Exact, Closed-Form Representations for the Time-Domain Surface Impedances of a Homogeneous, Lossy Half-Space

2004 ◽  
Vol 52 (10) ◽  
pp. 2659-2665 ◽  
Author(s):  
H.-Y. Pao ◽  
Z. Zhu ◽  
S.L. Dvorak
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Time Domain ◽  
The Time Domain

Time‐domain solution for horizontal coaxial dipoles on a half‐space

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1850-1852 ◽  
Author(s):  
David C. Bartel
Keyword(s):  
Frequency Domain ◽  
Half Space ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
Direct Solution ◽  
Current Waveform ◽  
Laplace Domain ◽  
Homogeneous Half Space ◽  
The Time Domain ◽  
The Magnetic Field

The practice of transforming frequency‐domain results into the time domain is fairly common in electromagnetics. For certain classes of problems, it is possible to obtain a direct solution in the time domain. A summary of these solutions is given in Hohmann and Ward (1986). Presented here is another problem which can be solved directly in the time domain—the magnetic field of horizontal coaxial dipoles on the surface of a homogeneous half‐space. Solutions are presented for both an impulse transmitter current and a step turnon in the transmitter current. The solution in the time domain is obtained by taking the inverse Laplace transform of the product of the frequency‐domain solution and the Laplace‐domain representation of the current waveform.

scholarly journals A New Method to Calculate Induced Current of Thin Wire over Anisotropic Ground under HPM

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Le Cao
Keyword(s):  
Half Space ◽  
Time Domain ◽  
Response Analysis ◽  
Induced Current ◽  
Thin Wire ◽  
High Power Microwave ◽  
Time Response Analysis ◽  
Time Domain Integral Equation ◽  
The Time Domain ◽  
Power Microwave

The time response analysis of wire structures is often carried out in free space or isotropic half-space, but the real ground is usually layered and has anisotropic properties. In this paper, the induced current of a thin wire over layered anisotropic half-space under a high-power microwave (HPM) is calculated by using the time-domain integral equation (TDIE) method. The reflection coefficient of a layered anisotropic medium is obtained by the general transmitting matrix (GTM) method combined with Fourier transform. The variation of the induced current on the thin wire under different incident conditions is analyzed.

scholarly journals Analytic resolution of time-domain half-space Green's functions for internal loads by a displacement potential-Laplace-Hankel-Cagniard transform method

2020 ◽  
Vol 476 (2235) ◽  
pp. 20190610
Author(s):  
Ronald Y. S. Pak ◽  
Xiaoyong Bai
Keyword(s):  
Half Space ◽  
Time Domain ◽  
Surface Force ◽  
Point Load ◽  
Wave Group ◽  
Branch Points ◽  
Transform Method ◽  
Displacement Potential ◽  
Starting Point ◽  
The Time Domain

A refined yet compact analytical formulation is presented for the time-domain elastodynamic response of a three-dimensional half-space subject to an arbitrary internal or surface force distribution. By integrating Laplace and Hankel transforms into a method of displacement potentials and Cagniard's inversion concept, it is shown that the solution can be derived in a straightforward manner for the generalized classical wave propagation problem. For the canonical case of a buried point load with a step time function, the response is proved to be naturally reducible with the aid of a parametrized Bessel function integral representation to six wave-group integrals on finite contours in the complex plane that stay away from all branch points and the Rayleigh pole except possibly at the starting point of the contours. On the latter occasions, the possible singularities of the integrals can be rigorously extracted by an extended method of asymptotic decomposition, rendering the residual numerical computation a simple exercise. With the new solution format, the arrival time of each wave group is derivable by simple criteria on the contour. Typical results for the time-domain response for an internal point force as well as the degenerate case of a surface point source are included for comparison and illustrations.

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