## 3 Results
### Early Earthquake Magnitude Estimation as a Regression Task
This enables efficient modeling of temporal dependencies while preserving local amplitude variations. The RCGL integrates a GNN and residual connection to enhance signal denoising and retain essential amplitude and coda duration features, reducing noise interference. The performance of EQGraphNet is compared to other models such as MagNet [44], CREIME [4], and CNQI [66]; EQGraphNet demonstrates higher accuracy in estimating \(M_{L}\) and \(M_{D}\), with determination coefficients (\(R^{2}\)) of 0.9303 for \(M_{L}\) and 0.8621 for \(M_{D}\), as well as lower estimation errors. Unlike previous approaches that rely solely on convolutional or recurrent architectures, EQGraphNet integrates graph structures to leverage spatial-temporal relationships in the data. EQGraphNet is robust against natural noise, performing well even in signals with low SNR, making it ideal for adverse conditions. The model was also tested in regions such as Puerto Rico, Alaska, the Salish Sea, and the Hawaiian Islands, where EQGraphNet demonstrated its ability to generalize across different geological environments. However, the study highlights that performance deteriorates for very large magnitudes, suggesting that additional training data or transfer learning techniques could further enhance generalization. The proposed model is a promising tool for real-time magnitude estimation and early warning applications, especially in areas with limited seismic networks or noisy signals. Ref. [53] proposed a deep CRNN model with a multitask learning (MTL) approach for estimating epicentral distance and seismic magnitude. It processes three-component seismograms, combining deep convolutional blocks and Bi-LSTMs to extract static and temporal features. The feature extractor applies spectral normalization, leaky ReLU activations, and dropout to improve stability and prevent overfitting, while Bi-LSTMs model temporal dependencies, ensuring sensitivity to waveform variations over time. The model incorporates an embedding network based on a multilayer perceptron (MLP) to process the maximum amplitude of the waveform, transforming it into feature vectors that enhance magnitude estimation and epicentral distance predictions. Unlike previous models, this approach explicitly integrates amplitude features into the feature representation, reducing bias in magnitude estimation. The estimator employs a shared MTL structure with task-specific output layers for magnitude and distance, optimizing a joint loss function that combines L1 loss for accuracy and weight decay for regularization. The model was implemented using PyTorch (version 2.0.0) and compared to the following three existing models: Mousavi and Beroza [67], complex CNN [48], and MagNet [44]. Experimental results show that explicitly modeling amplitude enhances distance estimation, particularly for low-amplitude events, while Bi-LSTMs improve temporal feature extraction. Compared to previous models, the proposed approach achieves lower MAE for both magnitude and distance, with higher \(R^{2}\) values, indicating strong prediction accuracy. The study also suggests that incorporating additional waveform attributes, such as envelope functions or coda duration, could further improve generalization and robustness to regional variability. Ref. [42] presented a CNN-based deep learning model for earthquake magnitude estimation using high-frequency GNSS (HR-GNSS) displacement data. The proposed architecture consists of six 2D convolutional layers, three max-pooling layers for dimensionality reduction, and three fully connected layers for final magnitude estimation. The model processes three-component displacement data, utilizing kernel sizes of (1,3) and ReLU activation functions. Unlike traditional approaches that rely on empirical scaling relationships, this model directly learns patterns from raw HR-GNSS signals. The model was primarily trained on a synthetic dataset consisting of 36,800 rupture scenarios generated for the Chilean subduction zone.