A novel half space time-domain measurement technique for one-dimensional microwave imaging

The electromagnetic (EM) fields in a one‐dimensional (1-D) earth due to a dipole or loop transmitter have been studied by a number of authors, including Lewis and Lee (1978), Pridmore (1978), Nabighian (1979), and Hoversten and Morrison (1982). Nabighian (1979) aptly described the time‐domain‐induced current system in a homogeneous half‐space as resembling a “smoke ring” blown by the transmitter, which moves outwards and downwards and diminishes in amplitude with increasing time after the transmitter is turned off. In a homogeneous half‐space, the physical electric field maximum moves outward from the transmitter loop edge at an angle of approximately 30° with the surface. Hoversten and Morrison (1982) show how the direction of propagation of the time‐domain electric field maximum is affected by conductivity structure. In the case of a highly conductive overburden over a resistive basement, the electric field maximum travels essentially horizontally away from the transmitter, and is effectively trapped in the upper layer.

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Numerical solution to a nonlinear, one-dimensional problem of anisotropic thermoelasticity with volume force and heat supply in a half-space: interaction of displacements

Archive of Applied Mechanics ◽

10.1007/s00419-014-0921-3 ◽

2014 ◽

Vol 85 (4) ◽

pp. 433-454 ◽

Cited By ~ 2

Author(s):

W. Mahmoud ◽

A. F. Ghaleb ◽

E. K. Rawy ◽

H. A. Z. Hassan ◽

A. A. Mosharafa

Keyword(s):

Numerical Solution ◽

Half Space ◽

Heat Supply ◽

Dimensional Problem ◽

Volume Force ◽

One Dimensional

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Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method

Applied Sciences ◽

10.3390/app11083421 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3421

Author(s):

Cheng-Yu Ku ◽

Li-Dan Hong ◽

Chih-Yu Liu ◽

Jing-En Xiao ◽

Wei-Po Huang

Keyword(s):

Porous Media ◽

Time Domain ◽

Numerical Solutions ◽

Space Time ◽

Two Dimensional ◽

Transient Flows ◽

Layered Porous Media ◽

Time Marching ◽

Time Basis ◽

Marching Scheme

In this study, we developed a novel boundary-type meshless approach for dealing with two-dimensional transient flows in heterogeneous layered porous media. The novelty of the proposed method is that we derived the Trefftz space–time basis function for the two-dimensional diffusion equation in layered porous media in the space–time domain. The continuity conditions at the interface of the subdomains were satisfied in terms of the domain decomposition method. Numerical solutions were approximated based on the superposition principle utilizing the space–time basis functions of the governing equation. Using the space–time collocation scheme, the numerical solutions of the problem were solved with boundary and initial data assigned on the space–time boundaries, which combined spatial and temporal discretizations in the space–time manifold. Accordingly, the transient flows through the heterogeneous layered porous media in the space–time domain could be solved without using a time-marching scheme. Numerical examples and a convergence analysis were carried out to validate the accuracy and the stability of the method. The results illustrate that an excellent agreement with the analytical solution was obtained. Additionally, the proposed method was relatively simple because we only needed to deal with the boundary data, even for the problems in the heterogeneous layered porous media. Finally, when compared with the conventional time-marching scheme, highly accurate solutions were obtained and the error accumulation from the time-marching scheme was avoided.

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