ON THE VIBRATION OF SATURATED LAYERED HALF-SPACE DUE TO LOW FREQUENCY EXCITATION

1998 ◽  
Vol 213 (3) ◽  
pp. 561-568
Author(s):  
J. Yang ◽  
T. Sato
Keyword(s):  
Half Space ◽  
Low Frequency ◽  
Frequency Excitation ◽  
Layered Half Space

Very low‐frequency electromagnetic response of a perfectly conducting half‐plane in a layered half‐space

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 1059-1067 ◽  
Author(s):  
M. Poddar
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Half Plane ◽  
Tilt Angle ◽  
Low Frequency ◽  
Method Of Successive Approximations ◽  
Very Low Frequency ◽  
Depth Of Burial ◽  
Layered Half Space ◽  
Conductivity Contrast

Following Dmitriev (1961), a rigorous theoretical solution for the problem of scattering by a perfectly conducting inclined half‐plane in a layered half‐space in a plane‐wave field has been obtained. The solution is in the form of a Fredholm integral equation of the second kind, where the unknown is the Laplace transform of scattering current in the half‐plane. The integral equation is solved numerically by the method of successive approximations. The scattered fields at the surface of the half‐space are found by integrating the half‐space Green’s function over the transform of the scattering current. The effects of depth of burial and inclination of the half‐plane, conductivity contrast between the overburden and the substratum, and thickness of the overburden are studied in some detail. As expected, the tangent of the tilt angle and the ellipticity of the ellipse of magnetic polarization decrease rapidly with increasing depth of burial, conductivity contrast, and thickness. Inclination introduces asymmetry in the anomaly profile besides affecting its magnitude. Depth of exploration is greater for the ellipticity than for the tilt angle. A target depth equal to half of the skin depth in the substratum is the limiting depth of detection in the very low‐frequency, electromagnetic (VLF-EM) method. An interpretation scheme for VLF-EM field data is presented, based on peak‐to‐peak separation and difference between peaks of the two polarization parameters.

Seismic Waves in a Laterally Inhomogeneous Layered Medium, Part I: Theory

1997 ◽  
Vol 64 (1) ◽  
pp. 50-58 ◽  
Author(s):  
Ruichong Zhang ◽  
Liyang Zhang ◽  
Masanobu Shinozuka
Keyword(s):  
Wave Field ◽  
Half Space ◽  
Seismic Waves ◽  
Scattered Wave ◽  
Inhomogeneous Layer ◽  
Dislocation Source ◽  
Seismic Dislocation ◽  
Body Forces ◽  
The Mean ◽  
Layered Half Space

Seismic waves in a layered half-space with lateral inhomogeneities, generated by a buried seismic dislocation source, are investigated in these two consecutive papers. In the first paper, the problem is formulated and a corresponding approach to solve the problem is provided. Specifically, the elastic parameters in the laterally inhomogeneous layer, such as P and S wave speeds and density, are separated by the mean and the deviation parts. The mean part is constant while the deviation part, which is much smaller compared to the mean part, is a function of lateral coordinates. Using the first-order perturbation approach, it is shown that the total wave field may be obtained as a superposition of the mean wave field and the scattered wave field. The mean wave field is obtainable as a response solution for a perfectly layered half-space (without lateral inhomogeneities) subjected to a buried seismic dislocation source. The scattered wave field is obtained as a response solution for the same layered half-space as used in the mean wave field, but is subjected to the equivalent fictitious distributed body forces that mathematically replace the lateral inhomogeneities. These fictitious body forces have the same effects as the existence of lateral inhomogeneities and can be evaluated as a function of the inhomogeneity parameters and the mean wave fleld. The explicit expressions for the responses in both the mean and the scattered wave fields are derived with the aid of the integral transform approach and wave propagation analysis.

Accurate Low-Frequency Approximation for Wires Within a Conducting Half-Space

2020 ◽  
Vol 62 (1) ◽  
pp. 272-275
Author(s):  
Blagoja Markovski ◽  
Leonid Grcev ◽  
Vesna Arnautovski-Toseva
Keyword(s):  
Half Space ◽  
Low Frequency ◽  
Frequency Approximation
Sign in / Sign up

Export Citation Format

Share Document