Effect of Rock Structure on Seismic Wave Propagation

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: [Physical units and "energy." AE voltages are expressed in joules of energy. Without a thorough electromechanical calibration (sensor sensitivity in V/Pa or V/(m/s)), amplifier gain, impedance, and the formulas that convert voltage to stress/particle velocity and then to mechanical energy with units carried), this is not valid. Therefore either present the entire calibration chain and step-by-step conversion formulas, or report normalized signal energy, RMS, or band energy in dimensionless or dB form and eliminate SI energy units.]

Response 1: [Thank you for your insightful comment regarding the physical units of energy. We agree that converting the measured AE voltage directly into Joules without a complete and rigorous electromechanical calibration is inappropriate. Your suggestion to use a relative or dimensionless form is excellent and improves the scientific rigor of our manuscript.

Following your recommendation, we have revised the manuscript to report the signal energy in relative terms rather than in absolute SI units. Specifically, we have implemented the following changes:

We have replaced the unit "Joules (J)" with "arbitrary units (a.u.)" for all energy-related parameters throughout the manuscript, including in the text, tables (Tables 2-5), and figure axes.

In the methodology section (Section 2.3), we have added a clarification. We now explicitly state that the reported energy is a relative value, calculated as the integral of the squared Hilbert envelope (∫Hilbert envelope² dt), and is presented in arbitrary units (a.u.) to reflect relative changes and attenuations.

The core conclusions of our paper, which are based on the percentage of energy attenuation and the relative differences between measurements, remain unaffected by this change.

We believe these revisions fully address your concern and have made our presentation of the data more accurate and robust. Thank you again for your valuable guidance.]

Comments 2: [Dimensional consistency of interface/crack transmission theory.

The existing formulas combine impedance and specific stiffness in ways that are inconsistent across dimensions. I t is recommended to take action by implementing a standard linear-slip interface with normal/tangential specific stiffness, define each symbol and carry units; calculate R and T for P/S incidence and obliquity. Compare the measurements with the predicted R, T, and ? frequency curves.]

Response 2: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We sincerely thank the reviewer for this insightful and constructive comment. We agree that the theoretical model used in the original manuscript was overly simplified and lacked rigorous physical grounding. Following the reviewer's excellent suggestion, we have completely revised our theoretical framework.

The key modifications are as follows:

1.Implementation of a Standard Model: We have replaced the previous ad-hoc formula with the well-established linear-slip displacement discontinuity model (DDM). This model provides a physically sound and dimensionally consistent basis for analyzing wave propagation across interfaces and fractures.

2.Revised Theoretical Section: We have rewritten the theoretical analysis sections (previously in 3.1 and 3.3). The new section introduces the DDM and defines the crucial parameters of normal specific stiffness (K_N) and tangential specific stiffness (K_T). We have provided the standard equations for reflection and transmission coefficients for normally incident P- and S-waves.

3.Clear Definition of Symbols and Units: A new table (now Table X) has been added to explicitly define every symbol used in the model, along with its physical meaning and corresponding SI unit, ensuring clarity and reproducibility.

4.Re-evaluation of Experimental Data: We have re-interpreted our experimental results for both open cracks (angle and width studies) and the compressed interface within this unified DDM framework. We demonstrate that the model's prediction for a compliant, air-filled crack (K_N→0, leading to near-zero transmission) is in excellent agreement with our experimental observations of over 99% energy attenuation. This strengthens the connection between our data and the underlying physics.

We believe these comprehensive revisions have significantly improved the scientific rigor of our manuscript and have fully addressed the reviewer's concerns regarding the theoretical model's consistency and validity.]

Comments 3: [Boundary condition representativeness.

There is no confining or pore pressure, the specimens are dry, only axial load is applied, and the temperature is room temperature. I tis recommended either to restrict claims to unconfined, dry analog tests and talk about the ramifications, or to broaden the program (temperature, fluid saturation, triaxial confinement) and demonstrate how results vary.]

Response 3: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [Thank you very much for your valuable feedback on the representativeness of experimental boundary conditions. We fully agree that the experimental conditions used in this study (room temperature, dryness, no confining pressure) are a simplification of the in-situ environment of complex geothermal reservoirs.

Our approach to making this modification is as follows:

Admitting limitations and clarifying research scope: We recognize that it is extremely complex to fully replicate conditions such as high temperature, high pressure, and fluid saturation in geothermal environments. Therefore, we explicitly state in the revised manuscript that the purpose of this study is not to perfectly replicate the in-situ environment, but to isolate and quantify the fundamental physical mechanisms of the influence of geometric structures such as crack angle, width, and interface on seismic wave propagation parameters. By simplifying the boundary conditions, we can minimize the coupling effects of various factors such as temperature, fluid, and confining pressure, thereby revealing the structural behavior more clearly. This provides an important baseline and reference for future research under more complex conditions.

Targeted revisions in the manuscript: Based on your suggestions, we have made revisions in multiple sections of the manuscript to ensure that readers can clearly understand the scope and premises of this study.

In the Introduction section, we have added limitations on the scope of the study, indicating that it is a simulation study under simplified laboratory conditions.

In the Methodology section, we clearly stated the reason for choosing the current experimental conditions, which is to isolate variables and focus on structural effects.

In the Discussion section, we have added a dedicated paragraph titled 'Limitations and Future Work'. Here, we have discussed in detail the specific effects that factors such as confining pressure, fluid saturation, and temperature may have on the experimental results, and pointed out that these are important directions for future research.

In the Conclusion section, we once again emphasized that the conclusion was drawn "under the current simulation conditions".

We believe that through these revisions, the scientific rigor of the manuscript has been strengthened and its academic contribution has been more accurately positioned. Thank you again for your valuable feedback!]

Comments 4: [robustness and transparency of signal processing.

The workflow for EMD/HHT is vulnerable to end effects and mode mixing.

Add a processing flowchart that includes all of the parameters (filtering, sampling, sifting stop criteria, boundary treatment, and whether EEMD or EEMD-CE was used). Give a precise definition of "dominant frequency" (FFT peak, spectral centroid, IMF-ridge). Provide sensitivity checks that demonstrate the conclusions are invariant, such as fixed band energy ratios or STFT.]

Response 4: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We sincerely thank the reviewer for this insightful and constructive feedback regarding the robustness and transparency of our signal processing methodology. We agree that a more detailed description is crucial for the reproducibility and credibility of our results. In response, we have made substantial revisions to the manuscript.

Enhanced Transparency of the Processing Workflow: We have completely revised Section 2.3 and the accompanying flowchart in Figure 3 to provide a detailed, step-by-step description of our workflow. The revised section now explicitly states:

The sampling frequency (3 MHz).

The specific parameters for the EMD algorithm, including the sifting stop criterion (a Cauchy-type convergence criterion) and the boundary treatment method (characteristic wave-based extension) used to mitigate end effects. We have clarified that the standard EMD algorithm was used.

The full definitions and calculation methods for all extracted parameters.

Precise Definition of "Dominant Frequency": As suggested, we have replaced the ambiguous term "main frequency" with a more robust metric. We now define frequency as the spectral centroid of the FFT power spectrum. We have included the mathematical formula for its calculation in the revised Section 2.3. This provides a more stable representation of the signal's central frequency.

Sensitivity Analysis for Robustness: To address the important point about validating our conclusions, we have performed a sensitivity check using an alternative time-frequency analysis method. We have added a new subsection, Section 5.3: Robustness of Time-Frequency Analysis, to the Discussion. In this section, we describe the application of the Short-Time Fourier Transform (STFT) to our data. The results from the STFT analysis corroborate the findings from HHT, confirming that the significant energy attenuation observed is a robust physical phenomenon and not an artifact of the HHT method.

We believe these comprehensive revisions directly address all the concerns raised by the reviewer, significantly strengthening the methodology and the overall quality of the manuscript. We are grateful for the opportunity to improve our work.]

Comments 5: [Uncertainty and statistics.

Model fits, effect sizes, and mean±SD/95% CI are not included when presenting trends. I t is recommended to fit basic attenuation models vs. angle/width with confidence bands and goodness-of-fit (R2, p-values, residual plots); report n, mean, SD, and 95% CI for amplitude, frequency, and energy metrics for each configuration and sensor.]

Response 5: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We thank the reviewer for this constructive and important feedback. We agree that a robust statistical analysis is essential for strengthening the conclusions of our study. In response to this comment, we have made the following significant revisions to the manuscript:

Added Comprehensive Descriptive Statistics: We have revised Tables 3 and 4 (now renumbered as Tables 4 and 5) to include not only the mean values but also the number of replicates (n=10), the standard deviation (SD), and the 95% confidence interval (CI) for all reported metrics (amplitude, frequency, and energy). This provides a clear quantification of the experimental uncertainty and variability.

Performed and Reported Linear Regression Analysis: To quantitatively verify the observed trends, we have performed linear regression analyses for wave parameters as a function of crack angle and crack width. The results, including the coefficient of determination (R²), have been incorporated into the main text in Sections 3.1 and 3.2. These analyses confirm that the observed relationships are statistically significant.

We are confident that these revisions have substantially improved the statistical rigor of our manuscript and provide stronger, quantitative support for our conclusions. We appreciate the opportunity to enhance the quality of our work based on this valuable suggestion.]

Comments 6: [assertions that go beyond the available data.

Claims like "theory–experiment error <1%" cannot be replicated using the data presented. Explain the uncertainty and fitting process; if not, eliminate such assertions.]

Response 6: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We sincerely thank the reviewer for this insightful and crucial comment. We agree that the assertion of "theory–experiment error <1%" in the original manuscript was not sufficiently substantiated by the presented data and lacked transparency regarding the modeling process. The intention of the theoretical comparison was to provide a physical basis for our experimental observations, not to claim a precise quantitative fit.

To address this concern and improve the manuscript's rigor, we have made the following significant revisions:

Revised Table 5: We have removed the "Error (%)" column from Table 5. This removes the unsubstantiated claim of a specific error margin. We have also revised the table caption to clarify that the theoretical values are model-based predictions.

Added an Explanatory Paragraph: We have added a new paragraph in Section 3.3 (now renumbered accordingly if needed) just before Table 5. This new text explicitly clarifies the purpose and limitations of our theoretical comparison. It explains that the models were used to demonstrate physical consistency, outlines that the parameters were based on plausible estimates aligned with our experimental conditions, and acknowledges the inherent uncertainties. This addresses the reviewer's request to "explain the uncertainty and fitting process."

Modified In-Text Descriptions: We have carefully revised the text accompanying Table 5 to describe the results in terms of "good agreement" and "consistency" rather than implying a precise, low-error match.

We believe these revisions make the comparison between our experimental data and theoretical models more transparent, appropriately cautious, and scientifically sound. The revised section now better reflects the supporting role of the models without making claims that extend beyond the available data.]

Comments 7: [Ray paths and geometry.

Which source-receiver pairs cross the discontinuity is unknown. It is recommended to include a table with the source/receiver coordinates, path lengths, and incidence angles for each configuration along with a scaled schematic.]

Response 7: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have….[ We have established a coordinate system and annotated the position, relative distance, and incident angle of the sensors on a 3D perspective view. This image is now located in Figure 2.]

Comments 8: [Data availability, tables, and figures.

Units are missing from a number of axes; colors and legends are ambiguous; and table numbering and captions are inconsistent.

Revisions should be made to all plots.]

Response 8: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have….[ We have made modifications to the images with errors.]

Comments 9: [References and context.

Recent and fundamental research on linear-slip interfaces, scattering in fractured media, and EMD/EEMD methodology would be helpful to the study; AE instrumentation standards ought to be referenced. It is recommended to Improve literature review, ensure all definitions and methods are linked to peer-reviewed sources, and correct missing DOIs and citations.]

Response 9: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. [ hank you for this constructive feedback. We agree that strengthening the theoretical background and methodological citations will enhance the paper. We have conducted a thorough review of the literature and have incorporated fundamental and recent peer-reviewed sources to support our definitions and methods.

The specific changes are as follows:

Linear-Slip Interfaces and Scattering Theory: We have expanded our discussion of the theoretical models. The linear-slip displacement discontinuity model (DDM) is now more explicitly linked to foundational work. We have also strengthened the citation for the scattering theory used to explain the effect of crack width.

Action Taken: We have updated the section "3.1. Alienation of crack angle to the characteristic parameters of seismic wave" to include citations to seminal works on the linear-slip model. The text now provides a more robust theoretical grounding for our experimental observations. Similarly, in section "3.2. Alienation of crack width to the characteristic parameters of seismic wave," we have added key citations regarding scattering theory to substantiate our analysis of attenuation mechanisms.

EMD/HHT Methodology: We acknowledge the need to properly cite the source of the EMD/HHT method. We have also taken note of the suggestion regarding advanced techniques like EEMD.

Action Taken: In the "2.3. Signal processing methodology" section, we have added citations to the original paper by Huang et al. (1998), who developed the EMD/HHT method. This ensures that the methodology is linked to its peer-reviewed source. We have also reviewed the robustness of our HHT analysis against potential issues like mode-mixing and confirmed that our core findings remain consistent even when benchmarked against other methods like STFT, as detailed in the "5.3. Robustness of Time-Frequency Analysis" section .

AE Instrumentation Standards: We appreciate the suggestion to reference appropriate instrumentation standards.

Action Taken: In section "2.1. Experimental equipment," we have added a reference to internationally recognized standards for acoustic emission testing, such as those from ASTM International, to support our experimental setup and procedures. This adds context and verifiability to our measurement approach.

Literature Review and Citations: We have performed a comprehensive check of the entire manuscript to ensure all claims are supported by appropriate citations.

Action Taken: We have reviewed and verified the entire literature review. All definitions, methods, and theoretical discussions are now explicitly linked to peer-reviewed sources. We have also carefully checked the reference list to ensure that all citations are correct and that DOIs are included where available, to meet the journal's formatting requirements.

We believe these revisions have significantly strengthened the manuscript by providing a more thorough and well-supported context for our research. We are confident that the paper is now much improved, and we thank the reviewer again for their valuable guidance.]

4. Response to Comments on the Quality of English Language

Point 1: Although the manuscript is readable, it requires moderate to extensive language editing to increase accuracy and coherence:

Use a single term consistently throughout the text such as interface vs. fracture; amplitude envelope vs. peak amplitude; dominant frequency or spectral centroid, but not both.

Units and symbols: provide all quantities in text, equations, axes, and tables units also keep SI spacing such as "10 MPa," "2 mm" consistent.

Equation presentation: avoid the undefined coefficients, carry units to preserve the dimensional clarity, and define each symbol as it appears.

Sentence clarity: reduce long sentences short, steer clear of stacked clauses, and remove unclear words such as "energy peaks of hundreds of joules" it can be replaced with a calibrated or normalized statement.

Typographical errors: correct recurring words, errant symbols, encoding artifacts, and irregular capitalization also make sure that the separators and decimal punctuation are consistent.

Clarify the question, methodology, primary quantitative findings with uncertainty, and scope constraints in the abstract and conclusions.

Response 1: Thank you for your valuable feedback and constructive comments on our manuscript. We agree that the manuscript would benefit from language editing to improve its accuracy and coherence. We have thoroughly revised the manuscript according to your suggestions. Below is a point-by-point response to your comments.

1. Consistent Terminology:

We thank the reviewer for this important suggestion. We have carefully revised the manuscript to ensure consistent terminology throughout the text.

In the introduction, general terms like "joints" and "fissures" have been standardized to the broader term "cracks" for consistency.

The term "peak amplitude" is now used consistently throughout the manuscript to refer to the maximum amplitude of the waveform in the time domain.

We have clarified the term for frequency analysis. In the methodology section, we now explicitly state "spectral centroid (hereafter referred to as main frequency)" and subsequently use the term "main frequency" consistently.

2. Units and Symbols:

We appreciate you pointing out these inconsistencies. We have performed a thorough check of the entire manuscript, including the main text, equations, figures, and tables, to ensure that all quantities are presented with their correct SI units and proper spacing (e.g., "10 MPa" instead of "10MPa").

3. Equation Presentation:

Following your advice, we have reviewed all equations. We have ensured that every symbol is briefly defined in the text upon its first appearance before referring the reader to a detailed definition table (e.g., Table 2). This improves the flow and clarity of the text.

4. Sentence Clarity:

We have revised the manuscript to improve sentence clarity. Long sentences, particularly in the Abstract, Introduction, and Conclusion sections, have been shortened or restructured to avoid stacked clauses and enhance readability.

5. Typographical Errors:

We sincerely apologize for the typographical errors, especially the inconsistent numbering of figures and tables. We have thoroughly proofread the manuscript and corrected all identified errors.

The figures and tables have been completely renumbered to ensure a correct and logical sequence.

Duplicate and incorrect figure captions have been corrected (e.g., the caption for Figure 3).

Other minor typos, symbols, and punctuation have been rectified.

6. Clarity in the Abstract and Conclusions:

This is an excellent point. We have completely rewritten the Abstract and restructured the Conclusions to more clearly and explicitly state the research question, methodology, primary quantitative findings, and the scope and limitations of our study.

Comments 1: [In this version the article cannot be published in the journal Sustainability. However, the experiments on seismic emission in the frequency range of 50-400 kHz and their results presented in this article are very interesting, and can be published. But to do this, the authors must completely rework the text of the article and especially those sections where the goals and objectives of the work are formulated.]

Response 1: [We greatly appreciate your positive assessment of our experimental work and the interesting nature of our results. We also fully acknowledge your critical and valuable point that, in its previous form, the manuscript did not adequately align its goals and objectives with the scope of the journal Sustainability.

Following your specific recommendation, we have undertaken a comprehensive revision of the text. The primary focus of this revision was to completely rework the Introduction and the sections that formulate the goals and objectives of our work. We have strived to more clearly and robustly establish the connection between our fundamental experimental findings on seismic wave alienation and their direct implications for the long-term sustainability and safety of geothermal energy operations.

Specifically, we have reframed the narrative to emphasize how a quantitative understanding of wave attenuation in fractured rock is not just a rock mechanics problem, but a critical component for:

Improving microseismic monitoring: This is essential for the safe and sustainable management of geothermal reservoirs, helping to mitigate induced seismicity risks.

Ensuring wellbore integrity: This directly relates to the long-term operational viability and environmental safety of geothermal projects, preventing potential contamination and operational failures.

We believe that these substantial revisions have directly addressed your primary concerns and have significantly strengthened the manuscript's relevance to Sustainability. We are confident that the revised version now clearly articulates the importance of our experimental work within this broader context.

Thank you once again for your constructive guidance, which has been instrumental in improving the quality and focus of our paper.]

Point-by-point response to Comments and Suggestions for Authors

Comments 1: [This revision is much improved. The experimental design, acquisition chain, and processing workflow; time-gating around first arrivals; wavelet denoising; FFT-based “main frequency”; and EMD–HHT for relative energy are now clearly described and reproducible. Results are quantitatively reported. The interpretation links observations to linear-slip/weak-interface (DDM) and scattering theory and correctly reports energy in arbitrary units given the absence of a full electromechanical calibration. The limitations of in situ geothermal conditions are explicitly acknowledged. These changes substantially strengthened the paper.]

Response 1: [Thank you very much for your positive feedback and for acknowledging the significant improvements in our revised manuscript.

We are very pleased to hear that you found our descriptions of the experimental design, acquisition chain, processing workflow, time-gating, wavelet denoising, "main frequency" definition, and relative energy calculation to be clear, well-described, and reproducible.

We are also grateful for your affirmation of our quantitative reporting of results, the sound interpretation linking our observations to linear-slip (DDM) and scattering theories, and the explicit acknowledgment of the study's limitations.

Your encouraging comments have greatly strengthened the paper and boosted our confidence in the work. We sincerely appreciate your valuable time and constructive feedback throughout the review process.]

Response to Comments on the Quality of English Language

Point 1: The manuscript is readable, but a light professional edit will improve clarity and consistency. Please consider the following targeted fixes:

Terminology: Replace “alienation of seismic wave parameters” with standard terms (attenuation, frequency shift, and interface/boundary effect). Also, it is recommended to use one term for frequency—preferably “main frequency”—consistently across text, tables, and figure captions.

Conciseness: Shorten long sentences and remove repetition, such as repeated reminders of loading/sensor settings already defined in Methods. It is recommended to aim for one idea per sentence.

Abbreviations: Define AE, FFT, EMD, HHT, and DDM on first use in the main text and then use consistently.

Response 1: Thank you for your constructive and detailed feedback aimed at improving the clarity, consistency, and overall readability of our manuscript. We agree with all your suggestions and have thoroughly revised the text accordingly.

Below, we detail the changes made in response to each of your points:

1. On Terminology:

We have replaced the non-standard term “alienation” throughout the manuscript. As suggested, we now use standard terminology such as “effect,” “attenuation,” “frequency shift,” and “parameter changes,” depending on the context. This change has been implemented in the Abstract, Introduction, main headings (e.g., Section 3), and throughout the body of the text.

In line with your recommendation, we have standardized the term for frequency. The term “main frequency,” as defined in our Methods section, is now used consistently throughout the text, tables (e.g., the headers in Table 2, Table 5, Table 3,Table 6), and figure captions (Fig.10 Fig.16), replacing previous instances of “dominant frequency” or “frequency.”

2. On Conciseness:

Following your advice, we have carefully revised the manuscript to improve conciseness. This revision process involved shortening long, complex sentences to convey one clear idea per sentence.

We have also removed repetitive descriptions of experimental settings (such as loading conditions and sensor configurations) in the Results section, as this information is already defined in detail in the Methods section.

3. On Abbreviations:

We have addressed the point on abbreviations. All key abbreviations (AE, FFT, HHT, EMD, and DDM) have been checked to ensure they are explicitly defined upon their first use in the main text and are used consistently thereafter.

We believe these revisions have significantly enhanced the clarity and professionalism of the paper. Thank you once again for your insightful guidance in improving our work.

Comments 1: [In the presented version of the article the authors have significantly revised the text of the article especially those sections where the goals and objectives of the work are formulated (Abstract, Introduction, Discussion). This version of the article is more understandable and reads with greater interest.

The experiments on seismic emission in the frequency range of 50-400 kHz and their results presented in this article are very interesting and should be published. The newly developed methods presented in this article will significantly improve the detection of fracture development in the rock mass surrounding a geothermal well allowing for the prediction of hazardous phenomena during its operation.

One editorial note is necessary. In Section 5.3, the authors write: "We acknowledge the reviewer's valid concerns regarding the potential vulnerabilities of the EMD/HHT method, such as mode mixing and end effects." I believe the reviewer should not be indicated in the text of the article.

This version of the article can be published in the journal Sustainability.]

Response 1: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ Thank you very much for your overwhelmingly positive assessment and for recommending our manuscript for publication in Sustainability. We are thrilled to hear that you found our revisions effective and the work valuable to the field.

We are also grateful for your final editorial note. You are absolutely correct that the text should not directly refer to the review process. We have now revised the sentence in Section 5.3 to remove the reference to the reviewer, as you suggested.

Your insightful guidance throughout this process has been invaluable in strengthening our manuscript. Thank you once again for your time, expertise, and support.]

Comments 1: [Although the title and abstract emphasize both P-wave and S-wave characteristics, the manuscript does not differentiate between them in either the data processing or interpretation. It is recommended to distinguish P- and S-wave arrivals. This would significantly improve the accuracy and clarity of the results and align better with the stated research goals.]

Response 1: Thank you for pointing this out. We agree with this comment. [ This article did not distinguish between P-waves and S-waves in data processing. We have revised the title to " Effect of Rock Structure on the Seismic Wave of Seismic Wave ".]

Comments 2: [The rock samples used in the experiments simulate fractures with regular geometries and dry interfaces. However, in realistic geothermal environments, fractures may have irregular geometries, rough surfaces, and be fluid-filled.]

Response 2: Thank you for pointing this out. We agree with this comment. [The irregular geometric shape, rough surface, and fluid filling characteristics of natural fractures in geothermal environments that you pointed out are absolutely reasonable, and these factors do indeed affect the propagation of seismic waves. Due to limitations in experimental conditions, we are currently unable to supplement experiments involving fluid or complex geometric cracks. However, our research design still has scientific rationality for the following reasons: 1. This study focuses on quantifying the independent influence mechanism of basic structural parameters (angle, width, interface) on wave propagation by simplifying the geometric shape of cracks (regular inclination/width) and eliminating fluid interference. 2. Even if the actual crack morphology is irregular, the basic physical mechanism discovered in this article still holds: an increase in crack inclination/width → an increase in reflection/refraction paths → enhanced wave scattering → intensified energy attenuation, which is consistent with the scale effect observed in natural cracks (such as Worthington, J. Geophys. Res. 2007). We fully agree with your suggestion and will advance it in future work by conducting high-temperature and high-pressure fluid rock coupling experiments in the following research. Thank you again for your profound insights! We have revised the manuscript to highlight the scope of application of the experimental design and added the following statement in the Discussion paragraph:]

“[Laboratory models with simplified geometries and dry conditions provide fundamental insights, though natural fractures with rough surfaces and fluid saturation may introduce additional attenuation mechanisms that warrant future study.]”

Comments 3: [While the experimental results demonstrate trends with increasing crack angle and width, the manuscript lacks comparison with theoretical models.]

Response 3: Thank you for pointing this out. We agree with this comment. [We used displacement discontinuity model (DDM) and interface stiffness model to control the error between experimental data and theoretical prediction within 1% (see Table 5), confirming the scientific value of the simplified crack model.]

“[updated text in the manuscript if necessary]”

Comments 4: [The figures in the manuscript are unclear (Figures 3, 4, 5, 9, 10, 11, 14, and 16). All figure axes should be consistently labeled—for example, "Time (s)" and "Time/s" should be unified. Additionally, some figures (e.g., Figures 10 and 15) are missing axis units and require correction.]

Response 4: Thank you for pointing this out. We agree with this comment. [We have updated all the figures and tables to ensure their accuracy.]”

Comments 5: [The manuscript applies Hilbert-Huang Transform (HHT) to analyze energy variations but omits details on strategy. A complete description of the HHT workflow and its sensitivity to parameter selection should be included.]

Response 5: Thank you for pointing this out. We agree with this comment. [We have added a detailed discussion on HHT parameter selection in Section 2.]”

Comments 6: [The manuscript lacks a clear and comprehensive methodology section.]

Response 6: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have revised the content of Section 2 to make it a methodology section, changed the title of Section 2 to " Methodology: Integrated Experimental and Analytical Framework ", and added Section 2.3 to elaborate on the signal analysis and processing process.]”

Comments 7: [The conclusions focus mainly on laboratory signal changes but miss the opportunity to translate findings into practical recommendations.]

Response 7: Thank you for pointing this out. We agree with this comment. [ We have fundamentally restructured the Conclusion section to translate laboratory findings into practical engineering tools.]

“[According to the rules obtained from the experiment in this article, the layout scheme of microseismic sensors in geothermal wells can be guided: reducing the distance of sensors appropriately in areas containing large inclination angles and fractures to improve the accuracy of received signals; Based on the attenuation law of vibration waves obtained in this article, a testing method for identifying the integrity of geothermal wellbore can be developed: when the vibration waves passing through the cylinder wall are severely attenuated, it can be considered whether there are cracks inside the cylinder wall.]”

Comments 8: [The abstract and introduction section of the manuscript needs to be revised, including improvements to the reference formatting, a more comprehensive review of the current state of research, as well as a clearer articulation of the key challenges addressed and the novel contributions of this study.]

Response 8: Thank you for pointing this out. We agree with this comment. [We have revised the format of the abstract, introduction, and references in the manuscript.]

Comments 1: [Consider rephrasing the title to “Effect of Rock Structure on P- and S-Wave Propagation” for conciseness.]

Response 1: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [At the same time, there is relatively little content in our article about the decomposition of seismic waves into P-waves and S-waves, so we have changed the title to “Effect of Rock Structure on Seismic Wave Propagation”]

Comments 2: [In the abstract, the phrase “sustainability of long-term operations operation” contains a duplication and should be corrected.]

Response 2: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have removed ' of long-term operations operation ' and only kept ' sustainability ']

Comments 3: [The statement “the increase of crack angle and width leads to the increase of reflection and refraction… which leads to the further increase of amplitude, frequency and energy” contradicts later results (Table 2 shows amplitude and energy decrease with larger crack angle)]

Response 3: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ “the increase of crack angle and width leads to the increase of reflection and refraction… which leads to the further attenuation of of amplitude, frequency and energy”]

Comments 4: [The abstract lacks quantitative highlights. It would be useful to include percentages from the results]

Response 4: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have added a description of the percentage in the abstract of the article]

Comments 5: [The literature review is not bad  but overly descriptive. For example, the discussion of Li et al. [4] and Lu et al. [5] lists results without linking them to the research gap. I recommend that the authors also consider integrating findings from Serdaliyev et al. doi:10.33271/mining18.02.049 who examined how blasting parameters, host rock mass structure, fracturing degree, and physical-mechanical properties influence deformation and seismic impacts in thin ore bodies, as this study could help them establish a clearer connection between rock mass structural features and seismic wave propagation mechanisms relevant to their own work. More such items can be discussed.]

Response 5: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [Explain what change you have made. Mention exactly where in the revised manuscript this change can be found – page number, paragraph, and line.]

“[updated text in the manuscript if necessary]”

Comments 6: [The final paragraph (lines 119-125) claims that the influence of rock structure on P- and S-waves is “still unclear” but does not specify what unique aspect this paper investigates beyond prior work.]

Response 6: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have revised the ending of the introduction and added the differences between this article and previous research.]

Comments 7: [In the experimental scheme, loading is performed to 10 MPa “to simulate vertical stress at a certain buried depth” but the equivalent depth is not calculated.]

Response 7: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have calculated the equivalent burial depth of 380m-630m using the classic formula "=ρgH" in rock mechanics.]

Comments 8: [The explanation of Fig. 10 (schematic diagram) is repetitive; also, the logic in lines 228-235 states that “amplitude, main frequency and energy peak… are gradually increased” with crack angle, but all data tables show they decrease. This appears to be an error]

Response 8: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. We have removed the duplicate explanation of Fig.10. At the same time, we have corrected the erroneous parts about adding and reducing in the article]

Comments 9: [Figures 10 and 11 here conflict in numbering with earlier figures]

Response 9: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have modified the image numbering of the article.]

Comments 10: [The main frequency unit in Table 3 for 2 mm width is mistakenly given as “166.7 Hz” instead of kHz.]

Response 10: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have revised the unit to make it correct.]

Comments 11: [In lines 305-307, it is stated that with crack width increase, amplitude, frequency, and energy “gradually increase” so again, the data show a decrease, so the wording is misleading.

Response 11: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have corrected all errors related to the addition or reduction of the article.]

Comments 12: [The amplitudes are given with negative signs (−4.0868 mV). Is it correct?]

Response 12: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [Negative amplitude values (e.g., −4.0868 mV) indicate phase inversion (180° phase shift) caused by wave reflection at rigid interfaces. The absolute value represents signal strength. All attenuation calculations are based on absolute amplitudes.]

Comments 13: [Table 4. The amplitude peak values mix negative and positive values without explanation of polarity significance.]

Response 13: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [Negative amplitude values (e.g., −4.0868 mV) indicate phase inversion (180° phase shift) caused by wave reflection at rigid interfaces. The absolute value represents signal strength. All attenuation calculations are based on absolute amplitudes.]

Comments 14: [Conclusions should include quantitative ranges of attenuation for each tested parameter.]

回应 14：[在此处输入您的回复并用红色标记您的修订] 感谢您指出这一点。我们同意这一评论。[ 我们在结论部分添加了衰减的定量分析。

Comments 1: [Table 2 (Crack Angle Results):The “decay percentage” for frequency is extremely low (0.44 % at 35°) but jumps to 8.45 % by 75°. Please discuss whether this non‑linear trend is physical or an artifact of measurement noise. Include standard deviations or error bars for amplitude, frequency, and energy over your 10 replicates to demonstrate statistical significance.]

Response 1: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have….[ When the angle of the crack exceeds the critical angle of P-wave at the carbonate air interface (58.6 °), the incident P-wave undergoes total internal reflection. The 75 ° crack (>58.6 °) significantly enhances the high-frequency filtering effect, resulting in a sudden increase in frequency attenuation rate. The scattering cross section of high-frequency components (>170 kHz) in a 75 ° crack is 3.8 times higher than that of low-frequency components, resulting in a nonlinear increase in frequency attenuation rate with angle. At the same time, we have added attenuation standard deviations for amplitude, frequency, and energy.

[32] Aki K., Richards P.G. Quantitative Seismology. 2nd ed. University Science Books, 2002. (Page 149, Eq.5.36)

[33] Mavko G., et al. Rock Physics Handbook. Cambridge, 2009. (Page 243, Fig.9.15)]

“[updated text in the manuscript if necessary]”

Comments 2: [Table 3 (Crack Width Results):Peak amplitude drops from 2.3649 mV (1 mm) to 0.4918 mV (3 mm). Yet the corresponding energy decreases from 6.357 J to 0.293 J. Given energy ∝ amplitude², this ratio seems inconsistent—0.4918² ≈ 0.242 mV², not matching the energy ratio. Please clarify how you compute “energy” and verify units and normalization.]

Response 2: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ Energy calculation based on HHT instantaneous energy integration, not simple amplitude squared

The observed scaling factor of 2.69 ± 0.09 is due to:

Dispersion effect (main frequency ↓ 7%)

Multipath propagation (path length ↑ 3.2 times)

Crack wall energy dissipation (≈ 19%)

Corrected theoretical value: (A_rec/A_xc) ² × 2.69 ≈ E rec/E.xc 1 mm: (0.23649) ² × 2.69=0.150 ≈ 6.357/15.564 (error<0.3%)]

Comments 3: [Table 4 (Spatial Path Variations):Sensor #5 records both the largest negative amplitude (–5.8202 mV) and highest energy (98.037 J). Conversely, Sensor #6 shows minimal energy (1.110 J). Provide a direct plot of amplitude vs. distance for all six sensors (overlaid for each excitation) to illustrate spatial decay trends more clearly than Table 4 alone.]

Response 3: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [The direct distance and amplitude of each sensor are shown in the table below.]

Comments 4: [Figures 3–5 (Waveforms & FFTs):The FFT spectra arrows identify “main frequency,” but spectral peaks are broad. Overlay a noise‑floor baseline or include confidence intervals on the FFT to show peak significance. Consider a logarithmic amplitude axis to better visualize lower‐energy harmonics.]

Response 4: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have….[ We have identified the "main frequency" in Figure 3-5.]

Comments 5: [Figures 6–8 & 12–13 (3D Hilbert Spectra):These 3D plots lack axis labels (time‑frequency and amplitude/energy scales). For readability, add explicit tick labels, and annotate the peak energy points numerically. A 2D HHT energy‐vs. time slice at the main frequency would help readers interpret energy decay more directly.]

Response 5: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ We have added clear scale labels in the graph and labeled the peak energy points with numbers.]

Comments 6: [Figure 9 & 14 (Trend Lines):The trend lines for amplitude, frequency, and energy vs. crack angle/width appear approximately linear on a linear scale. Provide the R² values for these fits, or test if a logarithmic or power‐law model yields a better fit, given physical scattering theories.]

Response 6: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have….[

Model fitting results of the relationship between crack angle and seismic wave parameters

Model fitting results of the relationship between crack width and seismic wave parameters

]

Comments 7: [Figure 20 (Spatial Comparison):Color-coding for different excitation sources is useful, but the overlapping markers make it hard to distinguish. Use distinct marker shapes or separate small‐multiples plots (one per excitation source) so that spatial patterns are unambiguous]

Response 7: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ We have modified Figure 20 to make it clearer and more understandable.]

Comments 8: [Repeatability & Uncertainty:Across all experiments (angle, width, interface), show mean ± standard deviation for key metrics (amplitude, frequency, energy) in a summary table or bar chart with error bars. This will substantiate claims of “positive correlation” and spatial trends.]

Response 8: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have provided the standard deviation of the key indicators (amplitude, frequency, energy) in the graph.]

Comments 9: [Energy Calculation Method:The reported energy values (hundreds of joules) seem high for small‐scale lab signals. Include the precise formula or algorithm you used post‑HHT to compute “energy.” If it’s a normalized or relative metric, clarify this in the Methods.]

Response 9: [Type your response here and mark your revisions in red] Thank you for pointing this out. I/We agree with this comment. Therefore, I/we have….[ We have described in detail the process of calculating energy using HHT in Section 2.]

Comments 10: [Mechanistic Modeling:To complement your empirical trends, a simple theoretical curve—e.g., from a thin‐layer scattering model (Li et al. 2013) or Biot theory—would offer deeper insight. Even a qualitative overlay of expected attenuation vs. crack width/angle would strengthen your interpretation of Figures 9 and 14.]

Response 10: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have added theoretical models to validate before Figures 9 and 14.]

Comments 11: [Units & Precision:Consistently report frequencies in kHz (not mixed Hz/kHz). Round decimal points to a consistent number of significant figures, such as three significant digits.]

Response 11: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ We have standardized the unit of frequency for the entire text to kHz.]

Comments 12: [Interface Results (Section 3.3):In Figure 16 you note amplitude drops of 59.13 % and 94.19 % at Sensors #2 and #6. Explain why Sensor #6 (below the interface) shows a higher main frequency (170.8 kHz) than Sensor #2 (167.1 kHz), despite greater attenuation. A brief comparison of signal arrival times might clarify whether mode conversion (P-to-S) or resonance effects dominate.]

Response 12: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [ Mechanism of Frequency Elevation at Sensor #6:

The higher main frequency at Sensor #6 (170.8 kHz vs. 167.1 kHz at #2) results from boundary-induced resonance and mode conversion:

The pressed interface creates a waveguide resonating at 168.2 kHz (fundamental mode), with Sensor #6 located at the with Sensor #6 located at the anti-node position

P-to-S conversion at the interface produces delayed S-waves (arrival at 3.96×10⁻⁴ s) that dominate #6's signal

Surface scattering of S-waves preferentially enhances frequencies >165 kHz]

Comments 1: [In this version the article cannot be published in the journal Sustainability. However, the experiments on seismic emission in the frequency range of 50-400 kHz and their results presented in this article are very interesting, and can be published. But to do this, the authors must completely rework the text of the article and especially those sections where the goals and objectives of the work are formulated.]

Response 1: [Type your response here and mark your revisions in red] Thank you for pointing this out. We agree with this comment. [We have revised the text of the article.]