Location of Magnetic Dipoles in Chongcho Lake, Republic of Korea: An Application of the SOAPFI (Shape‐of‐Anomaly Potential Field Inversion) Program

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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Analysis of depth resolution in potential-field inversion

Geophysics ◽

10.1190/1.2122408 ◽

2005 ◽

Vol 70 (6) ◽

pp. A1-A11 ◽

Cited By ~ 53

Author(s):

Maurizio Fedi ◽

Per Christian Hansen ◽

Valeria Paoletti

Keyword(s):

Potential Field ◽

Real Data ◽

Depth Resolution ◽

Careful Study ◽

Piecewise Constant ◽

Data Errors ◽

Damped Least Squares ◽

Value Decomposition ◽

The Given ◽

Field Inversion

We study the inversion of potential fields and evaluate the degree of depth resolution achievable for a given problem. To this end, we introduce a powerful new tool: the depth-resolution plot (DRP). The DRP allows a theoretical study of how much the depth resolution in a potential-field inversion is influenced by the way the problem is discretized and regularized. The DRP also allows a careful study of the influence of various kinds of ambiguities, such as those from data errors or of a purely algebraic nature. The achievable depth resolution is related to the given discretization, regularization, and data noise level. We compute DRP by means of singular-value decomposition (SVD) or its generalization (GSVD), depending on the particular regularization method chosen. To illustrate the use of the DRP, we assume a source volume of specified depth and horizontal extent in which the solution is piecewise constant within a 3D grid of blocks. We consider various linear regularization terms in a Tikhonov (damped least-squares) formulation, some based on using higher-order derivatives in the objective function. DRPs are illustrated for both synthetic and real data. Our analysis shows that if the algebraic ambiguity is not too large and a suitable smoothing norm is used, some depth resolution can be obtained without resorting to any subjective choice of depth weighting.

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