Review Reports

Round 1

Reviewer 1 Report

In the results section a paragraph is required which indicates how the results from the frequency domain to the time-domain were obtained. i.e. the details of the numerical iFFT.  This would only take a short paragraph, no need to add a complete section. This brings me to the other small weakness: the authors produce a convergence graph, which is necessary and good to include. However there must be some limits on how high "N" must reach with respect to frequency? Indeed how "high" or sharp can the inhomogeneity be in terms of /beta?  Please elaborate with some detail here.

Also, it would be interesting for many readers who work on pipes for instance to consider the case where the interior region (1) has no material, i.e. is a vacuum - I understand including a fluid is beyond the interest here but a void would be interesting for readers.

Some English typos need treatment in the text: "Rick" instead of "Ricker" and line 185: "proof". It is not really a proof, is it. It's an ansatz to take the German phrase.

Overall, with some upgrades it is a nice paper.

Thank you

 

 

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

In this paper, an analytical solution to SH wave scattering by a cylindrical inclusion with inhomogeneous elastic modulus in a full space is derived based on the wave function expansion method. A comprehensive set of numerical examples are presented to illustrate the sensitivity of the underground motion to the rigidity profile of the geological inclusion. The paper is well written. I have only one question.

 

To reveal the mechanism of an inhomogeneous inclusion modifying the wave field, the wave function series solution to SH wave scattering by a cylindrical inclusion whose shear modulus varies continuously in the form of power function in the radial direction is derived in this paper. However, the paper only illustrates a couple of typical inhomogeneous examples. Can the author comment that how to analyze generous inhomogeneous inclusion? Do there any general analytical methods?

 

 

In addition, In line 149, “An” is not in the format of a formula.

Author Response

Please see the attachment

Author Response File: Author Response.docx