Analyzing Earthquake's Onset-Magnitude Correlation Using Machine Learning and Simulated and Seismic Data

Exploring the potential relationship between an earthquake’s onset and its final moment magnitude (M_w) is a fundamental question in earthquake physics. This has practical implications, as rapid and accurate magnitude estimation is essential for effective early warning systems.

This study employs a novel approach of a hybrid Convolutional Neural Network (CNN) - Recurrent Neural Network (RNN) models to estimate moment magnitude from just the first two seconds of source time functions (STFs), which is significantly shorter than the entire source duration. We use STFs of large earthquakes from the SCARDEC database, which applies a deconvolution method on teleseismic body waves, considering only events with a M_w > 7 and an initial STF value smaller than 10¹⁷ Nm/s to avoid potential bias. Additionally, we incorporate STFs from physics-based numerical simulations of earthquake cycles on nonplanar faults, varying in roughness levels and fault lengths. These simulations exhibit substantial variability in earthquake magnitude and slip behavior between events. The reported methodology uses the information contained in the initial characteristics of the STF, its temporal derivative, and the associated seismic moment, capturing the valuable insights present in the initial energy release about the final moment magnitude.

For the simulated data, the CNN-RNN model demonstrates a good correlation between the initial 2 seconds of the STF and the final event magnitude. Correlation coefficients close to 0.8 and root mean squared errors (RMSE) around 0.25 for magnitudes between 5 and 7.5 showcase the model’s ability to learn and generalize effectively from diverse earthquake scenarios. While results for natural earthquakes from the SCARDEC database remain promising (RMSE of 0.27), the correlation coefficient is lower (0.31), suggesting a weaker relationship than simulated data. This discrepancy might be attributed to the narrower band of magnitudes (7 to 7.5) within SCARDEC data used here, potentially limiting the model’s ability to discern subtle variations and establish a stronger correlation. Further, as an earthquake's fractional duration, 2 sec/source duration, increases, the model's error consistently decreases as expected. Finally, most predictions fall within a narrow range of 1% error, and nearly 90% of samples across diverse durations satisfy a set 5% error threshold. This consistent performance of the hybrid CNN-RNN model across varying source durations, magnitude ranges, and fault characteristics underscores the model's adaptability and robustness in handling diverse earthquake scenarios. While we mostly use here STFs from simulated earthquakes, continuous learning and refinement against reliable and diverse STFs obtained from teleseismic data, when available, are key to enhancing the potential of these CNN-RNN models for a better understanding of the onset-magnitude correlation in natural earthquakes.