Three-dimensional em modeling

Hohmann, Gerald W.

doi:10.1007/bf01453994

Cited by 66 publications

(14 citation statements)

References 25 publications

(28 reference statements)

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“…The numerical observations of the effects of current perturbations due to 3D bodies are growing as workers consider models of greater and greater complexity. Fortunately, the subject of electromagnetic induction in 3D structures has already been reviewed at an earlier workshop (Hewson-Browne and Kendal, 1977), and there is a complete session on it at this one (Hohmann, 1983). Hence, I will merely pick out some of the interesting results of numerical modelling that shed light on the problem of current channelling.…”

Section: Za(co ) = At(o)) Ha(co ) ~-L~'(co) Oa(co ) 3ff ~mentioning

confidence: 96%

The problem of current channelling: A critical review

Jones

1983

Geophysical Surveys

146

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Abstract. The notion that currents induced 'elsewhere', by external source fields, could wend their way in a frequency-independent ohmic-like manner through a region of interest has been the cause of many recent disputes within the geomagnetic induction community. In particular, two-dimensional (2D) models of the Rhinegraben, and of the region known as the 'Eskdalemuir anomaly' in southern Scotland, have been dismissed as erroneous by those who believe that the observations are more correctly interpreted as due to the effects of 'channelled' currents rather than 'induced' currents. In this review, attention is paid primarily to consider under what circumstances any perturbation of current flow, which may manifest itself as a 'DC-like' channelled current, could cause a 'problem' for those wishing to interpret their observations. Various concepts are introduced, particularly the ratio of 3D/2D current channelling numbers for the induction problem, which is shown to be the ratio of the length of the 3D body to the skin depth in the host medium. It is stressed that the worker must analyse his data by adequate statistical techniques, and that the simplest physical models possible, that describes the observations, must be sought. Finally, suggestions are made for further work to be undertaken.

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Section: Za(co ) = At(o)) Ha(co ) ~-L~'(co) Oa(co ) 3ff ~mentioning

confidence: 96%

The problem of current channelling: A critical review

Jones

1983

Geophysical Surveys

146

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“…The comparisons of our numerical results and their results are shown in the Appendix of Chen and Fung (1988). Another comparison for Hohmann's model (Hohmann, 1983) has also been carried out (Chen and Fung, 1989), and in that model the conductivity contrast is 200. All the results obtained by different methods agree well for the most part of the response curves.…”

Section: The 3-d Finite Difference Methodsmentioning

confidence: 94%

Comment on “EM induction in elongated conductors normal to a coastline with application to geomagnetic measurements in Nigeria” by J. Chen, H. W. Dosso and S. Kang

Chen

2014

Earth Planet Sp

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On the Frequency Response of Induction ArrowsThe induction frequency response of some analogue models shown in Chen, Dosso and Kang (1997; hereafter referred to as CDK), seems to be somewhat strange. The frequency behaviour of the in-phase and quadrature Parkinson arrows, shown in figures 2 and 4 of CDK, indicates that: 1) the magnitude of the in-phase arrow decreases rapidly with increasing period, and becomes negligible when T = 30 min; 2) the quadrature arrow does not change its sign in the studied inducing period from 1 min to 90 min. In order to examine the correctness of the experimental results for their models, I have carried out some 3-D numerical modelling calculations using the finite difference method. I shall devide this comment into two parts. The first part gives the numerical results of an example, a model suggested by Wannamaker et al. (1984) for demonstrating the applicability of the finite difference method. The second part shows my numerical results for the elongated parallel conductors model mentioned in CDK, indicating that their analogue result is suspect. The 3-D Finite Difference MethodThe outline of the 3-D finite difference method and the detailed algorithm can be found in Chen (1985) and Chen and Fung (1988). The accuracy obtained by our computer program has been tested by making calculations for Weidelt's model (Weidelt, 1975) and Ting and Hohmann's model (Ting and Hohmann, 1981). The comparisons of our numerical results and their results are shown in the Appendix of Chen and Fung (1988). Another comparison for Hohmann's model (Hohmann, 1983) has also been carried out (Chen and Fung, 1989), and in that model the conductivity contrast is 200. All the results obtained by different methods agree well for the most part of the response curves.Here I show another comparison with the third model constructed by Wannamaker et al. (1984). In the stated model the conductive body is a plate-like feature 1 km thick at a depth of 750 m, with the lower layer situated below 2250 m. Its width is 5 km and its strike length is 60 km (see Fig. 1 Fig. 2a). Accordingly, the 3-D and 2-D results of the quadrature induction arrow do not agree well either (see Fig. 2b). Nevertheless, it is worth noting that, if we reverse the signs both for obtaining the in-phase and quadrature arrows, the quadrature Parkinson arrows in this example (T = 1 sec) point away from the conductor. As a matter of fact, when T ≥ 7 sec, the quadrature Parkinson arrows will change their directions; in that case, they will point towards the conductor. The Elongated Parallel Conductors Model without the OceanFigure 1 of CDK shows the structure of the model and figure 2 of CDK shows the response of V y (the response of the elongated conductors without the ocean). There is a pair of surface elongated conductors (3.6 S/m): both conductors' lengths and thicknesses are 500 km and 5 km respectively, the width is 20 km for conductor b and 5 km for conductor a. The conductor separation distance (S) is 50 km. The conductivity of the first layer ...

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“…Second, because the materials in the earth's crust are only weakly magnetic the permeability of the subsurface rocks can be approximated by the permeability of free space ðμ ¼ μ 0 Þ. Moreover, in EM methods, the primary source of the EM fields can be either an impressed electric current density J p or magnetic dipole moment M p (Hohmann, 1983). Therefore, at any point, the total electric and magnetic fields (E and H) are related by the following form of Maxwell's equations in the frequency domain:…”

Section: Theorymentioning

confidence: 99%

A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

2014

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The application of unstructured grids can improve the solution of total field electromagnetic problems because these grids allow efficient local refinement of the mesh at the locations of high field gradients. Unstructured grids also provide the flexibility required for representing arbitrary topography and subsurface interfaces. We investigated the generalization of the standard Yee's staggered scheme to unstructured tetrahedral-Voronoï grids using a finite-volume approach. We discretized the Helmholtz equation for the electric field in the frequency domain and solved the problem to find the projection of the total electric field along the edges of the tetrahedral elements. To compute the electric and magnetic fields at the observation points, an interpolation technique was employed, which uses the edge vector interpolation functions of the tetrahedral elements. To verify the presented scheme, two examples were evaluated, which revealed the computation of the total and secondary fields due to electric and magnetic sources in half-spaces that contain anomalous bodies. The results had good agreement with those from the literature. For the second example, accuracy studies were conducted to better understand the relative importance of different refinements in the grid and also the effect of the general quality of the grid. The results revealed the utmost importance of the quality of the tetrahedral grid and refinement at the observation locations. To validate the versatility of the approach, we synthesized helicopter-borne data for a model of the Ovoid ore body at Voisey's Bay, Labrador, Canada, which had good agreement with real data.

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Three-dimensional em modeling

Cited by 66 publications

References 25 publications

The problem of current channelling: A critical review

The problem of current channelling: A critical review

Comment on “EM induction in elongated conductors normal to a coastline with application to geomagnetic measurements in Nigeria” by J. Chen, H. W. Dosso and S. Kang

A finite-volume solution to the geophysical electromagnetic forward problem using unstructured grids

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