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<p>Three-dimensional inversion of gravity data plays a fundamental role in subsurface imaging for mineral exploration, geothermal assessment, and tectonic studies, yet it remains a challenging ill-posed problem plagued by non-uniqueness, rapid sensitivity decay with depth, and sensitivity to noise. To overcome these limitations, we present a novel variational Bayesian (VB) framework that accommodates both isotropic and anisotropic Total Variation (TV) regularization as separate prior options within a fully hierarchical probabilistic setting. The non-quadratic TV prior is approximated as a Gaussian scale mixture using iteratively reweighted least-squares surrogates, enabling mean-field variational inference to jointly recover the subsurface density model, noise precision, and regularization strength without manual tuning. Stochastic Hutchinson trace estimation and matrix-free preconditioned conjugate-gradient solvers ensure computational tractability for large grids, while voxel-wise posterior variances provide approximate uncertainty maps directly from the variational approximation. Synthetic experiments on a dipping dyke and two buried prisms demonstrate that the algorithm accurately reconstructs sharp geological boundaries, with isotropic TV producing rotationally invariant dipping structures and anisotropic TV yielding distinctly blockier, axis-aligned features. Both variants achieve excellent data fits within the 5% noise level and correctly map higher uncertainty at depth and along anomaly edges, with anisotropic TV delivering lower and more localized standard deviations. Application to real gravity data from the Health Steele massive sulfide deposit (New Brunswick, Canada) successfully images the southwest-dipping ore body and associated gabbro intrusions, consistent with known geology, while highlighting well-resolved high-confidence zones suitable for targeted exploration. The proposed VB-TV approach unifies edge-preserving regularization, automatic hyperparameter learning, and practical uncertainty quantification, offering a practical and scalable alternative to classical deterministic and smooth-prior Bayesian methods for potential-field interpretation. The uncertainty maps also can reduce exploration risks.</p>

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A variational bayesian method for 3D inversion of gravity data with total variation regularization

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • Mohammad Rezaie

摘要

Three-dimensional inversion of gravity data plays a fundamental role in subsurface imaging for mineral exploration, geothermal assessment, and tectonic studies, yet it remains a challenging ill-posed problem plagued by non-uniqueness, rapid sensitivity decay with depth, and sensitivity to noise. To overcome these limitations, we present a novel variational Bayesian (VB) framework that accommodates both isotropic and anisotropic Total Variation (TV) regularization as separate prior options within a fully hierarchical probabilistic setting. The non-quadratic TV prior is approximated as a Gaussian scale mixture using iteratively reweighted least-squares surrogates, enabling mean-field variational inference to jointly recover the subsurface density model, noise precision, and regularization strength without manual tuning. Stochastic Hutchinson trace estimation and matrix-free preconditioned conjugate-gradient solvers ensure computational tractability for large grids, while voxel-wise posterior variances provide approximate uncertainty maps directly from the variational approximation. Synthetic experiments on a dipping dyke and two buried prisms demonstrate that the algorithm accurately reconstructs sharp geological boundaries, with isotropic TV producing rotationally invariant dipping structures and anisotropic TV yielding distinctly blockier, axis-aligned features. Both variants achieve excellent data fits within the 5% noise level and correctly map higher uncertainty at depth and along anomaly edges, with anisotropic TV delivering lower and more localized standard deviations. Application to real gravity data from the Health Steele massive sulfide deposit (New Brunswick, Canada) successfully images the southwest-dipping ore body and associated gabbro intrusions, consistent with known geology, while highlighting well-resolved high-confidence zones suitable for targeted exploration. The proposed VB-TV approach unifies edge-preserving regularization, automatic hyperparameter learning, and practical uncertainty quantification, offering a practical and scalable alternative to classical deterministic and smooth-prior Bayesian methods for potential-field interpretation. The uncertainty maps also can reduce exploration risks.