Non-parametric simulation of spatially varying geo-data from sparse measurements by the tree-structured wavelet-based Bayesian compressive sensing

Huafu Pei, Fanhua Meng and Na You

Reliability Engineering and System Safety, 2025, vol. 264, issue PA

Abstract: Direct interpretation of spatially varying geotechnical properties from sparse in-situ measurements presents a significant challenge, yet remains critical for stochastic analysis of geological systems. While conventional random field (RF) theory and Kriging techniques offer theoretical foundations, Bayesian compressive sensing (BCS) has gained prominence in site characterization due to its data-driven nature and statistical uncertainty quantification capabilities. This study pioneers the integration of a hierarchical tree structure into wavelet-based BCS, effectively addressing the oversimplified independence assumption of wavelet coefficients in existing BCS for geo-data interpolation, thereby fundamentally advancing reconstruction fidelity. A Bayesian inference framework that considers the tree structure in the Markov Chain Monte Carlo (MCMC) is proposed in detail, establishing an innovative Tree-Structured BCS (TS-BCS) paradigm. The proposed framework has been rigorously validated on diverse datasets, including the synthetic undrained shear strength, real-life soil electrical conductivity, and cone penetration test data, in both randomly distributed sampling schemes and borehole‑aligned linear configurations. Evaluation results demonstrate that the TS-BCS gives consistent robustness of superior reconstruction accuracy, refined uncertainty quantification, and enhanced estimation of spatial autocorrelation structures compared to conventional BCS methods through explicitly encoding the statistical dependencies among wavelet coefficients as domain-specific regularization.

Keywords: Discrete wavelet transform; Tree structure; Gibbs sampling; Data-driven method; Spatially varying geo-data; Sparse measurements (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:264:y:2025:i:pa:s0951832025004831

DOI: 10.1016/j.ress.2025.111282

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