Hybrid‐ray approximation in electromagnetic sounding

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1846-1861 ◽  
Author(s):  
Tze‐Kong Kan ◽  
C. S. Clay
Keyword(s):  
Half Space ◽  
Wave Theory ◽  
Transverse Magnetic ◽  
Image Method ◽  
Multiple Reflections ◽  
Current Dipole ◽  
Electromagnetic Sounding ◽  
Transmission Coefficients ◽  
Magnetic Components ◽  
A Current

Our purpose is to develop electromagnetic (EM) transient sounding methods that can handle resistivity structures having dipping interfaces. The method is an approximation that uses wave theory for part of the calculation and ray theory for the rest. The approximation is a refinement of Yost’s (1952) image method in which the source on a half‐space becomes the image beneath the reflecting interface. This approach shows excellent agreement with experiment and promises simple applications. To test the approximation, we compare numerical integration of the fields over a two‐layer half‐space with approximate values. We separate the EM integrals into integrals for the surface wave, primary, and multiple reflections. For a current dipole along the x‐axis, the electric field [Formula: see text] is the sum of the transverse electric and transverse magnetic components. For skin depths >1, the main contributions to the integrals come from directions near the specular direction, and by moving the reflection coefficients at the lower interface outside of the integral, we obtain the hybrid‐ray approximation. The transmission coefficients from the source into the earth remain inside because the source is near the interface. Computations for a two‐layer model that includes the geometry, and system functions for deep dipole‐dipole soundings in the Precambrian shield of northern Wisconsin, give time‐domain signals that closely approximate the measurements. The theoretical model consists of a layer 18 to 23 km thick with a conductivity of [Formula: see text] over a half‐space with a conductivity of [Formula: see text].

scholarly journals Scattering from a Buried PEMC Cylinder Illuminated by a Normally Incident Plane Wave Propagating in Free Space

2018 ◽  
Vol 8 (1) ◽  
pp. 1-7 ◽  
Author(s):  
A. Hamid ◽  
F. Cooray
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Free Space ◽  
Transverse Magnetic ◽  
Planar Interface ◽  
Burial Depth ◽  
Multiple Reflections ◽  
Incident Plane ◽  
Plane Wave Incident ◽  
Expansion Coefficients

A rigorous solution is presented to the problem of scattering by a perfect electromagnetic conducting (PEMC) circular cylinder buried inside a dielectric half-space that is excited by a normally incident transverse magnetic (TM) plane wave propagating in free space. The plane wave incident on the planar interface separating the two media creates fields transmitting into the dielectric half- space becoming the known primary incident fields for the buried cylinder. When the fields scattered by the cylinder, in response to those fields incident on it, are incident at the interface, they generate fields reflected into the dielectric half-space and fields transmitted into free space. These fields, and the fields scattered by the cylinder are expressed in terms of appropriate cylindrical waves consisting of unknown expansion coefficients which are to be determined. Imposing boundary conditions at the surface of the cylinder and at a point on the planar interface, enables the evaluation of the unknown coefficients. This procedure is then replicated, by considering multiple reflections and transmissions at the planar interface, and multiple scattering by the cylinder, till a preset accuracy is obtained for the reflection coefficient at the particular point on the interface. The refection coefficient at this point is then computed for cylinders of different sizes, to show how it varies with the PEMC admittance of the cylinder, its burial depth, and the permittivity of the dielectric half-space.

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

scholarly journals Mathematical analogies in physics. Thin-layer wave theory

2014 ◽  
Vol 57 (1) ◽  
Author(s):  
José M. Carcione ◽  
Vivian Grünhut ◽  
Ana Osella
Keyword(s):  
Quantum Mechanics ◽  
Thin Layer ◽  
Quantum Physics ◽  
Constitutive Relations ◽  
Normal Incidence ◽  
Wave Theory ◽  
Transverse Magnetic ◽  
Momentum Conservation ◽  
Tunnel Effect ◽  
Basic Equations

<p>Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law). In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies) between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission) problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect). The analogy is mainly illustrated with geophysical examples of propagation of S (shear), P (compressional), TM (transverse-magnetic) and TE (transverse-electric) waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.</p>

Magnetic localisation of a current dipole implanted in dogs

1987 ◽  
Vol 32 (1) ◽  
pp. 65-70 ◽  
Author(s):  
E Costa Monteiro ◽  
A C Bruno ◽  
S R W Louro ◽  
P Costa Ribeiro ◽  
A Fonseca Costa
Keyword(s):  
Current Dipole ◽  
A Current

Part II magnetic field produced by a current dipole

1976 ◽  
Vol 9 (4) ◽  
pp. 409-417 ◽  
Author(s):  
David Cohen ◽  
Hidehiro Hosaka
Keyword(s):  
Magnetic Field ◽  
Current Dipole ◽  
A Current

Wave Scattering From Multiple Horizontal Plates as a Breakwater

2009 ◽  
Author(s):  
Guoyu Wang ◽  
Yongxue Wang
Keyword(s):  
Water Depth ◽  
Plate Thickness ◽  
Wave Theory ◽  
Linear Potential ◽  
Antisymmetric Part ◽  
Transmission Coefficients ◽  
Present Solution ◽  
Relative Water ◽  
Constant Coefficients ◽  
Finite Water Depth

The multiple horizontal plates breakwater is proposed in this article, which mainly consists of several horizontal plates. The regular wave test results demonstrate that it has good performance of dissipating waves. Based on the linear potential wave theory, the scattering of waves normally incident on the multiple horizontal plates in a channel of finite water depth is investigated. The velocity potential is split to the symmetric and antisymmetric part, and the method of eigenfunction expansions is used to obtain the unknown constant coefficients determined from the matching conditions. The thickness of the plates is considered in the theoretical analysis. The present solution is compared with the existing theoretical, numerical and experimental results with good agreements. The parameters such as the relative water depth, relative plate width, relative plate thickness and number of plates, those identified with the performance of the breakwater are investigated and discussed. The variation of reflection and transmission coefficients alone with the above mentioned parameters are also presented.

Dynamic Distribution of Displacement and Stress Considerations in the Ultrasonic Immersion Nondestructive Evaluation of Multilayered Plates

1990 ◽  
Vol 112 (3) ◽  
pp. 260-265 ◽  
Author(s):  
A. H. Nayfeh ◽  
T. W. Taylor
Keyword(s):  
Nondestructive Evaluation ◽  
Half Space ◽  
Elastic Solid ◽  
Ultrasonic Waves ◽  
Theoretical Treatment ◽  
Multilayered Media ◽  
Transmission Coefficients ◽  
Interfacial Conditions ◽  
Smooth Interface ◽  
Multilayered Plates

A unified theoretical treatment is presented for the calculation of displacements and stresses within multilayered media subjected to incident ultrasonic waves. The wave is supposed to be incident from water, at an arbitrary angle, upon a plate consisting of an arbitrary number of different isotropic material layers. In the first part of the analysis displacements and stresses are determined as functions of position within the plate while all layer interfaces are assumed to be rigidly bonded. A smooth interface is subsequently introduced to simulate debonding of two material layers. The composite plate is assumed to be bounded at the bottom by either a free surface, a fluid half-space or an elastic solid half-space. A byproduct of the analysis is the derivation of the reflection and transmission coefficients for the systems. Extensive numerical results are given in order to delineate the influence of the plate material orderings, layer thicknesses and interfacial conditions on the displacements and stresses within the plate. The model developed here will be of value in material characterization and in the nondestructive evaluation of advanced material applications.

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