Proposal of a Methodology Based on Using a Wavelet Transform as a Convolution Operation in a Convolutional Neural Network for Feature Extraction Purposes

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

- Lines 11–18. Overly verbose and lacks focus. :“This work proposes a novel CNN architecture that replaces standard convolution with Discrete Wavelet Transform (DWT) for multi-scale feature extraction in seismic data. A Self-Organizing Map (SOM) is integrated for unsupervised classification. Case studies on synthetic and real seismic data demonstrate improved sensitivity to localized features and reduced computational costs compared to traditional CNNs.”

- Lines 20–30: Unsupported claim about hybrid CNNs (Lines 27–30). Please add empirical support. “Hybrid CNNs, such as wavelet-integrated architectures [8, 9], have demonstrated advantages in computational efficiency and multi-resolution analysis, particularly in geophysical applications [11], where preserving high-frequency seismic signatures is critical.”

- Same page, clarify the motivation: “Wavelet Transform has gained traction in CNNs for its ability to capture both time and frequency domain features, making it particularly suitable for analyzing complex seismic data.”

- Lines 60–63: Superficial description of CNN steps. Please clarify methodology, maybe a flowchart or algorithmic summary of the modified CNN workflow (e.g., “Sliding Window → DWT Convolution → Pooling → SOM Classification”).

- Lines 234–238: Overly technical explanation of wavelet decomposition. Break down equations with annotations. Add a table mapping wavelet levels (e.g., Level 1: approximation/detail coefficients) to their physical interpretation in seismic analysis (e.g., low-frequency trends vs. high-frequency anomalies).

- Synthetic examples (Lines 441–477) lack relevance to seismic data. “Synthetic experiments on geometric shapes (e.g., rotated lines, ellipsoids) validate the method’s ability to detect orientation-invariant features, analogous to seismic horizons with varying dips.” Please strengthen connection to some real-world applications.

- Line 441-443: The synthetic data examples (straight line, circle, and ellipsoid) are not well-integrated with the overall methodology. Explain how these synthetic examples validate the proposed methodology and their relevance to seismic data analysis.

- Lines 498–501: “The proposed method achieved a 92% accuracy in identifying hydrocarbon-bearing zones, compared to 78% for a traditional CNN, with a 30% reduction in training time (Table 3).” Qualitative results without metrics. Please clarify.

- Line 326-328: “Within Machine Learning, we find different types of learning [10]. The one that interests us due to the nature of some problems that are represented in the selection of characteristics in a multi-scale way is Unsupervised Learning.” This sentence is overly generic and lacks specificity. It could be written more concisely and with more technical detail.

- Line 534–536: Non-specific. Please add technical details for “Pseudocode initializes the seismic cube with a sliding window (β=64, γ=8) and applies Daubechies-4 DWT for decomposition.”

- Figure 1: Described as “handling information from an information cube” but missing.

- Section 3.1: The explanation of Wavelet Transform application is overly technical and hard to follow. The readability will be improved if authors can break down the explanation into smaller steps with annotations or visual aids (e.g., a flowchart).

- Pooling Strategy (Section 3.2): No comparison to traditional methods.

- Parameter Optimization (Lines 53–58): Mentions 26 variables but no discussion.

- Please add quantitative metrics (F1-score, runtime) and compare against baselines (e.g., standard CNN, wavelet pre-processing).

- For Figure 11, please provide parameter optimization details.

- In general, the manuscript is logically structured but suffers from excessive verbosity and lack of focus in some sections. The method and results sections could benefit from tighter organization and clearer subsections.

- The novelty may be questioned without direct comparison to recent hybrid CNNs (e.g., [8, 15]).

- Claims about computational efficiency (Line 40) need validation via runtime metrics.

- “Clasification” → “Classification”

Author Response

 Reviewers Lines 11–18. Overly verbose and lacks focus. : “This work proposes a novel CNN architecture that replaces standard convolution with Discrete Wavelet Transform (DWT) for multi-scale feature extraction in seismic data. A Self-Organizing Map (SOM) is integrated for unsupervised classification. Case studies on synthetic and real seismic data demonstrate improved sensitivity to localized features and reduced computational costs compared to traditional CNNs.”

Response: We agree with this comment. We have extensively modified this paper, changing several parts of the manuscript and creating three annexes to better explain the algorithm.

Reviewer:

 Lines 20–30: Unsupported claim about hybrid CNNs (Lines 27–30). Please add empirical support. “Hybrid CNNs, such as wavelet-integrated architectures [8, 9], have demonstrated advantages in computational efficiency and multi-resolution Analysis, particularly in geophysical applications [11], where preserving high-frequency seismic signatures is critical.”

Same page, clarify the motivation: “Wavelet Transform has gained traction in CNNs for its ability to capture both time and frequency domain features, making it particularly suitable for analyzing complex seismic data.”

Lines 60–63: Superficial description of CNN steps. Please clarify methodology, maybe a flowchart or algorithmic summary of the modified CNN workflow (e.g., “Sliding Window → DWT Convolution → Pooling → SOM Classification”).

Lines 234–238: Overly technical explanation of wavelet decomposition. Break down equations with annotations. Add a table mapping wavelet levels (e.g., Level 1: approximation/detail coefficients) to their physical interpretation in seismic analysis (e.g., low-frequency trends vs. high-frequency anomalies).

Response: We thank the reviewer for these comments. Since we modified Sections two and three to explain our proposal, the main differences from CNN, and how the use of DWT may defer to a physical engagement from seismic analysis, we have integrated one similar comment. 

Reviewer:

Synthetic examples (Lines 441–477) lack relevance to seismic data. “Synthetic experiments on geometric shapes (e.g., rotated lines, ellipsoids) validate the method’s ability to detect orientation-invariant features, analogous to seismic horizons with varying dips.” Please strengthen the connection to some real-world applications.

Line 441-443: The synthetic data examples (straight line, circle, and ellipsoid) are not well integrated with the overall methodology. Explain how these synthetic examples validate the proposed methods and their relevance to seismic data Analysis.

Lines 498–501: “The proposed method achieved a 92% accuracy in identifying hydrocarbon-bearing zones, compared to 78% for a traditional CNN, with a 30% reduction in training time (Table 3).” Qualitative results without metrics. Please clarify.

Line 326-328: “Within Machine Learning, we find different types of learning [10]. The one that interests us due to the nature of some problems that are represented in the selection of characteristics in a multi-scale way is Unsupervised Learning.” This sentence is overly generic and lacks specificity. It could be written more concisely and with more technical detail.

Line 534–536: Non-specific. Please add technical details for “Pseudocode initializes the seismic cube with a sliding window (β=64, γ=8) and applies Daubechies-4 DWT for decomposition.”

Response: 

We thank the reviewer for these meaningful comments. We have modified section 4, decided to withdraw the synthetic examples, and concentrated on the seismic analysis. We have used the Mean square Error and presented several cases for comparison, pointing out the contribution by using this proposal. 

Reviewer:

 Figure 1: Described as “handling information from an information cube” but missing.

Section 3.1: The explanation of Wavelet Transform application is overly technical and hard to follow. The readability will be improved if authors can break down the explanation into smaller steps with annotations or visual aids (e.g., a flowchart).

Pooling Strategy (Section 3.2): No comparison to traditional methods.

Parameter Optimization (Lines 53–58): Mentions 26 variables but no discussion.

Response:

Firstly, we thank the reviewer for these comments. We have created a table from the parameters feasible to be optimized, and we concentrated on the most important and sensible data to obtain a valuable response following a group of cases according to the most important parameters to be followed.

Reviewer:

In general, the manuscript is logically structured but suffers from excessive verbosity and lack of focus in some sections. The method and results sections could benefit from tighter organization and clearer subsections.

The novelty may be questioned without direct comparison to recent hybrid CNNs (e.g., [8, 15]).

Claims about computational efficiency (Line 40) need validation via runtime metrics.

Response: 

We thank the reviewer for these comments. We have cleaned our paper substantially following these comments 

Reviewer 2 Report

Comments and Suggestions for Authors

I have following comments:

1. The paper proposes replacing the conventional convolution operation in CNNs with a wavelet transform but lacks a strong justification for why this modification is superior. Why the authors did such work and is it really necessary to have such model?
2. Provide a comparative analysis showing the advantages of wavelet-based convolution over traditional CNN convolutions, particularly in seismic data analysis.
3. The study does not compare the proposed method’s performance against state-of-the-art deep learning approaches for seismic data processing. Also, maybe ensemble machine learning methods can be other possible methods for comparison.
4. Introduce comparative experiments with existing CNN architectures to validate the performance gains and computational efficiency of the proposed approach.
5. The methodology is applied to synthetic and real seismic data, but there is no discussion on how robust it is under noise, different seismic conditions, or variations in data resolution.
6. The paper lacks the novel approaches of optimizing the hyperparameters. How they included in paper? see eswa.2024.124897.
7. The paper is dense with mathematical derivations, making it challenging for readers. Reduce or remove them to appendix.
8. The study mentions that wavelet-based convolution reduces computational costs, but no quantitative analysis or comparison of computational efficiency is provided.
9. Complex Morlet wavelet-based refined feature may help to better results, see j.jobe.2020.101847, and improve the paper by this method.

Author Response

REVIEWER

The paper proposes replacing the conventional convolution operation in CNNs with a wavelet transform but lacks a strong justification for why this modification is superior. Why the authors did such work and is it really necessary to have such model?

COMMENTS

We thank the reviewer for this comment. We have modified the introduction to focus on this particular issue, giving a clear Idea that our algorithms do not mean an improvement over CNN, but more likely a suitable and accurate approximation for Feature Extraction.

Reviewer

Provide a comparative analysis showing the advantages of wavelet-based convolution over traditional CNN convolutions, particularly in seismic data analysis

The study does not compare the proposed method’s performance against state-of-the-art deep learning approaches for seismic data processing. Also, maybe ensemble machine learning methods can be other possible methods for comparison.

Introduce comparative experiments with existing CNN architectures to validate the proposed approach's performance gains and computational efficiency.

Comments 

We thank the reviewer for this comment. Therefore, we have largely modified the manuscript in order to compare in terms of the identification from circumstances where it is possible to detect certain seismic features.

Reviewer

The methodology is applied to synthetic and real seismic data, but there is no discussion on how robust it is under noise, different seismic conditions, or variations in data resolution.

The paper lacks the novel approaches of optimizing the hyperparameters. How they included in paper? see eswa.2024.124897.

The paper is dense with mathematical derivations, making it challenging for readers. Reduce or remove them to appendix.

The study mentions that wavelet-based convolution reduces computational costs, but no quantitative analysis or comparison of computational efficiency is provided.

Complex Morlet wavelet-based refined feature may help to better results, see j.jobe.2020.101847, and improve the paper by this method.

COMMENTS:

 

We thank the reviewer for these comments. We have created three annexes in order to focus the main body of this manuscript on the construction from the algorithm. Furthermore, we have modified the results section, eliminating the synthetic data 

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Abstract

- Line 14-16: “focusing the processing of the convolution, and the shifting of data from a window to an end with the classification based onself-organising maps.”

→ Rephrase for clarity: “focusing on convolution processing, windowed data shifting, and classification via self-organizing maps.”

Section 2

- Line 95-100: “This is the approximation followed in this manuscript.” → Redundant phrasing. Simplify to “This manuscript employs Max Pooling for dimensionality reduction.”

- Line 82-89: The analogy to “smoothing operation” is misleading. Clarify how DWT convolution differs from traditional CNN convolution (e.g., multi-scale filtering vs. learned kernels).

Section 3

- Add a brief explanation of wavelet decomposition levels and their role in feature extraction for Equations (1)-(2).

- Line 258-263: “competitive learning” is undefined. Introduce the concept briefly

- Line 188-189: “This condition is crucial to define several parameters around this algorithm” → Non-specific. Specify which parameters (e.g., window size, wavelet type).

Over all

- Missing details on data preprocessing and parameter selection.

- The caption of figure and table should be self explained. Please add more explanations (e.g. Table 3).

- Logical flow is fragmented. Sections 2 and 3 lack clear transitions. Methodological steps (e.g., DWT integration) need deeper explanation.

- Novel integration of DWT and SOM in CNNs for seismic data, but novelty is overstated without comparisons to existing hybrid models (e.g., wavelet-CNNs in [14,16]).

- Claims about computational efficiency (Line 45) and accuracy lack empirical validation. Citations [30,31] are loosely connected to the methodology.

- Explain why MSE is suitable for evaluating SOM weight matrices.

- Typos (e.g., “self-organising mapis”).

- No baseline comparison (e.g., traditional CNN vs. proposed DWT-CNN-SOM).

- Please provide a point-to-point response and highlight the changes in the cover letter.

Author Response

please check the related file

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper was improved accordigly and I recommend it.

Author Response

We thank you for your valuable comments.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Line 32: "...computational costs..", the current work didn't show case any runtime comparisons between proposed method and traditional CNN in terms of computational expense. This claim should be changed. 
Line 319: Missing equation reference. 
Undefined parameter c_{i,j} for euqation 15.  
Line 518: Missing figure reference

Author Response

please review the attached file 

Author Response File: Author Response.docx