## 3 Results
### Early Earthquake Magnitude Estimation as a Regression Task
These synthetic signals provided a controlled environment to analyze performance without noise interference. However, applying the model to real earthquake data revealed that the lack of noise in training could affect generalization. Tests with synthetic data yielded a root mean square (RMS) error between 0.06 and 0.11, while real data tests, including events from regions such as Cascadia and Chile, showed RMS values ranging up to 0.09 when station configurations were consistent with the training data. One of the key findings is the impact of temporal signal window length on magnitude estimation accuracy. Shorter time windows sometimes led to the underestimation of large events (\(M_{w}>9.5\)), while smaller earthquakes (\(M_{w}<6.9\)) tended to be overestimated. Additionally, factors such as SNR and maximum signal amplitude significantly influenced performance when working with real data. The study highlights the potential of deep learning in HR-GNSS-based earthquake magnitude estimation but also emphasizes the challenges of adapting models trained on synthetic data to real-world applications. Future work could focus on incorporating realistic noise during training and refining the model's ability to generalize across different seismogenic regions. Ref. [43] introduced a method for estimating seismic magnitudes with low uncertainty, even when data from only a few stations is available. It combines three-dimensional (3D) physical corrections with boosted tree regression to reduce variability in single-station magnitude estimates. The approach was tested on the IPOC seismic catalog from northern Chile, which included over 100,000 events recorded between 2007 and 2014. Unlike traditional methods, this approach extracts 110 waveform features, such as displacement, velocity, acceleration, and cumulative energy. These features are corrected for source, station, and path effects using a non-parametric function that depends on epicentral distance and depth, while also incorporating station-specific adaptive 3D corrections. The boosting tree regression further enhances prediction stability by integrating multiple features, reducing standard deviation by 57%, with 40% of this improvement attributed to the regression model itself. Compared to standard correction models, this approach achieves up to a 47% reduction in RMSE for horizontal displacement and 39% for vertical acceleration. P-wave-derived features and envelope values prove crucial in reducing uncertainties. However, despite these improvements, the method's reliance on a large dataset for training and the computational cost of 3D corrections may limit its application in real-time scenarios. Future studies could explore hybrid models combining boosting trees with neural networks to further enhance efficiency and adaptability. Ref. [40] proposed an SVM-based model (SVM-M) for magnitude estimation within the first three seconds of the P-wave arrival, similar to other models that utilize this early time window for rapid magnitude estimation. The model operates without constraints on SNR or epicentral distance, enhancing its flexibility across different seismic conditions. It utilizes a Gaussian radial basis function kernel to optimize a regression function mapping 12 input parameters to magnitude estimates. Compared to traditional methods like \(\tau_{c}\) and \(P_{d}\), SVM-M significantly reduces prediction error, achieving a standard deviation of 0.297, in contrast to 1.637 for \(\tau_{c}\) and 0.425 for \(P_{d}\). Notably, while increasing the time window from 1 s to 10 s improves performance, particularly for large earthquakes, using only 3 s of P-wave data still provides reliable magnitude estimates, suggesting that essential information is present even in the early portion of the waveform. Additionally, the model demonstrates strong generalization capabilities, reinforcing its potential for earthquake early warning applications. Ref. [32] presented MEANet, a model for magnitude estimation that integrates physics-based features with deep learning.