Spectral Graph Convolution Networks for Microbialite Lithology Identification Based on Conventional Well Logs

Keran Li^a,1, Jinmin Song^a,*, Han Wang^a, Haijun Yan^b, Shugen Liu^a, Yang Lan^c,2, Xin Jin^a, Jiaxin Ren^a, Lizhou Tian^a, Haoshuang Deng^a, Wei Chen^a

^aState Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu 610059, China

^bResearch Institute of Petroleum Exploration and Development, Beijing, 100083, China

^cUniversity College London, Gower Street, London, WC1E 6BT, UK

¹Present address: State Key Laboratory of Critical Earth Material Cycling and Mineral Deposits, Frontiers Science Center for Critical Earth Material Cycling, School of Earth Sciences and Engineering, Nanjing University, Nanjing, 210023, China

²Present address: School of Economics and Management, Beihang University, Beijing, 100191, China

^*Corresponding authors

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📄 Paper • 🌐 Project Page • 📊 Dataset • 🚀 Quick Start

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🎯 Overview

This repository provides the official implementation of Spectral Graph Convolutional Networks (GCN) for automated microbialite lithology identification from conventional well logs. Unlike traditional methods that shuffle time-series data (destroying sedimentary sequence information), this approach treats well logs as graph-structured spectral data, preserving both vertical temporal dependencies and inter-log correlations.

🔬 Key Innovations

• 🕸️ Graph Representation: Transforms well logs into latent graphs (spectra + adjacency matrix) using GRU and self-attention
• 🎵 Spectral Processing: Utilizes Graph Fourier Transform (GFT) and Discrete Fourier Transform (DFT) to capture frequency-domain features
• ⏱️ Sequence Preservation: Maintains depth-series (time-series) order without shuffling, modeling actual sedimentary deposition sequences
• ⚖️ Data Balance: Implements SMOTE to handle class imbalance in microbialite distribution
• 🔄 Transfer Learning: Demonstrates fine-tuning strategies for adapting to new formations (Dengying-2, Leikoupo-4³) with limited samples

📊 Performance Highlights

Model	Accuracy	Precision	Recall	F1-Score	AUC
GCN (Ours)	0.90	0.93	0.94	0.90	0.95
LSTM	0.80	0.79	0.78	0.80	0.78
RNN	0.61	0.60	0.65	0.61	0.72
TCN	0.70	0.69	0.72	0.70	0.78
ANN	0.61	0.50	0.56	0.61	0.58

Results on Dengying Formation (Z2dn4), Moxi Gas Field, Sichuan Basin

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🏗️ Architecture

Workflow: Raw Logs → GRU Encoder → Self-Attention (Adjacency) → GFT/DFT → GLU → Graph Conv → Classification

Core Components

1. 📈 GRU Block: Processes depth-series sequences to generate latent graph representations
2. 🔗 Self-Attention: Dynamically constructs adjacency matrices from hidden states (Q, K, V mechanism)
3. 🌊 Spectral Transform:
   • GFT: Graph Fourier Transform using Laplacian eigen-decomposition
   • DFT: Discrete Fourier Transform for frequency-domain convolution
4. 🎛️ GLU (Gated Linear Unit): Controls information flow in spectral domain
5. 🕸️ Graph Convolution: Spectral graph convolution with symmetric normalized Laplacian

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📁 Dataset

Geological Setting

• Location: Moxi Gas Field, Central Sichuan Basin, China
• Formation: 4th Member of Ediacaran Dengying Formation (Z2dn4)
• Wells: 44 wells (42 for training, 2 preserved for generalization testing)
• Samples: 10,367 valid data points (after SMOTE augmentation: 12,570)

Well Log Features (8 Curves)

Curve	Description	Unit	Geological Significance
AC	Acoustic (Sonic)	μs/m	Velocity, porosity indicator
CAL	Caliper	inch	Borehole diameter, caving
CNL	Compensated Neutron	%	Porosity, hydrogen index
DEN	Density	g/cm³	Bulk density, lithology
GR	Gamma Ray	API	Shale content, clay volume
PE	Photoelectric Factor	b/e	Mineral composition, lithology
RLLD	Deep Resistivity	Ω·m	True formation resistivity
RLLS	Shallow Resistivity	Ω·m	Invasion zone resistivity

Lithological Classes (5 Microbialite Types)

Code	Full Name	Description	Characteristics
MICR	Dolomicrite	Micritic dolomite	Dark, fine-grained, rare structures
SSTR	Stratiform Stromatolite	Layered microbial mats	Parallel laminations, intermittent dark lines
WSTR	Wavy Stromatolite	Undulating microbial structures	Large curvature, semi-circular, porous
THRO	Thrombolite	Clotted microbial structure	Dark clots, diffusing fabric, dissolving pores
SILIS	Siliceous Stromatolite	Silica-rich microbialite	Curved stripes, interlayer quartz, brittle

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📦 Installation

Prerequisites

• Python ≥ 3.8
• CUDA ≥ 11.3 (optional, for GPU acceleration)
• 8GB+ RAM

Setup

# Clone repository
git clone https://github.com/KeranLi/GCN-Microbialite-Lithology.git
cd GCN-Microbialite-Lithology

# Install dependencies
pip install -r requirements.txt

# Install package
pip install -e .

Key Dependencies:

torch>=1.11.0
numpy>=1.20.0
pandas>=1.3.0
scikit-learn>=0.24.0
scipy>=1.7.0
imbalanced-learn>=0.8.0  # For SMOTE

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🚀 Quick Start

1. Data Preparation

Prepare CSV files with the following columns:

Depth,AC,CAL,CNL,DEN,GR,PE,RLLD,RLLS,Lithology
5000.0,55.2,8.5,2.1,2.45,15.0,3.2,100.0,95.0,SSTR
5000.125,56.1,8.6,2.2,2.46,16.2,3.1,105.0,98.0,SSTR
...

2. Training

Train GCN Model (Full Pipeline)

python scripts/train.py --config configs/config.yaml --model gcn

Train Baseline Models (for Comparison)

# LSTM (Time-series sequential)
python scripts/train.py --model lstm

# RNN (Basic recurrent)
python scripts/train.py --model rnn

# TCN (Temporal Convolutional Network)
python scripts/train.py --model tcn

# ANN (Standard feed-forward)
python scripts/train.py --model ann

3. Evaluation

python scripts/evaluate.py --checkpoint checkpoints/best_gcn.pth --test_data data/test.csv

Expected output:

Test Metrics:
- Accuracy: 0.90
- Precision: 0.93
- Recall: 0.94
- F1-Score: 0.90
- AUC: 0.95

Confusion Matrix:
       SSTR  THRO  WSTR  SILIS  MICR
SSTR   0.97  0.01  0.02   0.00  0.00
THRO   0.00  0.99  0.00   0.00  0.00
WSTR   0.03  0.01  0.95   0.00  0.01
SILIS  0.00  0.00  0.00   0.99  0.01
MICR   0.00  0.04  0.00   0.00  0.95

4. Inference on New Wells

import torch
from models.gcn import MicrobialiteGCN
from utils.data_loader import WellLogDataset

# Load model
model = MicrobialiteGCN(input_dim=8, num_classes=5)
checkpoint = torch.load('checkpoints/best_gcn.pth')
model.load_state_dict(checkpoint['model_state_dict'])

# Prepare data (8 log curves)
logs = [[55.2, 8.5, 2.1, 2.45, 15.0, 3.2, 100.0, 95.0], ...]  # [seq_len, 8]
input_tensor = torch.FloatTensor(logs).unsqueeze(0)  # [1, seq_len, 8]

# Predict
logits, adjacency_matrix = model(input_tensor)
predicted_class = torch.argmax(logits, dim=1)
# Returns: SSTR (Stratiform Stromatolite)

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🔄 Transfer Learning (Fine-tuning)

The model supports rapid adaptation to new formations with limited data, as demonstrated in the paper for:

• Dengying-2 Member (Taihe Gas Field) - 6 lithologies
• Leikoupo-4³ Submember (Pengzhou Gas Field) - 3 lithologies

Strategy 1: Standard Fine-tuning (Medium Dataset: >1000 samples)

python scripts/transfer_learning.py     --source_model checkpoints/best_gcn.pth     --target_data data/dengying2.csv     --num_classes 6     --strategy fine_tune     --epochs 50

Strategy 2: GCN + SVM (Small Dataset: <500 samples)

When target data is extremely limited, freeze GCN layers and use SVM classifier:

from scripts.transfer_learning import TransferLearningGCN

# Initialize transfer learning
tl = TransferLearningGCN(
    pretrained_path='checkpoints/best_gcn.pth',
    num_new_classes=3,  # Leikoupo-43 has 3 classes
    freeze_layers=True
)

# Use GCN as feature extractor + SVM
tl.fine_tune_with_svm(X_train, y_train, X_test, y_test)

Results with Fine-tuning:

Formation	Samples	Strategy	Accuracy	Notes
Dengying-4 (Source)	8,000	Baseline	0.90	Original training
Dengying-2	500	GCN+SVM	0.86	Limited data
Dengying-2	8,000	Fine-tune	0.91	Full adaptation
Leikoupo-4³	2,000	Fine-tune	0.84	Cross-formation

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📊 Experimental Results

Main Results (Test Set, Moxi Gas Field)

Model	Architecture	Acc	Pre	Rec	F1	AUC	Params
GCN	GRU+GFT+GLU+GCN	0.90	0.93	0.94	0.90	0.95	2.1M
LSTM	5-layer LSTM	0.80	0.79	0.78	0.80	0.78	1.8M
RNN	5-layer RNN	0.61	0.60	0.65	0.61	0.72	1.2M
TCN	Dilated Conv	0.70	0.69	0.72	0.70	0.78	1.5M
FC-ANN	Fully Connected	0.61	0.50	0.56	0.61	0.58	2.8M
Dropout-ANN	ANN + Dropout	0.67	0.70	0.63	0.67	0.62	2.8M

Key Findings

1. GCN Superiority: GCN achieves 90% accuracy, outperforming LSTM by 10% and RNN by 29%
2. Overfitting in ANNs: Standard ANNs show severe overfitting (train acc 0.82 → test acc 0.61), mitigated by dropout but still inferior to sequential models
3. Temporal Information: Shuffling time-series destroys sedimentary patterns, reducing all models to ~20% accuracy
4. Class-wise Performance:
   • THRO (Thrombolite): Best identified (Accuracy >0.95)
   • SSTR vs WSTR: Main confusion pair (3% misclassification due to similar lamination patterns)
   • SILIS: Easily distinguished by quartz signature in PE logs

Ablation Study

Components removed and performance impact:

Configuration	Accuracy Drop	Analysis
Full Model	0.90	Baseline
w/o GRU	-0.18	Graph construction is critical
w/o Self-Attention	-0.06	Attention provides moderate gain
w/o DFT	-0.08	Frequency domain important
w/o GFT	-0.10	Graph Fourier Transform essential
w/o Convolution	-0.28	Most vital component
Single GCN Layer	-0.08	Two layers optimal

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🔍 Geological Insights

Stratigraphic Sequence Analysis

The model captures Walther's Law in the vertical direction:

• Window=2 (0.25m): Dominated by same-lithology transitions (self-transitions)
• Window=3 (0.375m): Optimal for detecting lithology changes
• Window>4: Self-transitions dominate again

This 0.375m scale matches the GCN's receptive field, validating that the model learns actual depositional cyclicity.

Log Correlation Analysis

Despite high correlation between RLLD and RLLS (Pearson 0.81), removing either reduces accuracy by ~5%, indicating they provide complementary latent information through spectral graph convolution.

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📂 Project Structure

gcn-lithology-identification/
├── configs/
│   └── config.yaml              # Configuration parameters
├── models/
│   ├── gcn.py                   # Main GCN architecture (GRU + Spectral GCN)
│   ├── layers.py                # Custom layers (GLU, GFT, GraphConv)
│   └── baselines.py             # LSTM, RNN, TCN, ANN comparators
├── utils/
│   ├── data_loader.py           # Data loading with SMOTE augmentation
│   ├── graph_utils.py           # Adjacency matrix construction
│   ├── metrics.py               # Evaluation metrics (Acc, F1, AUC)
│   └── visualizer.py            # Confusion matrix & log visualization
├── scripts/
│   ├── train.py                 # Main training loop
│   ├── evaluate.py              # Model evaluation
│   ├── predict.py               # Inference script
│   └── transfer_learning.py     # Fine-tuning for new formations
├── notebooks/
│   └── tutorial.ipynb           # Step-by-step tutorial
├── requirements.txt
└── README.md

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📚 Citation

If you use this code or dataset in your research, please cite:

@article{li2025spectral,
  title={Spectral graph convolution networks for microbialite lithology identification based on conventional well logs},
  author={Li, Ke-Ran and Song, Jin-Min and Wang, Han and Yan, Hai-Jun and Liu, Shu-Gen and Lan, Yang and Jin, Xin and Ren, Jia-Xin and Zhao, Ling-Li and Tian, Li-Zhou and Deng, Hao-Shuang and Chen, Wei},
  journal={Petroleum Science},
  volume={22},
  pages={1513--1533},
  year={2025},
  publisher={Elsevier},
  doi={10.1016/j.petsci.2025.02.008}
}

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⚠️ Usage Notes

1. Data Quality: Ensure logs are environmentally corrected and depth-aligned. Missing values should be interpolated before training.

2. Class Imbalance: Microbialite distributions are naturally imbalanced (SSTR: 33%, THRO: 27%, WSTR: 12%, etc.). Always use SMOTE or class-weighted loss to avoid bias toward majority classes.

3. Sequence Preservation: Do not shuffle the training data along the depth axis. The model relies on temporal dependencies in sedimentary sequences. Shuffling reduces accuracy to ~20%.

4. Transfer Learning: When applying to new formations:

   • If >1000 samples available: Use standard fine-tuning
   • If 500-1000 samples: Use GCN+SVM strategy
   • If <500 samples: Consider domain adaptation or data augmentation

5. Hyperparameters: The paper uses 1200 epochs with early stopping (patience=50). Learning rate 5e-4 works best for Adam optimizer.

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📝 License

This project is licensed under MIT License.