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<p>Three-dimensional gravity data inversion is an ill-posed and non-unique problem that requires effective regularization to obtain stable and geologically meaningful subsurface density models. Although sparse regularization methods based on Lp-norms enhance structural sharpness, fixed-norm approaches—particularly L<sub>1</sub>-norm regularization—often produce overly smooth or diffuse anomalies at depth due to the limited resolving power of gravity data. To address this limitation, we introduce a sensitivity-based adaptive L<sub>p</sub>-norm regularization framework for gravity inversion, implemented using an iterative reweighted least squares (IRLS) algorithm formulated in data space. The proposed approach spatially adapts the norm parameter <i>p</i> according to data sensitivity, which decreases with depth. Higher <i>p</i> values are assigned to shallow, well-constrained regions to promote smooth and stable solutions, while lower <i>p</i> values are assigned to deeper, weakly constrained regions to encourage sparsity, compactness, and sharper boundaries. This strategy is physically motivated and aims to counteract the inherent loss of resolution with depth, thereby reducing the tendency of conventional sparse norms to smear deep structures. Reformulating the IRLS algorithm in data space significantly improves computational efficiency by reducing memory requirements and computational cost, making the method well suited for large-scale three-dimensional inversions. The effectiveness of the method is demonstrated using two synthetic models of increasing complexity and a real airborne gravity gradiometer dataset from the chromite-bearing Black Thor Intrusive Complex in Ontario, Canada. Results show that the sensitivity-based adaptive L<sub>p</sub>-norm inversion consistently outperforms conventional L<sub>1</sub>-norm regularization in resolving deep bodies, producing sharper geometries, and geologically plausible depth extents while maintaining good data fits.</p>

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Sensitivity-based adaptive Lp-norm regularization for gravity data inversion in data space

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Mohammad Rezaie

摘要

Three-dimensional gravity data inversion is an ill-posed and non-unique problem that requires effective regularization to obtain stable and geologically meaningful subsurface density models. Although sparse regularization methods based on Lp-norms enhance structural sharpness, fixed-norm approaches—particularly L1-norm regularization—often produce overly smooth or diffuse anomalies at depth due to the limited resolving power of gravity data. To address this limitation, we introduce a sensitivity-based adaptive Lp-norm regularization framework for gravity inversion, implemented using an iterative reweighted least squares (IRLS) algorithm formulated in data space. The proposed approach spatially adapts the norm parameter p according to data sensitivity, which decreases with depth. Higher p values are assigned to shallow, well-constrained regions to promote smooth and stable solutions, while lower p values are assigned to deeper, weakly constrained regions to encourage sparsity, compactness, and sharper boundaries. This strategy is physically motivated and aims to counteract the inherent loss of resolution with depth, thereby reducing the tendency of conventional sparse norms to smear deep structures. Reformulating the IRLS algorithm in data space significantly improves computational efficiency by reducing memory requirements and computational cost, making the method well suited for large-scale three-dimensional inversions. The effectiveness of the method is demonstrated using two synthetic models of increasing complexity and a real airborne gravity gradiometer dataset from the chromite-bearing Black Thor Intrusive Complex in Ontario, Canada. Results show that the sensitivity-based adaptive Lp-norm inversion consistently outperforms conventional L1-norm regularization in resolving deep bodies, producing sharper geometries, and geologically plausible depth extents while maintaining good data fits.