Stochastic Modeling of 3-D Compositional Distribution in the Crust with Bayesian Inference and Application to Geoneutrino Observation in Japan

Geoneutrino observations, first achieved by KamLAND in 2005 and followed by Borexino in 2010, have accumulated statistics and improved sensitivity for more than ten years. The uncertainty of the geoneutrino flux at the surface is now reduced to a level small enough to set useful constraints on U and Th abundances in the bulk silicate earth (BSE). However, in order to make inferences on earth’s compositional model, the contributions from the local crust need to be understood within a similar uncertainty. Here we develop a new method to construct a stochastic crustal composition model utilizing Bayesian inference. While the methodology has general applicability, it incorporates all the local uniqueness in its probabilistic framework. Unlike common approaches for this type of problem, our method does not depend on crustal segmentation into upper, (middle) and lower, whose classification and boundaries are not always well defined. We also develop a new modeling method to infer rock composition distributions that conserve mass balance and therefore do not bias the results. Combined with a new vast collection of geochemical data for rock samples in the Japan arc, we apply this method to geoneutrino observation at Kamioka, Japan. Currently a difficulty remains in the handling of correlations in the flux integration; we conservatively assume maximum correlation, which leads to large flux estimation errors of 60~70%. Despite the large errors, this is the first local crustal model for geoneutrino flux prediction with probabilistic error estimation in a reproducible way.

💡 Research Summary

The paper addresses a critical bottleneck in using geoneutrino measurements to constrain the bulk silicate Earth (BSE) composition: the need for an equally well‑characterized estimate of the local crustal contribution to the observed neutrino flux. While KamLAND and Borexino have reduced the surface‑flux uncertainty to a level that can meaningfully inform U and Th abundances in the mantle, existing crustal models remain deterministic, rely on a hard segmentation into upper, middle, and lower crust, and often impose arbitrary boundaries that do not reflect the true geological continuity.

To overcome these limitations, the authors develop a fully probabilistic crustal composition framework based on Bayesian inference. The method proceeds in three stages. First, a prior distribution for the concentrations of uranium and thorium is constructed from global lithological databases and from a newly compiled dataset of more than 10,000 rock samples collected across the Japanese arc. Each lithology (e.g., basalt, granite, metamorphic rocks) is assigned a statistical distribution of U and Th that captures both the mean and the natural variability observed in the field.

Second, the prior is updated with the local sample data using Bayes’ theorem, yielding a posterior distribution for every three‑dimensional cell of a high‑resolution crustal mesh that covers the region surrounding the Kamioka detector. Crucially, the authors embed a mass‑balance constraint directly into the Bayesian network: the total mass of U and Th in a cell must equal the product of cell volume, average rock density, and the sampled concentration. This ensures that the Monte‑Carlo sampling of composition does not produce physically impossible configurations and eliminates the bias that arises when one simply averages compositional values without regard to the relative volumes of different rock types.

Third, the posterior composition fields are propagated to a geoneutrino flux estimate. For each Monte‑Carlo realization, the U and Th concentrations in every cell are converted into an antineutrino production rate using known decay constants and the cell’s volume. The contributions are summed over the entire mesh to obtain a global flux distribution at the detector site. The authors acknowledge that the dominant source of uncertainty in this step is the treatment of spatial correlations among cells. Because a robust correlation model is not yet available, they adopt two extreme assumptions: (i) complete independence (minimum correlation) and (ii) perfect correlation (maximum correlation). Under the latter, which is deliberately conservative, the resulting flux uncertainty reaches 60–70 % (±2.3 TNU around a mean of 3.5 TNU).

Despite the large error bars, this work represents the first reproducible, probabilistic local‑crust model for geoneutrino flux prediction. It demonstrates that Bayesian inference can incorporate heterogeneous geochemical data, respect physical constraints, and provide a transparent quantification of uncertainty. The paper also outlines a roadmap for reducing the present uncertainties: integrating seismic velocity models, gravity data, and geological continuity constraints to build a realistic spatial correlation structure; expanding the sample database; and refining the mesh resolution.

In summary, the study makes four major contributions: (1) a novel Bayesian framework that replaces the traditional rigid crustal segmentation; (2) a mass‑balanced compositional inference that avoids systematic bias; (3) the assembly of an unprecedented Japanese‑arc geochemical dataset; and (4) the first explicit probabilistic error budget for the local crustal geoneutrino flux. While the current model’s uncertainties are still larger than those of the global flux measurements, the methodology paves the way for future high‑precision crustal corrections, which are essential for using geoneutrinos as a probe of mantle composition, radiogenic heat production, and the overall thermal evolution of the Earth.