Electromagnetic induction by a finite electric dipole source over a 2-D earth

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Martyn J. Unsworth ◽  
Bryan J. Travis ◽  
Alan D. Chave
Keyword(s):  
Finite Element ◽  
Electromagnetic Fields ◽  
Electric Dipole ◽  
Numerical Solutions ◽  
Current Source ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Horizontal Electric Dipole

A numerical solution for the frequency domain electromagnetic response of a two‐dimensional (2-D) conductivity structure to excitation by a three‐dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite‐element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far‐field. In combination with an iterative solution for the along‐strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air‐earth interface are presented to illustrate the usefulness of the code.

Effect of a Conducting Overburden on the Fields of a Buried Dipole Source

1975 ◽  
Vol 53 (6) ◽  
pp. 598-609 ◽  
Author(s):  
V. Ramaswamy ◽  
H. W. Dosso
Keyword(s):  
Magnetic Fields ◽  
Electromagnetic Fields ◽  
Analytical Solutions ◽  
Electric Dipole ◽  
Lower Layer ◽  
Low Frequency ◽  
Dipole Source ◽  
Vertical Electric Dipole ◽  
Electric And Magnetic Fields ◽  
Horizontal Electric Dipole

Analytical solutions for the low frequency electromagnetic fields of a dipole source situated in the lower layer of a two layer conductor are derived. The sources considered are a vertical electric dipole, a horizontal electric dipole, and a horizontal magnetic dipole. The numerical results discussed in this paper describe the general behavior of the electric and magnetic fields for various upper layer conductivities, upper layer thickness, and source depths. The results are of interest in the application of electromagnetic techniques to locate miners trapped underground following a mine disaster.

Three-dimensional Land FD-CSEM Regularized Inversion Based on Edge Finite-element Method

2018 ◽  
Vol 23 (2) ◽  
pp. 211-222
Author(s):  
Jianxin Liu ◽  
Pengmao Liu ◽  
Xiaozhong Tong
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Three Dimensional ◽  
Dipole Source ◽  
Unique Problem ◽  
Three Dimensional Modeling ◽  
Homogeneous Half Space ◽  
Electromagnetic Responses ◽  
Horizontal Electric Dipole ◽  
The Galerkin Method

There is a desire to obtain rapid and stable inversion results and clearly reconstruct subsurface resistivity structure in frequency domain (FD) electromagnetics. Three-dimensional modeling of land FD controlled-source electromagnetic (CSEM) data is vital to improve the understanding of electromagnetic responses collected in increasingly complex geologic settings. Three-dimensional inversion of land FD-CSEM data is a mathematically non-unique problem with instability, due to the noise contained in the data and its inherent incompleteness. The main difference between our method and those from previous work is that the edge finite-element approach is applied to solve the three-dimensional FD-CSEM generated by a horizontal electric dipole source. Firstly, we formulate the edge finite-element equation through the Galerkin method, based on the Helmholtz equation of the electric fields. Secondly, in order to check the validity of the modeling code, we compare the numerical results with the analytical solutions for a homogeneous half-space model. For further tests, we calculate the electromagnetic responses for another two models with more practical structures. Finally, the three-dimensional inversion is carried out based on a regularization method with smoothness-constraints to obtain stable solutions.

Electromagnetic Response for Horizontal Electric Dipole Source Considering Conduct & Displacement Current

2014 ◽  
Vol 513-517 ◽  
pp. 3340-3344
Author(s):  
Jia Bin Yan ◽  
Xiang Yu Huang ◽  
Peng Yu Wu
Keyword(s):  
Electric Dipole ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Displacement Current ◽  
Geophysical Application ◽  
Horizontal Electric Dipole ◽  
Em Field ◽  
Transform Zone ◽  
Displacement Currents ◽  
And Diffusion

Electromagnetic (EM) field is often referred to diffusion (quasi-static assumption) that displacement currents are neglected during data processing in geophysical application, while the ratio of conduct currents to displacement currents is higher than 10, that is ,we think EM field is diffusion dominated and wave dominate for the ratio less than 0.1. Our simulating with Horizontal Electric Dipole Field indicated that frequency range of wave dominated is that the ratio is less than 0.007, the magnitude curves of EM component and impedance referring to diffusion and wave are different from those of diffusion. And in transform zone () the curves are different from those of wave and diffusion.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Layered Media Under Thermomechanical Surface Loading

2002 ◽  
Vol 125 (1) ◽  
pp. 52-59 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Layered Medium ◽  
Numerical Solutions ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Thin Layers ◽  
Surface Loading ◽  
Elastic Plastic ◽  
Thermomechanical Surface

The simultaneous effects of mechanical and thermal surface loadings on the deformation of layered media were analyzed with the finite element method. A three-dimensional model of an elastic sphere sliding over an elastic-plastic layered medium was developed and validated by comparing finite element results with analytical and numerical solutions for the stresses and temperature distribution at the surface of an elastic homogeneous half-space. The evolution of deformation in the layered medium due to thermomechanical surface loading is interpreted in light of the dependence of temperature, von Mises equivalent stress, first principal stress, and equivalent plastic strain on the layer thickness, Peclet number, and sliding distance. The propensity for plastic flow and microcracking in the layered medium is discussed in terms of the thickness and thermal properties of the layer, sliding speed, medium compliance, and normal load. It is shown that frictional shear traction and thermal loading promote stress intensification and plasticity, especially in the case of relatively thin layers exhibiting low thermal conductivity.

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