Recovering sparse models in 3D potential‐field inversion without bound dependence or staircasing problems using a mixed L p ‐norm regularization

In potential-field inversion, careful management of singular value decomposition components is crucial for obtaining information about the source distribution with respect to depth. In principle, the depth-resolution plot provides a convenient visual tool for this analysis, but its computational complexity has hitherto prevented application to large-scale problems. To analyze depth resolution in such problems, we developed a variant ApproxDRP, which is based on an iterative algorithm and therefore suited for large-scale problems because we avoid matrix factorizations and the associated demands on memory and computing time. We used the ApproxDRP to study retrievable depth resolution in inversion of the gravity field of the Neapolitan Volcanic Area. Our main contribution is the combined use of the Lanczos bidiagonalization algorithm, established in the scientific computing community, and the depth-resolution plot defined in the geoscience community.

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3-D POTENTIAL FIELD INVERSION OF CAMP CLUBHOUSE CROSSROADS MAFIC INTRUSIVE PLUTON, COASTAL PLAIN, SOUTH CAROLINA

10.1130/abs/2019se-327325 ◽

2019 ◽

Author(s):

Kubra Sibel Albayrak ◽

◽

James N. Kellogg

Keyword(s):

South Carolina ◽

Coastal Plain ◽

Potential Field ◽

Field Inversion

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Uncertainty analysis of 3D potential-field deterministic inversion using mixed Lp norms

Geophysics ◽

10.1190/geo2020-0672.1 ◽

2021 ◽

pp. 1-103

Author(s):

Xiaolong Wei ◽

Jiajia Sun

Keyword(s):

Uncertainty Analysis ◽

Potential Field ◽

Physical Property ◽

Uniqueness Problem ◽

Data Set ◽

Regularization Term ◽

Lp Norm ◽

Box Plots ◽

Model Features ◽

Field Inversion

The non-uniqueness problem in geophysical inversion, especially potential-field inversion, is widely recognized. It is argued that uncertainty analysis of a recovered model should be as important as finding an optimal model. However, quantifying uncertainty still remains challenging, especially for 3D inversions in both deterministic and Bayesian frameworks. Our objective is to develop an efficient method to empirically quantify the uncertainty of the physical property models recovered from 3D potential-field inversion. We worked in a deterministic framework where an objective function consisting of a data misfit term and a regularization term is minimized. We performed inversions using a mixed Lp-norm formulation where various combinations of L p (0 <= p <= 2) norms can be implemented on different components of the regularization term. Specifically, we randomly sampled the p-norm values in multiple times, and generated a large and diverse sequence of physical property models that all reproduce the observed geophysical data equally well. This suite of models offers practical insights into the uncertainty of the recovered model features. We quantified the uncertainty through calculation of standard deviations and interquartile range, as well as visualizations in box plots and histograms. The numerical results for a realistic synthetic density model created based on a ring-shaped igneous intrusive body quantitatively illustrate uncertainty reduction due to different amounts of prior information imposed on inversions. We also applied the method to a field data set over the Decorah area in the northeastern Iowa. We adopted an acceptance-rejection strategy to generate 31 equivalent models based on which the uncertainties of the inverted models as well as the volume and mass estimates are quantified.

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