Smoothest Model and Sharp Boundary Based Two‐Dimensional Magnetotelluric Inversion

Zhang, Luolei; Yu, Peng; Wang, Jialin; Wu, Jiansheng

doi:10.1002/cjg2.1461

Cited by 16 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zhdanov (2009) also applied the MGS functional to invert gravity and EM data. Zhang et al (2009Zhang et al ( , 2010 used this theory to invert 2-D MT data and obtain clear images of geo-electrical interfaces.…”

Section: -D Mt Inversion With Minimum Gradient Support 297mentioning

confidence: 99%

“…These algorithms provide smooth solutions, but few are suitable for clearly imaging geo-electrical interfaces. Zhang et al (2009Zhang et al ( , 2010 used this theory to invert 2-D MT data and obtain clear images of geo-electrical interfaces. Portniaguine & Zhdanov (1999, 2002 proposed a focusing geophysical inversion using the minimum gradient support (MGS) functional and used the MGS functional in gravity and magnetic inversion (Zhdanov et al 2004).…”

mentioning

confidence: 99%

See 1 more Smart Citation

A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint

Zhang¹,

Koyama²,

Utada³

et al. 2012

Geophysical Journal International

Self Cite

View full text Add to dashboard Cite

SUMMARY Most 3‐D magnetotelluric (MT) inversions are classified as a regularized inversion with a smoothness constraint. These inverse algorithms provide smooth solutions but cannot clearly image sharp geo‐electrical interfaces. In this paper, we introduce the minimum gradient support (MGS) functional to regularize the 3‐D MT inverse problem. This functional has a property whereby the functional seeks a structure with minimum volume containing large conductivity gradients. Therefore, the MGS functional can be used to search for a model with a sharp boundary. We apply the MGS functional to 3‐D MT inversion to obtain a clear and accurate image of geo‐electrical interfaces. In addition, the modified scattering equation approach introduced in the modified iterative dissipative method (MIDM) is applied to forward calculation, which is based on integral equation (IE) formulation and allows us to efficiently reduce the time required for forward calculation with high accuracy. The quasi‐Newton iterative method is used to optimize the objective functional. It is a kind of iterative method with simplified calculation of the inverse Hessian matrix using Broyden–Fletcher–Goldfarb–Shanno (BFGS) update. The convergence of this iterative method is guaranteed with inexact line searches. We also modify the adaptive approach for optimum selection of the regularization parameter so as to fit the inverse algorithm of this study. Three synthetic models are investigated, and the obtained results are compared with those obtained by a smoothing inversion. Based on the comparison, we confirm that the MGS inversion can provide higher resolution when geo‐electrical interfaces are sharp. This property will help us to determine reliable electrical structures by the MT exploration method.

show abstract

Section: -D Mt Inversion With Minimum Gradient Support 297mentioning

confidence: 99%

mentioning

confidence: 99%

A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint

Zhang¹,

Koyama²,

Utada³

et al. 2012

Geophysical Journal International

Self Cite

View full text Add to dashboard Cite

show abstract

“…7a, b). The 2D wedge model configuration is the same as that used by de Groot-Hedlin and Constable (2004) and Zhang et al (2009). The upper boundary of the wedge has a slope of 5.7°, and the lower boundary has a slope of 16.6°.…”

Section: Two-dimensional Wedge Modelmentioning

confidence: 99%

“…However, it needs to build a layered model to invert both resistivity and thickness of each layer for every horizontal mesh, which is very complicated in the model construction and inversion calculation. Meanwhile, Zhang et al (2009Zhang et al ( , 2010 added diagonal gradient support to the objective functional, which consists of both smoothing and focusing constraints, and obtained better inversion results in imaging an inclined geoelectrical interface. Recently, Grayver and Kuvshinov (2016) applied arbitrary norms for residual and regularization terms to produce classes of equivalent solutions of smooth or compact models, in which a L 1.5 norm was shown to be most efficient for a stable inversion with sharp boundary.…”

Section: Introductionmentioning

confidence: 99%

Regularized magnetotelluric inversion based on a minimum support gradient stabilizing functional

Xiang

Zhang

et al. 2017

Earth Planets Space

Self Cite

View full text Add to dashboard Cite

Regularization is used to solve the ill-posed problem of magnetotelluric inversion usually by adding a stabilizing functional to the objective functional that allows us to obtain a stable solution. Among a number of possible stabilizing functionals, smoothing constraints are most commonly used, which produce spatially smooth inversion results. However, in some cases, the focused imaging of a sharp electrical boundary is necessary. Although past works have proposed functionals that may be suitable for the imaging of a sharp boundary, such as minimum support and minimum gradient support (MGS) functionals, they involve some difficulties and limitations in practice. In this paper, we propose a minimum support gradient (MSG) stabilizing functional as another possible choice of focusing stabilizer. In this approach, we calculate the gradient of the model stabilizing functional of the minimum support, which affects both the stability and the sharp boundary focus of the inversion. We then apply the discrete weighted matrix form of each stabilizing functional to build a unified form of the objective functional, allowing us to perform a regularized inversion with variety of stabilizing functionals in the same framework. By comparing the one-dimensional and twodimensional synthetic inversion results obtained using the MSG stabilizing functional and those obtained using other stabilizing functionals, we demonstrate that the MSG results are not only capable of clearly imaging a sharp geoelectrical interface but also quite stable and robust. Overall good performance in terms of both data fitting and model recovery suggests that this stabilizing functional is effective and useful in practical applications.

show abstract

“…Algorithms with better fitting performance have smaller errors. For example, the MODEM inversion method has poor boundary convergence, while the Bayesian 2D inversion method performs well in boundary inversion [ 20 , 21 ]. However, many inversion algorithms, including machine learning algorithms, may have errors to varying degrees [ 22 , 23 ].…”

Section: Introductionmentioning

confidence: 99%

Study on the shielding effect of low resistance body when using transient electromagnetic to detect urban underground space

An,

Yong,

Liu

et al. 2023

PLoS ONE

View full text Add to dashboard Cite

Transient electromagnetic Method (TEM) is an efficient geophysical detection technology suitable for detection of urban near-surface space. However, its detection results are well affected by the low resistance anomaly, which interferes with the interpretation of the inversion results. This article used finite element method to simulate the entire process of urban underground pipeline under TEM detection. The causes of interference and the degree of interference under different working conditions were analyzed. The results demonstrate that low resistance anomaly in magnetic field will caused electromagnetic energy absorption and resulting eddy current losses, which lead to a distortion of the primary magnetic field in the vicinity of the pipeline, and formation of a weak field zone beneath the pipeline. The size and shape of the shielding zone are affected by burial depth, transmitter coil diameter, and anomaly size. When the burial depth exceeds 10 times the diameter of the coil or pipeline, the shielding range stabilizes at 1.5–2 times the pipeline’s transverse diameter. Moreover, when the pipeline’s transverse diameter exceeds twice the transmitter coil diameter, the weak field zone beneath the pipeline will transform into a strong field zone, this is due to the refractive and reflective effects of the electromagnetic field. Finally, experiments were conducted and the inverted results was found to be larger than the actual pipeline diameter, with an error margin similar to that explained by the simulation. These results have implications for high accuracy detecting underground pipelines in urban areas.

show abstract

Smoothest Model and Sharp Boundary Based Two‐Dimensional Magnetotelluric Inversion

Cited by 16 publications

References 21 publications

A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint

A regularized three-dimensional magnetotelluric inversion with a minimum gradient support constraint

Regularized magnetotelluric inversion based on a minimum support gradient stabilizing functional

Study on the shielding effect of low resistance body when using transient electromagnetic to detect urban underground space

Contact Info

Product

Resources

About