Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids

Wang, Feiyan; Morten, Jan Petter; Spitzer, Klaus

doi:10.1093/gji/ggy029

Cited by 43 publications

(7 citation statements)

References 53 publications

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“…It is a standard choice in the geo-electromagnetic induction community to minimise the above l 2 -norm variant of the cost function Q (Menke 2012;Aster et al 2012;Farquharson and Oldenburg 2004;Krakauer et al 2004;Schwarzbach and Haber 2013;Usui 2015;Mojica and Bassrei 2015;Jahandari and Farquharson 2017;Wang et al 2018a). However, it may be desirable to use general l p norms instead.…”

Section: Methods Of Model Analysismentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, mostsquares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important Extended author information available on the last page of the article applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitation...

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Section: Methods Of Model Analysismentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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“…Most of the recently published 3D TEM inversion methods are based on structured hexahedron grids for timedomain EM Ren et al, 2018). The inversions based on unstructured grids are generally for frequency-domain EM problems (Jahandari & Farquharson, 2017;Schwarzbach & Haber, 2013;Wang et al, 2018), except for Liu et al (2019), who proposed a 3D TEM inversion method based on unstructured grids. For the complex structure of spontaneous coal combustion areas, the unstructured grids can faithfully represent the complex geometry and hence result in higher forward modeling accuracy.…”

Section: Introductionmentioning

confidence: 99%

Detection of Coal Spontaneous Combustion Using the TEM Method: A Synthetic Study

Hui

Liu

Yin

et al. 2021

Pure Appl. Geophys.

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Spontaneous coal combustion is a serious hazard that affects mining safety. Since the coal seams are thin and their resistivity dramatically changes during spontaneous combustion, locating the burned cavities or caving zones using electromagnetic (EM) methods is challenging. The conventional transient electromagnetic (TEM) method with a loop transmitter is ineffective, as the main targets are mostly horizontal and resistive. We propose in this paper to apply TEM with an electrical source to detect the resistive targets of spontaneous coal combustion. Considering that its areas generally have very complex geometry, we adopt the unstructured finite-element method for accurate EM forward modeling. For the time discretization, we choose the unconditionally stable backward Euler scheme. Numerical experiments for typical spontaneous combustion models show the high sensitivity of TEM for an electrical source to the burned cavities, and based on this we further use the limited-memory BFGS method to do 3D inversions. To obtain high-resolution imaging results, we bound the resistivity based on the measurements to the coal mine. The inversion results show that the 3D TEM inversions can effectively recover the locations and resistivities of the burned cavities, implying TEM is a valid tool for detecting spontaneous coal combustion.

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“…Unstructured tetrahedral mesh can readily fit an undulating Earth surface and complex underground structures with fewer cells (Jahandari and Farquharson, 2018). It has been used increasingly widely in 3D electromagnetic modeling and inversions with the finite element method (Ren et al, 2013;Jahandari and Farquharson, 2018;Wang et al, 2018). Although the 3D joint inversion of MT and ZTEM data considering topography have not been well-studied to date, it is ideal for developing a robust 3D joint inversion MT and ZTEM data using the finite element method with unstructured tetrahedral grids.…”

Section: Introductionmentioning

confidence: 99%

3D joint inversion of airborne ZTEM and ground MT data using the finite element method with unstructured tetrahedral grids

et al. 2023

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As an airborne electromagnetic method induced by natural sources, the Z-axis tipper electromagnetic (ZTEM) system can primarily recover near-surface shallow structures, due to band-limited frequencies (usually 30–720 Hz) of the airborne survey and high sample rate acquisition along the terrain. In contrast, traditional ground magnetotellurics (MT) allows better recovery of deep structures as the data acquired are typical of large site intervals (usually higher than 1 km) and lower frequencies (usually lower than 400 Hz). High-resolution MT surveys allow for shallow small and deep large anomalies to be adequately interpreted but need large site intervals and broadband frequency range, which are seldom used as they are quite costly and laborious. ZTEM data are tippers that relate local vertical to orthogonal horizontal fields, measured at a reference station on the ground. As the 1D structures produce zero vertical magnetic fields, ZTEM is not sensitive to background resistivity. Thus, in general, ZTEM can only reveal relative resistivities and not real resistivities. A combination of the ZTEM and MT methods can be an effective technique, alleviating the shortcomings of the individual methods. At present, complex underground structures and topography introduce difficulties for data inversion and interpretation, as conventional ZTEM and MT forward modeling are generally used on structured grids with limited accuracy. To effectively recover complex underground structures with topography, we developed a 3D framework for joint MT and ZTEM inversion with unstructured tetrahedral grids. The finite element method is used for the forward problem because of its flexibility with unstructured tetrahedral meshes. The limited-memory quasi-Newton algorithm (L-BFGS) for optimization is used to solve the joint inverse problem, which saves memory and computational time by avoiding the explicit calculation of the Hessian matrix. To validate our joint inversion algorithm, we run numerical experiments on two synthetic models. The first synthetic model uses two conductive anomalous bodies of different sizes and depths. At the same time, a simple quadrangular is used for comparing the inversions with and without topography. In contrast, the second synthetic model represents a realistic topography with two different conductivities and the same depth. Both single-domain and joint inversions of the ZTEM and MT data are carried out for the two synthetic models to demonstrate the complementary advantages of joint inversion, while the second model is also used to test the adaptability of the joint inversion to complex topography. The results demonstrate the effectiveness of the finite element method with unstructured tetrahedral grids and the L-BFGS method for joint MT and ZTEM inversion. In addition, the inversion results prove that joint MT and ZTEM inversion can recover deep structures from the MT data and small near-surface structures from the ZTEM data by alleviating the weaknesses of the individual methods.

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Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids

Cited by 43 publications

References 53 publications

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Detection of Coal Spontaneous Combustion Using the TEM Method: A Synthetic Study

3D joint inversion of airborne ZTEM and ground MT data using the finite element method with unstructured tetrahedral grids

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