Vector Decomposition of Elastic Seismic Wavefields Using Self-Attention Deep Convolutional Generative Adversarial Networks

Round 1

Reviewer 1 Report

From my point of view, the article sent is quite interesting because the study of the interaction between S and P waves as a function of the apparent relative velocities seems very useful to understand, even more, the behavior of buildings as a function of the progression of the seismic wave. In this sense, the progression of the wave in different media, elastic - plastic, anisotropic - isotropic, non-linear, must be better explained. to clarify the interaction of the S and P waves in the whole seismic wave.

In summary, I think the article presented is interesting and suitable to publish in the journal.

Author Response

Point 1: From my point of view, the article sent is quite interesting because the study of the interaction between S and P waves as a function of the apparent relative velocities seems very useful to understand, even more, the behavior of buildings as a function of the progression of the seismic wave. In this sense, the progression of the wave in different media, elastic - plastic, anisotropic - isotropic, non-linear, must be better explained. to clarify the interaction of the S and P waves in the whole seismic wave.

In summary, I think the article presented is interesting and suitable to publish in the journal.

 

Response 1: Dear reviewer, first of all, thank you for your recognition of our manuscript. In our manuscript, we mainly develop a vector decomposition method of P- and S-wave modes from the coupled elastic seismic wavefields using self-attention deep convolutional generative adversarial networks (SADCGANs) for isotropic elastic media. In theory, P-wavefields are curl-free and S-wavefields are divergence-free in isotropic elastic media, and we can use the divergence and curl operators to separate the P- and S-wavefields, but it cannot generate all components of decomposed vector P- and S-wave modes and will damage their amplitude and phase characteristics. To overcome the shortcomings of conventional methods, our work goal is to develop an effective intelligent data-driven vector decomposition method of P- and S-wave modes which are not dependent on elastic model parameters and certain prior conditions. Numerical examples of different models demonstrate the effectiveness and feasibility of our developed method. In this manuscript, our research object only considers the isotropic elastic media, and therefore we do not add the contents related to more complex media in the revised manuscript, such as viscoelastic media, anisotropic media, etc. Of course, as the type of geological model becomes more complex, the separation and decomposition of different wave modes will become more difficult. To achieve this goal, we must understand the wavefield characteristics and differences of different wave modes in different media, such as P- , S- and converted-waves. In future work, we will extend this developed method in our manuscript to anisotropic media. In anisotropic media, the P- and S-wave polarizations are no longer parallel or perpendicular to their propagation directions, and they are called quasi-P (qP) and quasi-S (qS) waves to distinguish them from the isotropic wave modes. In this case, divergence and curl operators cannot separate the anisotropic wavefields accurately. In my opinion, our developed method can be theoretically applied to anisotropic media, and the key step is how to generate the corresponding training dataset. If the relevant research results are obtained in the future, we will publish them publicly.

If you have any further questions, please don’t hesitate to contact us. We will further discuss and modify the corresponding contents according to your comments. Thanks!

Best regards.

Author Response File: Author Response.docx

Reviewer 2 Report

The article "Vector Decomposition of Elastic Seismic Wavefields Using..." presents an interesting development of the vector decomposition method of P- and S-wave fashions using SADCGAN. To demonstrate the advantages of the proposed approach, the authors applied it to a simple isotropic elastic model and an isotropic Hess elastic model, which is a complex elastic model with an anomalous body. The article has the character of a good technical report. It is worth extending the paper with a description of applied (practical) examples of using it. The article has some editorial inadequacies, e.g., in the abstract, too long sentences which could be more straightforward (lines 17-19), unnecessarily recalling known elementary relations (lines 94-96), the conclusion chapter more like a summary.

Best regards

The article "Vector Decomposition of Elastic Seismic Wavefields Using..." presents an interesting development of the vector decomposition method of P- and S-wave fashions using SADCGAN. To demonstrate the advantages of the proposed approach, the authors applied it to a simple isotropic elastic model and an isotropic Hess elastic model, which is a complex elastic model with an anomalous body. The article has the character of a good technical report. It is worth extending the paper with a description of applied (practical) examples of using it. The article has some editorial inadequacies, e.g., in the abstract, too long sentences which could be more straightforward (lines 17-19), unnecessarily recalling known elementary relations (lines 94-96), the conclusion chapter more like a summary.

Best regards

 

Author Response

Point 1: The article "Vector Decomposition of Elastic Seismic Wavefields Using..." presents an interesting development of the vector decomposition method of P- and S-wave fashions using SADCGAN. To demonstrate the advantages of the proposed approach, the authors applied it to a simple isotropic elastic model and an isotropic Hess elastic model, which is a complex elastic model with an anomalous body. The article has the character of a good technical report. It is worth extending the paper with a description of applied (practical) examples of using it. The article has some editorial inadequacies, e.g., in the abstract, too long sentences which could be more straightforward (lines 17-19), unnecessarily recalling known elementary relations (lines 94-96), the conclusion chapter more like a summary.

 

Response 1: Dear reviewer, first of all, thank you for your recognition of our manuscript. As your comments, the testing of our developed method is only applied to numerical isotropic elastic models at present and these experimental results demonstrate the effectiveness and feasibility of our developed method in our manuscript. Our next research work is to extend this intelligent data-driven vector decomposition method to the multi-wave imaging process of elastic reverse-time migration (ERTM) for the real multi-component seismic data. At present, we are preprocessing a set of real multi-component seismic data, including denoising, static correction, deconvolution, etc. Once the preprocessing work is completed, we will apply the developed method proposed in this manuscript to the wavefield separation and decomposition of real multi-component seismic data and wavefields. If the relevant research results are obtained in the future, we will publish them publicly. According to your suggestions, we have carefully revised the editorial inadequacies which you pointed out in our manuscript, and these modifications have been marked in the revised manuscript. According to your suggestions, we have carefully revised the conclusion chapter of our manuscript, and these modifications have been marked in the revised manuscript.

If you have any further questions, please don’t hesitate to contact us. We will further discuss and modify the corresponding contents according to your comments. Thanks!

Best regards.

Author Response File: Author Response.docx

Reviewer 3 Report

Overall, the article sound  good, however,  lacks specific details on the shortcomings of existing methods, does not sufficiently explain the proposed method, lacks comprehensive evaluation and validation, Insufficient discussion on the limitations of training data and does not discuss the broader implications of the research. These critical shortcomings should be addressed to improve the clarity and impact of the article.  Author shall add following details

1- Detailed Information on the proposed method

2- Discussion on the limitations of training data

      3-Consideration for real-world applications and data

N/A

Author Response

Overall, the article sound good, however, lacks specific details on the shortcomings of existing methods, does not sufficiently explain the proposed method, lacks comprehensive evaluation and validation, Insufficient discussion on the limitations of training data and does not discuss the broader implications of the research. These critical shortcomings should be addressed to improve the clarity and impact of the article. Author shall add following details.

 

Dear reviewer, first of all, thank you for your recognition of our manuscript. According to your comments, we have carefully made comprehensive revisions to our manuscript, and these modifications have been marked in the revised manuscript. My response to the three questions you raised is as follows:

 

Point 1: Detailed Information on the proposed method

 

Response 1: According to your suggestions, we have carefully added more detailed information on our developed method. For example, we have added the relevant contents about the self-attention module in the revised manuscript. In addition, some descriptions of our developed method have been modified and adjusted, and the relevant modifications have been marked in the revised manuscript.

 

Point 2: Discussion on the limitations of training data

 

Response 2: According to your suggestions, we have carefully added the discussion on the limitations of training dataset in Section 4, and the relevant modifications have been marked in the revised manuscript. In my opinion, the training dataset in our research process mainly have the following limitations. Firstly, the training results of the neural network theoretically improve as the number of sample labels gradually increases, but we can only select the simulated wavefields at some certain times as training dataset for a given elastic model, and therefore this number needs to be carefully considered. Secondly, due to only testing two models, the training dataset we used in our work lacks diversity, which may result in our developed method not achieving good vector decomposition results for more complex elastic models, and this problem can be effectively solved by introducing various theoretical elastic models. Thirdly, various theoretical models are only the approximation of the real geological models, and therefore the simulated wavefields with fixed simulation parameters as training dataset are different from the real elastic seismic wavefields in subsurface media, such as time and space grid sizes, source and receiver positions, etc, which may cause that our developed method cannot effectively and accurately separate the horizontal and vertical components of vector P- and S-wave modes from the real elastic seismic wave-fields. Fourthly, at present, there is no effective method to completely separate the vector P- and S-wave modes from the coupled elastic seismic wavefields, and therefore the training dataset which we can use in our work is not absolutely perfect. Of course, there are some other limitations to training dataset, and we will not elaborate on them in the revised manuscript.

 

Point 3: Consideration for real-world applications and data

 

Response 3: As your comments, the application objects of our developed method are mainly the numerical isotropic elastic models at present and the testing results of two theoretical isotropic elastic models demonstrate the effectiveness and feasibility of our developed method in our manuscript. Our next research work is to apply this developed method to the real multi-component seismic data and wavefields. At present, we are preprocessing a set of real multi-component seismic data, including denoising, static correction, deconvolution, etc. Once the preprocessing work is completed, we will test the feasibility of our developed method in real-world applications. If the relevant research results are obtained in the future, we will publish them publicly.

If you have any further questions, please don’t hesitate to contact us. We will further discuss and modify the corresponding contents according to your comments. Thanks!

Best regards.

Author Response File: Author Response.docx

Reviewer 4 Report

I think the work has significant material for readers and correction has been improved the level of work, however I suggest to add the following work in the text:

Site classification using deep‐learning‐based image recognition techniques , published in Earthquake Engineering & Structural Dynamics

Author Response

Point 1: I think the work has significant material for readers and correction has been improved the level of work, however I suggest to add the following work in the text:

Site classification using deep-learning-based image recognition techniques, published in Earthquake Engineering & Structural Dynamics.

 

Response 1: Dear reviewer, first of all, thank you for your recognition of our manuscript. According to your suggestions, we have carefully read this reference titled “Site classification using deep-learning-based image recognition techniques”. This reference studies an image recognition method using a deep convolutional neural network (DCNN) to effectively classify sites, which can effectively improve the highest total accuracy rate. Similar neural networks may be applied to the vector decomposition of elastic seismic wavefields. However, at present, we only study the developed vector decomposition method based on SADCGANs in our manuscript, and in future work, we will test other neural networks used in elastic wavefield decomposition and conduct a comprehensive comparative analysis of their performance, such as DCNN, DenceNet and ResNet, etc. If the relevant research results are obtained in the future, we will publish them publicly. In addition, we have added this literature as a reference in the revised manuscript, and these modifications have been marked in the revised manuscript.

If you have any further questions, please don’t hesitate to contact us. We will further discuss and modify the corresponding contents according to your comments. Thanks!

Best regards.

Author Response File: Author Response.docx

Reviewer 5 Report

I think the subject of research is interesting to the readers and the manuscript is well written. The problem definition, theoretical background presentation, multiple experiments and discussion are all well presented.

Author Response

Point 1: I think the subject of research is interesting to the readers and the manuscript is well written. The problem definition, theoretical background presentation, multiple experiments and discussion are all well presented.

 

Response 1: Dear reviewer, first of all, thank you for your recognition of our manuscript. According to the comments from all reviewers, we have carefully revised our manuscript, and these modifications have been marked in the revised manuscript.

If you have any further questions, please don’t hesitate to contact us. We will further discuss and modify the corresponding contents according to your comments. Thanks!

Best regards.

Author Response File: Author Response.docx

Reviewer 6 Report

This paper develops a vector decomposition method of P- and S-wave modes using self-attention deep convolutional generative adversarial networks (SADCGANs) to effectively separate the horizontal and vertical components. The paper is potentially interesting to Applied Sciences readers. However, the paper is not clearly explained. So I encourage authors to look at these comments to improve the readiness of the paper.

Comments:

1. Some traditional approaches for wavefield decomposition should be discussed, such as the Hilbert transform based method.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition, Geophysics, 2017

2. Can you show the residual between the original wavefield and decomposed trace by different methods in Figure 7.

3. How about the computational efficiency between the Helmholtz decomposition and proposed AI method? Can you show the computational details about the AI method?

4. Can the authors provide some metrics to evaluate the performance of the proposed SADCGANs? Can you show the loss functions during the training and testing?

5. Many networks such as DnCNN, Dencenet or Resnet are common in seismic data processing, what are the advantages or disadvantages of your proposed network compared to them?

Moderate editing of English language required

Author Response

Please refer to the attachment for a detailed response.

 

This paper develops a vector decomposition method of P- and S-wave modes using self-attention deep convolutional generative adversarial networks (SADCGANs) to effectively separate the horizontal and vertical components. The paper is potentially interesting to Applied Sciences readers. However, the paper is not clearly explained. So I encourage authors to look at these comments to improve the readiness of the paper.

 

Dear reviewer, first of all, thank you for your recognition of our manuscript. Your suggestions and comments can help us improve the quality of our manuscript. We have studied your comments and suggestions carefully and have tried our best to revise our manuscript according to these comments. We hope that these corrections meet with approval. Revised portion are marked in different colours in the revised manuscript. The responds to your comments are as follows:

 

Point 1: Some traditional approaches for wavefield decomposition should be discussed, such as the Hilbert transform based method.

Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition, Geophysics, 2017.

 

Response 1: According to your suggestions, we have carefully read this reference titled “Reverse time migration of multiples: Reducing migration artifacts using the wavefield decomposition imaging condition”. This reference studies an effective method to separate the up-going and down-going wavefields from the acoustic seismic wavefields based on Hilbert transform. However, our manuscript studies a vector wavefield decomposition method based on SADCGANs to effectively separate the different wave modes from the coupled elastic seismic wavefields, such as P- and S-wave modes. Strictly speaking, the research objects and contents of this reference are different from those of our manuscript. Hilbert transform can effectively separate the up-going and down-gonging wavefields from the acoustic seismic wavefields, but it is unable to effectively separate the P- and S-wave modes from the coupled elastic seismic wavefields. At present, there are four methods to achieve the separation and decomposition of P- and S-wave modes from the coupled elastic seismic wavefields, such as the Helmholtz decomposition algorithm, the vector decomposition algorithm based on the decoupled elastic wave equations, the vector decomposition algorithm in wavenumber domain and the novel data-driven decomposition algorithm based on deep learning, and the above four methods are mentioned in our manuscript. In summary, we do not add any content related to Hilbert transform in the revised manuscript, because it cannot effectively achieve our goals.

 

Point 2: Can you show the residual between the original wavefield and decomposed trace by different methods in Figure 7.

 

Response 2: Dear reviewer, we are not sure if we understand this comment correctly. For this comment, we have the following understanding. Firstly, the original wavefields are the coupled elastic seismic wavefields (u_x, u_z), the decomposed wavefields generated by the Helmholtz decomposition algorithm are the scalar P- and S-wavefields (u_P, u_S), and the decomposed wavefields generated by the wavenumber domain decomposition algorithm or the developed algorithm based on SADCGANs are the horizontal and vertical components of decoupled vector P- and S-wave modes (u_xP, u_xS, u_zP, u_zS). The residuals between the original wavefields and decomposed wavefields (u_x-u_P, u_x-u_S, u_z-u_P, u_z-u_S, u_x-u_xP, u_x-u_xS, u_z-u_zP, u_z-u_zS) do not represent the accuracy error caused by different algorithms. The following Figure 1A shows these residuals mentioned above. From Figure 1A, we cannot intuitively find the accuracy differences between the separation results of different algorithms, and therefore we think that it is not necessary to add such figures in the revised manuscript. Secondly, we should discuss the residuals between the ideally decomposed wavefields (called as ideal solutions) and the decomposed wavefields by different algorithms, because these residuals can truly reflect the accuracy of different algorithms. However, there is currently no perfect algorithm to completely separate the horizontal and vertical components of decoupled vector P- and S-wave modes (u_xP, u_xS, u_zP, u_zS) from the coupled elastic seismic wavefields (u_x, u_z). In other words, at present, the ideally decomposed results of the coupled elastic seismic wavefields do not exist, and we can only find the reference solutions to effectively evaluate the accuracy of our developed vector decomposition algorithm based on SADCGANs. In our manuscript, we use the wavefield decomposition results of this wavenumber domain decomposition algorithm as the reference solutions. Thirdly, through consulting a large number of references, there are several similar conclusions: Helmholtz decomposition algorithm will seriously damage the amplitude and phase characteristics of decoupled P- and S-wave modes; the wavenumber domain decomposition algorithm can effectively preserve the vector, amplitude and phase characteristics of decoupled P- and S-wave modes, and therefore the accuracy of the latter is higher than that of the former. Due to the fact that we use the wavefield decomposition results of the wavenumber domain decomposition algorithm as training samples during the experimental process, the wavefield decomposition results of our developed algorithm based on SADCGANs should be as close as possible to the wavefield decomposition results of the wavenumber domain decomposition algorithm, which will prove the effectiveness and feasibility of our developed method. In our manuscript, the above conclusions can be well demonstrated in Figures 7, 10, 14 and 17. In summary, we think that these figures which show the residual between the original wavefields and decomposed wavefields by different algorithms are not necessary.

 

 

Figure1A The residuals between the original wavefields and decomposed wavefields by different algorithms.

 

Point 3: How about the computational efficiency between the Helmholtz decomposition and proposed AI method? Can you show the computational details about the AI method?

 

Response 3: As your comments, we have correspondingly added the contents on the computational efficiency between the Helmholtz decomposition algorithm, the wavenumber domain vector decomposition algorithm and the vector decomposition algorithm based on SADCGANs in Discuss Section in the revised manuscript. Generally speaking, among the three decomposition algorithms used in our numerical experiments, Helmholtz decomposition algorithm has the highest computational efficiency, the vector decomposition algorithm in wavenumber domain requires longer computing time than Helmholtz decomposition algorithm, and our developed algorithm based on SADCGANs requires the longest computing time. The biggest concern of using SADCGANs is the computational cost for the training process. Once trained, the computational cost for the prediction process of neural network is comparatively inexpensive. During our numerical experiments, the central processing unit (CPU) which is used for elastic wavefield decomposition is the Intel Xeon Gold 5218 16-core 2.30 GHz processor, and the graphics processing unit (GPU) which is used for elastic wavefield decomposition is the 32G NVIDIA Tesla V100 processor. To obtain the decomposed wave modes from the coupled elastic seismic wavefields, the computing time of Helmholtz decomposition algorithm is so small that it can be ignored, the vector decomposition algorithm in wavenumber domain usually takes approximately 12 to 16 seconds, and our developed method based on SADCGANs with 5000 training samples requires approximately 48 hours for the training process and 10 to 15 seconds for the subsequent prediction process. Based on these statistical time data, the significant computational cost of our developed algorithm based on SADCGANs is mainly caused by the training process. With the rapid development of advanced hardware, such as CPU, GPU and computer cluster, the computational cost will not be a problem for our developed method based on SADCGANs in the future.

 

Point 4: Can the authors provide some metrics to evaluate the performance of the proposed SADCGANs? Can you show the loss functions during the training and testing?

 

Response 4: As your comments, we have added the corresponding contents in Discuss Section in the revised manuscript. To evaluate the performance of our developed method based on SADCGANs, we use two popular performance metrics to effectively quantify the neural network output. The first performance metric is the structural similarity index (SSIM), and the second performance metric is the coefficient of determination (R²). The loss functions of SADCGANs during the training and testing are described as Equation (8), which can be called as Wasserstein GAN with gradient penalty (WGAN-GP). Compared with the conventional loss functions, this WGAN-GP can more effectively stabilize the training and testing process. These above modifications have been marked in the revised manuscript.

 

Point 5: Many networks such as DnCNN, Dencenet or Resnet are common in seismic data processing, what are the advantages or disadvantages of your proposed network compared to them?

 

Response 5: As your comments, we have added the corresponding contents in Discuss Section in the revised manuscript. With the rapid development of deep learning methods, more and more neural networks are widely used in seismic data processing, such as DCNN, DenceNet, ResNet and GANs, etc. To achieve the vector decomposition of coupled elastic seismic wavefields, we use the SADCGANs which is an improvement of conventional GANs in this paper. Compared with other generative models, GANs is a type of generative model with several advantages. Firstly, GANs can be well generalized without requiring a large amount of annotated training data. Secondly, Markov chains may have lower efficiency in high-dimensional spaces because it convergence rate may be slower, and therefore GANs has the advantage of not requiring Markov chains. Most of the other neural networks either use stochastic approximations to select the training samples to minimize the objective function or use the Markov chains to repeatedly extract samples from the distribution and update them to ultimately converge to the true model. Thirdly, GANs can use multimodal outputs where a single input may correspond to multiple correct answers. Compared with the conventional machine learning models, this significant advantage can minimize the mean squared error (MSE) between the predicted and the desired outputs and thus lead to blurring of the detailed features because of the averaging effect. Finally, the GAN framework is a promising alternative to the neural networks operating on MSE, because it provides a rich internal representation of the structural information of the datasets without any blurring or averaging effect. However, the conventional GANs also has some disadvantages, the most serious problem of which is the difficulty of training. To effectively alleviate this problem, we use the more effective SADCGANs instead of the conventional GANs to stabilize the entire training process and obtain better wavefield decomposition results. At present, we only study the developed vector decomposition method based on SADCGANs, and in future work, we will test other neural networks used in elastic wavefield decomposition and conduct a comprehensive comparative analysis of their performance, such as DCNN, DenceNet and ResNet, etc. If the relevant research results are obtained in the future, we will publish them publicly.

 

Point 6: Moderate editing of English language required.

Response 6: According to your suggestions, we have carefully revised the English language for our manuscript, and these modifications have been marked in the revised manuscript.

 

If you have any further questions, please don’t hesitate to contact us. We will further discuss and modify the corresponding contents according to your comments. Thanks!

Best regards.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Hello, this version of the manuscript looks better. Best regards

Native speaker proofreading

Author Response

Dear reviewer, thank you for your recognition of our manuscript.

Reviewer 6 Report

The authors have made related corrections, no more comments

The authors have made related corrections, no more comments