Deciphering Earth’s deep mantle hemispheric geochemical dichotomy with machine learning

Deciphering Earth’s deep mantle hemispheric geochemical dichotomy with machine learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Deciphering Earth’s deep mantle hemispheric geochemical dichotomy with machine learning Zefeng Li, Shang Ma, Ling Chen, Ji Shen, Yunguo Li, Wenzhong Wang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4268316/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Global geochemical zoning of the mantle provides critical constraints on Earth’s internal dynamics and evolutionary history. However, whether geochemical heterogeneities in the deep mantle are dominated by the hemispheric DUPAL anomaly 1,2 or by the two large low shear-wave velocity provinces (LLSVPs) has recently been debated 3 . Here, we employ machine learning to objectively assess the credibility of the two hypotheses on two different datasets of radiogenic isotopic records from global ocean island basalts. We observe discrepant classification accuracies for the LLSVP-based dichotomy and contradictory roles of the most characteristic 87 Sr/ 86 Sr isotopic ratio in two different datasets where the hemispheric DUPAL dichotomy remains robust and consistent. The two most important isotopic ratios, i.e., 87 Sr/ 86 Sr and 206 Pb/ 204 Pb, effectively distinguish the austral and boreal domains to the same extent as all the isotopic ratios combined. This discovery concisely defines the DUPAL anomaly in the 87 Sr/ 86 Sr - 206 Pb/ 204 Pb diagram, which highlights the key role of the Enriched Mantle 1 (EM1) component. The importance of EM1 supports the historical large-scale mass transfer of lower continental crust into the deep mantle in the Southern Hemisphere and could be attributed to widespread lithospheric delamination caused by continental collisions during Gondwana amalgamation at ~600-500 Ma. These observations illustrate how machine learning from large geochemical datasets contributes to revealing robust patterns in heterogeneous and evolutionarily deep Earth. Earth and environmental sciences/Solid Earth sciences/Geochemistry Earth and environmental sciences/Solid Earth sciences/Geodynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Highlights Machine learning reveals that hemispheric geochemical differences in the Earth’s mantle are more predominant than those between LLSVPs. Enriched Mantle 1 plays a key role in differentiating the DUPAL anomaly, as revealed by the data-driven classification boundary. The DUPAL anomaly could have resulted from large-scale lithospheric delamination during Gondwana amalgamation. Introduction Global geochemical and geophysical observations have revealed the heterogeneous nature of the Earth's mantle 4 – 9 , which plays an important role in governing the thermal and chemical geodynamics of the deep Earth. Radiogenic isotopic signatures, including Sr, Nd, and Pb, observed in oceanic island basalts (OIBs) reveal chemical heterogeneities in the deep mantle 10 , 11 . The sources of these oceanic basalts have been conventionally attributed to several isotopically distinct mantle endmembers, such as Enriched Mantle 1 (EM1) 6 , Enriched Mantle 2 (EM2) 6 , High-µ (HIMU, µ = 238 U/ 204 Pb) 6 and the Focus Zone (FOZO) 12 , or mixtures between them. FOZO is a common component of many OIBs 12 , 13 and could represent the primitive mantle 14 . HIMU is believed to result from subducted oceanic crust and/or the extraction of Pb from the mantle to the core 6 , 15 , 16 . The EM signatures are often associated with the recycling of continental crust 6 , 17 – 20 . Specifically, EM1 is associated with recycled continental lower crust and subcontinental lithospheric mantle 6 – 8 , 14 , whereas EM2 is thought to contain recycled upper continental crust and sediments 6 , 7 . Particularly notable are the EM signatures observed in OIBs from the Southern Hemisphere, characterized by higher 208 Pb/ 204 Pb, 207 Pb/ 204 Pb and 87 Sr/ 86 Sr, which is termed the DUPAL anomaly 1 . However, the mechanisms responsible for such hemispheric mantle distinction, which include core–mantle–crust differentiation 1 and/or lower crustal delamination 20 , remain largely unresolved. The southern hemispheric DUPAL anomaly has been debated, partly because the isotopic data from East Pacific Rise basalts and South Pacific OIBs appear to be inconsistent with the DUPAL anomaly 21 , 22 observed elsewhere. Doucet et al . 3 observed that the large-scale heterogeneities in the deep mantle are predominantly divided by the African and Pacific large low shear-wave velocity provinces (LLSVPs, Fig. 1 ), rather than by hemispheres, as the DUPAL anomaly suggests. However, this finding could be associated with the selection of OIBs from deep plume oceanic hotspots 2 . Based on the OIBs characterized by 143 Nd/ 144 Nd from all oceanic hotspots, Jackson & Macdonald 2 confirmed the existence of the austral DUPAL anomaly and attributed it to the deep subduction of continental crust during Gondwana and Pangea assembly. A comprehensive and objective evaluation of global OIB geochemical signatures is needed to clarify the predominant zoning characteristics of the deep mantle. Here, we harness the power of machine learning to resolve two debated geochemical dichotomies, i.e., whether the deep mantle is mainly divided by hemispheres (hereafter referred to as the DUPAL dichotomy) or by LLSVPs (hereafter referred to as the LLSVP dichotomy). We train random forest classifiers 23 for the DUPAL dichotomy and LLSVP dichotomy using two different isotopic datasets (Fig. 1 ). By observing the stability of the classification accuracies and the consistency of the isotopic contributions on the two datasets, we find that the DUPAL dichotomy is generally more robust than the LLSVP dichotomy. The DUPAL dichotomy has two most important isotopic ratios, 87 Sr/ 86 Sr and 206 Pb/ 204 Pb, which underscores the significant role of EM1. We interpret the hemispherically distributed deep-mantle geochemical heterogeneities as a result of material mixing from massive lithospheric delamination during Gondwana supercontinent assembly at ~ 600 − 500 Ma. Resolving geochemical dichotomies with machine learning Radiogenic isotopic data of OIBs from mantle plume sources offer critical constraints on geochemical heterogeneities in the deep mantle 11 , 24 . We analyse two isotopic datasets: the dataset presented by Doucet et al . 3 (hereafter referred to as the DC20 dataset) and an expanded dataset that encompasses the DC20 dataset and additional isotopic data of all OIBs from the EarthChem portal ( http://portal.earthchem.org ). The DC20 dataset contains 1,809 samples from 8 hotspots, whereas the expanded dataset contains 3,464 samples from 34 hotspots (Fig. 1 ). All the samples have complete 87 Sr/ 86 Sr, 143 Nd/ 144 Nd, 206 Pb/ 204 Pb, 207 Pb/ 204 Pb and 208 Pb/ 204 Pb measurements. We further derive 207 Pb*/ 206 Pb* and 208 Pb*/ 206 Pb* (ref. 25 ) from 207 Pb/ 204 Pb, 206 Pb/ 204 Pb and 208 Pb/ 204 Pb. These derived ratios represent the time-integrated growth of U/Pb and Th/U ratios and are associated with enriched lithospheric material 26 . These isotopic ratios are organized into 7-element feature vectors and input into random forest classifiers, which map them to their respective source domains: African versus Pacific LLSVPs and DUPAL versus non-DUPAL domains. The contribution of each isotopic ratio to the classification is evaluated by the Shapley value 27 , 28 , which represents the average impact of an individual isotopic ratio by considering all combinations it forms with other isotopic ratios. Further details regarding the data selection, random forest classification and feature importance evaluation are outlined in the Methods section. In the case of the DC20 dataset (Fig. 1 ), the classification accuracy using the LLSVP dichotomy reaches 92.1 ± 4.4% (Fig. 2 ), indicating high distinguishability between the two LLSVPs. The two most important isotopic ratios in the classification are 87 Sr/ 86 Sr and 208 Pb*/ 206 Pb*, with average Shapley values of 0.143 and 0.129 (significantly greater than 0), respectively (Fig. 3 a). In comparison, the least important isotopic ratio, 207* Pb/ 206* Pb, exhibits an average Shapley value of 0.013 (approximately equivalent to 0). It is worth noting that samples from the Pacific LLSVP exhibit low 87 Sr/ 86 Sr (< 0.705), 207 Pb/ 206 Pb and 208 Pb/ 206 Pb ratios, generally following the Northern Hemisphere Reference Line (NHRL) (Supplementary Fig. S1 ). For the most important isotopic ratio, 87 Sr/ 86 Sr, the Pacific LLSVP displays negative Shapley values (Fig. 3 a). These results agree with previous findings by Doucet et al . 3 . However, with the expanded dataset, the classification accuracy using the LLSVP dichotomy decreases dramatically to 83.3 ± 3.7% (Fig. 2 ). 87 Sr/ 86 Sr and 208 Pb/ 204 Pb are the most important features (average Shapley values of 0.103 and 0.079, respectively; Fig. 3 b). This experiment reveals that a high 87 Sr/ 86 Sr ratio is more indicative of the Pacific LLSVP (Supplementary Fig. S2), contradicting the observations with the DC20 dataset. These results suggest that the LLSVP dichotomy is supported by the DC20 dataset but not by the expanded dataset, suggesting that the LLSVP dichotomy is not a universal feature of global OIBs. In comparison with that of the DC20 dataset, the classification accuracy of the DUPAL dichotomy reached 94.5 ± 3.6% (Fig. 2 ). The two most important isotopic ratios controlling this classification are 87 Sr/ 86 Sr and 206 Pb/ 204 Pb, with average Shapley values of 0.204 and 0.102, respectively. High 87 Sr/ 86 Sr, 207 Pb*/ 206 Pb* and 208 Pb*/ 206 Pb* ratios yield positive Shapley values (Fig. 3 c), thus serving as positive indicators of the DUPAL domain (Fig. 3 c and Supplementary Fig. S3), consistent with previous investigations 1 , 17 . With the expanded dataset, the classification accuracy reaches 91.9 ± 2.7% (Fig. 2 ). This accuracy is significantly greater than the accuracy of the LLSVP dichotomy (83.3 ± 3.7%) with the expanded dataset and is comparable to the accuracy of the DUPAL dichotomy with the DC20 data. Moreover, 87 Sr/ 86 Sr and 206 Pb/ 204 Pb remain the most important isotopic ratios, with average Shapley values of 0.148 and 0.103, respectively (Fig. 3 d). Similarly, high 87 Sr/ 86 Sr, 207 Pb*/ 206 Pb* and 208 Pb*/ 206 Pb* are positive indicators of the DUPAL domain (Fig. 3 d and Supplementary Fig. S4). These observations demonstrate the robustness and consistency of the DUPAL dichotomy with both the DC20 and expanded datasets, suggesting a universal feature of global OIBs. To further examine the stability of the DUPAL dichotomy, we retrain the random forest classifiers using the two most important isotopic ratios ( 87 Sr/ 86 Sr and 206 Pb/ 204 Pb for the DUPAL dichotomy and 87 Sr/ 86 Sr and 208 Pb*/ 206 Pb* for the LLSVP dichotomy) and visualize their decision boundaries (Supplementary Fig. S5). These boundaries are obtained by inputting the virtual values of 87 Sr/ 86 Sr - 206 Pb/ 204 Pb and 87 Sr/ 86 Sr - 208 Pb*/ 206 Pb* into the retrained classifiers (details in Methods). We observe that the decision boundaries of the LLSVP dichotomy significantly differ between the two datasets (Supplementary Fig. S5a, b). The boundary on the expanded dataset appears to be extremely complex, which is a sign of overfitting. In contrast, the DUPAL dichotomy shows relatively simple and similar boundaries with both datasets (Supplementary Fig. S5c, d), supporting that the DUPAL dichotomy is a more reliable geochemical zoning model. Primary signatures of the DUPAL anomaly To evaluate the net contributions of different isotopic ratios to the DUPAL dichotomy, we track the changes in classification accuracy by progressively inputting the isotopic ratios from the most to the least important. The results reveal that with only the two most important isotopic ratios, 87 Sr/ 86 Sr and 206 Pb/ 204 Pb, the classification accuracies reach 94.2 ± 2.6% and 87.9 ± 2.9%, respectively, for the two datasets (Figs. 4 a, b). The predominance of 87 Sr/ 86 Sr and 206 Pb/ 204 Pb likely results from the high incompatibility of their respective parent elements (Rb and U), which have greater partition coefficients than the Sm/Nd system. Consequently, the enrichment of these elements in melts is less susceptible to contamination and/or measurement uncertainties, making them effective for distinguishing between the DUPAL and non-DUPAL domains. Importantly, the discrimination accuracies using only 87 Sr/ 86 Sr and 206 Pb/ 204 Pb are almost identical to those obtained using all the isotopic ratios. This suggests that the other isotopic ratios provide little additional discriminative power beyond that provided by 87 Sr/ 86 Sr and 206 Pb/ 204 Pb. Although different isotopic characteristics could represent different geochemical components, our results imply that here, they seem to reflect the same geochemical reservoirs. The complete distinguishability of 87 Sr/ 86 Sr and 206 Pb/ 204 Pb thus warrants a concise definition of the DUPAL anomaly in the 87 Sr/ 86 Sr - 206 Pb/ 204 Pb diagram. Machine learning automatically derives a data-driven decision boundary between the DUPAL and non-DUPAL domains (Fig. 5 ). The delineated DUPAL domain is encompassed by the curves of the mixing mantle endmembers of EM1, EM2 and FOZO. The non-DUPAL domain, on the other hand, is mainly positioned within HIMU, EM2 and FOZO (Fig. 5 ). Therefore, the DUPAL and non-DUPAL domains share the EM2 and FOZO components but exhibit different predominance of EM1 and HIMU components. Specifically, EM1 is more prevalent relative to HIMU within the DUPAL domain, while HIMU exhibits a higher proportion compared to EM1 within the non-DUPAL domain. Our refined definition of the DUPAL anomaly in the 87 Sr/ 86 Sr- 206 Pb/ 204 Pb diagram underscores the predominant role of EM1, distinguishing it from the conventional definition using deviations from the NHRL (Supplementary Fig. S6). The machine learning classifiers effectively categorize most of the OIB samples into their respective hemispheric geochemical regimes. However, a small subset of samples is misclassified more frequently than others (misclassification rate > 10%; Fig. 5 and Supplementary Fig. S7). They are mostly from the Hawaii, Pitcairn, Samoa and Society hotspots (Supplementary Fig. S8), which fall within the conventionally defined geographic DUPAL domain but exhibit non-DUPAL geochemical signatures (Fig. 5 ). Basalts from these hotspots exhibit a wide variety of geochemical characteristics ranging from DUPAL to non-DUPAL. The observed intra-hotspot geochemical variations are possibly associated with the sampling locations relative to the Pacific LLSVP 24 (Fig. 1 ): the spatial pattern of heterogeneities situated above the core-mantle boundary could be preserved through plume conduits, resulting in different geochemical compositions in OIBs from the same plume 29 . Implications for genesis of the mantle hemispheric dichotomy The origin of the large-scale austral DUPAL anomaly is thought to be associated with supercontinent evolution during the Gondwana period 2 , 19 , partly because the DUPAL anomaly was located in the Southern Hemisphere and coincident with the majority of the global continents’ location at ~ 550 Ma (Supplementary Fig. S9). Our results highlight the key role of the EM1 component in the deep mantle, implying the involvement of continental lower crust and subcontinental lithospheric material. Geodynamic modelling has demonstrated that continental collision can cause lithospheric thickening, increased crustal density and negative buoyancy, eventually resulting in the foundering of subcontinental lithospheric mantle and lower crust 30 , 31 . Hence, intensive lithospheric delamination in the Southern Hemisphere during Gondwana assembly could have been responsible for the genesis of the hemispheric geochemical dichotomy (Fig. 6 ). The Gondwana delamination hypothesis is further supported by global zircon measurements. Much larger negative ε Hf values at ~ 600 − 500 Ma 32 were observed than those obtained during the formation of other supercontinents (Supplementary Fig. S10), indicating an unusually high level of continental mass loss during Gondwana amalgamation 33 . Hence, extra lithospheric material was added to the ubiquitous FOZO, along with the shared EM2 in all the OIBs, which may have resulted from pervasive global subduction over supercontinental cycles 34 . The austral localization of the DUPAL anomaly may indicate its source depth at which the majority of the delaminated material was situated. If the delaminated material stays in the upper mantle, due to vigorous convection in the upper mantle, EM1 reservoirs would tend to be distributed across all latitudes rather than being confined to the Southern Hemisphere. Moreover, the delaminated lithosphere after metamorphic densification is unlikely to remain in the upper mantle and most of the mantle transition zone 35 , 36 and can potentially sink into the lower mantle 37 . It has a large chance to persist in the Southern Hemisphere to present day owing to the much slower convection of the lower mantle 38 , 39 . Consequently, the delaminated lithosphere is sampled by upwelling plumes to form the observed EM1 component in OIBs. This hypothesis favours that the DUPAL anomaly is predominantly originated from the lower mantle, which readily explains the two key characteristics of the DUPAL anomaly, i.e. dominance of the EM1 endmember and localization in the Southern Hemisphere (Fig. 6 ). The occurrence of Gondwana crustal recycling at ~ 600 − 500 Ma also accommodates the necessary time for the sinking of crustal mass 40 and the upwelling of enriched mantle material 41 . The present DUPAL signature of OIBs possibly represents a snapshot of the evolving deep Earth bearing the imprint of Gondwana formation at ~ 600 − 500 Ma. Our findings reveal the relationship between modern geochemical anomalies and ancient geological evolution, potentially reflecting a long period (~ 600 Myr) of large-scale material recycling in the deep mantle. Comparatively, mid-oceanic ridge basalts from shallow reservoirs likely represent material recycling during a shorter period (< 200 Myr) of the tectonic history of upper mantle convection 42 . Our study illustrates that machine learning applied to large geochemical datasets can contribute to identifying deep-mantle geochemical heterogeneities and revealing robust patterns of geodynamic evolution in the deep Earth. Declarations Acknowledgements This project is supported by National Science Foundation of China (Nos. 42274063, 42288201). Data availability The DC20 dataset can be accessed from the supplementary data in ref. 3 ( https://doi.org/10.1038/s41561-020-0599-9 , last accessed on 12 August 2022). The expanded dataset was compiled from the EarthChem Portal ( http://portal.earthchem.org , last accessed on 2 March 2023) and is available in the Supplementary Data. Code availability The random forest classifiers were developed with the open-source Python package scikit-learn ( https://scikit-learn.org , last accessed on 16 March 2023), and the Shapley value was calculated with the open-source Python package SHAP ( https://shap.readthedocs.io , last accessed on 20 August 2023). The complete set of developed codes is available via Zenodo at https://doi.org/10.5281/zenodo.10373594 . Competing interests The author declares no competing interests. References Hart, S. R. A large-scale isotope anomaly in the Southern Hemisphere mantle. Nature 309 , 753–757 (1984). Jackson, M. G. & Macdonald, F. A. Hemispheric Geochemical Dichotomy of the Mantle Is a Legacy of Austral Supercontinent Assembly and Onset of Deep Continental Crust Subduction. AGU Advances 3 , (2022). Doucet, L. S. et al. Distinct formation history for deep-mantle domains reflected in geochemical differences. Nat. Geosci. 13 , 511–515 (2020). Hart, S. R., Schilling, J.-G. & Powell, J. L. Basalts from Iceland and Along the Reykjanes Ridge: Sr Isotope Geochemistry. Nature Physical Science 246 , 104–107 (1973). Hedge, C. E. Strontium isotopes in basalts from the Pacific Ocean basin. Earth and Planetary Science Letters 38 , 88–94 (1978). Zindler, A. & Hart, S. Chemical Geodynamics. Annual Review of Earth and Planetary Sciences 14 , 493–571 (1986). Hofmann, A. W. Mantle geochemistry: the message from oceanic volcanism. Nature 385 , 219–229 (1997). Stracke, A., Hofmann, A. W. & Hart, S. R. FOZO, HIMU, and the rest of the mantle zoo. Geochemistry, Geophysics, Geosystems 6 , (2005). Goes, S., Yu, C., Ballmer, M. D., Yan, J. & Van Der Hilst, R. D. Compositional heterogeneity in the mantle transition zone. Nat Rev Earth Environ 3 , 533–550 (2022). Zindler, A., Staudigel, H. & Batiza, R. Isotope and trace element geochemistry of young Pacific seamounts: implications for the scale of upper mantle heterogeneity. Earth and Planetary Science Letters 70 , 175–195 (1984). Adams, J. V. et al. Extreme isotopic heterogeneity in Samoan clinopyroxenes constrains sediment recycling. Nat Commun 12 , 1234 (2021). Hart, S. R., Hauri, E. H., Oschmann, L. A. & Whitehead, J. A. Mantle Plumes and Entrainment: Isotopic Evidence. Science 256 , 517–520 (1992). White, W. M. Isotopes, DUPAL, LLSVPs, and Anekantavada. Chemical Geology 419 , 10–28 (2015). Huang, S. & Zheng, Y. Mantle geochemistry: Insights from ocean island basalts. Sci. China Earth Sci. 60 , 1976–2000 (2017). Vollmer, R. Terrestrial lead isotopic evolution and formation time of the Earth’s core. Nature 270 , 144–147 (1977). Allègre, C. J. Chemical geodynamics. Tectonophysics 81 , 109–132 (1982). Dupré, B. & Allègre, C. J. Pb–Sr isotope variation in Indian Ocean basalts and mixing phenomena. Nature 303 , 142–146 (1983). Hawkesworth, C. J., Mantovani, M. S. M., Taylor, P. N. & Palacz, Z. Evidence from the Parana of south Brazil for a continental contribution to Dupal basalts. Nature 322 , 356–359 (1986). Arndt, N. T. & Goldstein, S. L. An open boundary between lower continental crust and mantle: its role in crust formation and crustal recycling. Tectonophysics 161 , 201–212 (1989). Escrig, S., Capmas, F., Dupré, B. & Allègre, C. J. Osmium isotopic constraints on the nature of the DUPAL anomaly from Indian mid-ocean-ridge basalts. Nature 431 , 59–63 (2004). Macdougall, J. D. & Lugmair, G. W. Sr and Nd isotopes in basalts from the East Pacific Rise: significance for mantle heterogeneity. Earth and Planetary Science Letters 77 , 273–284 (1986). Staudigel, H. et al. The longevity of the South Pacific isotopic and thermal anomaly. Earth and Planetary Science Letters 102 , 24–44 (1991). Breiman, L. Random Forests. Machine Learning 45 , 5–32 (2001). Huang, S., Hall, P. S. & Jackson, M. G. Geochemical zoning of volcanic chains associated with Pacific hotspots. Nature Geosci 4 , 874–878 (2011). Stacey, J. S. & Kramers, J. D. APPROXIMATION OF TERRESTRIAL LEAD ISOTOPE EVOLUTION BY A TWO-STAGE MODEL. Earth and Planetary Science Letters 26 , 207–221 (1975). Williams, C. D., Mukhopadhyay, S., Rudolph, M. L. & Romanowicz, B. Primitive Helium Is Sourced From Seismically Slow Regions in the Lowermost Mantle. Geochem. Geophys. Geosyst. 20 , 4130–4145 (2019). Lundberg, S. M. & Lee, S.-I. A Unified Approach to Interpreting Model Predictions. in Advances in Neural Information Processing Systems (eds. Guyon, I. et al.) vol. 30 (Curran Associates, Inc., 2017). Štrumbelj, E. & Kononenko, I. Explaining prediction models and individual predictions with feature contributions. Knowl Inf Syst 41 , 647–665 (2014). Farnetani, C. G. & Hofmann, A. W. Dynamics and internal structure of a lower mantle plume conduit. Earth and Planetary Science Letters 282 , 314–322 (2009). Chen, L. The Role of Lower Crustal Rheology in Lithospheric Delamination During Orogeny. Front. Earth Sci. 9 , 755519 (2021). Li, Z., Liu, M. & Gerya, T. Lithosphere delamination in continental collisional orogens: A systematic numerical study. JGR Solid Earth 121 , 5186–5211 (2016). Belousova, E. A. et al. The growth of the continental crust: Constraints from zircon Hf-isotope data. Lithos 119 , 457–466 (2010). Roberts, N. M. W. Increased loss of continental crust during supercontinent amalgamation. Gondwana Research 21 , 994–1000 (2012). Evans, D. True polar wander and supercontinents. Tectonophysics (2002) doi:10.1016/S0040-1951(02)00642-X. Wang, Y., Zhang, L. & Li, Z.-H. Metamorphic densification can account for the missing felsic crust of the Greater Indian continent. Commun Earth Environ 3 , 166 (2022). Ganguly, J., Freed, A. M. & Saxena, S. K. Density profiles of oceanic slabs and surrounding mantle: Integrated thermodynamic and thermal modeling, and implications for the fate of slabs at the 660km discontinuity. Physics of the Earth and Planetary Interiors 172 , 257–267 (2009). Ballmer, M. D., Houser, C., Hernlund, J. W., Wentzcovitch, R. M. & Hirose, K. Persistence of strong silica-enriched domains in the Earth’s lower mantle. Nature Geosci 10 , 236–240 (2017). Čížková, H., Van Den Berg, A. P., Spakman, W. & Matyska, C. The viscosity of Earth’s lower mantle inferred from sinking speed of subducted lithosphere. Physics of the Earth and Planetary Interiors 200–201 , 56–62 (2012). Steinberger, B. & Calderwood, A. R. Models of large-scale viscous flow in the Earth’s mantle with constraints from mineral physics and surface observations. Geophysical Journal International 167 , 1461–1481 (2006). Domeier, M., Doubrovine, P. V., Torsvik, T. H., Spakman, W. & Bull, A. L. Global correlation of lower mantle structure and past subduction. Geophysical Research Letters 43 , 4945–4953 (2016). Steinberger, B., Nelson, P. L., Grand, S. P. & Wang, W. Yellowstone Plume Conduit Tilt Caused by Large‐Scale Mantle Flow. Geochem Geophys Geosyst 20 , 5896–5912 (2019). Yang, A. Y. et al. A subduction influence on ocean ridge basalts outside the Pacific subduction shield. Nat Commun 12 , 4757 (2021). Breiman, L. Bagging predictors. Mach Learn 24 , 123–140 (1996). Ho, T. K. The random subspace method for constructing decision forests. IEEE Transactions on Pattern Analysis and Machine Intelligence 20 , 832–844 (1998). Simmons, N. A., Forte, A. M., Boschi, L. & Grand, S. P. GyPSuM: A joint tomographic model of mantle density and seismic wave speeds. J. Geophys. Res. 115 , B12310 (2010). Jackson, M. G., Becker, T. W. & Steinberger, B. Spatial Characteristics of Recycled and Primordial Reservoirs in the Deep Mantle. Geochem Geophys Geosyst 22 , (2021). Hauri, E. H., Whitehead, J. A. & Hart, S. R. Fluid dynamic and geochemical aspects of entrainment in mantle plumes. Journal of Geophysical Research: Solid Earth 99 , 24275–24300 (1994). Merdith, A. S. et al. Extending full-plate tectonic models into deep time: Linking the Neoproterozoic and the Phanerozoic. Earth-Science Reviews 214 , 103477 (2021). Campbell, I. H. & Allen, C. M. Formation of supercontinents linked to increases in atmospheric oxygen. Nature Geosci 1, 554–558 (2008). Methods Construction of radiogenic isotopic datasets The filtered DC20 dataset 3 comprises six oceanic hotspots (Fig. 1), i.e., Iceland, Tristan, Reunion, Hawaii, Easter and Galapagos, and two plateaus, i.e., Kerguelen and Louisville. A total of 1,809 samples with complete 87 Sr/ 86 Sr, 143 Nd/ 144 Nd, 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, and 208 Pb/ 204 Pb data were selected. 207 Pb*/ 206 Pb* and 208 Pb*/ 206 Pb* are calculated using Equation (1) for both datasets to assess the time-integrated growth of 206 Pb, 207 Pb and 208 Pb since the Earth’s formation. 207 Pb*/ 206 Pb* = ( 207 Pb/ 204 Pb – 10.294)/( 206 Pb/ 204 Pb – 9.307) 208 Pb*/ 206 Pb*= ( 208 Pb/ 204 Pb – 29.476)/( 206 Pb/ 204 Pb – 9.307) 25 (Eq. 1) The expanded isotopic dataset consists of 1,809 samples from the DC20 dataset and 1,655 additional samples from all 26 oceanic hotspots compiled in the EarthChem portal (http://portal.earthchem.org). The expanded dataset includes hotspots situated around and within the African LLSVP or the Pacific LLSVP (Fig. 1). All the samples have complete records of 87 Sr/ 86 Sr, 143 Nd/ 144 Nd, 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, 208 Pb/ 204 Pb, and calculated 207 Pb*/ 206 Pb* and 208 Pb*/ 206 Pb* (Supplementary Data). The definition of the DUPAL domain follows that of Jackson and Macdonald 2 , with primary characterization of 143 Nd/ 144 Nd. The DUPAL domain comprises 11 hotspots (Fig. 1): Tristan, Discovery, Samoa, Pitcairn, Meteor/Shona, Tasmantid, Kerguelen, Hawaii, San Felix, Societies and Amsterdam/St. Paul. The non-DUPAL domain comprises the remaining 23 hotspots. The geographic distribution of the DUPAL domain closely aligns with the distribution of the DUPAL hotspots reported by Hart 1 , who focused on the deviations of 207 Pb/ 204 Pb and 208 Pb/ 204 Pb from the NHRL 1 and absolute values of 87 Sr/ 86 Sr. Random forest classifications of geochemical data The random forest algorithm 23 is an ensemble learning algorithm that consists of multiple decision trees. Each decision tree starts at the root node and progresses toward the leaves. At each node, a split is made based on a single feature. This process continues until it reaches one of the leaf nodes at the top of the tree. Each decision tree predicts a class, and the class receiving the most votes from the decision trees becomes the model's final prediction. A random forest repeatedly subsamples both the data and features to train decision trees 43,44 , which mitigates potential overfitting and enhances model generalizability. Four random forest classifiers are constructed to test two dichotomies using two datasets: (a) classification between the LLSVPs using the DC20 dataset; (b) classification between the LLSVPs using the expanded dataset; (c) classification between the DUPAL and non-DUPAL domains using the DC20 dataset; and (d) classification between the DUPAL and non-DUPAL domains using the expanded dataset. The isotopic ratios include 87 Sr/ 86 Sr, 143 Nd/ 144 Nd, 206 Pb/ 204 Pb, 207 Pb/ 204 Pb, 208 Pb/ 204 Pb, 207 Pb*/ 206 Pb* and 208 Pb*/ 206 Pb*. To avoid data leakage, we divide the training and test datasets at the geographical location level rather than into individual samples. That is, all samples from the same geographical location are either in the training set or in the test set. In each run, 70% of the locations are randomly selected for training, and the remaining 30% are used for testing. The number of locations for two classes remains equal during training and testing to ensure that the classification accuracy is not affected by imbalanced data. This procedure is repeated 1,000 times to determine the optimal hyperparameter pair (tree depth and forest size) for each classifier. The average accuracy and standard deviation of the four classifiers are calculated using the searched optimal tree depth and forest size: 6 and 95 for the LLSVP dichotomy using the DC20 dataset, 15 and 95 for the LLSVP dichotomy using the expanded dataset, 13 and 100 for the DUPAL dichotomy using the DC20 dataset, and 15 and 95 for the DUPAL dichotomy using the expanded dataset (Supplementary Fig. S11). Feature importance of geochemical measurements Feature importance, i.e., the relative importance of each isotopic ratio in classification, is evaluated by the Shapley value. The Shapley value is measured with the Shapley additive explanation approach 27,28 , which is defined as follows: Data-driven decision boundaries for separating geochemical regimes To map the decision boundaries of the two dichotomies, we retrain the random forest classifiers with only the two most important isotopic ratios as inputs: 87 Sr/ 86 Sr and 206 Pb/ 204 Pb for the DUPAL dichotomy and 87 Sr/ 86 Sr and 208 Pb*/ 206 Pb* for the LLSVP dichotomy. The trained classifiers predict the possibilities of virtual grid points across the 87 Sr/ 86 Sr- 206 Pb/ 204 Pb or 87 Sr/ 86 Sr- 208 Pb*/ 206 Pb* diagrams. These predicted possibilities are plotted as heatmaps. Each heatmap is generated from a random data split of training and testing sets. This process is repeated 1,000 times, and the decision boundary is the contour with a predicted probability of approximately 0.5 in the average heatmap. Additional Declarations There is NO Competing Interest. Supplementary Files Maetalisotopessupp.docx Supplementary Information African.csv Dataset 1 Pacific.csv Dataset 2 Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4268316","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":300700141,"identity":"ca5723c1-818c-460a-a580-580d0636d58a","order_by":0,"name":"Zefeng Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYFACxgdAwoKHH8ZtIKyF2QBISPBINkBUE6+FweAAsVrk25sZHxf8kpAxvpH+/MEPBhvZDQeYnz3Ap4Wx5zCz8cw+CR6zGzmGjT0MacYbDrCZG+B1lkT+MWneHrAWxmYGhsOJGw7wsEng08Im/5j9N0iL8Yz0h0At/wlr4ZFgZmPm+SHBYyCRYAjUcoCwFgmeZGZp3gYJHokzbwxn9hgkG888zGaGV4t8+2HGzzx/bOz529MffPhRYSfbd7z5GV4tYMDYBmOBgoqZoHoQ+EOUqlEwCkbBKBipAADhJEHyL7tNGwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-4405-8872","institution":"University of Science and Technology of China","correspondingAuthor":true,"prefix":"","firstName":"Zefeng","middleName":"","lastName":"Li","suffix":""},{"id":300700143,"identity":"5147cef3-8593-4c58-88f2-1515109510f9","order_by":1,"name":"Shang Ma","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Shang","middleName":"","lastName":"Ma","suffix":""},{"id":300700145,"identity":"c2278e52-b429-4bb6-999e-7f9a7467a438","order_by":2,"name":"Ling Chen","email":"","orcid":"https://orcid.org/0000-0001-7170-5954","institution":"Institute of Geology and Geophysics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Ling","middleName":"","lastName":"Chen","suffix":""},{"id":300700147,"identity":"90ea9092-1933-4be8-bec1-4e67490746a3","order_by":3,"name":"Ji Shen","email":"","orcid":"","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Ji","middleName":"","lastName":"Shen","suffix":""},{"id":300700149,"identity":"ef840772-ffc4-412b-8ac7-4c5f986d491e","order_by":4,"name":"Yunguo Li","email":"","orcid":"https://orcid.org/0000-0002-6221-7585","institution":"University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Yunguo","middleName":"","lastName":"Li","suffix":""},{"id":300700151,"identity":"98a3e7a1-ae3e-415b-90ad-b18ab72048e4","order_by":5,"name":"Wenzhong Wang","email":"","orcid":"https://orcid.org/0000-0002-8824-7475","institution":"Carnegie Institution for Science","correspondingAuthor":false,"prefix":"","firstName":"Wenzhong","middleName":"","lastName":"Wang","suffix":""},{"id":300700153,"identity":"f956bcf0-f860-4068-b1f2-ccb63a2ca77d","order_by":6,"name":"Wei Leng","email":"","orcid":"","institution":"School of Earth and Space Sciences, University of Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Leng","suffix":""}],"badges":[],"createdAt":"2024-04-15 08:30:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4268316/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4268316/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":56236068,"identity":"11f2ef77-8dcb-4a7d-8126-1cd8d50cfbf3","added_by":"auto","created_at":"2024-05-10 08:44:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1901751,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eGeographic distribution of oceanic hotspots. \u003c/strong\u003eThe background is the seismic shear-wave velocity anomaly at 2850 km from the seismic tomography model GyPSuM\u003csup\u003e45\u003c/sup\u003e. The boundaries of the LLSVPs are indicated by the white lines (-0.7% δV\u003csub\u003es\u003c/sub\u003e\u0026nbsp;velocity contour of GyPSuM\u003csup\u003e45\u003c/sup\u003e at 2850 km). The triangles represent hotspot conduit bases at 2850 km within the DUPAL domain, whereas the dots represent those outside the DUPAL domain. The DC20 dataset includes the hotspots marked by red dots and triangles. The expanded dataset includes those marked by all dots and triangles. The locations of hotspot conduit bases at 2850 km are adopted from Jackson et al.\u003csup\u003e46\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/0d5cecf5376a8d196cd6ca66.png"},{"id":56236070,"identity":"81c3d7f2-2c97-4c42-937f-936b0183b3aa","added_by":"auto","created_at":"2024-05-10 08:44:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":203838,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAccuracy histograms for DUPAL and LLSVP dichotomies on two datasets using 1,000 random data selections.\u003c/strong\u003e The LLSVP dichotomy achieves average accuracies of 92.1 ± 4.4% and 83.3 ± 3.7% for the DC20 dataset and the expanded dataset, respectively. The DUPAL dichotomy achieves average accuracies of 94.5 ± 3.6% and 91.9.5 ± 2.7% with the DC20 dataset and the expanded dataset, respectively.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/ba67bb18a2f4077a99aa130e.png"},{"id":56236528,"identity":"f900a4b4-9514-41ad-9b12-348f9337efa8","added_by":"auto","created_at":"2024-05-10 08:52:38","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":591656,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eShapley maps for DUPAL and LLSVP dichotomies with two datasets.\u003c/strong\u003e (a) Shapley map from 1,000 iterations of the LLSVP dichotomy with the DC20 dataset. Next to the feautre names are the average Shapley values of all the data, where a larger value suggests greater feature importance. (b)(c)(d) Similar to (a) but for the LLSVP dichotomy with the expanded dataset, the DUPAL dichotomy with the DC20 dataset, and the DUPAL dichotomy with the expanded dataset, respectively.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/6ee4ecb666d4eaf891fdedc6.png"},{"id":56236075,"identity":"124e5d17-daeb-414f-8513-669ad1946c0c","added_by":"auto","created_at":"2024-05-10 08:44:39","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":295064,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFeature importance and dependency of the classification accuracy of the DUPAL dichotomy on different features. \u003c/strong\u003eThe average accuracies (green dots, left-hand y-axis) and error bars are obtained by progressively inputting features in order of feature importance (pink dots, right-hand y-axis) from 1,000 classifications of the DUPAL dichotomy with the DC20 dataset (a) and with the expanded dataset (b).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/4b4f69aa889205c372493b41.png"},{"id":56236069,"identity":"fb09c835-5c45-4561-b382-4dc7db0573d1","added_by":"auto","created_at":"2024-05-10 08:44:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":878593,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIsotopic variation and decision boundaries between the DUPAL and non-DUPAL domains. \u003c/strong\u003eThe red lines mark the decision boundaries of the DUPAL (green) and non-DUPAL (pink) domains. Only 5.8% of the samples (yellow dots) are misclassified at a rate \u0026gt; 10% (Supplementary Figure S7). EM1, EM2 and HIMU were defined by Zindler and Hart\u003csup\u003e6\u003c/sup\u003e, and FOZO was defined by Hauri et al.\u003csup\u003e47\u003c/sup\u003e. The black lines are constructed using the following concentrations for Sr and Pb (in ppm): 200 and 10 for EM1, 300 and 20 for EM2, and 18.4 and 0.1 for FOZO.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/284f8c2a934933831baf2999.png"},{"id":56236071,"identity":"51ca3625-3389-481b-8619-3c386d0dfbfa","added_by":"auto","created_at":"2024-05-10 08:44:37","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":456684,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic illustration of the formation of the DUPAL anomaly.\u003c/strong\u003e Gondwana assembly at ~600-500 Ma in the Southern Hemisphere resulted in large-scale lithospheric thickening and unstable lithospheric bases. The lower continental and lithospheric material sinks into the deep mantle. The primitive magma originating from the deep mantle base sampled these materials through ascending plumes, forming the present observed EM1 component in the DUPAL anomaly.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/4930ec894af353743ae78b6e.png"},{"id":61567944,"identity":"fb236ccd-2659-4247-91da-8645583b40d2","added_by":"auto","created_at":"2024-08-01 10:13:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4251538,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/50eb7b93-ead6-458a-b6c7-f2a485055bb5.pdf"},{"id":56236073,"identity":"e4022706-4efc-4394-98af-cbf6e0c4deed","added_by":"auto","created_at":"2024-05-10 08:44:38","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":6822747,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Information\u003c/p\u003e","description":"","filename":"Maetalisotopessupp.docx","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/9a14c0302f89c8516158b760.docx"},{"id":56236067,"identity":"52d44749-e334-4b27-b329-764515fc26e8","added_by":"auto","created_at":"2024-05-10 08:44:36","extension":"csv","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":232085,"visible":true,"origin":"","legend":"Dataset 1","description":"","filename":"African.csv","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/67dd5309c28d288c5966e0a1.csv"},{"id":56236074,"identity":"b4b71977-7b70-47ef-bc1d-fee40244b47b","added_by":"auto","created_at":"2024-05-10 08:44:39","extension":"csv","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":61962,"visible":true,"origin":"","legend":"Dataset 2","description":"","filename":"Pacific.csv","url":"https://assets-eu.researchsquare.com/files/rs-4268316/v1/977dad93e018f6e806e71403.csv"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Deciphering Earth’s deep mantle hemispheric geochemical dichotomy with machine learning","fulltext":[{"header":"Highlights","content":"\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003eMachine learning reveals\u0026nbsp;that hemispheric geochemical differences in the Earth\u0026rsquo;s mantle are more predominant than those between LLSVPs.\u003c/li\u003e\n \u003cli\u003eEnriched Mantle 1 plays a key role in differentiating the DUPAL anomaly, as revealed by the data-driven classification boundary.\u003c/li\u003e\n \u003cli\u003eThe DUPAL anomaly could have resulted from large-scale lithospheric delamination during Gondwana amalgamation.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Introduction","content":"\u003cp\u003eGlobal geochemical and geophysical observations have revealed the heterogeneous nature of the Earth's mantle\u003csup\u003e\u003cspan additionalcitationids=\"CR5 CR6 CR7 CR8\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, which plays an important role in governing the thermal and chemical geodynamics of the deep Earth. Radiogenic isotopic signatures, including Sr, Nd, and Pb, observed in oceanic island basalts (OIBs) reveal chemical heterogeneities in the deep mantle\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. The sources of these oceanic basalts have been conventionally attributed to several isotopically distinct mantle endmembers, such as Enriched Mantle 1 (EM1)\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, Enriched Mantle 2 (EM2)\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, High-\u0026micro; (HIMU, \u0026micro; = \u003csup\u003e238\u003c/sup\u003eU/\u003csup\u003e204\u003c/sup\u003ePb)\u003csup\u003e6\u003c/sup\u003e and the Focus Zone (FOZO)\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003c/sup\u003e or mixtures between them. FOZO is a common component of many OIBs\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e and could represent the primitive mantle\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. HIMU is believed to result from subducted oceanic crust and/or the extraction of Pb from the mantle to the core\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. The EM signatures are often associated with the recycling of continental crust\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan additionalcitationids=\"CR18 CR19\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Specifically, EM1 is associated with recycled continental lower crust and subcontinental lithospheric mantle\u003csup\u003e\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, whereas EM2 is thought to contain recycled upper continental crust and sediments\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Particularly notable are the EM signatures observed in OIBs from the Southern Hemisphere, characterized by higher \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb and \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, which is termed the DUPAL anomaly\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. However, the mechanisms responsible for such hemispheric mantle distinction, which include core\u0026ndash;mantle\u0026ndash;crust differentiation\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e and/or lower crustal delamination\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, remain largely unresolved.\u003c/p\u003e \u003cp\u003eThe southern hemispheric DUPAL anomaly has been debated, partly because the isotopic data from East Pacific Rise basalts and South Pacific OIBs appear to be inconsistent with the DUPAL anomaly\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e observed elsewhere. Doucet \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e observed that the large-scale heterogeneities in the deep mantle are predominantly divided by the African and Pacific large low shear-wave velocity provinces (LLSVPs, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), rather than by hemispheres, as the DUPAL anomaly suggests. However, this finding could be associated with the selection of OIBs from deep plume oceanic hotspots\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Based on the OIBs characterized by \u003csup\u003e143\u003c/sup\u003eNd/\u003csup\u003e144\u003c/sup\u003eNd from all oceanic hotspots, Jackson \u0026amp; Macdonald\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e confirmed the existence of the austral DUPAL anomaly and attributed it to the deep subduction of continental crust during Gondwana and Pangea assembly.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA comprehensive and objective evaluation of global OIB geochemical signatures is needed to clarify the predominant zoning characteristics of the deep mantle. Here, we harness the power of machine learning to resolve two debated geochemical dichotomies, i.e., whether the deep mantle is mainly divided by hemispheres (hereafter referred to as the DUPAL dichotomy) or by LLSVPs (hereafter referred to as the LLSVP dichotomy). We train random forest classifiers\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e for the DUPAL dichotomy and LLSVP dichotomy using two different isotopic datasets (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). By observing the stability of the classification accuracies and the consistency of the isotopic contributions on the two datasets, we find that the DUPAL dichotomy is generally more robust than the LLSVP dichotomy. The DUPAL dichotomy has two most important isotopic ratios, \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, which underscores the significant role of EM1. We interpret the hemispherically distributed deep-mantle geochemical heterogeneities as a result of material mixing from massive lithospheric delamination during Gondwana supercontinent assembly at ~\u0026thinsp;600\u0026thinsp;\u0026minus;\u0026thinsp;500 Ma.\u003c/p\u003e"},{"header":"Resolving geochemical dichotomies with machine learning","content":"\u003cp\u003eRadiogenic isotopic data of OIBs from mantle plume sources offer critical constraints on geochemical heterogeneities in the deep mantle\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. We analyse two isotopic datasets: the dataset presented by Doucet \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e (hereafter referred to as the DC20 dataset) and an expanded dataset that encompasses the DC20 dataset and additional isotopic data of all OIBs from the EarthChem portal (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://portal.earthchem.org\u003c/span\u003e\u003cspan address=\"http://portal.earthchem.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The DC20 dataset contains 1,809 samples from 8 hotspots, whereas the expanded dataset contains 3,464 samples from 34 hotspots (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). All the samples have complete \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, \u003csup\u003e143\u003c/sup\u003eNd/\u003csup\u003e144\u003c/sup\u003eNd, \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb and \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb measurements. We further derive \u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* (ref. \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e) from \u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb and \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb. These derived ratios represent the time-integrated growth of U/Pb and Th/U ratios and are associated with enriched lithospheric material\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. These isotopic ratios are organized into 7-element feature vectors and input into random forest classifiers, which map them to their respective source domains: African versus Pacific LLSVPs and DUPAL versus non-DUPAL domains. The contribution of each isotopic ratio to the classification is evaluated by the Shapley value\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, which represents the average impact of an individual isotopic ratio by considering all combinations it forms with other isotopic ratios. Further details regarding the data selection, random forest classification and feature importance evaluation are outlined in the Methods section.\u003c/p\u003e \u003cp\u003eIn the case of the DC20 dataset (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the classification accuracy using the LLSVP dichotomy reaches 92.1\u0026thinsp;\u0026plusmn;\u0026thinsp;4.4% (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), indicating high distinguishability between the two LLSVPs. The two most important isotopic ratios in the classification are \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb*, with average Shapley values of 0.143 and 0.129 (significantly greater than 0), respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). In comparison, the least important isotopic ratio, \u003csup\u003e207*\u003c/sup\u003ePb/\u003csup\u003e206*\u003c/sup\u003ePb, exhibits an average Shapley value of 0.013 (approximately equivalent to 0). It is worth noting that samples from the Pacific LLSVP exhibit low \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr (\u0026lt;\u0026thinsp;0.705), \u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e206\u003c/sup\u003ePb and \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e206\u003c/sup\u003ePb ratios, generally following the Northern Hemisphere Reference Line (NHRL) (Supplementary Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). For the most important isotopic ratio, \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, the Pacific LLSVP displays negative Shapley values (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). These results agree with previous findings by Doucet \u003cem\u003eet al\u003c/em\u003e.\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. However, with the expanded dataset, the classification accuracy using the LLSVP dichotomy decreases dramatically to 83.3\u0026thinsp;\u0026plusmn;\u0026thinsp;3.7% (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb are the most important features (average Shapley values of 0.103 and 0.079, respectively; Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). This experiment reveals that a high \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr ratio is more indicative of the Pacific LLSVP (Supplementary Fig. S2), contradicting the observations with the DC20 dataset. These results suggest that the LLSVP dichotomy is supported by the DC20 dataset but not by the expanded dataset, suggesting that the LLSVP dichotomy is not a universal feature of global OIBs.\u003c/p\u003e \u003cp\u003eIn comparison with that of the DC20 dataset, the classification accuracy of the DUPAL dichotomy reached 94.5\u0026thinsp;\u0026plusmn;\u0026thinsp;3.6% (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The two most important isotopic ratios controlling this classification are \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, with average Shapley values of 0.204 and 0.102, respectively. High \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, \u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* ratios yield positive Shapley values (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec), thus serving as positive indicators of the DUPAL domain (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec and Supplementary Fig. S3), consistent with previous investigations\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. With the expanded dataset, the classification accuracy reaches 91.9\u0026thinsp;\u0026plusmn;\u0026thinsp;2.7% (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). This accuracy is significantly greater than the accuracy of the LLSVP dichotomy (83.3\u0026thinsp;\u0026plusmn;\u0026thinsp;3.7%) with the expanded dataset and is comparable to the accuracy of the DUPAL dichotomy with the DC20 data. Moreover, \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb remain the most important isotopic ratios, with average Shapley values of 0.148 and 0.103, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). Similarly, high \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, \u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* are positive indicators of the DUPAL domain (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed and Supplementary Fig. S4). These observations demonstrate the robustness and consistency of the DUPAL dichotomy with both the DC20 and expanded datasets, suggesting a universal feature of global OIBs.\u003c/p\u003e \u003cp\u003eTo further examine the stability of the DUPAL dichotomy, we retrain the random forest classifiers using the two most important isotopic ratios (\u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb for the DUPAL dichotomy and \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* for the LLSVP dichotomy) and visualize their decision boundaries (Supplementary Fig. S5). These boundaries are obtained by inputting the virtual values of \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr - \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb and \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr - \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* into the retrained classifiers (details in Methods). We observe that the decision boundaries of the LLSVP dichotomy significantly differ between the two datasets (Supplementary Fig. S5a, b). The boundary on the expanded dataset appears to be extremely complex, which is a sign of overfitting. In contrast, the DUPAL dichotomy shows relatively simple and similar boundaries with both datasets (Supplementary Fig. S5c, d), supporting that the DUPAL dichotomy is a more reliable geochemical zoning model.\u003c/p\u003e"},{"header":"Primary signatures of the DUPAL anomaly","content":"\u003cp\u003eTo evaluate the net contributions of different isotopic ratios to the DUPAL dichotomy, we track the changes in classification accuracy by progressively inputting the isotopic ratios from the most to the least important. The results reveal that with only the two most important isotopic ratios, \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, the classification accuracies reach 94.2\u0026thinsp;\u0026plusmn;\u0026thinsp;2.6% and 87.9\u0026thinsp;\u0026plusmn;\u0026thinsp;2.9%, respectively, for the two datasets (Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, b). The predominance of \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb likely results from the high incompatibility of their respective parent elements (Rb and U), which have greater partition coefficients than the Sm/Nd system. Consequently, the enrichment of these elements in melts is less susceptible to contamination and/or measurement uncertainties, making them effective for distinguishing between the DUPAL and non-DUPAL domains. Importantly, the discrimination accuracies using only \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb are almost identical to those obtained using all the isotopic ratios. This suggests that the other isotopic ratios provide little additional discriminative power beyond that provided by \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb. Although different isotopic characteristics could represent different geochemical components, our results imply that here, they seem to reflect the same geochemical reservoirs.\u003c/p\u003e \u003cp\u003eThe complete distinguishability of \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb thus warrants a concise definition of the DUPAL anomaly in the \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr - \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb diagram. Machine learning automatically derives a data-driven decision boundary between the DUPAL and non-DUPAL domains (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The delineated DUPAL domain is encompassed by the curves of the mixing mantle endmembers of EM1, EM2 and FOZO. The non-DUPAL domain, on the other hand, is mainly positioned within HIMU, EM2 and FOZO (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Therefore, the DUPAL and non-DUPAL domains share the EM2 and FOZO components but exhibit different predominance of EM1 and HIMU components. Specifically, EM1 is more prevalent relative to HIMU within the DUPAL domain, while HIMU exhibits a higher proportion compared to EM1 within the non-DUPAL domain. Our refined definition of the DUPAL anomaly in the \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr-\u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb diagram underscores the predominant role of EM1, distinguishing it from the conventional definition using deviations from the NHRL (Supplementary Fig. S6).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe machine learning classifiers effectively categorize most of the OIB samples into their respective hemispheric geochemical regimes. However, a small subset of samples is misclassified more frequently than others (misclassification rate\u0026thinsp;\u0026gt;\u0026thinsp;10%; Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Supplementary Fig. S7). They are mostly from the Hawaii, Pitcairn, Samoa and Society hotspots (Supplementary Fig. S8), which fall within the conventionally defined geographic DUPAL domain but exhibit non-DUPAL geochemical signatures (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Basalts from these hotspots exhibit a wide variety of geochemical characteristics ranging from DUPAL to non-DUPAL. The observed intra-hotspot geochemical variations are possibly associated with the sampling locations relative to the Pacific LLSVP\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e): the spatial pattern of heterogeneities situated above the core-mantle boundary could be preserved through plume conduits, resulting in different geochemical compositions in OIBs from the same plume\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Implications for genesis of the mantle hemispheric dichotomy","content":"\u003cp\u003eThe origin of the large-scale austral DUPAL anomaly is thought to be associated with supercontinent evolution during the Gondwana period\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, partly because the DUPAL anomaly was located in the Southern Hemisphere and coincident with the majority of the global continents\u0026rsquo; location at ~\u0026thinsp;550 Ma (Supplementary Fig. S9). Our results highlight the key role of the EM1 component in the deep mantle, implying the involvement of continental lower crust and subcontinental lithospheric material. Geodynamic modelling has demonstrated that continental collision can cause lithospheric thickening, increased crustal density and negative buoyancy, eventually resulting in the foundering of subcontinental lithospheric mantle and lower crust\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. Hence, intensive lithospheric delamination in the Southern Hemisphere during Gondwana assembly could have been responsible for the genesis of the hemispheric geochemical dichotomy (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The Gondwana delamination hypothesis is further supported by global zircon measurements. Much larger negative ε\u003csub\u003eHf\u003c/sub\u003e values at ~\u0026thinsp;600\u0026thinsp;\u0026minus;\u0026thinsp;500 Ma\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e were observed than those obtained during the formation of other supercontinents (Supplementary Fig. S10), indicating an unusually high level of continental mass loss during Gondwana amalgamation\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Hence, extra lithospheric material was added to the ubiquitous FOZO, along with the shared EM2 in all the OIBs, which may have resulted from pervasive global subduction over supercontinental cycles\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe austral localization of the DUPAL anomaly may indicate its source depth at which the majority of the delaminated material was situated. If the delaminated material stays in the upper mantle, due to vigorous convection in the upper mantle, EM1 reservoirs would tend to be distributed across all latitudes rather than being confined to the Southern Hemisphere. Moreover, the delaminated lithosphere after metamorphic densification is unlikely to remain in the upper mantle and most of the mantle transition zone\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e and can potentially sink into the lower mantle\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. It has a large chance to persist in the Southern Hemisphere to present day owing to the much slower convection of the lower mantle\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. Consequently, the delaminated lithosphere is sampled by upwelling plumes to form the observed EM1 component in OIBs. This hypothesis favours that the DUPAL anomaly is predominantly originated from the lower mantle, which readily explains the two key characteristics of the DUPAL anomaly, i.e. dominance of the EM1 endmember and localization in the Southern Hemisphere (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe occurrence of Gondwana crustal recycling at ~\u0026thinsp;600\u0026thinsp;\u0026minus;\u0026thinsp;500 Ma also accommodates the necessary time for the sinking of crustal mass\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e and the upwelling of enriched mantle material\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The present DUPAL signature of OIBs possibly represents a snapshot of the evolving deep Earth bearing the imprint of Gondwana formation at ~\u0026thinsp;600\u0026thinsp;\u0026minus;\u0026thinsp;500 Ma. Our findings reveal the relationship between modern geochemical anomalies and ancient geological evolution, potentially reflecting a long period (~\u0026thinsp;600 Myr) of large-scale material recycling in the deep mantle. Comparatively, mid-oceanic ridge basalts from shallow reservoirs likely represent material recycling during a shorter period (\u0026lt;\u0026thinsp;200 Myr) of the tectonic history of upper mantle convection\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Our study illustrates that machine learning applied to large geochemical datasets can contribute to identifying deep-mantle geochemical heterogeneities and revealing robust patterns of geodynamic evolution in the deep Earth.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis project is supported by National Science Foundation of China (Nos. 42274063, 42288201).\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eThe DC20 dataset can be accessed from the supplementary data in ref. 3 (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41561-020-0599-9\u003c/span\u003e\u003cspan address=\"10.1038/s41561-020-0599-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, last accessed on 12 August 2022). The expanded dataset was compiled from the EarthChem Portal (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://portal.earthchem.org\u003c/span\u003e\u003cspan address=\"http://portal.earthchem.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, last accessed on 2 March 2023) and is available in the Supplementary Data.\u003c/p\u003e\u003ch2\u003eCode availability\u003c/h2\u003e \u003cp\u003eThe random forest classifiers were developed with the open-source Python package scikit-learn (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://scikit-learn.org\u003c/span\u003e\u003cspan address=\"https://scikit-learn.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, last accessed on 16 March 2023), and the Shapley value was calculated with the open-source Python package SHAP (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://shap.readthedocs.io\u003c/span\u003e\u003cspan address=\"https://shap.readthedocs.io\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, last accessed on 20 August 2023). The complete set of developed codes is available via Zenodo at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.5281/zenodo.10373594\u003c/span\u003e\u003cspan address=\"10.5281/zenodo.10373594\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe author declares no competing interests.\u003c/p\u003e "},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eHart, S. R. A large-scale isotope anomaly in the Southern Hemisphere mantle. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e309\u003c/strong\u003e, 753\u0026ndash;757 (1984).\u003c/li\u003e\n\u003cli\u003eJackson, M. G. \u0026amp; Macdonald, F. A. Hemispheric Geochemical Dichotomy of the Mantle Is a Legacy of Austral Supercontinent Assembly and Onset of Deep Continental Crust Subduction. \u003cem\u003eAGU Advances\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, (2022).\u003c/li\u003e\n\u003cli\u003eDoucet, L. S. \u003cem\u003eet al.\u003c/em\u003e Distinct formation history for deep-mantle domains reflected in geochemical differences. \u003cem\u003eNat. Geosci.\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 511\u0026ndash;515 (2020).\u003c/li\u003e\n\u003cli\u003eHart, S. R., Schilling, J.-G. \u0026amp; Powell, J. L. Basalts from Iceland and Along the Reykjanes Ridge: Sr Isotope Geochemistry. \u003cem\u003eNature Physical Science\u003c/em\u003e \u003cstrong\u003e246\u003c/strong\u003e, 104\u0026ndash;107 (1973).\u003c/li\u003e\n\u003cli\u003eHedge, C. E. Strontium isotopes in basalts from the Pacific Ocean basin. \u003cem\u003eEarth and Planetary Science Letters\u003c/em\u003e \u003cstrong\u003e38\u003c/strong\u003e, 88\u0026ndash;94 (1978).\u003c/li\u003e\n\u003cli\u003eZindler, A. \u0026amp; Hart, S. Chemical Geodynamics. \u003cem\u003eAnnual Review of Earth and Planetary Sciences\u003c/em\u003e \u003cstrong\u003e14\u003c/strong\u003e, 493\u0026ndash;571 (1986).\u003c/li\u003e\n\u003cli\u003eHofmann, A. W. Mantle geochemistry: the message from oceanic volcanism. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e385\u003c/strong\u003e, 219\u0026ndash;229 (1997).\u003c/li\u003e\n\u003cli\u003eStracke, A., Hofmann, A. W. \u0026amp; Hart, S. R. FOZO, HIMU, and the rest of the mantle zoo. \u003cem\u003eGeochemistry, Geophysics, Geosystems\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, (2005).\u003c/li\u003e\n\u003cli\u003eGoes, S., Yu, C., Ballmer, M. D., Yan, J. \u0026amp; Van Der Hilst, R. D. Compositional heterogeneity in the mantle transition zone. \u003cem\u003eNat Rev Earth Environ\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, 533\u0026ndash;550 (2022).\u003c/li\u003e\n\u003cli\u003eZindler, A., Staudigel, H. \u0026amp; Batiza, R. Isotope and trace element geochemistry of young Pacific seamounts: implications for the scale of upper mantle heterogeneity. \u003cem\u003eEarth and Planetary Science Letters\u003c/em\u003e \u003cstrong\u003e70\u003c/strong\u003e, 175\u0026ndash;195 (1984).\u003c/li\u003e\n\u003cli\u003eAdams, J. V. \u003cem\u003eet al.\u003c/em\u003e Extreme isotopic heterogeneity in Samoan clinopyroxenes constrains sediment recycling. \u003cem\u003eNat Commun\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 1234 (2021).\u003c/li\u003e\n\u003cli\u003eHart, S. R., Hauri, E. H., Oschmann, L. A. \u0026amp; Whitehead, J. A. Mantle Plumes and Entrainment: Isotopic Evidence. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e256\u003c/strong\u003e, 517\u0026ndash;520 (1992).\u003c/li\u003e\n\u003cli\u003eWhite, W. M. Isotopes, DUPAL, LLSVPs, and Anekantavada. \u003cem\u003eChemical Geology\u003c/em\u003e \u003cstrong\u003e419\u003c/strong\u003e, 10\u0026ndash;28 (2015).\u003c/li\u003e\n\u003cli\u003eHuang, S. \u0026amp; Zheng, Y. Mantle geochemistry: Insights from ocean island basalts. \u003cem\u003eSci. China Earth Sci.\u003c/em\u003e \u003cstrong\u003e60\u003c/strong\u003e, 1976\u0026ndash;2000 (2017).\u003c/li\u003e\n\u003cli\u003eVollmer, R. Terrestrial lead isotopic evolution and formation time of the Earth\u0026rsquo;s core. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e270\u003c/strong\u003e, 144\u0026ndash;147 (1977).\u003c/li\u003e\n\u003cli\u003eAll\u0026egrave;gre, C. J. Chemical geodynamics. \u003cem\u003eTectonophysics\u003c/em\u003e \u003cstrong\u003e81\u003c/strong\u003e, 109\u0026ndash;132 (1982).\u003c/li\u003e\n\u003cli\u003eDupr\u0026eacute;, B. \u0026amp; All\u0026egrave;gre, C. J. Pb\u0026ndash;Sr isotope variation in Indian Ocean basalts and mixing phenomena. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e303\u003c/strong\u003e, 142\u0026ndash;146 (1983).\u003c/li\u003e\n\u003cli\u003eHawkesworth, C. J., Mantovani, M. S. M., Taylor, P. N. \u0026amp; Palacz, Z. Evidence from the Parana of south Brazil for a continental contribution to Dupal basalts. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e322\u003c/strong\u003e, 356\u0026ndash;359 (1986).\u003c/li\u003e\n\u003cli\u003eArndt, N. T. \u0026amp; Goldstein, S. L. An open boundary between lower continental crust and mantle: its role in crust formation and crustal recycling. \u003cem\u003eTectonophysics\u003c/em\u003e \u003cstrong\u003e161\u003c/strong\u003e, 201\u0026ndash;212 (1989).\u003c/li\u003e\n\u003cli\u003eEscrig, S., Capmas, F., Dupr\u0026eacute;, B. \u0026amp; All\u0026egrave;gre, C. J. Osmium isotopic constraints on the nature of the DUPAL anomaly from Indian mid-ocean-ridge basalts. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e431\u003c/strong\u003e, 59\u0026ndash;63 (2004).\u003c/li\u003e\n\u003cli\u003eMacdougall, J. D. \u0026amp; Lugmair, G. W. Sr and Nd isotopes in basalts from the East Pacific Rise: significance for mantle heterogeneity. \u003cem\u003eEarth and Planetary Science Letters\u003c/em\u003e \u003cstrong\u003e77\u003c/strong\u003e, 273\u0026ndash;284 (1986).\u003c/li\u003e\n\u003cli\u003eStaudigel, H. \u003cem\u003eet al.\u003c/em\u003e The longevity of the South Pacific isotopic and thermal anomaly. \u003cem\u003eEarth and Planetary Science Letters\u003c/em\u003e \u003cstrong\u003e102\u003c/strong\u003e, 24\u0026ndash;44 (1991).\u003c/li\u003e\n\u003cli\u003eBreiman, L. Random Forests. \u003cem\u003eMachine Learning\u003c/em\u003e \u003cstrong\u003e45\u003c/strong\u003e, 5\u0026ndash;32 (2001).\u003c/li\u003e\n\u003cli\u003eHuang, S., Hall, P. S. \u0026amp; Jackson, M. G. Geochemical zoning of volcanic chains associated with Pacific hotspots. \u003cem\u003eNature Geosci\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 874\u0026ndash;878 (2011).\u003c/li\u003e\n\u003cli\u003eStacey, J. S. \u0026amp; Kramers, J. D. APPROXIMATION OF TERRESTRIAL LEAD ISOTOPE EVOLUTION BY A TWO-STAGE MODEL. \u003cem\u003eEarth and Planetary Science Letters\u003c/em\u003e \u003cstrong\u003e26\u003c/strong\u003e, 207\u0026ndash;221 (1975).\u003c/li\u003e\n\u003cli\u003eWilliams, C. D., Mukhopadhyay, S., Rudolph, M. L. \u0026amp; Romanowicz, B. Primitive Helium Is Sourced From Seismically Slow Regions in the Lowermost Mantle. \u003cem\u003eGeochem. Geophys. Geosyst.\u003c/em\u003e \u003cstrong\u003e20\u003c/strong\u003e, 4130\u0026ndash;4145 (2019).\u003c/li\u003e\n\u003cli\u003eLundberg, S. M. \u0026amp; Lee, S.-I. A Unified Approach to Interpreting Model Predictions. in \u003cem\u003eAdvances in Neural Information Processing Systems\u003c/em\u003e (eds. Guyon, I. et al.) vol. 30 (Curran Associates, Inc., 2017).\u003c/li\u003e\n\u003cli\u003e\u0026Scaron;trumbelj, E. \u0026amp; Kononenko, I. Explaining prediction models and individual predictions with feature contributions. \u003cem\u003eKnowl Inf Syst\u003c/em\u003e \u003cstrong\u003e41\u003c/strong\u003e, 647\u0026ndash;665 (2014).\u003c/li\u003e\n\u003cli\u003eFarnetani, C. G. \u0026amp; Hofmann, A. W. Dynamics and internal structure of a lower mantle plume conduit. \u003cem\u003eEarth and Planetary Science Letters\u003c/em\u003e \u003cstrong\u003e282\u003c/strong\u003e, 314\u0026ndash;322 (2009).\u003c/li\u003e\n\u003cli\u003eChen, L. The Role of Lower Crustal Rheology in Lithospheric Delamination During Orogeny. \u003cem\u003eFront. Earth Sci.\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 755519 (2021).\u003c/li\u003e\n\u003cli\u003eLi, Z., Liu, M. \u0026amp; Gerya, T. Lithosphere delamination in continental collisional orogens: A systematic numerical study. \u003cem\u003eJGR Solid Earth\u003c/em\u003e \u003cstrong\u003e121\u003c/strong\u003e, 5186\u0026ndash;5211 (2016).\u003c/li\u003e\n\u003cli\u003eBelousova, E. A. \u003cem\u003eet al.\u003c/em\u003e The growth of the continental crust: Constraints from zircon Hf-isotope data. \u003cem\u003eLithos\u003c/em\u003e \u003cstrong\u003e119\u003c/strong\u003e, 457\u0026ndash;466 (2010).\u003c/li\u003e\n\u003cli\u003eRoberts, N. M. W. Increased loss of continental crust during supercontinent amalgamation. \u003cem\u003eGondwana Research\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 994\u0026ndash;1000 (2012).\u003c/li\u003e\n\u003cli\u003eEvans, D. True polar wander and supercontinents. \u003cem\u003eTectonophysics\u003c/em\u003e (2002) doi:10.1016/S0040-1951(02)00642-X.\u003c/li\u003e\n\u003cli\u003eWang, Y., Zhang, L. \u0026amp; Li, Z.-H. Metamorphic densification can account for the missing felsic crust of the Greater Indian continent. \u003cem\u003eCommun Earth Environ\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, 166 (2022).\u003c/li\u003e\n\u003cli\u003eGanguly, J., Freed, A. M. \u0026amp; Saxena, S. K. Density profiles of oceanic slabs and surrounding mantle: Integrated thermodynamic and thermal modeling, and implications for the fate of slabs at the 660km discontinuity. \u003cem\u003ePhysics of the Earth and Planetary Interiors\u003c/em\u003e \u003cstrong\u003e172\u003c/strong\u003e, 257\u0026ndash;267 (2009).\u003c/li\u003e\n\u003cli\u003eBallmer, M. D., Houser, C., Hernlund, J. W., Wentzcovitch, R. M. \u0026amp; Hirose, K. Persistence of strong silica-enriched domains in the Earth\u0026rsquo;s lower mantle. \u003cem\u003eNature Geosci\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 236\u0026ndash;240 (2017).\u003c/li\u003e\n\u003cli\u003eČ\u0026iacute;žkov\u0026aacute;, H., Van Den Berg, A. P., Spakman, W. \u0026amp; Matyska, C. The viscosity of Earth\u0026rsquo;s lower mantle inferred from sinking speed of subducted lithosphere. \u003cem\u003ePhysics of the Earth and Planetary Interiors\u003c/em\u003e \u003cstrong\u003e200\u0026ndash;201\u003c/strong\u003e, 56\u0026ndash;62 (2012).\u003c/li\u003e\n\u003cli\u003eSteinberger, B. \u0026amp; Calderwood, A. R. Models of large-scale viscous flow in the Earth\u0026rsquo;s mantle with constraints from mineral physics and surface observations. \u003cem\u003eGeophysical Journal International\u003c/em\u003e \u003cstrong\u003e167\u003c/strong\u003e, 1461\u0026ndash;1481 (2006).\u003c/li\u003e\n\u003cli\u003eDomeier, M., Doubrovine, P. V., Torsvik, T. H., Spakman, W. \u0026amp; Bull, A. L. Global correlation of lower mantle structure and past subduction. \u003cem\u003eGeophysical Research Letters\u003c/em\u003e \u003cstrong\u003e43\u003c/strong\u003e, 4945\u0026ndash;4953 (2016).\u003c/li\u003e\n\u003cli\u003eSteinberger, B., Nelson, P. L., Grand, S. P. \u0026amp; Wang, W. Yellowstone Plume Conduit Tilt Caused by Large‐Scale Mantle Flow. \u003cem\u003eGeochem Geophys Geosyst\u003c/em\u003e \u003cstrong\u003e20\u003c/strong\u003e, 5896\u0026ndash;5912 (2019).\u003c/li\u003e\n\u003cli\u003eYang, A. Y. \u003cem\u003eet al.\u003c/em\u003e A subduction influence on ocean ridge basalts outside the Pacific subduction shield. \u003cem\u003eNat Commun\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 4757 (2021).\u003c/li\u003e\n\u003cli\u003eBreiman, L. Bagging predictors. \u003cem\u003eMach Learn\u003c/em\u003e \u003cstrong\u003e24\u003c/strong\u003e, 123\u0026ndash;140 (1996).\u003c/li\u003e\n\u003cli\u003eHo, T. K. The random subspace method for constructing decision forests. \u003cem\u003eIEEE Transactions on Pattern Analysis and Machine Intelligence\u003c/em\u003e \u003cstrong\u003e20\u003c/strong\u003e, 832\u0026ndash;844 (1998).\u003c/li\u003e\n\u003cli\u003eSimmons, N. A., Forte, A. M., Boschi, L. \u0026amp; Grand, S. P. GyPSuM: A joint tomographic model of mantle density and seismic wave speeds. \u003cem\u003eJ. Geophys. Res.\u003c/em\u003e \u003cstrong\u003e115\u003c/strong\u003e, B12310 (2010).\u003c/li\u003e\n\u003cli\u003eJackson, M. G., Becker, T. W. \u0026amp; Steinberger, B. Spatial Characteristics of Recycled and Primordial Reservoirs in the Deep Mantle. \u003cem\u003eGeochem Geophys Geosyst\u003c/em\u003e \u003cstrong\u003e22\u003c/strong\u003e, (2021).\u003c/li\u003e\n\u003cli\u003eHauri, E. H., Whitehead, J. A. \u0026amp; Hart, S. R. Fluid dynamic and geochemical aspects of entrainment in mantle plumes. \u003cem\u003eJournal of Geophysical Research: Solid Earth\u003c/em\u003e \u003cstrong\u003e99\u003c/strong\u003e, 24275\u0026ndash;24300 (1994).\u003c/li\u003e\n\u003cli\u003eMerdith, A. S. \u003cem\u003eet al.\u003c/em\u003e Extending full-plate tectonic models into deep time: Linking the Neoproterozoic and the Phanerozoic. \u003cem\u003eEarth-Science Reviews\u003c/em\u003e \u003cstrong\u003e214\u003c/strong\u003e, 103477 (2021).\u003c/li\u003e\n\u003cli\u003eCampbell, I. H. \u0026amp; Allen, C. M. Formation of supercontinents linked to increases in atmospheric oxygen. \u003cem\u003eNature Geosci\u003c/em\u003e 1, 554\u0026ndash;558 (2008).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eConstruction of radiogenic isotopic datasets\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe filtered\u0026nbsp;DC20 dataset\u003csup\u003e3\u003c/sup\u003e comprises six oceanic hotspots (Fig. 1), i.e., Iceland, Tristan, Reunion, Hawaii, Easter and Galapagos, and two plateaus, i.e., Kerguelen and Louisville. A total of 1,809 samples with complete \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, \u003csup\u003e143\u003c/sup\u003eNd/\u003csup\u003e144\u003c/sup\u003eNd, \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb,\u003csup\u003e\u0026nbsp;207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, and \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb data were selected. \u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* are calculated using Equation (1) for both datasets to assess the time-integrated growth of \u003csup\u003e206\u003c/sup\u003ePb,\u003csup\u003e\u0026nbsp;207\u003c/sup\u003ePb and \u003csup\u003e208\u003c/sup\u003ePb since the Earth\u0026rsquo;s formation.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* = (\u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb \u0026ndash; 10.294)/(\u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb \u0026ndash; 9.307)\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb*= (\u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb \u0026ndash; 29.476)/(\u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb \u0026ndash; 9.307)\u003csup\u003e25\u003c/sup\u003e (Eq. 1)\u003c/p\u003e\n\u003cp\u003eThe expanded isotopic dataset consists of 1,809 samples from the DC20 dataset and 1,655 additional samples from all 26 oceanic hotspots compiled in the EarthChem portal (http://portal.earthchem.org). The expanded dataset includes hotspots situated around and within the African LLSVP or the Pacific LLSVP (Fig. 1). All the samples have complete records of \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, \u003csup\u003e143\u003c/sup\u003eNd/\u003csup\u003e144\u003c/sup\u003eNd, \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb,\u003csup\u003e\u0026nbsp;207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, and calculated \u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* (Supplementary Data).\u003c/p\u003e\n\u003cp\u003eThe definition of the DUPAL domain follows that of Jackson and Macdonald\u003csup\u003e2\u003c/sup\u003e\u003csup\u003e,\u003c/sup\u003e with primary characterization of \u003csup\u003e143\u003c/sup\u003eNd/\u003csup\u003e144\u003c/sup\u003eNd. The DUPAL domain comprises 11 hotspots (Fig. 1): Tristan, Discovery, Samoa, Pitcairn, Meteor/Shona, Tasmantid, Kerguelen, Hawaii, San Felix, Societies and Amsterdam/St. Paul. The non-DUPAL domain comprises the remaining 23 hotspots. The geographic distribution of the DUPAL domain closely aligns with the distribution of the DUPAL hotspots reported by Hart\u003csup\u003e1\u003c/sup\u003e, who focused on the deviations of \u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb and \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb from the NHRL\u003csup\u003e1\u003c/sup\u003e and absolute values of \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRandom forest classifications of geochemical data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe random forest algorithm\u003csup\u003e23\u003c/sup\u003e is an ensemble learning algorithm that consists of multiple decision trees. Each decision tree starts at the root node and progresses toward the leaves. At each node, a split is made based on a single feature. This process continues until it reaches one of the leaf nodes at the top of the tree. Each decision tree predicts a class, and the class receiving the most votes from the decision trees becomes the model\u0026apos;s final prediction. A random forest repeatedly subsamples both the data and features to train decision trees\u003csup\u003e43,44\u003c/sup\u003e, which mitigates potential overfitting and enhances model generalizability.\u003c/p\u003e\n\u003cp\u003eFour random forest classifiers are constructed to test two dichotomies using two datasets: (a) classification between the LLSVPs using the DC20 dataset; (b) classification between the LLSVPs using the expanded dataset; (c) classification between the DUPAL and non-DUPAL domains using the DC20 dataset; and (d) classification between the DUPAL and non-DUPAL domains using the expanded dataset. The isotopic ratios include \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr, \u003csup\u003e143\u003c/sup\u003eNd/\u003csup\u003e144\u003c/sup\u003eNd, \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e207\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e208\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, \u003csup\u003e207\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb*.\u003c/p\u003e\n\u003cp\u003eTo avoid data leakage, we divide the training and test datasets at the geographical location level rather than into individual samples. That is, all samples from the same geographical location are either in the training set or in the test set. In each run, 70% of the locations are randomly selected for training, and the remaining 30% are used for testing. The number of locations for two classes remains equal during training and testing to ensure that the classification accuracy is not affected by imbalanced data. This procedure is repeated 1,000 times to determine the optimal hyperparameter pair (tree depth and forest size) for each classifier. The average accuracy and standard deviation of the four classifiers are calculated using the searched optimal tree depth and forest size: 6 and 95 for the LLSVP dichotomy using the DC20 dataset, 15 and 95 for the LLSVP dichotomy using the expanded dataset, 13 and 100 for the DUPAL dichotomy using the DC20 dataset, and 15 and 95 for the DUPAL dichotomy using the expanded dataset (Supplementary Fig. S11).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFeature importance of geochemical measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFeature importance, i.e., the relative importance of each isotopic ratio in classification, is evaluated by the Shapley value. The Shapley value is measured with the Shapley additive explanation approach\u003csup\u003e27,28\u003c/sup\u003e, which is defined as follows:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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width=\"689\" height=\"344\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData-driven decision boundaries for separating geochemical regimes\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo map the decision boundaries of the two dichotomies, we retrain the random forest classifiers with only the two most important isotopic ratios as inputs: \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb for the DUPAL dichotomy and\u003csup\u003e\u0026nbsp;87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* for the LLSVP dichotomy. The trained classifiers predict the possibilities of virtual grid points across the \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr-\u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb or \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr-\u003csup\u003e208\u003c/sup\u003ePb*/\u003csup\u003e206\u003c/sup\u003ePb* diagrams. These predicted possibilities are plotted as heatmaps. Each heatmap is generated from a random data split of training and testing sets. This process is repeated 1,000 times, and the decision boundary is the contour with a predicted probability of approximately 0.5 in the average heatmap.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4268316/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4268316/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGlobal geochemical zoning of the mantle provides critical constraints on Earth’s internal dynamics and evolutionary history. However, whether geochemical heterogeneities in the deep mantle are dominated by the hemispheric DUPAL anomaly\u003csup\u003e1,2\u003c/sup\u003e or by the two large low shear-wave velocity provinces (LLSVPs) has recently been debated\u003csup\u003e3\u003c/sup\u003e. Here, we employ machine learning to objectively assess the credibility of the two hypotheses on two different datasets of radiogenic isotopic records from global ocean island basalts. We observe discrepant classification accuracies for the LLSVP-based dichotomy and contradictory roles of the most characteristic \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr isotopic ratio in two different datasets where the hemispheric DUPAL dichotomy remains robust and consistent. The two most important isotopic ratios, i.e., \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr and \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb, effectively distinguish the austral and boreal domains to the same extent as all the isotopic ratios combined. This discovery concisely defines the DUPAL anomaly in the \u003csup\u003e87\u003c/sup\u003eSr/\u003csup\u003e86\u003c/sup\u003eSr - \u003csup\u003e206\u003c/sup\u003ePb/\u003csup\u003e204\u003c/sup\u003ePb diagram, which highlights the key role of the Enriched Mantle 1 (EM1) component. The importance of EM1 supports the historical large-scale mass transfer of lower continental crust into the deep mantle in the Southern Hemisphere and could be attributed to widespread lithospheric delamination caused by continental collisions during Gondwana amalgamation at ~600-500 Ma. These observations illustrate how machine learning from large geochemical datasets contributes to revealing robust patterns in heterogeneous and evolutionarily deep Earth.\u003c/p\u003e","manuscriptTitle":"Deciphering Earth’s deep mantle hemispheric geochemical dichotomy with machine learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-10 08:44:28","doi":"10.21203/rs.3.rs-4268316/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7b10f72f-8143-4c4d-8996-786fb8d97995","owner":[],"postedDate":"May 10th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":31728973,"name":"Earth and environmental sciences/Solid Earth sciences/Geochemistry"},{"id":31728974,"name":"Earth and environmental sciences/Solid Earth sciences/Geodynamics"}],"tags":[],"updatedAt":"2024-08-01T10:05:41+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-10 08:44:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4268316","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4268316","identity":"rs-4268316","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}