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Effectiveness of Neural Kriging for Three-Dimensional Modeling of Sparse and Strongly Biased Distribution of Geological Data with Application to Seafloor Hydrothermal Mineralization


Three-dimensional modeling of geoscientific data of limited amounts and strongly biased locations is difficult and impractical using almost any method. To obtain a correct spatial model from data under such constraints, this study systematically demonstrated the effectiveness of neural kriging (NK), which is based on a deep neural network (DNN) with a semivariogram learning criterion. As a novel case study of resource geology, NK was applied to clarify the three-dimensional deposit structure of an active seafloor hydrothermal vent area, Izena Hole in the middle Okinawa Trough, using Cu, Zn, Pb, Ag, and Ba content data, geological columns, and resistivity data from drill core samples obtained at six drill sites aligned nearly E–W and two drill sites far from these six. Two high-content zones clearly appeared for all five elements, in the sulfide mound and underlying sediment, and about 30 m below the seafloor as a stratiform shape. Advantages of NK were demonstrated as follows. The NK results showed the locations of these high-content zones and their horizontal extent along the pathway of hydrothermal fluids more clearly than the result of typical geostatistical simulation, turning bands simulation (TBS), by enabling content estimations even in areas without data. NK also estimated the uppermost high-content zones more accurately than the ordinal DNN methods or TBS. Next, NK was tested for a region 20 times wider than the first target, and the resultant Cu and Zn content models showed indistinct horizontal linear features and vertical continuity, which may have been caused by the fault structure and small amounts of metal precipitation in the deep part, respectively. Thus, one advantage of NK is that its spatial model can contribute to constructing hypotheses of transport and enrichment mechanisms of target metals.

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This work was financially supported by the Cross-ministerial Strategic Innovation Promotion Program (SIP). Sincere thanks are extended to two anonymous reviewers for essential and constructive comments and suggestions that improved the clarity of this manuscript.

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All authors contributed to the study conception and design. Material preparation and data collection were performed by TN, YT and SK, and data analysis and spatial modeling were performed by KK, OY, VRS and SAT. The first draft of the manuscript was written by KK and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Katsuaki Koike.

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The authors declare that they have no competing interests.

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Koike, K., Yono, O., de Sá, V.R. et al. Effectiveness of Neural Kriging for Three-Dimensional Modeling of Sparse and Strongly Biased Distribution of Geological Data with Application to Seafloor Hydrothermal Mineralization. Math Geosci 54, 1183–1206 (2022).

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  • Deep neural network
  • Learning criterion
  • Semivariogram
  • Metal content
  • Turning bands simulation
  • Seafloor hydrothermal deposit