A combining earthquake forecasting model between deep learning and Epidemic-Type Aftershock Sequence (ETAS) model (2310.02574v1)

Abstract: The scientific process of earthquake forecasting involves estimating the probability and intensity of earthquakes in a specific area within a certain timeframe, based on seismic activity laws and observational data. Epidemic-Type Aftershock Sequence (ETAS) models, which rely on seismic empirical laws, is one of the most commonly used methods for earthquake forecasting. However, it underestimates feature in short-term time scale and overestimates in long-term time scale. Convolutional Long Short-Term Memory (ConvLSTM), has emerged as a promising approach capable of extracting spatio-temporal features. Hence, we propose a novel composite model named CL-ETAS model, which combines the strengths of ConvLSTM and ETAS model. We conduct experimental verification on real seismic data in Southern California. Our results show that CL-ETAS model outperforms both ETAS model and ConvLstm in accurately forecasting the number of earthquake events, their magnitude, and spatial distribution. Additionally, CL-ETAS model demonstrates notable enhancements in forecast stability and interpretability. These results offer valuable insights and recommendations for future earthquake forecasting endeavors.

• The paper proposes a novel CL-ETAS framework combining ConvLSTM and the ETAS model to improve spatio-temporal earthquake forecasting accuracy.
• The model leverages convolutional LSTM layers with empirical seismic laws to effectively capture spatial features and temporal dependencies.
• Results using Southern California seismic data demonstrate superior performance compared to standalone ETAS and ConvLSTM models across multiple evaluation metrics.

Combining Earthquake Forecasting Using Deep Learning and ETAS Model

Introduction

The paper presents a composite earthquake forecasting model that integrates Convolutional Long Short-Term Memory (ConvLSTM) networks and the Epidemic-Type Aftershock Sequence (ETAS) statistical model. Earthquake forecasting remains a complex challenge owing to the inherently unpredictable nature of seismic activities. Traditional models like ETAS utilize empirical seismic laws but face limitations in accurately predicting the short-term occurrence and dynamics of seismic events. On the other hand, deep learning approaches, particularly those leveraging ConvLSTM, offer advancements in capturing spatio-temporal patterns in seismic data but fall short in leveraging underlying seismic empirical laws.

CL-ETAS Model Structure

The CL-ETAS model combines the stochastic modeling capabilities of the ETAS model with the spatio-temporal prediction strength of ConvLSTM. The ETAS component models earthquake occurrences as a space-time point process incorporating empirical laws such as the Gutenberg-Richter law, Utsu law, and Omori law. It provides initial statistical forecasting based on historical seismic events. The ConvLSTM component is then employed to refine these forecasts using a neural network architecture that processes sequential spatial-temporal seismic data.

ConvLSTM Architecture

The architecture of the ConvLSTM involves a series of ConvLSTM2D layers adapted to forecast seismic activities. Each layer uses convolutional operations to capture spatial features, while the LSTM units capture temporal dependencies. The ability of ConvLSTM to utilize convolutional operations allows the model to account for complex spatial correlations in seismic data, something traditional LSTMs struggle with.

Methodology

Data from Southern California's earthquake catalog was used to train and evaluate the model, focusing on earthquakes of magnitude 3 and above. The CL-ETAS model’s training procedure involved augmenting ConvLSTM's input with ETAS-generated forecasting matrices. This hybrid approach allows the model to retain the empirical forecasting strength of ETAS while leveraging deep learning to improve accuracy and interpretability.

Results

The CL-ETAS model demonstrated superior performance in forecasting the number of earthquake events, their magnitudes, and spatial distribution compared to standalone ETAS and ConvLSTM models. It consistently outperformed the other models in several key evaluation metrics, including N-Test, M-Test, S-Test, and PL-Test.

Evaluation Metrics

1. N-Test: CL-ETAS surpassed ETAS and ConvLSTM in matching the real number of seismic events.
2. M-Test: Predicted frequency-magnitude distribution more closely aligned with observed data.
3. S-Test: The spatial forecast accuracy indicating spatial event distribution was better captured.
4. PL-Test: Demonstrated robustness in the likelihood alignment between observed and predicted seismic catalogs.

Implications and Future Research

The integration of ConvLSTM with the ETAS model introduces a robust forecasting tool that enhances both the accuracy and stability of earthquake predictions. The fusion of deep learning with statistical modeling provides improved adaptability to spatial and temporal complexities inherent in seismic data. Future research may focus on optimizing ConvLSTM parameters, exploring more complex neural architectures, and refining ETAS statistical inputs. Advanced calibrations in historical seismic data treatments could further enhance model outputs, paving the way for broader applications in seismic risk mitigation.

Conclusion

The proposed CL-ETAS model marks an advancement in earthquake forecasting methodology by effectively combining the empirical prediction strength of ETAS with the pattern recognition capabilities of ConvLSTM. This approach not only enhances prediction accuracies across several metrics but also promises improvements in the spatial and temporal precision of forecasting systems. As the model undergoes further refinement, its potential to significantly impact seismic hazard prediction and risk management becomes increasingly apparent.