## 4 Materials and Methods
### Methodology
#### 4.2.1 Convolutional Neural Networks
To address the spatial heterogeneity of sedimentary facies images, this study designed a three-stage augmentation framework incorporating geometric transformations, illumination perturbations, and domain adaptation (Figure 8). The geometric transformation module employs random rotations (\(\pm\)45\({}^{\circ}\)), non-uniform translations (horizontal/vertical offsets: 0.3\(\times\) image dimensions), scale adjustments (0.6-1.5\(\times\)), and shear deformations (0.3 radians), simulating geometric distortions during seismic wave propagation via affine transformation matrices. The illumination perturbation module introduces brightness range modulation (0.5-1.5\(\times\)) and contrast enhancement (0.7-1.3\(\times\)) to emulate imaging variations under different lighting conditions. Notably, a class-specific augmentation intensity adjustment mechanism was developed for underrepresented categories (e.g., main channels, natural levees): dynamically tuning brightness perturbation magnitudes (1.2\(\times\) enhancement for channels, 1.5\(\times\) for levees) to increase sample diversity while preserving geological semantics. Our model employed five key optimization strategies: (1) thickness-adaptive input scaling (64 \(\times\) 64 to 256 \(\times\) 256) to preserve geological features across bed thicknesses; (2) class-specific augmentation intensities to address imbalance; (3) dual-rate learning  
Figure 8: A thickness-adaptive input sizing algorithm diagram. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyperparameter Category** & **Parameter Name** & **Value/Configuration** \\ \hline \multirow{8}{*}{Data Preprocessing} & Rotation Range & \(\pm\)45\({}^{\circ}\) \\ \cline{2-3}  & Width Shift Range & 0.3 \\ \cline{2-3}  & Height Shift Range & 0.3 \\ \cline{2-3}  & Zoom Range & [0.6, 1.5] \\ \cline{2-3}  & Shear Range & 0.3 \\ \cline{2-3}  & Brightness Range & [0.5, 1.5] \\ \cline{2-3}  & Horizontal Flip & True \\ \cline{2-3}  & Class-specific Enhancement & Main Channel: \(\times\)1.2 \\ \cline{2-3}  & Natural Levee: \(\times\)1.5 \\ \hline \multirow{8}{*}{Model Architecture} & 0: (64 \(\times\) 64) \\  & Input Size (Dynamic) & 1: (128 \(\times\) 128) \\ \cline{2-3}  & 2: (192 \(\times\) 192) \\ \cline{2-3}  & Convolutional Layer 1 & Filters = 16, Kernel Size = (3 \(\times\) 3), \\  & Activation = ’relu’, Padding = ’same’ \\ \cline{2-3}  & Convolutional Layer 2 & Filters = 32, Kernel Size = (3 \(\times\) 3), \\  & Activation = ’relu’, Padding = ’same’ \\ \cline{2-3}  & Dense Layer (Feature Fusion) & Units = 8, Activation = ’relu’ \\ \cline{2-3}  & Output Layer & Units = 6, Activation = ’softmax’ \\ \cline{2-3}  & Dropout & Rate = 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The hyperparameter optimization results. scheduling (initial \(1\times 10^{-3}\) with exponential decay and plateau detection); (4) a balanced dual-input architecture (3 convolutional blocks + 2 dense layers) with concatenation-based fusion; (5) automated class weighting. These choices were informed by iterative ablation and validated through 5-fold cross-validation. The configuration balances computational efficiency with geological plausibility, particularly for underrepresented facies like channels.