Accurate and timely information about earthquake source parameters, including focal mechanisms, is vital for post-earthquake response and hazard mitigation. Traditional methods for determining focal mechanisms, such as those based on P-wave first motions or moment tensors, are often time-consuming, taking minutes to tens of minutes. This delay hinders rapid assessments of damage, emergency response, and understanding of the earthquake's impact. Artificial intelligence (AI) offers the potential to automate and accelerate these processes. While AI has been applied successfully to other seismological tasks like earthquake detection and magnitude estimation, real-time focal mechanism determination remains a challenge. This study addresses this gap by developing a novel deep learning approach, aiming to provide near-instantaneous focal mechanism estimations after an earthquake.

Existing methods for focal mechanism determination rely on various data types and methodologies. Techniques using P-wave first motions, moment tensors, and full waveforms have been employed, each with its advantages and limitations. Deep learning has emerged as a promising tool for improving seismological analyses, showing success in areas like earthquake detection and phase picking. However, previous attempts to utilize deep learning for real-time focal mechanism estimation have either required extensive real-world datasets or faced computational constraints. Some efforts used deep learning for focal mechanism inversion or combined first motions with methods like HAS (hypocentral analysis system) improving focal mechanism estimations. Other fast methods, like those leveraging advanced search engines, exist but often require enormous databases and pre-processing steps, reducing practicality. The need for a fully automated, efficient, and widely applicable real-time solution remains.

This research proposes FMNet, a deep convolutional neural network (CNN) designed to rapidly estimate earthquake focal mechanisms using full waveforms. Unlike many deep learning models requiring extensive real-world data for training, FMNet leverages a large dataset of synthetic waveforms. The study area, centered on the 2019 Ridgecrest earthquake sequence in Southern California, was discretized into a 3D grid. Synthetic waveforms were generated for a variety of focal mechanisms at each grid point using a double-couple source model and a 1D velocity model. This resulted in a training dataset of 787,320 synthetic samples. Realistic noise and random time shifts were added to the synthetic data to improve the model's robustness. The FMNet architecture is a deep CNN with 16 trainable layers, including compression and expansion components, allowing it to learn global waveform characteristics. The network was trained using the Adam optimizer and a mean squared error loss function. The trained model was then used to predict the focal mechanisms of four real Ridgecrest earthquakes (Mw ≥ 5.4). To evaluate the model's performance, a separate test dataset of 1000 synthetic samples was used. The Kagan angle, which quantifies the difference between predicted and true focal mechanisms, was used as a performance metric. An encoder layer within the FMNet was also analyzed to understand the model's internal representation of waveforms and to assess its robustness.

FMNet successfully estimated the focal mechanisms of four significant earthquakes in the 2019 Ridgecrest sequence. The predicted focal mechanisms largely matched those from the Southern California Seismic Network (SCSN) moment tensor catalog, with consistent strike-slip faulting and steep dipping fault planes. A comparison of real and synthetic waveforms, generated using FMNet's predicted focal mechanisms, showed high correlation coefficients (0.86), validating the accuracy of the predictions. Analysis of the encoder layer showed that the FMNet learns a sparse representation of the input waveforms, maintaining essential information for focal mechanism determination. The L2-norm misfits between the encoded features and waveforms in the training data showed strong similarity, indicating that feature similarity corresponds to waveform similarity. The entire prediction process, once the model is trained, takes less than 200 milliseconds on a single CPU. Testing on an unseen synthetic dataset revealed that 97.8% of the Kagan angles were within 20 degrees of the true values. The model's robustness was further analyzed through scenarios with added noise, random time shifts, missing data, and inaccurate velocity models. While these factors can affect accuracy, they generally do not significantly impact the prediction's ability to correctly identify strike and dip angles. However, inaccurate velocity models introduce greater errors in rake angle estimation, while the absence of data points lowers confidence in rake angle predictions.

The results demonstrate the potential of FMNet as a tool for real-time earthquake focal mechanism determination. Its ability to learn from synthetic data allows application in areas with limited seismicity but high seismic hazard. The speed and accuracy of FMNet represent a significant advancement over traditional methods. While the training requires computational resources, the deployment and prediction are extremely fast, enabling near real-time earthquake characterization. The analysis of the encoder layer provides insights into the network's internal workings and its ability to effectively compress and represent waveform data. The success of FMNet in handling scenarios with noise and missing data demonstrates its robustness. The study's findings suggest that FMNet could substantially improve the speed and automation of earthquake early warning systems.

FMNet offers a novel and efficient deep learning approach for real-time earthquake focal mechanism determination. Its ability to utilize synthetic data, rapid prediction speed, and demonstrated accuracy on real-world data are significant contributions. Future work could focus on improving the handling of smaller earthquakes, incorporating 3D velocity models, and enhancing the model's ability to predict focal depth more accurately. The development of a fully integrated system for real-time earthquake monitoring and early warning systems leveraging FMNet is a promising direction for future research.

The current FMNet relies on a 1D velocity model and is best suited for low-frequency data, limiting its applicability to moderate and large earthquakes. The accuracy of predictions can be affected by inaccuracies in the velocity model, poor azimuthal coverage of seismic stations, and events occurring outside the training area. While FMNet handles missing data reasonably well, extensive data loss can impact accuracy, particularly for rake angle prediction. Further refinement is needed to improve the accuracy and reliability of focal depth estimations. The model's performance on smaller earthquakes needs further investigation.