GeoSAE: A 3D Stratigraphic Modeling Method Driven by Geological Constraint

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I have the following recommendations. 

1. Provide a diagram which describes all your proposed methodology

2. Provide the parameters of the Neural Network models and the hardware and softwar setup. 

3. Provide clearer explanation of the employed datasets and how can it be realted to the use of a Neural Network like Self Staked-Encoder Network. 

Author Response

Dear Reviewer,
Thank you for your valuable feedback and thoughtful recommendations. We have carefully considered your suggestions and made the necessary revisions. Below are our responses to your comments:

Comments 1: Provide a diagram which describes all your proposed methodology
Response1: In response to your suggestion, we have added a diagram in Section 2.3 (page 12, line 419) that clearly describes the entire proposed methodology. This addition is intended to provide readers with a more intuitive and comprehensive overview of our approach.

Comments 2:  Provide the parameters of the Neural Network models and the hardware and software setup
Response 2: As requested, we have provided the parameters of the Neural Network models and detailed the hardware and software setup in Section 3(page 13, line 429). The experimental setup now includes the following configurations:
GPU: NVIDIA GeForce RTX-3080Ti
CPU: Intel i7-10 (single-core)
CUDA Version: 11.6
Python Version: 3.8
Additionally, in Section 2.2.1 (page 9, line 345), we have revised the description of the network model for predicting the 3D potential field. 
Original:
"A network model for predicting the 3D potential field is presented in this paper, built from multiple stacked autoencoders with an encoder-decoder structure, as shown in Fig. 5. The model is composed of convolutional layers, fully connected layers, and activation functions. The convolutional layers are used with a kernel size of 1 and a stride of 1, ensuring that the input tensor's dimensions are preserved while producing output tensors with the same height and width but varying channel depth."
Revised:
"A network model for predicting the 3D potential field is presented in this paper, built from stacked autoencoders with an encoder-decoder structure. Each autoencoder consists of an encoder-decoder structure, as shown in Fig. 5, where the encoder is composed of two convolutional layers with kernel sizes of 3×128 and 128×256, followed by a fully connected layer of 256×256. The decoder is composed of two convolutional layers with kernel sizes of 256×128 and 128×1. The convolutional layers are used with a kernel size of 1 and a stride of 1, ensuring that the input tensor's dimensions are preserved while producing output tensors with the same height and width but varying channel depth."

Comments 3: Provide clearer explanation of the employed datasets and how can it be related to the use of a Neural Network like Self Stacked-Encoder Network
Response 3: First, we apologize for the translation error in the manuscript. The correct term should be "Stacked Autoencoder," and we have made the necessary correction. Regarding your query, we have provided a clearer explanation of the datasets used in Section 2.3(page 11, line 396). This section now includes both a textual description and a visual illustration, explaining how the datasets are used and how they relate to the application of Neural Networks, such as the Stacked Autoencoder.
Added Text:
2.3. Overall Modeling Workflow Architecture(page 11, line395)
According to Sections 2.1 and 2.2, this paper outlines the framework for the overall modeling workflow, which includes three main subprocesses as shown below:
First, the network parameters of the autoencoder (AE) are pre-trained. This process, described in Section 2.2.2, uses the planar geometry shown in Fig 7 and combines L1 and L2 loss functions for pre-training the network parameters.
Next, the pre-trained AE network parameters are loaded into the stacked autoencoder (SAE), and the model continues training to accelerate convergence. Training utilizes the geology knowledge-driven loss function introduced in Section 2.1, aiming to predict the scalar field values of stratigraphic interface sampling points by learning the internal features of these points. The stratigraphic interface sampling points can be obtained from various geological data sources, such as borehole data, geological profiles, geological maps, etc. Training continues until the predicted scalar field values meet the convergence conditions of the loss function, completing the training of the GeoSAE model.
Finally, the trained GeoSAE model is used to predict scalar field values for grid points. The grid points are generated based on the modeling range and specified grid resolution, covering the range of stratigraphic interface sampling points used during training. The prediction results can be extracted using isosurface extraction or attribute classification methods to generate 3D stratigraphic surface models or 3D geological attribute models.
Added Diagram:

We believe these revisions address your concerns and significantly improve the manuscript. Once again, thank you for your constructive feedback, and we look forward to any further comments you may have.

Best regards,
Jinbo Zhou
Hainan Key Laboratory of Marine Geological Resources and Environment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors submitted a well written and an interesting manuscript dealing 3D geological modelling using deep learning techniques. The methodological approach is well described, and the conclusions are supported by experimental results. With the current technological advances and increasing need for natural resources, this study would contribute greatly to modern geological studies and potentially provide a useful tool for geological mapping. However, the authors should improve the manuscript before it could be considered for publication. Some references are written in language other language than English which make it difficult to review the statements attributed to them in the main manuscript. Please check references 7, 22, 23, 36, 37, 38, 39, 40 and replace them with other reference studies.

Author Response

Dear Reviewer,
Thank you for your kind comments and positive feedback on our manuscript. We are delighted to hear that you found the methodology well-described and the experimental results supporting the conclusions. We also appreciate your valuable suggestion regarding the non-English references.

Comment1:The authors submitted a well written and an interesting manuscript dealing 3D geological modelling using deep learning techniques. The methodological approach is well described, and the conclusions are supported by experimental results. With the current technological advances and increasing need for natural resources, this study would contribute greatly to modern geological studies and potentially provide a useful tool for geological mapping. However, the authors should improve the manuscript before it could be considered for publication. Some references are written in language other language than English which make it difficult to review the statements attributed to them in the main manuscript. Please check references 7, 22, 23, 36, 37, 38, 39, 40 and replace them with other reference studies.
Response 1:In response to your comments, I have carefully reviewed the references you pointed out (7, 22, 23, 36, 37, 38, 39, 40) and made the following changes:     
Reference 40 has been removed.
The other references have been replaced with appropriate English references. We believe these modifications enhance the quality of the manuscript and ensure that the cited works are accessible to a broader international audience.
Replaced References:
7. Gonçalves, Í. G.; Kumaira, S.; Guadagnin, F. A Machine Learning Approach to the Potential-Field Method for Implicit Modeling of Geological Structures. Comput. Geosci. 2017, 103, 173–182.
22. Liu, L.; Li, T.; Ma, C. Research on 3D Geological Modeling Method Based on Deep Neural Networks for Drilling Data. Appl. Sci. 2024, 14, 423.
23. Zhou, C.; Ouyang, J.; Ming, W.; Zhang, G.; Du, Z.; Liu, Z. A Stratigraphic Prediction Method Based on Machine Learning. Appl. Sci. 2019, 9(17), 3553.
36. Liu, L.; Zhou, J.; Jiang, D.; Zhuang, D.; Mansaray, L. R. Lithological Discrimination of the Mafic-Ultramafic Complex, Huitongshan, Beishan, China: Using ASTER Data. J. Earth Sci. 2014, 25, 529–536.
37. Su, Q.; Li, Z.; Li, G.; Zhu, D.; Hu, P. Coastal Erosion Risk Assessment of Hainan Island, China. Acta Oceanol. Sin. 2023, 42(7), 79–90.
38.Dilek, Y.; Tang, L. Magmatic Record of the Mesozoic Geology of Hainan Island and Its Implications for the Mesozoic Tectonomagmatic Evolution of SE China: Effects of Slab Geometry and Dynamics in Continental Tectonics. Geol. Mag. 2021, 158(1), 118–142.
39. Yao, W.; Li, Z. X.; Li, W. X.; Li, X. H. Proterozoic Tectonics of Hainan Island in Supercontinent Cycles: New Insights from Geochronological and Isotopic Results. Precambrian Res. 2017, 290, 86–100.
We hope that these revisions meet your expectations and improve the manuscript’s accessibility for international readers. Thank you again for your thoughtful feedback.

Best regards,
Jinbo Zhou
Hainan Key Laboratory of Marine Geological Resources and Environment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors

 

Many thanks for submitting your interesting manuscript to Applied Sciences. I was very pleased to review it and I hope that my remarks can contribute to its improvement.

I think that the work have conditions to be published after some revisions, which I would like to see considered. 

 

#1.

As for the acronym GeoSAE, which is the essential element in the title and the main object of this work, the meaning of the letters S, A and E is explained in line 125 though It would be important to have this explanation the first time it appears in the main text.

 

#2

The regional framework of the study area in China and East Asia should be included in figure 8 to improve readability for international readers who are not familiar with the Chinese geographical context.

 

#3

I suggest removing the numerical indication [(1) (2) ... ] of items in various parts of the text, so as not to confuse them with the chapter numbering.

 

#4

Please revise all the titles (captions) of figures in order to include always the study context or study area. These should be as comprehensive and legible as possible, without the need to consult the main text.

 

#5

I suggest revising the final part of chapter 1 (‘Introduction’). The last paragraph contains a summary of the work, with information about the methods that are described in the following chapter. I suggest removing this paragraph.

 

#6

I suggest the rearrangement of the chapters structure. For instance, the chapter 3 (“Data verification”) should be entitled “Results” and a Discussion chapter must be included. It is expected that this chapter includes an interpretation of the results obtained, such as the main patterns in the observations made, the relationships, trends and generalisations of the results, exceptions to these trends, agreement or novelty in relation to previous work, etc.  The main limitations should be mentioned (if applicable), as well as the advances in knowledge that have been made as a result of the work. The discussion can be supplemented with data from other works.

 

#7

I suggest avoiding the repeated use of the expression ‘this paper’ or ‘the paper’, replacing it with something like ‘our approach’ or ‘this work’.

 

 

Regards

Author Response

Dear Reviewer,
Thank you very much for your thoughtful and constructive comments on our manuscript. We greatly appreciate the time and effort you took to review our work, and we believe that your suggestions have significantly improved the manuscript. Below are the changes we have made in response to your recommendations:

Comments 1:As for the acronym GeoSAE, which is the essential element in the title and the main object of this work, the meaning of the letters S, A and E is explained in line 125 though It would be important to have this explanation the first time it appears in the main text.
Response 1:As you suggested, we have now provided a full explanation of the acronym "GeoSAE" at the first occurrence in the introduction (page3, line 119). This ensures that readers are introduced to the meaning of the acronym early in the text. Modification：
“To address this challenge, this work presents GeoSAE, a geological constraint-driven 3D modeling method that incorporates geological constraints into the modeling process. In GeoSAE, the ‘S,’ ‘A,’ and ‘E’ represent Stacked Autoencoder, which is a neural network architecture where multiple autoencoders are stacked to simultaneously predict several potential field values.”

Comments 2:The regional framework of the study area in China and East Asia should be included in figure 8 to improve readability for international readers who are not familiar with the Chinese geographical context.
Response 2:We have revised Figure 8 to include a clearer depiction of the regional framework, highlighting the position of China within East Asia, as well as the location of Haikou City in Hainan Province. This addition will help improve readability for international readers unfamiliar with the geographical context.The updated figure is now labeled as Figure 9 and is presented in Section 3.1, "Data preparation and analysis," on page 14, line 466. The new title of the figure is:
Figure 9: Borehole Distribution and Modeling Scope of Jiangdong New District, Haikou City.

Comments 3: I suggest removing the numerical indication [(1) (2) ... ] of items in various parts of the text, so as not to confuse them with the chapter numbering.
Response 3: We have removed the numerical indications [(1), (2), etc.] from the various sections of the manuscript, as per your recommendation, to avoid confusion with chapter numbering.
Example of Modification:
In Section 2.1.2 (page 5, line 186), the original text was:
(1) "Above" relationship: For a given potential field representing consecutive strata, the potential field value at the sampling point of the upper stratum is required to be greater than that of the lower stratum if one stratum is above another.
(2) "Below" relationship: In all potential fields, the potential field value at the sampling point of the lower stratum is required to be less than that of the upper stratum if one stratum is beneath another.
(3) "Overlap" relationship: If two stratigraphic surfaces overlap, equality of the potential field values at the sampling points along the interface of these strata is required.
We have modified it to:
"Above" relationship: For a given potential field representing consecutive strata, the potential field value at the sampling point of the upper stratum is required to be greater than that of the lower stratum if one stratum is above another.
"Below" relationship: In all potential fields, the potential field value at the sampling point of the lower stratum is required to be less than that of the upper stratum if one stratum is beneath another.
"Overlap" relationship: If two stratigraphic surfaces overlap, equality of the potential field values at the sampling points along the interface of these strata is required.

Comments 4: Please revise all the titles (captions) of figures in order to include always the study context or study area. These should be as comprehensive and legible as possible, without the need to consult the main text.
Response 4: We have revised all figure captions to include the study context or study area, making them more comprehensive and self-explanatory, so that readers do not need to refer to the main text for clarification.
Examples of Modification:
Original:
Figure 1: Potential field representation based on stratigraphic contact relations (Section 2.1.2, page 5, line 186)
Figure 3: Relationship between stratigraphic surfaces based on the sequence of potential field values (Section 2.1.2, page 6, line 220)
Figure 8: Borehole distribution and modeling scope (Section 3.1, page 14, line 470)
Figure 9: Schematic diagram of stratigraphic columns in the modeled area (Section 3.1, page 15, line 479)
Revised:
Figure 1: Potential field representation based on stratigraphic contact relationships, showing six stratigraphic surfaces, including two unconformable and four conformable interfaces.
Figure 3: Layer ordering relationships between stratigraphic surfaces based on potential field value sequence, illustrating the "above," "below," and "overlap" relationships in the stratigraphic model.
Figure 9: Borehole Distribution and Modeling Scope of Jiangdong New District, Haikou City
Figure 10: Schematic diagram of stratigraphic columns in the modeled area of Jiangdong New District

Comments 5: I suggest revising the final part of chapter 1 (‘Introduction’). The last paragraph contains a summary of the work, with information about the methods that are described in the following chapter. I suggest removing this paragraph.
Response 5: As per your suggestion, we have removed the last paragraph of the introduction, which contained a summary of the work and methods. We have integrated relevant content into the conclusion section to improve readability and flow.
Added in Section 5: Conclusion (page 22, line 619):
Three-dimensional geological modeling is essential for advancing our understanding of the formation and evolution of subsurface structures. However, incorporating geological knowledge directly into the modeling process is challenging, often leading to discrepancies between the generated 3D geological models and actual geological conditions. To address this issue, this work presents a geological constraint-driven 3D geological modeling approach, GeoSAE, which effectively integrates multiple geological constraints—such as stratigraphic sequence relationships, interface consistency, attitude point orientation, and interface smoothness—into the deep learning training process. The core contributions of this work are: the construction of a geological constraint loss function that incorporates stratigraphic geometric features and smoothing effects to guide the training process; the design of a stacked autoencoder (SAE) structure that enables the simultaneous prediction of multiple potential field values; and the development of a comprehensive framework for geological constraint-driven 3D geological modeling, which is validated through modeling experiments. 
The proposed method utilizes a deep learning approach with integrated geological constraints, overcoming the limitations of traditional implicit interpolation techniques. The experimental results show that GeoSAE accurately predicts stratigraphic surfaces and fits stratigraphic points with high precision. Additionally, the stratigraphic smoothness constraint effectively mitigates abrupt transitions in potential field modeling, enhancing the quality of the generated model.
This method's key advantage lies in its ability to incorporate geological constraints directly into the modeling process, improving both model accuracy and geological relevance. Future work may focus on extending the method to model more complex geological structures, such as faults and overturned strata. Additionally, incorporating more geological constraints and expanding the dataset could further refine the framework's ability to handle complex geological challenges. Exploring more flexible network architectures and integrating multivariate geological data may also improve the model's generalization and performance.

Comments 6: I suggest the rearrangement of the chapters structure. For instance, the chapter 3 (“Data verification”) should be entitled “Results” and a Discussion chapter must be included. It is expected that this chapter includes an interpretation of the results obtained, such as the main patterns in the observations made, the relationships, trends and generalisations of the results, exceptions to these trends, agreement or novelty in relation to previous work, etc.  The main limitations should be mentioned (if applicable), as well as the advances in knowledge that have been made as a result of the work. The discussion can be supplemented with data from other works.
Response 6: We have revised the structure of the manuscript as recommended. The title of Chapter 3 has been changed to "Experimental Verification and Results," and we have added a new Chapter 4 titled "Discussion." In this new chapter, we interpret the results obtained, discuss patterns, trends, and relationships observed, compare our findings with previous work, and address any limitations and advances in knowledge resulting from the study.
Added in Chapter 4: Discussion (page 21, line 583):
The modeling results indicate that the GeoSAE method excels in constructing 3D geological models that incorporate multiple unconformities and continuous strati-graphic interfaces. It is particularly effective in generating scalar field values that ad-here to geological principles, even when handling noisy regional datasets. Although the stratigraphic sequence relationship loss and global smoothing loss contribute in-crementally to model optimization, they provide crucial support for validating the model's effectiveness. Particularly in data scarce areas, such as outcrop regions with limited profile data, these constraints offer significant improvements. They enable the integration of geological maps into the modeling process by sampling points within unit polygons and incorporating these points as constraints with weighting terms to guide the model toward results that better reflect geological structures. 
Furthermore, the GeoSAE model effectively handles both internal and external constraints on stratigraphic relationships, demonstrating its potential to integrate new geological constraints. For example, the model automatically learns the optimal isosurface for each stratigraphic surface, thus overcoming the limitations of manually specified isosurfaces. This method is more flexible in adapting to complex geological structures, especially when modeling areas with varying or significant thickness changes. Compared to the limitations of manually specified isosurfaces in traditional methods, GeoSAE significantly enhances the expression of stratigraphic structures.
Experimental results show that the Softplus function effectively captures high-frequency details in the data while avoiding unnatural folding features when generating structures with good geological representation. The ReLU activation function typically results in sharper geometric shapes, which may be more suitable for brittle structural environments, while the smoother geometric shapes produced by the Softplus function better align with the actual features of geological structures. Experimental results show that the Softplus function effectively captures high-frequency de-tails in the data while avoiding unnatural folding features when generating structures with good geological representation.  In contrast, while the ReLU activation function generates sharper geometric shapes, in certain cases, the model's fitting performance may be compromised, especially when higher stratigraphic smoothness is required. 
However, although the GeoSAE model performs excellently in fitting most stratigraphic surfaces, some layers (such as N1d and N2h) exhibit significant fitting errors. These errors may stem from the inherent complexity of the actual geological data, such as vertical folding of strata and erosional unconformities, which make it difficult for the model to fully capture the subtle variations in the strata. Moreover, while the glob-al smoothing constraint reduces the impact of data noise to some extent, excessive smoothing weights may suppress important geological features in the strata, leading to overly smooth stratigraphic surfaces, which could affect the model's accuracy. Therefore, future research could further optimize the weight of the smoothing constraint to better balance the smoothness of the model with the retention of details.
Overall, the GeoSAE method provides a new and effective approach for 3D geo-logical modeling, excelling in handling complex geological structures and large-scale regional modeling. This method not only enhances the accuracy of modeling but also improves the model's adaptability to complex geological environments, offering important references for future geological modeling and data analysis. In future work, further optimization of constraint conditions and improving the model's ability to capture special geological phenomena remains a promising area for in-depth research.

Comments 7: I suggest avoiding the repeated use of the expression ‘this paper’ or ‘the paper’, replacing it with something like ‘our approach’ or ‘this work’.
Response 7: We have revised instances of the expression "this paper" or "the paper" and replaced them with terms such as "our approach" or "this work" to improve clarity and avoid redundancy.
Original:
"To address this, this paper introduces GeoSAE, a geological constraint-driven 3D modeling method that incorporates geological constraints into the modeling process." (Section 1, page 3, line 118)
"In response, various geological constraints are effectively transformed into inequality forms in this paper." (Section 2.1, page 3, line 138)
Modified:
"To address this challenge, this work presents GeoSAE, a geological constraint-driven 3D modeling method that incorporates geological constraints into the modeling process."
"In response, various geological constraints are effectively transformed into inequality forms in this approach."

We hope these revisions adequately address your concerns and enhance the quality of the manuscript. Thank you again for your valuable feedback. We look forward to your further comments.

Best regards,
Jinbo Zhou
Hainan Key Laboratory of Marine Geological Resources and Environment

Author Response File: Author Response.pdf