A finite‐element solution for the transient electromagnetic response of an arbitrary two‐dimensional resistivity distribution

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1450-1461 ◽  
Author(s):  
Y. Goldman ◽  
C. Hubans ◽  
S. Nicoletis ◽  
S. Spitz
Keyword(s):  
Finite Element ◽  
Sparse Matrix ◽  
Equation System ◽  
Electromagnetic Response ◽  
Implicit Time ◽  
Two Dimensional ◽  
Time Step ◽  
Transient Electromagnetic ◽  
Exact Boundary ◽  
The Time Domain

We present a numerical method for solving Maxwell’s equations in the case of an arbitrary two‐dimensional resistivity distribution excited by an infinite current line. The electric field is computed directly in the time domain. The computations are carried out in the lower half‐space only because exact boundary conditions are used on the free surface. The algorithm follows the finite‐element approach, which leads (after space discretization) to an equation system with a sparse matrix. Time stepping is done with an implicit time scheme. At each time step, the solution of the equation system is provided by the fast system ICCG(0). The resulting algorithm produces good results even when large resistivity contrasts are involved. We present a test of the algorithm’s performance in the case of a homogeneous earth. With a reasonable grid, the relative error with respect to the analytical solution does not exceed 1 percent, even 2 s after the source is turned off.

The Calculation of 2.5D Transient Electromagnetic Response

2010 ◽  
Vol 36 ◽  
pp. 349-354
Author(s):  
Guo Hong Fu ◽  
Bin Xiong
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Equation System ◽  
Background Field ◽  
Electromagnetic Response ◽  
Response Curves ◽  
Forward Algorithm ◽  
Element Mesh ◽  
Geoelectric Section ◽  
Transient Electromagnetic

A 2.5D finite element forward algorithm for TEM with block linear conductivity was put forward in this paper. Firstly, based on the Maxwell equations, 2-order dual differential equation along strike was obtained by Laplace and Fourier transform. Then finite element linear equation system was obtained from coupling differential equation by using the Galerkin method, and yields the numerical solution of 2.5D transient electromagnetic field. The conductivity in finite element mesh is linear but uniform. In addition, the total field is decomposed into background field and secondary field: the former is solved by analytical method, and the latter is calculated by numerical method. Finally, 2.5D transient electromagnetic response curves of several typical geoelectric section models were computed.

scholarly journals Numerical Simulation of Transient Electromagnetic Response of Unfavorable Geological Body in Tunnel

2011 ◽  
Vol 90-93 ◽  
pp. 37-40 ◽  
Author(s):  
Lu Bo Meng ◽  
Tian Bin Li ◽  
Zheng Duan
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Electromagnetic Field ◽  
Electromagnetic Response ◽  
Detection Distance ◽  
Geological Body ◽  
Response Characteristics ◽  
Finite Element Software ◽  
Transient Electromagnetic ◽  
Field Decay

To investigate the transient electromagnetic method of response characteristics in the tunnel geological prediction, the finite element numerical simulation of unfavorable geological body of different location, different resistivity sizes, different shapes, and different volume size were carried out by ANSYS finite element software. The results show that secondary electromagnetic field of different location of unfavorable geological body have same decay rate, when detection distance from 30m to 70m, transient electromagnetic responses are strongest, followed distance from 10m to 30m and from 70m to 90m. The shape, volume and resistivity of unfavorable geological body have strong influence on transient electromagnetic response, unfavorable geological body more sleek, the greater the volume and the smaller the resistivity of unfavorable geological body, the secondary electromagnetic field decay slower.

Contribution to Bridge Damage Analysis

2014 ◽  
Vol 704 ◽  
pp. 435-441 ◽  
Author(s):  
Mohammed Lamine Moussaoui ◽  
Abderrahmane Kibboua ◽  
Mohamed Chabaat
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Damage Detection ◽  
Sparse Matrix ◽  
System Of Equations ◽  
Shape Functions ◽  
Time Step ◽  
Analytical Geometry ◽  
Matrix Algorithms ◽  
Bridge Damage

Structural damage detection has become an important research area since several works [2] were focused on the crack zones detection in order to foresee the appropriate solutions. The present research aims to carry out the reinforced concrete bridge damage detection with the finite element mathematical model updating method (MMUM). Unknown degrees of freedom dof are expanded from measured ones. The partitioned system of equations has provided a large sub-system of equations which can be solved efficiently by handling sparse matrix algorithms at each time step of the finite time centered space FTCS discretization. A new and efficient method for the calculation of the constant strain tetrahedron shape functions has been developed [1,3,4,5,6]. The topological and analytical geometry of the tetrahedron and its useful formulae enabled us to develop its shape functions and its corresponding finite element matrices. The global finite element matrices and sparse matrix computations have been achieved with a calculus source code. The reinforced concrete mixture has been modeled with the mixture laws [16] which led to its material properties matrix as an orthotropic case with 9 constants and 2 planes of symmetry from the generalizedHooke’slaw [1]. It is noticed that the material is made of steel, cement, gravels, sand and impurities. The data computations have been implemented with optimized cpu time and data storage using vectorial programming of efficient algorithms [11,12]. The sparse matrix algorithms used in this study are: solution of symmetric systems of equations UTDUd=R, multiplication, addition, transposition, permutation of rows and columns, and ordering of the matrices representations. All the sparse matrices are given in row-wise sparse format.

Diffusion of electromagnetic fields into a two‐dimensional earth: A finite‐difference approach

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 870-894 ◽  
Author(s):  
M. L. Oristaglio ◽  
G. W. Hohmann
Keyword(s):  
Finite Difference ◽  
Half Space ◽  
Small Time ◽  
Two Dimensional ◽  
Time Step ◽  
Small Peak ◽  
Transient Electromagnetic ◽  
The Earth ◽  
Air Interface ◽  
Equation Boundary

We describe a numerical method for time‐stepping Maxwell’s equations in the two‐dimensional (2-D) TE‐mode, which in a conductive earth reduces to the diffusion equation. The method is based on the classical DuFort‐Frankel finite‐difference scheme, which is both explicit and stable for any size of the time step. With this method, small time steps can be used at early times to track the rapid variations of the field, and large steps can be used at late times, when the field becomes smooth and its rates of diffusion and decay slow down. The boundary condition at the earth‐air interface is handled explicitly by calculating the field in the air from its values at the earth’s surface with an upward continuation based on Laplace’s equation. Boundary conditions in the earth are imposed by using a large, graded grid and setting the values at the sides and bottom to those for a haft‐space. We use the 2-D model to simulate transient electromagnetic (TE) surveys over a thin vertical conductor embedded in a half‐space and in a half‐space with overburden. At early times (microseconds), the patterns of diffusion in the earth are controlled mainly by geometric features of the models and show a great deal of complexity. But at late times, the current concentrates at the center of the thin conductor and, with a large contrast (1000:1) between conductor and half‐space, produces the characteristic crossover and peaked anomalies in the surface profiles of the vertical and horizontal emfs. With a smaller contrast (100:1), however, the crossover in the vertical emf is obscured by the halfspace response, although the horizontal emf still shows a small peak directly above the target.

scholarly journals Laplace Transform for Finite Element Analysis of Electromagnetic Interferences in Underground Metallic Structures

2022 ◽  
Vol 12 (2) ◽  
pp. 872
Author(s):  
Andrea Cristofolini ◽  
Arturo Popoli ◽  
Leonardo Sandrolini ◽  
Giacomo Pierotti ◽  
Mattia Simonazzi
Keyword(s):  
Finite Element ◽  
Laplace Transform ◽  
Electromagnetic Interference ◽  
Inverse Laplace Transform ◽  
Element Analysis ◽  
Metallic Structures ◽  
Numerical Inverse Laplace Transform ◽  
Transient Electromagnetic ◽  
The Time Domain ◽  
High Voltage Power Lines

A numerical methodology is proposed for the calculation of transient electromagnetic interference induced by overhead high-voltage power lines in metallic structures buried in soil—pipelines for oil or gas transportation. A series of 2D finite element simulations was employed to sample the harmonic response of a given geometry section. The numerical inverse Laplace transform of the results allowed obtaining the time domain evolution of the induced voltages and currents in the buried conductors, for any given condition of the power line.

Transient electromagnetic field computations for polygonal loops on layered earths

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 785-793 ◽  
Author(s):  
A. P. Raiche
Keyword(s):  
Digital Filters ◽  
Computation Time ◽  
Hankel Transform ◽  
Electromagnetic Response ◽  
System Response ◽  
Current Response ◽  
Loop Area ◽  
Transient Electromagnetic ◽  
The Time Domain ◽  
Dipole Response

The transient electromagnetic response (vertical and horizontal components of dB/dt) of a large polygonal transmitting loop on a layered earth is calculated using a nested interpolation scheme based on the dipole‐dipole response function. The frequency‐domain field of a vertical magnetic dipole is inverse Laplace transformed into the time domain, for selected values of the Hankel transform variable, using the Gaver‐Stehfest method. After interpolation, the result is inverse Hankel transformed (for selected values of distance) using digital filters. Interpolating over distance allows integration of the dipole response over the area of one or more transmitting loops. An interpolation over time gives the step‐current response, which in turn is convolved with the transmitter‐receiver characteristics to yield the system response. This method allows robust calculation of several transmitting loops (with different signal parameters) and several receiver positions in little more time than that required for one loop with one receiver. The computation time for the single transmitter‐receiver response can be decreased by analytical integration of the Bessel function over the transmitter loop area before performing the inverse Hankel transform. Since this procedure precludes the use of standard digital filters for the inverse Hankel transform, it is not efficient for multireceiver computations.

The Dispersion in One- and Two-Dimensional Finite Element Solutions to the Heat Equation

2002 ◽  
Author(s):  
W. Dauksher ◽  
A. F. Emery
Keyword(s):  
Finite Element ◽  
Heat Equations ◽  
Two Dimensional ◽  
Step Size ◽  
Matrix Formulation ◽  
Time Step ◽  
Time Step Size ◽  
Time Stepping ◽  
Dimensional Finite Element ◽  
The One

The dispersive errors in the finite element solution to the one- and two-dimensional heat equations are examined as a function of element type and size, capacitance matrix formulation, time stepping scheme and time step size.

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