| 18 May 2026
Three-Dimensional Geological Modeling based on Dual-Task Stratigraphy-Aware Attention Networks (Geo-SAN v1.0)
Abstract. The current three-dimensional (3D) geological implicit modelling methods are mainly based on interpolation methods, such as Kriging and radial basis functions (RBFs), which struggle to capture the nonlinear characteristics of complex geological structures and are limited in their capacity to integrate multi-source modeling data. To overcome these limitations, we proposed a 3D geological modelling framework, Geo-SAN, which consists of a dual-task stratigraphy-aware attention network. The framework starts with graph neural networks (GNNs) with a multi-scale neighborhood aggregation mechanism which is aimed to identify critical sampled points adjacent to fault planes and aggregate the lithological features. Subsequently, a stratigraphy-aware attention mechanism is introduced to explicitly incorporate similarities in stratigraphic sequence into the framework. A unidirectional stratigraphic scalar field penalty to lithological classification is developed and incorporated into loss functions, thereby denoising lithological classification. Finally, a dual-task prediction head is designed to simultaneously complete lithological classification and scalar field interpolation. Ablation experiment further validates the contributions of the three core components, that is, graph neighborhood aggregation, stratigraphy-aware attention, and dual-task learning. A case study at the Lingnian-Ningping region of Guangxi Zhuang Autonomous Region (GZAR), China, demonstrates that the proposed Geo-SAN framework, with an accuracy of 92.1% in lithological classification and a coefficient of determination (R²) of 0.96 in predicting the scalar field, outperforms the Hermite RBFs (HRBFs). In summary, the proposed framework is an important innovation of intelligent modelling of intricate geological formations, which is promising in the application of concealed mineral exploration.
1. The physical basis for the stratigraphic sequence similarity matrix is insufficient. In the learnable lithology similarity matrix defined in Section 2.1.2, the denominator value of σ(x) lacks geological basis and sensitivity analysis, and the impact of this hyperparameter on the distinguishability of the 13 lithology types is not discussed.
2. The weight settings for the dual-task loss lack an adaptive mechanism. In the total loss function in Section 2.2.4, the specific values of the four weight coefficients α, β, γ, and δ are not explicitly given in the text, and a fixed weighting strategy is used instead of a dynamic adaptive balancing strategy. In the early stages of training, the scalar field loss and the lithology classification loss differ significantly in magnitude; fixed weights may lead to one task dominating gradient updates. It is recommended to supplement the experimental basis for weight selection.
3. The baseline settings for the ablation experiments are not comprehensive enough. Table 2 only compares four internal variants in the ablation experiments, lacking a horizontal comparison with current mainstream deep learning geological modeling methods, and therefore cannot demonstrate the advantages of Geo-SAN over other methods. Furthermore, whether the accuracy difference between M3 and M4 is entirely attributable to the SAN module or the contribution of the dual-task structure is unclear, lacking ablation experiments that isolate the dual-task module.
4. The coupling mechanism between scalar field prediction and lithological classification is not sufficiently demonstrated. The paper claims that the dual-task framework establishes an "intrinsic coupling" between the scalar field and lithological categories, but Section 2.1.3 only describes a simple shared backbone + dual-branch structure, without explaining the specific interaction between the two tasks at the feature level. The KL divergence term in L_strat transforms the scalar field into lithological prior probabilities, but the mapping function from scalar values to probability distributions in this transformation process is not defined in detail. The confusion between T₁m and P₁m, and D₂d and D₁y, occurs precisely between adjacent stratigraphic units, indicating that cross-task constraints cannot completely resolve the classification ambiguity problem at stratigraphic boundaries.
5. The research depth on fault handling methods is insufficient. Section 2.1.1 mentions that "faults are encoded as a feature of nodes in relation to fault planes," but only encodes faults as a 0/1 binary feature, without considering key parameters such as fault displacement and fault type (normal fault/reverse fault/strike-slip fault). For left-lateral strike-slip reverse faults like the Nacha fault, it is unclear whether the model can accurately characterize the stratigraphic shift relationship between the two sides of the fault. The magnified view of region A in Figure 15b shows abrupt changes in stratigraphic thickness near the fault, requiring quantitative evaluation of the prediction error near the fault area.
6. The model's generalization ability and sample imbalance issues are not adequately discussed. Figure 13d shows extreme imbalance in the training samples. The paper claims the model has "strong small-sample generalization ability" for sparse classes, but does not provide performance tests under conditions of fewer or zero samples. Furthermore, the experiment uses a fixed 8:2 training-to-test split without cross-validation. This limitation of the modeling method, which often occurs in actual exploration where "new stratigraphic units do not appear in the training set," should be explained in the discussion.
7. Inconsistencies between the claim of "geological interpretability" and empirical evidence. Section 5 mentions that "model interpretability is still limited," but the abstract and conclusion emphasize that the method "reflects prior geological knowledge." It is recommended to supplement the analysis with spatial distribution of attention weights to support the core innovation claim of "stratigraphic awareness."