RESPONSE OF THIN DYKE TO OSCILLATING DIPOLE

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 134-143 ◽  
Author(s):  
James Paul Wesley
Keyword(s):  
Exact Solution ◽  
Magnetic Dipole ◽  
Analytical Continuation ◽  
Dipole Source ◽  
Finite Conductivity ◽  
First Approximation ◽  
Sulfide Ore ◽  
Infinite Slab ◽  
Infinite Conductivity

A dyke of sulfide ore may be geophysically prospected by observing its response to a slowly oscillating magnetic dipole source. To a first approximation the field produced by a thin dyke is given by a dyke of infinite conductivity and vanishing thickness in a vacuum (Wesley, 1958, Geophysics, v. 23, p. 128). In order to identify the ore and to estimate the size of the deposit, it is necessary to consider further approximations involving the conductivity and thickness of the dyke. By a type of analytical continuation an approximation is found which agrees both with the exact solution for a dyke of infinite conductivity and vanishing thickness and with the exact solution (approximated only for ωσ large and also for σ small) for an infinite slab of finite conductivity and nonvanishing thickness, the dyke appearing as an infinite slab when both source and observer are near the dyke but far removed from the edge. The solution is very good provided the dyke is geometrically thin.

RESPONSE OF DYKE TO OSCILLATING DIPOLE

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 128-133 ◽  
Author(s):  
James Paul Wesley
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Scalar Potential ◽  
Three Dimensions ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
First Approximation ◽  
Sulfide Ore ◽  
Infinite Conductivity ◽  
The Magnetic Field

A dyke of sulfide ore may be geophysically prospected by observing its electromagnetic response to a slowly oscillating magnetic dipole source. An excellent first approximation of the fields generated is obtained by considering the idealized case of a dyke of infinite conductivity and vanishing thickness in a vacuum. Surprisingly, this idealized problem can be solved exactly in terms of a newly discovered Green’s function for Laplace’s equation (in three dimensions) which is simply expressed in closed form. The magnetic scalar potential and the magnetic field are given for final results.

A general solution for a spherical conductor in a magnetic dipole field

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 781-800 ◽  
Author(s):  
Melvyn E. Best ◽  
Basil R. Shammas
Keyword(s):  
Magnetic Dipole ◽  
Spherical Model ◽  
Massive Sulfide ◽  
Ore Deposits ◽  
Dipole Field ◽  
First Approximation ◽  
Sulfide Ore ◽  
Magnetic Dipole Field ◽  
Airborne Em ◽  
Spherical Conductor

In electromagnetic (EM) prospecting for volcanogenic massive sulfide ore deposits, a significant number of the responses are associated with compact conductors. As a first approximation, these bodies are studied using a conducting sphere model. An exact solution is given for a spherical conductor excited by a magnetic dipole field in free space for arbitrary transmitter‐receiver (T-R) configurations with receiver positions inside or outside the conductor. In this general approach, it is possible to investigate the lateral attenuation of EM systems. In particular, the effects of flight‐line displacement from the center of the spherical conductor on several airborne EM responses are presented. For example, at normal flying heights, the standard Dighem system has a lateral attenuation 50 times larger than the EM-30 system (for a sphere of 100 m radius). Field results from the Clearwater deposit in New Brunswick are compared to the spherical model attenuations for the Dighem, Otter, and F-500 systems. The behavior of the total magnetic fields [Formula: see text] and [Formula: see text] inside the conductor are presented in the form of magnitude and phase contours. The [Formula: see text] amplitude was found to be approximately the same inside and outside the sphere; the [Formula: see text] amplitude, however, differs significantly in these two regions. Observations such as these may provide some guidance in subdividing anomalous inhomogeneities in future numerical modeling.

Torsional oscillations of a fluid sphere with a rigid boundary in a uniform magnetic field

1966 ◽  
Vol 24 (2) ◽  
pp. 275-284
Author(s):  
R. A. Wentzell
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Uniform Magnetic Field ◽  
Perfect Conductor ◽  
Rigid Boundary ◽  
Torsional Oscillations ◽  
Magnetic Viscosity ◽  
Eigen Values ◽  
Infinite Conductivity ◽  
Axis Of Symmetry

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

Ferrofluid Convection in a Lid-Driven Cavity

2018 ◽  
Vol 388 ◽  
pp. 407-419
Author(s):  
Fatih Selimefendigil ◽  
Ali Jawad Chamkha
Keyword(s):  
Heat Transfer ◽  
Magnetic Dipole ◽  
Richardson Number ◽  
Vertical Wall ◽  
Thermal Characteristics ◽  
Dipole Source ◽  
Dipole Strength ◽  
Square Enclosure ◽  
Lower Temperature ◽  
The Right

This study numerically investigates the mixed convection of ferrofluids in a partially heated lid driven square enclosure. The heater is located to the left vertical wall and the right vertical wall is kept at constant lower temperature while other walls of the cavity are assumed to be adiabatic. The governing equations are solved with Galerkin weighted residual finite element method. The influence of the Richardson number (between 0.01 and 100), heater location (between 0.25 H and 0.75H), strength of the magnetic dipole (between 0 and 4), and horizontal location of the magnetic dipole source (between-2H and-0.5H) on the fluid flow and heat transfer are numerically investigated. It is found that local and averaged heat transfer deteriorates with increasing values of Richardson number and magnetic dipole strength. The flow field and thermal characteristics are sensitive to the magnetic dipole source strength and its position and heater location.

Inverse Scattering from a Perfectly Conducting Prolate Spheroid in the Quasi-Static Domain

1973 ◽  
Vol 51 (2) ◽  
pp. 219-222
Author(s):  
D. A. Hill
Keyword(s):  
Magnetic Fields ◽  
Magnetic Dipole ◽  
Inverse Scattering ◽  
Oblate Spheroid ◽  
Prolate Spheroid ◽  
Dipole Source ◽  
Intermediate Step

The problem of inverse scattering from a perfectly conducting prolate spheroid in the quasistatic region of a magnetic dipole source is considered. From one observation of the radial and transverse scattered magnetic fields, the parameters which identify the spheroid (interfocal distance and eccentricity) are uniquely determined. The intermediate step requires the determination of the two magnetic polarizabilities. Similar results are also obtained for the oblate spheroid by a transformation.

scholarly journals Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
S. S. Ganji ◽  
M. G. Sfahani ◽  
S. M. Modares Tonekaboni ◽  
A. K. Moosavi ◽  
D. D. Ganji
Keyword(s):  
Exact Solution ◽  
Order Approximation ◽  
Expansion Method ◽  
Higher Order ◽  
Coupled Systems ◽  
Parameter Expansion ◽  
Analytical Technique ◽  
First Approximation ◽  
Mass Spring ◽  
Parameter Expansion Method

We consider periodic solution for coupled systems of mass-spring. Three practical cases of these systems are explained and introduced. An analytical technique called Parameter Expansion Method (PEM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations. Comparing with exact solutions, the first approximation to the frequency of oscillation produces tolerable error 3.14% as the maximum. By the second iteration the respective error became 1/5th, as it is 0.064%. So we conclude that the first approximation of PEM is so benefit when a quick answer is required, but the higher order approximation gives a convergent precise solution when an exact solution is required.

Radio propagation over a flat Earth across a boundary separating two different media

1953 ◽  
Vol 246 (905) ◽  
pp. 1-55 ◽  
Keyword(s):  
Plane Wave ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Dipole Source ◽  
Radio Waves ◽  
Dual Integral Equations ◽  
Plane Wave Incident ◽  
General Complex ◽  
Infinite Conductivity ◽  
New Feature

A theoretical investigation is given of the phenomena arising when vertically polarized radio waves are propagated across a boundary between two homogeneous sections of the earth’s surface which have different complex permittivities. The problem is treated in a two-dimensional form, but the results, when suitably interpreted, are valid for a dipole source. The earth’s surface is assumed to be flat. In the first part of the paper one section of the earth is taken to have infinite conductivity and is represented by an infinitely thin, perfectly conducting half-plane lying in the surface of an otherwise homogeneous earth. The resulting boundary-value problem is initially solved for a plane wave incident at an arbitrary angle; the scattered field due to surface currents induced in the perfectly conducting sheet is expressed as an angular spectrum of plane waves, and this formulation leads to dual integral equations which are treated rigorously by the methods of contour integration. The solution for a line-source is then derived by integration of the plane-wave solutions over an appropriate range of angles of incidence, and is reduced to a form in which the new feature is an integral of the type missing text where a and b are in general complex within a certain range of argument.

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