Extracting and Predicting Earthquake Frequency Regularities in the Longmen Shan Fault Zone via the LSTM-GARCH Model

The Longmen Shan Fault Zone is marked by intricate geological structures and frequent seismic activity, which gives rise to persistent seismic hazards. To tackle the challenge of capturing the multi-temporal characteristics of earthquake frequency, this study combines machine learning with time series analysis to conduct earthquake frequency prediction research. Based on the 1970–2023 seismic dataset from the China Earthquake Networks Center, the seismic records were structured into four temporal scales: daily, weekly, monthly and quarterly. The minimum completeness magnitude (Mc) was determined as M3.0 by applying the G–R relationship. After conducting white noise tests and data normalization, ACF and PACF were utilized to select the optimal time-step parameters for the LSTM model. Considering the inherent characteristics of the seismic data, the 99th percentile of the frequency series was set as the threshold, and an auxiliary parameter was introduced to label high-frequency earthquake days for the construction of the LSTM model. Upon the completion of LSTM model fitting, heteroscedasticity tests were performed on the residuals between the predicted and observed values. Confirming the presence of significant heteroscedasticity, the GARCH model was incorporated to process these residuals, thus establishing a complete LSTM-GARCH coupled model. The results reveal that seismic activity in this region is normally low-frequency with occasional high-frequency occurrences. The proposed model achieves R2 above 0.80 across all four temporal scales, accompanied by superior performance in all error metrics. This study validates that the LSTM-GARCH model can effectively extract the multi-scale patterns of earthquake frequency, with the best performance observed at the daily scale. Ablation experiments further demonstrate that this coupled model outperforms both the ARIMA and single LSTM models, providing reliable technical support for short-to-long-term earthquake prediction and regional disaster risk assessment.