| Citation: | Dazheng Huang, Renguang Zuo, Jian Wang, Raimon Tolosana-Delgado. Spatially Constrained Variational Autoencoder for Geochemical Data Denoising and Uncertainty Quantification. Journal of Earth Science, 2025, 36(5): 2317-2336. doi: 10.1007/s12583-025-0180-y
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Geochemical survey data are essential across Earth Science disciplines but are often affected by noise, which can obscure important geological signals and compromise subsequent prediction and interpretation. Quantifying prediction uncertainty is hence crucial for robust geoscientific decision-making. This study proposes a novel deep learning framework, the Spatially Constrained Variational Autoencoder (SC-VAE), for denoising geochemical survey data with integrated uncertainty quantification. The SC-VAE incorporates spatial regularization, which enforces spatial coherence by modeling inter-sample relationships directly within the latent space. The performance of the SC-VAE was systematically evaluated against a standard Variational Autoencoder (VAE) using geochemical data from the gold polymetallic district in the northwestern part of Sichuan Province, China. Both models were optimized using Bayesian optimization, with objective functions specifically designed to maintain essential geostatistical characteristics. Evaluation metrics include variogram analysis, quantitative measures of spatial interpolation accuracy, visual assessment of denoised maps, and statistical analysis of data distributions, as well as decomposition of uncertainties. Results show that the SC-VAE achieves superior noise suppression and better preservation of spatial structure compared to the standard VAE, as demonstrated by a significant reduction in the variogram nugget effect and an increased partial sill. The SC-VAE produces denoised maps with clearer anomaly delineation and more regularized data distributions, effectively mitigating outliers and reducing kurtosis. Additionally, it delivers improved interpolation accuracy and spatially explicit uncertainty estimates, facilitating more reliable and interpretable assessments of prediction confidence. The SC-VAE framework thus provides a robust, geostatistically informed solution for enhancing the quality and interpretability of geochemical data, with broad applicability in mineral exploration, environmental geochemistry, and other Earth Science domains.
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