scholarly journals Calculating far field of an arbitrarily oriented electric dipole located above layered half space using reciprocity theorem

2012 ◽  
Vol 61 (5) ◽  
pp. 050301
Author(s):  
Ge De-Biao ◽  
Wei Bing
Keyword(s):  
Half Space ◽  
Electric Dipole ◽  
Reciprocity Theorem ◽  
Far Field ◽  
Layered Half Space

Note on the use of reciprocity theorem for obtaining radiation patterns

1965 ◽  
Vol 55 (2) ◽  
pp. 277-281 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Far Field ◽  
Radiation Patterns ◽  
Vertical Displacements ◽  
Field Radiation ◽  
P And Sv Waves

Abstract Expressions for the horizontal and vertical displacements at the surface of an elastic half space when plane harmonic P or SV waves are incident at any given angle are already known. On the basis of the reciprocity theorem, these expressions are used to obtain “far-field” radiation patterns of P and SV waves due to horizontal and vertical forces applied at the free surface.

Elastostatic Far-Field Behavior in a Layered Half Space Under Surface Pressure

1980 ◽  
Vol 47 (3) ◽  
pp. 504-512 ◽  
Author(s):  
R. Muki ◽  
S. B. Dong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Half Space ◽  
Asymptotic Expansions ◽  
Power Series Expansion ◽  
Surface Region ◽  
Far Field ◽  
Concentrated Force ◽  
Layered Half Space ◽  
Element Method

Elastostatic problem of a half space with a layer of possibly distinct mechanical properties under arbitrary normal tractions on the surface is reconsidered to establish far-field asymptotic expansions of the displacements. This work was motivated by application of such far field solutions to problems of the layered half space by Global-Local Finite-Element Method (GLFEM). When the traction is a unit concentrated force, the asymptotic expansion is found to coincide, up to the second term of its inverse power series expansion with respect to the distance from the point at interface below the point of load application, with that of the classical Boussinesq solution with a suitably chosen coordinate system. This agreement between the two solutions is also observed for normal tractions on a bounded surface region. Comparative numerical results are given to demonstrate the modeling capabilities of the far-field asymptotic expansions in a GLFEM example. It’s effectiveness is shown in terms of greater accuracy and computational efficiency over the conventional finite-element method.

Body wave radiation patterns from force applied within a half space

1966 ◽  
Vol 56 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Half Space ◽  
Body Wave ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Numerical Results ◽  
Wave Radiation ◽  
Far Field ◽  
Radiation Patterns ◽  
Sh Waves ◽  
Vertical Displacements

abstract Expressions are derived for the horizontal and vertical displacements at an arbitrary depth within a homogeneous, isotropic, elastic half space when plane harmonic P, SV or SH waves are incident at any given angle. On the basis of the reciprocity theorem, these expressions represent also the far-field polar radiation patterns of P, SV and SH waves due to horizontal and vertical forces applied at a point within the half space. Numerical results for a few selected values of depth are shown for a solid half space.

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