scholarly journals A parallel finite‐difference approach for 3D transient electromagnetic modeling with galvanic sources

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1192-1202 ◽  
Author(s):  
Michael Commer ◽  
Gregory Newman
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electric Field ◽  
Electric Fields ◽  
Time Derivative ◽  
Stable Solution ◽  
Parallel Computer ◽  
Staggered Grid ◽  
Electromagnetic Modeling ◽  
Transient Electromagnetic

A parallel finite‐difference algorithm for the solution of diffusive, three‐dimensional (3D) transient electromagnetic field simulations is presented. The purpose of the scheme is the simulation of both electric fields and the time derivative of magnetic fields generated by galvanic sources (grounded wires) over arbitrarily complicated distributions of conductivity and magnetic permeability. Using a staggered grid and a modified DuFort‐Frankel method, the scheme steps Maxwell's equations in time. Electric field initialization is done by a conjugate‐gradient solution of a 3D Poisson problem, as is common in 3D resistivity modeling. Instead of calculating the initial magnetic field directly, its time derivative and curl are employed in order to advance the electric field in time. A divergence‐free condition is enforced for both the magnetic‐field time derivative and the total conduction‐current density, providing accurate results at late times. In order to simulate large realistic earth models, the algorithm has been designed to run on parallel computer platforms. The upward continuation boundary condition for a stable solution in the infinitely resistive air layer involves a two‐dimensional parallel fast Fourier transform. Example simulations are compared with analytical, integral‐equation and spectral Lanczos decomposition solutions and demonstrate the accuracy of the scheme.

scholarly journals A finite‐difference, time‐domain solution for three‐dimensional electromagnetic modeling

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 797-809 ◽  
Author(s):  
Tsili Wang ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Execution Time ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Transient Electromagnetic ◽  
The Earth ◽  
The Magnetic Field

We have developed a finite‐difference solution for three‐dimensional (3-D) transient electromagnetic problems. The solution steps Maxwell’s equations in time using a staggered‐grid technique. The time‐stepping uses a modified version of the Du Fort‐Frankel method which is explicit and always stable. Both conductivity and magnetic permeability can be functions of space, and the model geometry can be arbitrarily complicated. The solution provides both electric and magnetic field responses throughout the earth. Because it solves the coupled, first‐order Maxwell’s equations, the solution avoids approximating spatial derivatives of physical properties, and thus overcomes many related numerical difficulties. Moreover, since the divergence‐free condition for the magnetic field is incorporated explicitly, the solution provides accurate results for the magnetic field at late times. An inhomogeneous Dirichlet boundary condition is imposed at the surface of the earth, while a homogeneous Dirichlet condition is employed along the subsurface boundaries. Numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth‐order difference method at early times and a second‐order method at other times. Numerical checks against analytical, integral‐equation, and spectral differential‐difference solutions show that the solution provides accurate results. Execution time for a typical model is about 3.5 hours on an IBM 3090/600S computer for computing the field to 10 ms. That model contains [Formula: see text] grid points representing about three million unknowns and possesses one vertical plane of symmetry, with the smallest grid spacing at 10 m and the highest resistivity at 100 Ω ⋅ m. The execution time indicates that the solution is computer intensive, but it is valuable in providing much‐needed insight about TEM responses in complicated 3-D situations.

scholarly journals Useful characteristics of shallow and deep marine CSEM responses inferred from 3D finite-difference modeling

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. F67-F76 ◽  
Author(s):  
Yutaka Sasaki ◽  
Max A. Meju
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electric Field ◽  
Shallow Water ◽  
Phase Response ◽  
Staggered Grid ◽  
Small Scale ◽  
Shallow Waters ◽  
Near Surface ◽  
Electric And Magnetic Field

Hydrocarbon reservoirs can be mapped if sufficient resistivity contrasts exist between them and their confining layers, but practical problems remain in target discrimination in deep and shallow waters, especially in the presence of heterogeneous overburden. We have developed an efficient 3D staggered-grid finite-difference controlled-source electromagnetic (CSEM) modeling code that enables study of the physics underlying some practical problems. We undertook a comparative analysis of reservoir detection in [Formula: see text]- and [Formula: see text]-deep waters using the simulated electric and magnetic field responses of a simple 3D reservoir. We examined the effect of two types of near-surface heterogeneity (mimicking disconnected gas clouds and/or patchy geochemical alteration halos) on the 3D reservoir response. We found that small-scale, shallow heterogeneities cause distortions that are almost independent of the source frequency. These persist at all source-receiver offsets in the electric amplitude response in deep and shallow waters and phase response in shallow water. They decrease in magnitude with increasing offset in deepwater phase response. Large-scale near-surface heterogeneities distort the horizontal electric field response more significantly than the small-scale ones, but the near-surface response gets smaller in amplitude as the offset increases. The distortions in shallow water are much smaller in magnitude than those for the deepwater case, so that the reservoir signatures still are visible on the response profiles. This might be considered as a positive feature for shallow-water inline electric field exploration. The magnetic field responses for the orthogonal direction provide diagnostic target signatures that are similar to the inline electric field responses in deep water but that are different in shallow water. The magnetic responses are affected by the airwave in a different manner from the electric field, suggesting that combined 3D electric and magnetic field analysis might be vital for handling the airwave problem.

scholarly journals Double layers in the downward current region of the aurora

2003 ◽  
Vol 10 (1/2) ◽  
pp. 45-52 ◽  
Author(s):  
R. E. Ergun ◽  
L. Andersson ◽  
C. W. Carlson ◽  
D. L. Newman ◽  
M. V. Goldman
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Phase Space ◽  
Electric Field ◽  
Electric Fields ◽  
Double Layers ◽  
Parallel Electric Field ◽  
Electrostatic Waves ◽  
Current Region ◽  
Decisive Evidence

Abstract. Direct observations of magnetic-field-aligned (parallel) electric fields in the downward current region of the aurora provide decisive evidence of naturally occurring double layers. We report measurements of parallel electric fields, electron fluxes and ion fluxes related to double layers that are responsible for particle acceleration. The observations suggest that parallel electric fields organize into a structure of three distinct, narrowly-confined regions along the magnetic field (B). In the "ramp" region, the measured parallel electric field forms a nearly-monotonic potential ramp that is localized to ~ 10 Debye lengths along B. The ramp is moving parallel to B at the ion acoustic speed (vs) and in the same direction as the accelerated electrons. On the high-potential side of the ramp, in the "beam" region, an unstable electron beam is seen for roughly another 10 Debye lengths along B. The electron beam is rapidly stabilized by intense electrostatic waves and nonlinear structures interpreted as electron phase-space holes. The "wave" region is physically separated from the ramp by the beam region. Numerical simulations reproduce a similar ramp structure, beam region, electrostatic turbulence region and plasma characteristics as seen in the observations. These results suggest that large double layers can account for the parallel electric field in the downward current region and that intense electrostatic turbulence rapidly stabilizes the accelerated electron distributions. These results also demonstrate that parallel electric fields are directly associated with the generation of large-amplitude electron phase-space holes and plasma waves.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Field Line ◽  
Geomagnetic Field ◽  
Geomagnetic Field Models ◽  
Spatial Derivatives ◽  
Field Lines ◽  
The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

INFLUENCE OF THE MAGNETIC FIELD ON THE TRANSVERSE RUNAWAY THRESHOLD

2007 ◽  
Vol 21 (10) ◽  
pp. 1715-1720 ◽  
Author(s):  
NANA METREVELI ◽  
ZAUR KACHLISHVILI ◽  
BEKA BOCHORISHVILI
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electric Fields ◽  
Applied Electric Field ◽  
Nonlinear Oscillations ◽  
Hot Electrons ◽  
Total Field ◽  
Practical Applications ◽  
Energy And Momentum ◽  
The Magnetic Field

The transverse runaway (TR) is a phenomenon whereby for a certain combination of energy and momentum scattering mechanisms of hot electrons, and for a certain threshold of the applied electric field, the internal (total) field tends to infinity. In this work, the effect of the magnetic field on the transverse runaway threshold is considered. It is shown that with increasing magnetic field, the applied critical electric fields relevant to TR decrease. The obtained results are important for practical applications of the TR effect as well as for the investigation of possible nonlinear oscillations that may occur near the TR threshold.

Transient fields of a current loop source above a layered earth

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 1068-1077 ◽  
Author(s):  
G. M. Hoversten ◽  
H. F. Morrison
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electric Fields ◽  
Current Loop ◽  
Wave Form ◽  
Sign Reversal ◽  
Circular Loop ◽  
Single Ring ◽  
Smoke Ring ◽  
A Current

The electric field induced within four layered models by a repetitive current wave form in a circular loop transmitter is presented along with the resulting magnetic fields observed on the surface. The behavior of the induced electric field as a function of time explains the observed sign reversal of the vertical magnetic field on the surface. In addition, the differences between magnetic field responses for different models are explained by the behavior of the induced electric fields. The pattern of the induced electric field is shown to be that of a single “smoke ring,” as described by Nabighian (1979), which is distorted by layering but which remains a single ring system rather than forming separate smoke rings in each layer.

Das toroidale schwachionisierte Magnetoplasma I

1967 ◽  
Vol 22 (12) ◽  
pp. 1890-1903
Author(s):  
F. Karger
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Electric Fields ◽  
Transverse Electric ◽  
Refined Theory ◽  
Toroidal Plasma ◽  
Dc Discharge ◽  
Transverse Electric Fields

In a previous paper31 discrepancies between theory and experiment were found on investigating the positive column in a curved magnetic field. The approximation derived in 31 for the torus drift in a weakly ionized magnetoplasma is therefore checked here (Part I) with a refined theory which also yields the transverse electric field strength. Experimentally, both the transverse electric fields and the density profiles in the DC discharge were determined in addition to the longitudinal electric field strength.The discrepancies occurring in 31 are ascribed to the fact that the plasma concentrates at the cathode end of the magnetic field coils, this effect having a considerable influence on the form of the transverse density profile and on the stability behaviour. Part II later will show how the influence of this concentration can be eliminated and what effect in the current-carrying toroidal plasma causes a marked reduction of the charge carrier losses.

Three‐dimensional induction logging problems, Part 2: A finite‐difference solution

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 484-491 ◽  
Author(s):  
Gregory A. Newman ◽  
David L. Alumbaugh
Keyword(s):  
Finite Difference ◽  
Electric Field ◽  
Krylov Subspace ◽  
Inverse Operator ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Linear System Of Equations ◽  
Order Of Magnitude ◽  
Finite Difference Solution ◽  
Difference Solution

A 3‐D finite‐difference solution is implemented for simulating induction log responses in the quasi‐static limit that include the wellbore and bedding that exhibits transverse anisotropy. The finite‐difference code uses a staggered grid to approximate a vector equation for the electric field. The resulting linear system of equations is solved to a predetermined error level using iterative Krylov subspace methods. To accelerate the solution at low induction numbers (LINs), a new preconditioner is developed. This new preconditioner splits the electric field into curl‐free and divergence‐free projections, which allows for the construction of an approximate inverse operator. Test examples show up to an order of magnitude increase in speed compared to a simple Jacobi preconditioner. Comparisons with analytical and mode matching solutions demonstrate the accuracy of the algorithm.

scholarly journals Ion energy increase in laser-generated plasma expanding through axial magnetic field trap

2007 ◽  
Vol 25 (3) ◽  
pp. 453-464 ◽  
Author(s):  
L. Torrisi ◽  
D. Margarone ◽  
S. Gammino ◽  
L. Andò
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Electric Fields ◽  
Axial Magnetic Field ◽  
Ion Beam ◽  
High Vacuum ◽  
Target Surface ◽  
Axial Direction ◽  
Ion Interactions ◽  
The Magnetic Field

Laser-generated plasma is obtained in high vacuum (10−7 mbar) by irradiation of metallic targets (Al, Cu, Ta) with laser beam with intensities of the order of 1010 W/cm2. An Nd:Yag laser operating at 1064 nm wavelength, 9 ns pulse width, and 500 mJ maximum pulse energy is used. Time of flight measurements of ion emission along the direction normal to the target surface were performed with an ion collector. Measurements with and without a 0.1 Tesla magnetic field, directed along the normal to the target surface, have been taken for different target-detector distances and for increasing laser pulse intensity. Results have demonstrated that the magnetic field configuration creates an electron trap in front of the target surface along the axial direction. Electric fields inside the trap induce ion acceleration; the presence of electron bundles not only focuses the ion beam but also increases its energy, mean charge state and current. The explanation of this phenomenon can be found in the electric field modification inside the non-equilibrium plasma because of an electron bunching that increases the number of electron-ion interactions. The magnetic field, in fact, modifies the electric field due to the charge separation between the clouds of fast electrons, many of which remain trapped in the magnetic hole, and slow ions, ejected from the ablated target; moreover it increases the number of electron-ion interactions producing higher charge states.

Sign in / Sign up

Export Citation Format

Share Document