Earthquake Magnitude Estimation Using Machine Learning from Single Station Seismic Data in Rwanda

Abstract Earthquake magnitude estimation is critical for seismic monitoring, particularly in data-constrained regions with sparse station coverage. This study investigates the use of machine learning techniques for rapid and reliable magnitude estimation from single-station seismic waveform data recorded at the HUYE station in Rwanda, located within the western branch of the East African Rift System. A machine learning framework was developed using three-second waveform windows centered on P-wave arrivals. Both raw waveform inputs and physics-informed engineered features were utilized, including logarithmic amplitude, cumulative displacement, signal energy, root-mean-square (RMS) amplitude, signal-to-noise ratio (SNR), dominant frequency, spectral centroid, and band-limited spectral energy (1–10 Hz). Three models were developed and evaluated: a Random Forest regressor, a Convolutional Neural Network (CNN), and a hybrid CNN integrating waveform data with engineered features. Model performance was assessed using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and the coefficient of determination (R²). The Random Forest model achieved the best performance (MAE = 0.274, RMSE = 0.351, R² = 0.684), outperforming both the hybrid model (MAE ≈ 0.278, R² ≈ 0.537) and the standalone CNN (MAE ≈ 0.329, R² ≈ 0.329). Feature importance analysis identified logarithmic displacement, band-limited spectral energy, and spectral centroid as the most influential predictors. Accurate and computationally efficient earthquake magnitude estimation can be achieved using single-station data through physics-informed feature engineering and machine learning. Feature-based models outperform deep learning approaches in data-limited environments, while hybrid models provide complementary improvements. The proposed framework offers a scalable solution for seismic monitoring and early warning systems in Rwanda and similar regions.