The result from the new algorithm also matched previously published data from others. However, I do have some concerns, which are listed below:

Although proper references were cited through out the manuscript, I believe the authors missed several significant and recent publication in the field of receiver function processing. For example, there are other methods and advances in H-k stacking method (e.g., Li, Jiangtao, et al. "A generalized H‐κ method with harmonic corrections on Ps and its crustal multiples in receiver functions." Journal of Geophysical Research: Solid Earth 124.4 (2019): 3782-3801.) that the authors seem just dismissed. It is also important to state clearly what deconvolution method is used to attain the receiver functions used for the data being used to test the new algorithm. It is also important to be aware of some of the new algorithms (e.g., Wang, Yinzhi, and Gary L. Pavlis. "Generalized iterative deconvolution for receiver function estimation." Geophysical Journal International 204.2 (2016): 1086-1099.) as well as their difference in the characteristic of the results, which can certainly affect how the H-k stacking method behave. Overall, the reference is a little thin, and that leads to some of the aspect of receiver function processing not being covered in the manuscript.

In addition, I think Figure 1 is not properly cited. This is apparently a figure adopted from Ammon, Charles J. "The isolation of receiver effects from teleseismic P waveforms." Bulletin of the seismological Society of America 81.6 (1991): 2504-2510. The authors did not properly cite it in the caption, which may lead to the misconception that it is original.

Figure 2 is an example of lacking discussion of deconvolution methods. It is not clear how those receiver functions were generated. Moreover, there is no labels or proper captions to help the user understand why there are this many panels in this figure. I can guess that these are just some traces being picked out as examples, but why these are chosen as opposed to others remains a puzzle to me.

The other major problem is in the implementation of the GPS method. The manuscript claims that the H-k stacking equation has five parameters, but in practice, people do not usually consider w1, w2, and w3 parameters. This is because they have a much less degree of freedom compared to H and k. In principle, w1 is always given the greatest weight, and w2 and w3 should be given similar weights. Also, people usually set a w1 that is greater than w2+w3. None of these conditions were presented or discussed in the implementation of the GPS method. However, later in Figure 3, it appears from the GUI that certain limits are implicitly posed to these weights such that the upper limit of w1, w2, w3 are set to 0.6, 0.6, 0.4. All three inversion results having w1 determined to be 0.6 seems indicating that the limit is also set in the inversion. I am not sure why this is not mentioned in the manuscript.

The last point I have is that the authors only used data from a single station to validate the new method. This might be OK to show that the method works, but I do believe the tests could be done with a better control over the factors that might affect the result. At least, a number of data from a range of geologic settings should be tested with the new method to validate the effectiveness. It might also help address this question that I end up wondering after reading through the manuscript: why do people need this new method?

Author Response

Addressing the comments by Reviewer 2:

1. We included many references including many recently published ones (References 27-34). In addition, many additional references are used and cited in the supplemental material.
2. We clearly stated the deconvolution method applied in our study and we also discussed some of the recent advances and developments in the area of deconvolution methods (lines 58-73). The added material here makes up almost one completely new paragraph.
3. The supplemental material associated with this article discusses some of the details of the practical aspects of computing receiver functions (Section 2.1) and also provides many additional information.
4. We added the proper citation for figure 1 [ J. Ammon, 1991 [21]].
5. Figure 2 has been re-assembled and new text is added on the figure caption to clarify some of the important points which are displayed on the figure. Moreover, some discussion points are added on how these receiver functions are generated as well (lines 226-232 and 253-254).
6. Comments and suggestions about the three weights used in the GPS implementation have been addressed through added new lines in the manuscript (lines 234-238).
7. The main purpose of our article is to show that the new GPS method of computation works for determining crustal thickness and k Thus, I agree with reviewer 2 in that aspect in which our displaying of the results from the one station is OK to show that the method works. However, if the focus of the article is changed to the application of the newly introduced method for a region, we may include many more results from different stations and different geographic locations. However, though this last suggestion and comment is very good for future extension of the current research, trying to include many more results takes a lot of article space, time and resources.

Round 2

Reviewer 2 Report

I am glad that most of my previous comments were addressed in this revision. While I'd still like to see a more extensive validation of the new method, I understand that it requires a lot more additional efforts. Thus, I am fine with accepting the paper in the present form.