Unsupervised machine learning reveals slab hydration variations from deep earthquake distributions beneath the northwest Pacific

Deep earthquakes, occurring at depths exceeding 300 km within subducting slabs, pose a significant challenge to our understanding of plate tectonics. The high temperatures and pressures at these depths should inhibit brittle failure, yet these events persist. Three main hypotheses attempt to explain their occurrence: thermal shear instability, dehydration embrittlement, and transformational faulting. While the debate continues, recent research suggests that dehydration embrittlement, based on fluid overpressure, is less likely, especially in the sinking lithospheric mantle. Growing evidence supports the transformational faulting hypothesis, which posits that deep earthquakes are triggered by the transformation of α-olivine to β-spinel (wadsleyite) in the rim of a metastable olivine wedge (MOW). The MOW's geometry is influenced by the slab's thermal state and hydration level; colder slabs are hypothesized to possess thicker MOWs compared to warmer ones. Hydrous defects play a crucial role, as water facilitates metamorphic transformations. While dehydration-driven stress transfer (DDST) involving grain size reduction explains intermediate-depth seismicity (30-300 km), its relevance to deep-focus earthquakes remains ambiguous. The *b*-value, the slope of the Gutenberg-Richter distribution, offers insights into seismic rupture mechanisms. Variations in the *b*-value with slab thermal state and magnitude are used to infer deep earthquake mechanisms. However, limitations in detecting smaller earthquakes hinder a full understanding of nucleation and propagation of deep ruptures. This study aims to address these limitations by analyzing a comprehensive earthquake catalog to estimate *b*-values for deep earthquakes and investigate their relationship to slab hydration and the MOW.

The literature surrounding deep-focus earthquakes highlights three primary mechanisms: thermal shear instability, dehydration embrittlement, and transformational faulting. While initially dehydration embrittlement, driven by fluid overpressure, was a prominent hypothesis, several studies suggest its limited applicability to deep intraslab events, especially within the sinking lithospheric mantle. Research increasingly supports transformational faulting in the metastable olivine wedge (MOW) as a crucial mechanism. Studies have observed metastable olivine wedges and conducted laboratory experiments supporting transformational faulting. The MOW's thickness is influenced by the thermal profile of the subducting slab, with colder slabs implying thicker wedges. Furthermore, the degree of slab hydration significantly impacts the MOW structure, influencing intermediate-depth seismicity. At intermediate depths, dehydration-driven stress transfer (DDST) involving grain size reduction has been proposed. However, its role in deep-focus seismicity requires further investigation. Previous research using the global CMT catalog explored *b*-value variations with slab thermal state and magnitude, suggesting a possible link between deep earthquake mechanisms, nucleation within the MOW rim, and rupture propagation outside the MOW due to thermal runaway for larger events. The lack of seismic constraints on the MOW rim's dimensions, due to the limited detection of small earthquakes, remains a challenge.

This study leverages the Japan Meteorological Agency (JMA) catalog, one of the most complete catalogs available, to analyze deep earthquakes (depth ≥ 300 km) in the northwestern Pacific subduction zones. The study area includes four regions known for abundant deep earthquakes: Kuril, Honshu, Izu, and Bonin. An unsupervised machine learning approach, specifically the K-means algorithm, is employed to cluster these earthquakes based on their hypocenter locations. The K-means clustering objectively groups similar data points, helping to avoid human bias in the selection process. The optimal number of clusters (four) is determined through silhouette analysis, maximizing the separation between clusters. The robustness of K-means is validated using spectral clustering and Gaussian mixture models (GMM). The generated clusters correspond to distinct segments of the subducting slab with varying degrees of hydration. After clustering, Gutenberg-Richter (GR) distribution analysis is performed in each cluster. The JMA magnitude scale (MJ) is converted to the moment magnitude (Mw) scale using an empirical relationship. Magnitude of completeness (Mc) is estimated from the non-cumulative distribution. *b*-values are calculated using three methods: maximum likelihood estimation, a modified formula, and an approach less affected by magnitude error, allowing for robust analysis and error estimation. The resulting *b*-values and their standard deviations are meticulously calculated and analyzed. The stability of the *b*-value analysis is further enhanced by Monte Carlo simulations (bootstrapping). These simulations check the impact of random variations in the dataset, validating the conclusions. The impact of specific large events is also considered and ruled out as a source of influence on the detected kinks. The study compares the observed kinks in the JMA catalog to those reported previously in the global CMT catalog and includes analysis of the CMT catalog to improve the results. For comparison purposes, this study also analyzes a larger dataset from the CMT catalog and the IRIS catalog, ensuring results are comprehensive and reliable.

The study reveals significant variations in *b*-values among the four clustered regions. The Kuril and Bonin clusters exhibit linear Gutenberg-Richter (GR) distributions with *b*-values around 1.0. However, the Honshu and Izu clusters display distinct kinks in their GR distributions at Mw ~3.7-3.8. Below this magnitude, *b*-values are anomalously high (1.4-1.7), while above it, they drop significantly to 0.6-0.7. This abrupt change signifies a reduction in fractal dimension for earthquakes above Mw 3.7-3.8 within the MOW. The elevated *b*-values for smaller earthquakes (Mw < 3.7-3.8) are linked to enhanced transformational faulting, likely facilitated by deep hydrous defects in the highly hydrated rim of the MOW. The thickness of the highly reactive, unstable rim is estimated to be ~1km based on the Mw 3.7-3.8 threshold and seismic characteristics. Analysis of additional seismic data from the CMT catalog show a clear kink at Mw 6.7 for deep earthquakes in warm subduction zones, with a doubling of *b*-values, while the cold Tonga subduction zone shows a constant *b*-value of 1.1. This difference in *b*-value behavior across various subduction zones is linked to differing hydration levels. The study demonstrates a clear correlation between high *b*-values and highly hydrated slabs. The Honshu and Izu regions, characterized by oblique subduction of spreading faults and fracture zones, exhibit enhanced water percolation and serpentinization, resulting in highly hydrated slabs. In contrast, the Kuril slab is relatively dry due to pre-existing faults that limit bending fault formation, while the Bonin slab's dryness is attributed to regional thermal anomalies associated with Cretaceous-Paleogene magmatism. This analysis suggests the existence of three distinct rupture domains contributing to earthquakes of different sizes: the unstable rim of the MOW (Mw < 3.7-3.8, rupture lengths ≤ 1 km), the interior of the MOW (3.8 < Mw < 6.7), and the warmer wadsleyite domain beyond the MOW (Mw > 6.7). The study proposes that for larger events, initial transformational faulting in the MOW rim triggers subsequent rupture propagation into the MOW via transformation-driven stress transfer, potentially extending beyond the MOW into wadsleyite via thermal runaway instability.

The findings provide crucial insights into deep earthquake mechanisms and their relationship to slab hydration. The observed *b*-value kinks at Mw 3.7-3.8 and Mw 6.7 suggest distinct rupture mechanisms operating across different earthquake magnitudes. The anomalously high *b*-values for small earthquakes in highly hydrated slabs (Honshu and Izu) highlight the importance of hydrous defects in catalyzing transformational faulting within the unstable MOW rim. This contrasts with drier slabs (Kuril and Bonin) exhibiting normal *b*-values, reinforcing the link between hydration and seismicity. The Mw 3.7-3.8 threshold provides a valuable seismic constraint on the MOW rim's thickness (~1 km), while the Mw 6.7 threshold suggests a larger rupture domain involving the entire MOW and beyond. The study's model implies that the evolution of ruptures from small to large magnitudes involves transitions between different rupture domains and mechanisms, including transformational faulting, transformation-driven stress transfer, and thermal runaway instability. This intricate interplay between slab hydration, MOW structure, and rupture mechanisms provides a comprehensive framework for understanding deep earthquake behavior. The study highlights the crucial role of pre-subduction oceanic plate features and fabrics in controlling slab hydration and subsequent deep seismicity.

This study provides novel insights into deep-focus earthquake mechanisms by analyzing the Gutenberg-Richter distribution of deep earthquakes in the northwestern Pacific using a comprehensive dataset and advanced machine learning techniques. The observed *b*-value kinks, coupled with varying slab hydration, reveal the importance of the metastable olivine wedge (MOW) rim in earthquake nucleation and propagation. The ~1 km thick, highly hydrated rim facilitates transformational faulting at low magnitudes (Mw < 3.7-3.8), while larger events (Mw > 6.7) likely involve thermal runaway instability extending beyond the MOW. Future research should focus on validating these findings in other subduction zones with varying hydration levels and improving earthquake detection capabilities to refine the understanding of deep earthquake processes.

The study's reliance on a specific regional catalog (JMA) limits its generalizability to other subduction zones. While the JMA catalog is comprehensive, the temporal coverage (2002-2016) might not fully capture long-term variations in seismicity. The conversion between different magnitude scales introduces inherent uncertainties that might slightly affect *b*-value estimations. The precise characterization of hydrous defects and their influence on transformational faulting requires further investigation, with more detailed experimental work needed to support the model proposed in the paper. The study's interpretations rely on current understanding of MOW formation and evolution. Future advancements in this area could refine the study's findings and expand our knowledge of deep-earthquake processes.