3D Geological Modeling Using Geostatistical, Deterministic, and Artificial Intelligence Algorithms: A Comparative Analysis for Delineating Mineralized Zones

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The reviewed manuscript (applsci-4542771) presents a comparative analysis of three geological modeling approaches (IK, NN, and ANN-MLP) for delineating oxide, supergene, and hypogene zones in a porphyry copper deposit. The authors used a dataset of 2097 samples from 51 exploration drill holes and applied a 3D block model containing 129507 blocks. The three models are compared through global zone proportions and vertical Z-direction swath plots. The topic is relevant to mineral-resource modeling. Please consider these comments to improve your manuscript:

1. Correct duplicated section numbering (3.2. and 4.1.).
2. Replace broad AI citations with literature directly supporting categorical spatial domain modelling and spatial validation.
3. Abstract: State the dataset size, block size, validation design, and proportion of unassigned blocks.
4. Keywords: Consider using more focused keywords such as 3D geological modeling and categorical classification
5. Lines 89:98: This gap in categorical deposit modeling is too broad.
6. Lines 153:157: Describe the source and resolution of the topographic surface.
7. Lines 204:227: This historical background is lengthy. Condense.
8. Lines 305:307: Translate to English
9. Line 308: Provide the rationale for choosing 800 epochs as the maximum limit, and batch size = 32.
10. Lines 362:372: Provide justification for the established probability thresholds of 0.6 for oxide and 0.51 for supergene/hypogene zones.
11. Line 379: Table 6 → Table 5
12. Table 5: Radio → Radius
13. Line 428: Table 7 → Table 6
14. Line 467: These thresholds are not clearly specified in Section 3.2.
15. Line 472: Furtheremore → Furthermore
16. Discussion: The discussion should be supported with recent and relevant literature.
17. Figures 13 and 14: Axis label “Frequency” or “proportion”
18. Line 555: “honors global mass balance” No formal mass-balance criterion is defined.
19. Limitations should be discussed.
20. Conclusion: Avoid using “exceptional generalization”, “captured geological uncertainty”, and “systematic bias” unless supported by independent validation and calibration analysis.

Comments on the Quality of English Language

English requires substantial language editing before publication.

Author Response

Found attached the author notes to reviewer in attached word file.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper addresses the geological uncertainty issues in the three-dimensional geological modeling of copper deposits' mineralization zones. Based on 51 exploration drill hole datasets, it conducts research on the division of mineralization zones (oxidation zones, secondary enrichment zones, and primary zones) using three algorithms: Kriging, Nearest Neighbor, and Multi-Layer Perceptron Neural Network. The main contributions of this paper include adapting the Z-axis swath plot as a quantitative evaluation method for the classification geological domain model; achieving multi-classification modeling of mineralization zones using MLP neural networks solely based on three-dimensional coordinates, and outputting the probability of occurrence of block geological variables; proposing to add boundary constraints to the MLP workflow to provide new ideas for automated resource estimation in intelligent mining environments.
1. The selection criteria for the hyperparameters (neuron quantity and number of layers) of the MLP model are missing. It is necessary to supplement the explanation of the grid search or trial-and-error screening process.
2. The literature support for the use of Swath plots for the evaluation of classification variables in the article is insufficient. It is recommended to supplement more published literature on similar applications.
3. The MLP model outputs the probabilities of each category, but the article does not analyze the calibration effect of probability prediction. It has not verified whether the high probability prediction represents a higher confidence level of the true category. The Softmax output in the classification task often has problems of over-confidence or under-confidence. Directly using a fixed probability threshold for block division may lead to systematic volume deviations. It is recommended to use reliability plots to evaluate probability calibration and discuss the risks of volume estimation in mineralization domains brought by the fixed threshold strategy.
4. The threshold setting for the Kriging indicator is > 0.6 for the oxidation zone and > 0.51 for the others. It is necessary to clarify the objective evaluation criteria for the determination of the threshold.
5. The conclusion part mentions modifying the Z-axis swath plots for the evaluation of the classification geological domain, but it does not clearly indicate the limitations of this evaluation method. It is recommended to supplement the applicable boundaries of this evaluation method.
6. The article points out that MLP performs unstably at sparse sampling boundaries and proposes to introduce boundary constraints as an improvement direction. However, no feasible implementation ideas have been given. Only raising the problem lacks a solution, reducing the practical value of this suggestion. It is recommended to briefly list feasible constraint methods, such as hard geological boundary masks, sampling boundary distance features as additional inputs, or boundary sample weighting strategies, and briefly describe the advantages and disadvantages of each method to facilitate subsequent research reference.
7. The conclusion states that ANNMLP has local sensitivity at low sampling boundaries, but does not clearly provide specific research directions for quantifying boundary constraints in future studies. It is recommended to refine the future research content.

Author Response

Found attached our comments to the reviewer

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a comparative study of three methods for three‑dimensional geological modelling of mineralised zones in a porphyry copper deposit. The strength of this work lies in its integration of conventional, deterministic, and state‑of‑the‑art data‑driven approaches within a unified framework, with rigorous validation using swath plots and an in‑depth discussion of the advantages and limitations of each method, as well as their roles in quantifying geological uncertainty. The manuscript is well structured, the methodology is thoroughly described, and the experimental design is sound. The results have significant practical value for mineral exploration and resource estimation. However, the following issues require revision:

Major Revisions

1. Although the authors provide a detailed description of the ANN‑MLP architecture (e.g., two hidden layers with 180 and 90 neurons), no justification is given for the selection of these specific numbers. Furthermore, the choice of key hyperparameters—including the initial learning rate of the Adam optimizer, batch size, and early stopping patience—is not supported by experimental or theoretical rationale.
2. The authors point out that the ANN‑MLP exhibits “continuous estimation” and “local instability” in the oxide zone within data‑sparse deep marginal areas (deep basal slices). However, the discussion attributes this behaviour to “the lack of a search ellipsoid as a geometric constraint,” which appears somewhat general and lacks a more detailed mechanistic explanation.
3. In Sections 3.1 and 3.2.2, the authors adopt different probability thresholds for generating the final geological models for the oxide zone (>0.6), secondary enrichment zone, and primary zone (>0.51). The rationale based on “metallurgical risk” is reasonable; however, it is essentially a subjective commercial decision rather than a purely scientific criterion.

Minor Revisions

1. The subheadings under Section 3 should be numbered as “3.2. Deterministic Geological Modelling” and “3.3. Geological Modelling using Artificial Intelligence.” The current numbering incorrectly repeats “3.2” and should be corrected.
2. In lines 304–307, a passage appears in Spanish: “El rendimiento de la ANN‑MLP se evaluó...”. Please translate this into English to maintain consistency in language throughout the manuscript.
3. When referring to the software, the authors predominantly use “RecMin Pro,” but “Recmin Pro” also appears (e.g., line 375). Please unify the capitalization and spelling.
4. In line 464, the authors cite “Figure 11. (c) Probability distribution profiles...”; however, the (c) and (d) subfigures of Figure 11 in this section appear to be incorrectly referenced in the text. Please check all figure numbers and citations for accuracy.
5. The reference list is generally of good quality; however, the authors are encouraged to check for recent (2024–2026) publications on the application of machine learning in geological modelling, particularly regarding uncertainty quantification and boundary constraints. Suggested references include: Study on Caving Characteristics of Roof and Floor and Law of Ground Pressure Behavior in Near‑Vertical Coal Seams Mining: A Three‑Dimensional Similarity Simulation Experiment, Study on Deformation Mechanism and Control Technology of Rock Pillar in Near‑Vertical Coal Seams Mining. Incorporating such recent work would further strengthen the depth of the discussion.

Author Response

Found attached our comments to the reviewer

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The revised manuscript has improved substantially. The reviewer appreciates the authors' detailed and specific responses to the comments, which have adequately addressed the major concerns raised during the review process. One more comment:

1. Please standardize terminology throughout the manuscript (Nearest Neighbor or Nearest Neighbour; mineralized zones or mineralized domains or geological domains; Multilayer Perceptron or Multi-Layer Perceptron).

Author Response

Found attached our answer to the reviewer

Author Response File: Author Response.docx