A new stabilizing functional to enhance the sharp boundary in potential field regularized inversion

Zhao, Chongjin; Yu, Peng; Zhang, Luolei

doi:10.1016/j.jappgeo.2016.10.033

Cited by 26 publications

(8 citation statements)

References 22 publications

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“…However, the result obtained by using a focusing stabilizing functional highly depends on the right choice of the focusing parameter. Zhao et al (2016) have introduced exponential stabilizer which doesn't need the focusing parameter.…”

Section: Introductionmentioning

confidence: 99%

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Zvara

Pašteka

Karcol

2021

Contrib. Geophys. Geod.

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Interpretation and inversion of microgravity anomalies belong to important tasks of near-surface geophysics, mostly in cavities detection in engineering, environmental and archaeological applications. One of the mostly used concepts of inversion in applied gravimetry is based on the approximation of the model space by means of 2D or 3D elementary sources with the aim to estimate their densities by means of the solution of a corresponding linear equation system. There were published several approaches trying to obtain correct and realistic results, which describe real parameters of the sources. In the proposed contribution we analyse the properties of two additional functionals, which describe additional properties of the searched solution – namely so-called L2-smoothing and minimum support focusing stabilizers. For the inversion itself, we have used the regularized conjugate gradient method. We have studied properties of these two stabilizers in the case of one synthetic model and one real-world dataset (microgravity data from St. Nicholas church in Trnava). Results have shown that proposed algorithm with the minimum support stabilizer can generate satisfactory model results, from which we can describe real geometry, dimensions and physical properties of interpreted cavities.

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Section: Introductionmentioning

confidence: 99%

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Zvara

Pašteka

Karcol

2021

Contrib. Geophys. Geod.

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“…For the Tikhonov regularization method, the data misfit term is responsible for fitting the observed data with predicted data for a given model, and the model misfit term is related to the structural characteristics of the model, which is also called the regularization term. The regularization term contains a priori information about the basic properties of the targets in the inversion, which means that the regularization term has a significant influence on the inversion result [9]. Thus, various regularization terms are provided for different types of models.…”

Section: Introductionmentioning

confidence: 99%

“…The MS and MGS are quasi L 0 -norm-type regularization methods, which means that they are often not convex, resulting in several local extrema and complicating the minimization of the Tikhonov parametric function [21]. Zhao proposed an exponential function-based regularization method that avoids selecting the focusing factor, which yields a performance similar to that of MS regularization [9]. Hybrid methods combining different L p -norms have been investigated in various publications, which can adopt their advantages and avoid their shortcomings.…”

Section: Introductionmentioning

confidence: 99%

Undersea Target Reconstruction Based on Coupled Laplacian-of-Gaussian and Minimum Gradient Support Regularizations

Shang

Xue

et al. 2019

IEEE Access

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In this paper, a novel inversion method is proposed to recover the sharp boundary of blocky targets buried beneath the seabed with conductivities different from that of the background environment. This method is implemented by combining the Laplacian-of-Gaussian (LoG) function with minimum gradient support (MGS) regularization. A two-stage inversion strategy is introduced to obtain stable and sharp boundary inversion results. We first use the LoG operator in 3D space to obtain the profile of the target and then switch to LoG-MGS coupled regularized inversion to obtain the sharp boundary of the target. It is crucial to choose an appropriate regularization parameter adjustment strategy. We use a bounded function to adjust the regularization parameters during the inversion, which can balance the observation information and the a priori information in a reasonable interval. Theoretical analysis and numerical simulations are conducted and the recovered results demonstrate that the proposed inversion method has a better performance in recovering blocky targets than canonical regularization terms. INDEX TERMS Block targets, inversion, sharp boundary, LoG-MGS coupled regularization.

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“…The second category of the stabilizing functions belongs to a class of functions that produce solutions with focused images (e.g. Last and Kubik ; Barbosa and Silva ; Portniaguine and Zhdanov ; Camacho, Montesinos and Vieira ; Bertete‐Aguirre, Cherkaev and Oristaglio ; Pilkington ; Zhao, Yu and Zhang ; Xiang et al . ; Meng ; Meng et al .…”

Section: Introductionmentioning

confidence: 99%

“…The second category of the stabilizing functions belongs to a class of functions that produce solutions with focused images (e.g. Last and Kubik 1983;Barbosa and Silva 1994;Portniaguine and Zhdanov 1999;Camacho, Montesinos and Vieira 2000;Bertete-Aguirre, Cherkaev and Oristaglio 2002;Pilkington 2009;Zhao, Yu and Zhang 2016;Xiang et al 2017;Meng 2018;Meng et al 2018). However, one of the most popular stabilizing functions for non-smooth inversion of geophysical data is minimum support (MS) stabilizing function which was used by different researchers (e.g.…”

Section: Introductionmentioning

confidence: 99%

A sigmoid stabilizing function for fast sparse 3D inversion of magnetic data

Rezaie

2019

Near Surface Geophysics

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An interesting geological objective of quantitative interpretation of magnetic data is to find inverse models which can determine sharp geological interfaces below the surface. The stabilizing function in the Tikhonov parametric functional governs sparseness constraint in the recovered model. This paper introduces a novel stabilizer based on a sigmoid function which can provide non‐smooth models in the inversion of magnetic data efficiently. An inversion algorithm is developed based on the reweighted regularized conjugate gradient to get the solution of the inverse problem using this stabilizing function. The performance of the proposed algorithm is checked on two synthetic data sets and real aeromagnetic data from McFaulds Lake in Ontario, Canada, in comparison with the results of the minimum support stabilizing function. The inverse problem converges to the solution faster when the sigmoid stabilizing function is used instead of the minimum support stabilizing function.

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A new stabilizing functional to enhance the sharp boundary in potential field regularized inversion

Cited by 26 publications

References 22 publications

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Density inversion of selected microgravity anomalies using L2-smoothing and minimum support focusing stabilizers

Undersea Target Reconstruction Based on Coupled Laplacian-of-Gaussian and Minimum Gradient Support Regularizations

A sigmoid stabilizing function for fast sparse 3D inversion of magnetic data

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