Precise eruption forecasting remains a significant challenge in volcanology due to the complex and varied nature of pre-eruptive behavior. Seismic signals are crucial for assessing eruptive activity, studying pre-eruptive stages, and identifying eruption precursors. Previous research has focused on seismic swarms, repeating earthquakes, and volcanic tremors as potential indicators. Volcanic tremors, continuous seismic signals frequently accompanying eruptions, are considered potential geophysical markers for eruption prediction. However, criteria for identifying reliable eruption precursors (recurrence, transferability, and differentiability) are debated. While earthquake swarms often precede eruptions, they can also result from non-eruptive activity. Volcanic tremors, another crucial seismic precursor, may be masked by the energy of earthquake swarms and can occur before and during eruptions, as well as during non-eruptive periods. Therefore, while neither guarantees an imminent eruption, their presence increases the likelihood. The 2021 Geldingadalir eruption, following 781 years of dormancy, presented an opportunity to test advanced methods for seismic data analysis. The eruption was preceded by seismic swarms and intrusion events, but no precursory volcanic tremor was initially reported, emphasizing the need for more sophisticated methods to analyze continuous seismic data streams and improve the speed and precision of eruption phase identification. This study employs machine learning to analyze the 2021 Geldingadalir eruption data to uncover patterns missed by traditional methods, potentially revealing insights into pre-eruptive signals and eruption evolution.

The authors review existing literature on eruption forecasting, highlighting the importance of seismic signals and the challenges of interpreting complex pre-eruptive behaviors. Studies on seismic precursors, including seismic swarms, repeating earthquakes, and volcanic tremors, are discussed. The criteria for identifying reliable precursors (recurrence, transferability, and differentiability) are reviewed, as is the limitations of relying on earthquake swarms or volcanic tremors alone due to their occurrence during both eruptive and non-eruptive periods. The use of volcanic tremor as a short-term precursor is explored, noting its potential to be obscured by earthquake swarms. The literature emphasizes the need for advanced, automated methods for analyzing continuous seismic data streams to improve the speed and accuracy of eruption forecasting. Existing studies on classifying volcano-related signals using neural networks are discussed, highlighting the need for unsupervised techniques, especially given the scarcity of labeled volcanic data.

The study used deep embedded clustering (DEC), a deep learning technique, to analyze continuous seismic data from the Geldingadalir 2021 eruption. Data from the east component of station NUPH, located 5.5 km southeast of the eruption site, was used due to its higher signal-to-noise ratio on horizontal components compared to the vertical component. The Short Time Fourier Transform (STFT) was applied to one-hour windows of the continuous seismic data, filtered from 1 to 4 Hz. A convolutional autoencoder extracted salient features from the spectrograms, which were then used for clustering with the DEC technique. This approach simultaneously optimizes feature extraction and clustering. The DEC method identified four clusters corresponding to distinct phases of volcanic activity: EQ (earthquakes), CT1 (continuous tremors 1), ET (episodic tremors), and CT2 (continuous tremors 2). A harmonic-percussive separation algorithm was used to further analyze the precursory tremor signal. To investigate the algorithm's ability to detect precursory tremors, a test was conducted using only pre-eruptive data (eight days before the eruption). Another DEC analysis was performed on episodic tremors between May 2 and June 14 to analyze their variations. Seven-minute-long windows of the seismic signal, starting from the onset time of each tremor episode, were used as input for this analysis. The autoencoder architecture is described, along with the training process and loss functions used (MSE for the autoencoder and KL divergence for the clustering layer). The selection of optimal frequency bands and window lengths is justified. The methods used for visualizing high-dimensional data in two dimensions (t-SNE) and determining the optimal number of clusters (Calinski-Harabasz index) are also explained.

The study identified four distinct seismic clusters representing different phases of the 2021 Geldingadalir eruption: 1. **EQ (earthquakes):** Dominated by transient earthquakes, primarily before the eruption, but also present later during the eruption. 2. **CT1 (continuous tremors 1):** Initiated three days before the eruption, lasting until April 27, representing continuous tremors related to continuous lava outflow. 3. **ET (episodic tremors):** From April 27 to June 13, linked to lava fountaining. 4. **CT2 (continuous tremors 2):** From June 13 to 24, characterized by continuous tremors with two dominant frequencies and higher amplitude than CT1. The study successfully detected precursory volcanic tremors three days before the eruption, which were previously overlooked. This detection was confirmed by applying a harmonic-percussive separation algorithm, which extracted the underlying tremor signal. The change in eruption style from continuous lava outflow to lava fountaining is linked to the transition between seismic clusters CT1 and ET. This transition, occurring around April 27, might be related to an increase in magma flow rate and a change in the depth of the melt generation source reported in other studies. Further analysis of episodic tremors (May 2 to June 14) revealed four sub-clusters (ET-1 to ET-4), each representing episodes with different durations, amplitudes, and frequency content. These sub-clusters are linked to the evolution of the shallow magma compartment, outgassed lava accumulating in the crater, and a widening conduit. The study found a strong correlation between the features extracted by the autoencoder (duration, amplitude, and frequency content) and the observed characteristics of the tremor episodes. This connection was stronger in the clustering of episodic tremors due to the reduced input data variation and shorter durations.

The findings demonstrate the effectiveness of unsupervised deep learning in analyzing continuous seismic data for volcano monitoring. The ability to detect concealed pre-eruptive signals and subtle changes in tremor patterns provides valuable insights into the eruption's evolution. The detection of precursory tremors three days before the eruption highlights the potential of the method for enhancing early warning systems. The observed link between changes in tremor patterns and the transition in eruption style emphasizes the importance of continuous monitoring and advanced signal processing techniques. The detailed analysis of episodic tremors reveals insights into the complex interactions within the volcanic system. The success of the algorithm even with a limited dataset demonstrates its robustness and potential for real-time applications. The strong correlation between extracted features and physical properties (duration, amplitude, frequency) further validates the method's ability to capture meaningful information from the seismic data.

This study demonstrates the power of unsupervised deep learning, specifically DEC, for revealing subtle pre-eruptive signals and charting the temporal evolution of volcanic eruptions. The identification of precursory tremors and the detailed characterization of different eruption phases enhance our understanding of volcanic processes. The method's ability to extract meaningful information from complex seismic signals opens avenues for improving eruption forecasting and early warning systems. Further research should focus on applying this method to other eruptions and exploring its integration into real-time monitoring systems, while addressing challenges related to data availability, noise, and varying eruption patterns across different volcanoes.

The study's reliance on data from a single seismic station limits the comprehensiveness of its analysis. The potential impact of noise levels on the accuracy of the method is acknowledged. The generalizability of the findings might be limited by the specific characteristics of the 2021 Geldingadalir eruption. The study’s focus on a single eruption limits the generalizability of the findings to other volcanic events. While the algorithm can identify clusters, it may struggle with new, previously unseen patterns and its performance may vary depending on the volcano and quality of data.