A grounded vertical long wire source system for plane wave magnetotelluric analog modeling

Geophysics ◽  
1980 ◽  
Vol 45 (10) ◽  
pp. 1523-1529 ◽  
Author(s):  
R. N. Edwards
Keyword(s):  
Plane Wave ◽  
Current Source ◽  
Skin Depth ◽  
Uniform Field ◽  
Induced Current ◽  
Horizontal Magnetic Field ◽  
Helmholtz Coils ◽  
Analog Modeling ◽  
Conductivity Anomalies ◽  
External Connections

A typical electromagnetic (EM) analog modeling apparatus consists of an electrolytic tank with embedded graphite blocks, representing conductivity anomalies. A plane wave magnetotelluric (MT) source is generated by alternating currents in a set of parallel horizontal overhead wires. A uniform horizontal magnetic field is produced over the surface of the electrolyte. A similar uniform field may also be generated by grounded semiinfinite vertical wires. Four such wires, two carrying current upward and two downward, when arranged at the corners of a rectangle of defined dimensions, generate a more uniform field than a corresponding pair of Helmholtz coils. If the size of the rectangle is large compared with a skin depth in the electrolyte, Cagniard’s MT relationships are obeyed both on and beneath the electrolyte. The vertical current source has the advantage over the horizontal current source since it requires no ancillary external connections between the ends of the modeling tank to complete the induced current circuit.

On: “A grounded vertical long‐wire source system for plane wave magnetotelluric analog modeling” by R. N. Edwards (GEOPHYSICS, October 1980, p. 1523–1529).

Geophysics ◽  
1981 ◽  
Vol 46 (6) ◽  
pp. 934-935 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Radial Distance ◽  
Skin Depth ◽  
Space Model ◽  
Homogeneous Half Space ◽  
The Earth ◽  
Analog Modeling ◽  
Vertical Wire ◽  
Electrical Skin

In an interesting analysis, Edwards shows that a vertical long wire source will produce electromagnetic (EM) fields that satisfy simple impedance relationships for a homogeneous half‐space model of the earth. The important restriction is that the radial distance to the observer be large compared with an electrical skin depth. Certainly the vertical wire structures provide a very convenient modeling scheme for the “average prospector” to interpret magnetotelluric (MT) data collected over confined inhomogeneities within the conductive host region.

Removal of static shift in two dimensions by regularized inversion

Geophysics ◽  
1991 ◽  
Vol 56 (12) ◽  
pp. 2102-2106 ◽  
Author(s):  
Catherine deGroot‐Hedlin
Keyword(s):  
Electric Fields ◽  
Apparent Resistivity ◽  
Skin Depth ◽  
Two Dimensions ◽  
Small Scale ◽  
Low Frequencies ◽  
Near Surface ◽  
Regularized Inversion ◽  
Conductivity Anomalies ◽  
Local Distortions

A common problem in magnetotelluric (MT) sounding is the presence of static shifts in the data, i.e., a vertical shifting of the log‐apparent‐resistivity versus period curves relative to regional values (Jones, 1988; Jiracek, 1990; Berdichevsky et al., 1989). These static shifts are due to the presence of small‐scale, shallow conductivity anomalies near the measurement site. Electric charge builds up on near‐surface anomalies that are small in comparison to the skin depth of the electromagnetic (EM) fields. The charge buildup produces a perturbation of the measured electric fields from their regional values that persists to arbitrarily low frequencies. Incorrect removal of these local distortions leads to incorrect interpretation of the deeper targets of investigation.

QUANTUM EFFECTS IN A COMBINATION OF A CONSTANT UNIFORM FIELD AND A PLANE WAVE FIELD

1991 ◽  
Vol 06 (25) ◽  
pp. 4437-4489 ◽  
Author(s):  
D.M. GITMAN ◽  
M.D. NOSKOV ◽  
SH. M. SHVARTSMAN
Keyword(s):  
Plane Wave ◽  
Wave Field ◽  
Quantum Electrodynamics ◽  
Quantum Effects ◽  
Uniform Field ◽  
Dirac Equations ◽  
Radiative Processes ◽  
Klein Gordon ◽  
Plane Wave Field ◽  
Uniform Electromagnetic Field

Quantum effects are considered in the external field, which is a superposition of a constant uniform electromagnetic field and a plane wave field. The complete and orthonormal sets of solutions to the Klein-Gordon and Dirac equations are constructed for this field. The probabilities of scattering and pair creation are calculated. The representations of various Green functions, which are used in quantum electrodynamics with unstable vacuum, are obtained. The radiative processes are explored for the field under consideration.

Calculation and Analysis of Geo-Magnetically Induced Current in Earth Based on Plane Wave Method

2013 ◽  
Vol 732-733 ◽  
pp. 1197-1201
Author(s):  
Xiao Wang ◽  
Lian Guang Liu ◽  
Chun Ming Liu
Keyword(s):  
Plane Wave ◽  
Maxwell Equations ◽  
Power Grid ◽  
Wave Method ◽  
Induced Current ◽  
Plane Wave Method ◽  
Conductivity Structure ◽  
The Relationship ◽  
Earth Conductivity ◽  
Conductivity Models

Geo-magnetically Induced Current (GIC) is not only flowing in conductors such as power grid and pipeline, but also flowing in earth and GIC in earth will affect GIC in conductors. Thus studying the relationship between GIC in earth and earth conductivity is significant to understand the impacts of conductivity on GIC in earth and conductors. This paper uses Maxwell equations and plane wave method to analyze GIC density lever and distribution characteristics in different earth depth of uniform/layered earth conductivity model and gives the relationship between conductivity and GIC in earth. The results indicate that, the smaller the earth conductivity, the deeper earth GIC distributes, and earth conductivity structure has great impact on GIC. At last, this paper proposes that to calculate GIC in power grid accurately, we need to establish more accurate earth conductivity models.

ELECTROMAGNETIC INVESTIGATION OF THE SEA FLOOR

Geophysics ◽  
1970 ◽  
Vol 35 (3) ◽  
pp. 476-489 ◽  
Author(s):  
J. H. Coggon ◽  
H. F. Morrison
Keyword(s):  
Mineral Exploration ◽  
Skin Depth ◽  
Electromagnetic Response ◽  
Horizontal Magnetic Field ◽  
Electromagnetic System ◽  
Sea Floor ◽  
Sea Bottom ◽  
Sea Bed ◽  
Receiver System ◽  
Field Strengths

Numerical evaluation of integral expressions for the fields about a vertical magnetic dipole in the sea allows analysis of the electromagnetic response over wide ranges of sea induction number and sea floor conductivity. Our analysis indicates that a marine electromagnetic system for measurement of bottom conductivity variations could readily be designed, with such applications as oceanographic and geologic studies, and mineral exploration. For a source‐receiver system on a homogeneous sea bottom, it is found that: (i) when the ratio k=(sea‐bed conductivity)/(seawater conductivity) is greater than about 0.03, both horizontal and vertical magnetic fields are useful for measurement of bottom conductivity at sea induction numbers less than 30 [induction number =√2 (horizontal transmitter‐receiver separation/skin depth)]. A separation of 30 m and frequencies in the range 300–3500 hz appear suitable for investigation of the upper few meters of unconsolidated bottom sediments. (ii) When the ratio k is less than 0.03, sea induction numbers from 10 to a few hundred are required for detection of seabed conductivity variations. In this case, the horizontal magnetic field, resulting from energy transmission mainly through the seafloor, is the suitable field to use. Electromagnetic sounding of indurated rocks may thus call for frequencies of 100 to 20,000 hz at a separation of 200 m. Field strengths vary strongly with relative sea depth D/R (D=sea depth, R=horizontal source‐receiver separation) when D/R is small; but sensitivity to bottom conductivity is little affected by D/R. Elevation of source and receiver above a seafloor less conductive than seawater reduces field strengths and sensitivity to seabed properties.

Doubling the effective skin depth with a local source

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 732-738 ◽  
Author(s):  
James E. Reid ◽  
James C. Macnae
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Survey Design ◽  
Data Interpretation ◽  
Skin Depth ◽  
Local Source ◽  
Electromagnetic Sounding ◽  
Homogeneous Half Space ◽  
Electric And Magnetic Fields ◽  
Thick Overburden

The depth at which the amplitude of the frequency‐domain electromagnetic fields due to dipole and square loop sources over a homogeneous half‐space fall to 1/e of their value at the surface is compared to the conventional plane‐wave skin depth. The skin depth due to a local source depends on the transmitter frequency, half‐space conductivity, transmitter altitude, and transmitter‐receiver offset, and may range from a fraction of to more than twice the plane‐wave skin depth. Unlike the plane‐wave skin depth, the “local‐source skin depth” is different for electric and magnetic fields, and may be nonunique for some transmitter geometries and field components. For all transmitter geometries, however, the local‐source skin depth approaches the plane‐wave skin depth as the transmitter altitude and/or receiver offset increase. The concept of the local‐source skin depth has direct application to survey design and data interpretation. A theoretical example demonstrates that it is possible to predict, for a given survey geometry and frequency range, whether or not an electromagnetic sounding can detect a conductive basement below a thick overburden layer.

Reflexion of a plane wave at a plasma slab

1979 ◽  
Vol 22 (3) ◽  
pp. 525-547 ◽  
Author(s):  
J. N. Elgin
Keyword(s):  
Electromagnetic Wave ◽  
Plane Wave ◽  
Boundary Conditions ◽  
Oblique Incidence ◽  
Plasma Layer ◽  
Plane Electromagnetic Wave ◽  
Current Source ◽  
Normal Incidence ◽  
Method Of Solution ◽  
Plasma Slab

The problem of a monochromatic plane electromagnetic wave incident from a vacuum onto a plasma slab is considered. The method of solution is based on the representation of the disturbance in the plasma layer as that generated by an appropriate current source in the complementary regions into which, for the purpose of the representation, the plasma is conceived to extend. The normal incidence case is treated first for both the specular reflexion and the absorption boundary conditions, with the extension to oblique incidence following in a later section of the paper.

Conservative modeling of 3-D electromagnetic fields, Part I: Properties and error analysis

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1308-1318 ◽  
Author(s):  
J. Torquil Smith
Keyword(s):  
Magnetic Flux ◽  
Plane Wave ◽  
Analytic Solutions ◽  
Skin Depth ◽  
Staggered Grid ◽  
Test Cases ◽  
Wave Component ◽  
Two Samples ◽  
Rms Error ◽  
Horizontal Wavelength

Conservation of electric current and magnetic flux can be explicitly enforced by modeling Maxwell’s equations on a staggered grid, where the different field components are sampled at points offset relative to each other. A staggered finite‐difference (SFD) approximation gives divergence‐free magnetic fields and electric currents ensuring good behavior at all periods. Comparisons of SFD solutions with 2-D quasi‐analytic solutions are very good (∼1% rms error). When a modeled region can be subdivided into uniform subdomains, comparison of analytic solutions and SFD approximations show that the greatest differences occur near the Nyquist wavenumbers; the SFD solutions do not attenuate in space as rapidly as the analytic solutions. The accuracy of a computed SFD solution can be estimated from its wavenumber content. For test cases the accuracy estimates are surprisingly close to the actual accuracies. Grid requirements for modeling short horizontal wavelength components of a solution seem more demanding than for modeling the infinite wavelength (plane‐wave) component: for 2% accuracy 4π samples are required per horizontal wavelength compared to two samples per skin depth for the plane‐wave component.

A new vertical continuation procedure for airborne electromagnetic field data from the modified image method

Geophysics ◽  
1999 ◽  
Vol 64 (5) ◽  
pp. 1364-1368 ◽  
Author(s):  
Clyde J. Bergeron ◽  
John R. Brusstar ◽  
Ningke Yi ◽  
Yan Wu ◽  
Juliette W. Ioup
Keyword(s):  
Accurate Method ◽  
Skin Depth ◽  
Flight Path ◽  
Integral Representations ◽  
Algebraic Expression ◽  
Image Method ◽  
Sommerfeld Integral ◽  
Horizontal Variation ◽  
Conductivity Anomalies ◽  
Airborne Electromagnetic

Airborne electromagnetic (AEM) data measured by equipment in a bird tethered to a helicopter have large variations caused by the unavoidable vertical excursions of the helicopter as it traverses its flight path. Such large changes tend to mask the smaller changes in field strength caused by lateral variations in the earth’s electrical conductivity along the flight path, which is the information that is the goal of AEM surveys. Signals produced by conductivity anomalies such as sea‐ice keels and pipelines in marshes or in the shallow ocean are enhanced and may be apparent directly in the continued fields. Furthermore, electronic or environmental noise is more easily detected in the continued fields and reduced by various methods of filtering and signal processing. In the modified image method (MIM) formalism for AEM fields, the algebraic expression for the secondary to primary field ratio [Formula: see text] is given in terms of R, where R is the total complex vertical separation of the primary and image dipoles [Formula: see text] scaled to the coil spacing ρ, [Formula: see text] is the complex effective skin depth, and h is the altitude of the bird. An inverse algebraic relation gives R as a function of [Formula: see text]. In this paper we present a simple and accurate method of continuing the field by way of continuing R. Because R is linear in h, the vertical continuation of R from h to h0 is accomplished by a simple linear translation. This method is applied to a flight line of an AEM survey of Barataria Bay, Louisiana, which includes both the marsh and a near‐shore region of the Gulf of Mexico. The smoothnesss of the continued data over the Gulf implies that the variability of the continued data over the marsh is attributable to horizontal variation in salinity, soil porosity, and water depth rather than noise. To produce more accurate values for R, we have also included details of an extended half‐space renormalization function which, in effect, removes residual differences between the fields calculated from the MIM algebraic and the numerical evaluation of the exact Sommerfeld integral representations of the [Formula: see text] field.

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