PROPAGATION OF RADIO WAVES OVER A STRATIFIED GROUND

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 416-422 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Dielectric Constant ◽  
General Expression ◽  
Numerical Calculations ◽  
Stratified Medium ◽  
Radio Waves ◽  
Number Of Layers ◽  
Special Case ◽  
Wave Tilt

The propagation of vertically polarized radio waves over a horizontally stratified medium is investigated. A general expression for the “wave tilt” is derived for the case of any number of layers with arbitrary properties in each layer. Numerical calculations are carried out for the special case of only two layers which show that the conductivity and dielectric constant variations of the lower layers will affect the magnitude and phase of the wave tilt.

scholarly journals A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
X. Bai ◽  
C. Hasan ◽  
M. Mobedi ◽  
A. Nakayama
Keyword(s):  
Thermal Conductivity ◽  
General Expression ◽  
Metal Foam ◽  
Solid Angle ◽  
Periodic Structures ◽  
Three Dimensional ◽  
High Thermal Conductivity ◽  
Numerical Calculations ◽  
The One ◽  
Good Agreement

A general expression has been obtained to estimate thermal conductivities of both stochastic and periodic structures with high-solid thermal conductivity. An air layer partially occupied by slanted circular rods of high-thermal conductivity was considered to derive the general expression. The thermal conductivity based on this general expression was compared against that obtained from detailed three-dimensional numerical calculations. A good agreement between two sets of results substantiates the validity of the general expression for evaluating the stagnant thermal conductivity of the periodic structures. Subsequently, this expression was averaged over a hemispherical solid angle to estimate the stagnant thermal conductivity for stochastic structures such as a metal foam. The resulting expression was found identical to the one obtained by Hsu et al., Krishnan et al., and Yang and Nakayama. Thus, the general expression can be used for both stochastic and periodic structures.

Radio-wave reflectivity from cold glaciers

2020 ◽  
Author(s):  
Olga Yushkova ◽  
Taisiya Dymova ◽  
Viktor Popovnin
Keyword(s):  
Dielectric Constant ◽  
Dielectric Permittivity ◽  
Reflection Coefficient ◽  
Surface Temperature ◽  
Frequency Dependence ◽  
Depth Profile ◽  
Loss Tangent ◽  
Thin Layers ◽  
The Arctic ◽  
Radio Waves

<p>Radio echo-sounding is a powerful technique for investigating the subsurface of the glaciers. However, physics underlying the formation of the reflected signal is sometimes oversimplified  in the geophysical glacier studies, leading to wrong results. Various remote sensing techniques use different wavelengths (e.g., 13.575 GHz for CryoSat and 20-25/200-600 MHz for ground-penetrating radar), but it is still not clear which particular wavelengths are the best to detect different characteristics of the ice. Possibly, the results gained using different wavelengths may not coincide but rather complement each other due to frequency dependence of the dielectric permittivity and conductivity of snow, ice and especially water.</p><p>Here we attempt to construct an electrophysical model of a cold glacier. This mathematical model considers the variability of the depth profile of the complex dielectric permittivity depending on the frequency of the probing radio signal and the surface temperature. A series of calculations of the reflection coefficients of radio waves from the modelled glacier show that at low temperatures for frequencies above 1 MHz the real part of the dielectric constant of the glacier does not change with frequency and surface temperature, but depends on the glacier structure, while the depth profile of the loss tangent is constant throughout the glacier.  As wavelength decreases, the absorption of radio-waves by the glacier decreases and the frequency dependence of the reflection coefficient becomes a periodic function, its period and amplitude depend on the glacier thickness, the dielectric constant of the bedrock and ice on the surface.</p><p>The range of radio-waves from 0.1 to 1 MHz is not optimal for sounding cold glaciers: the absorption of radio-waves by ice is large for studying thick layers of the glacier, and the wavelength does not allow studying thin layers. Hence, reflection from the glacier surface prevails upon reflection of the signal. The small absorption of short radio waves by ice leads to the fact that the frequency dependence of the reflection coefficient of short radio-waves is practically the sum of the partial reflections of radio-waves from the surface and internal snow/firn and firn/ice boundaries. Period and amplitude of oscillations of the function  depend on the depth of the internal boundaries and the gradient of dielectric characteristics of ice, snow, firn and bedrock.</p><p>Changes in surface temperature, leading to a change in the loss tangent of the upper glacier layers, are manifested in the phase magnitude of the reflection coefficient of radio-waves:it grows with the temperature. Theoretically, the high-frequency signal reflected from the glacier contains information about the structure of the cold glacier and the depth distribution of the dielectric constant, but to restore the electrophysical parameters of the glaciers, it is necessary to use a broadband signal with smooth spectrum and high digitization speed.</p><p>The reported study was funded by RFBR, project number 18-05-60080 (“Dangerous nival-glacial and cryogenic processes and their impact on infrastructure in the Arctic”).</p>

Comparative Study on the Effective Dielectric Constant of the Graded Composites

2013 ◽  
Vol 677 ◽  
pp. 192-196
Author(s):  
Chun Zhen Fan ◽  
Jun Qiao Wang ◽  
Er Jun Liang
Keyword(s):  
Dielectric Constant ◽  
Approximation Method ◽  
Dipole Approximation ◽  
Effective Dielectric Constant ◽  
Gradual Transition ◽  
Sum Rule ◽  
Number Of Layers ◽  
Continuous Band ◽  
Rule Method ◽  
Good Agreement

The effective dielectric constant of the graded composites was calculated with three different methods, namely, the nonlinear differential effective dipole approximation method (NDEDA), the Maxwell-Garnette method (MGT) and the sum rule method (Sum). In each layer of the graded composites, the distribution of the dielectric constant follows a Drude form. Our numerical results show that when the number of layers N inside the graded composites increases, a gradual transition from sharp peaks to an emerging broad continuous band is clearly obtained. Moreover, the results obtained by the MGT and sum rule methods achieve a good agreement with that by the NDEDA method when N is approaching infinity.

scholarly journals Identification and localization of layers in the ionosphere using the eikonal and amplitude of radio occultation signals

2011 ◽  
Vol 4 (2) ◽  
pp. 1465-1492
Author(s):  
A. G. Pavelyev ◽  
K. Zhang ◽  
J. Wickert ◽  
T. Schmidt ◽  
Y.-A. Liou ◽  
...  
Keyword(s):  
Radio Occultation ◽  
Stratified Medium ◽  
Communication Link ◽  
Radio Waves ◽  
Acceleration Technique ◽  
Ionosphere Model ◽  
Different Types ◽  
Phase Variations ◽  
Waves Propagation ◽  
Analytical Expressions

Abstract. Conditions for communication, navigation, and remote sensing in the ionosphere and atmosphere depend strongly on the ionospheric impact on the radio waves propagation. By use of the CHAllenge Minisatellite Payload (CHAMP) radio occultation (RO) data a description of different types of the ionospheric contributions to the RO signals at the altitudes 30–90 km of the RO ray perigee is introduced and compared with results of measurements obtained earlier in the communication link satellite-to-Earth at frequency 1.5415 GHz. An analytical model is introduced for description of the radio waves propagation in a stratified medium consisting of sectors having the spherically symmetric distributions of refractivity. Model presents analytical expressions for the phase path and refractive attenuation of radio waves. Model is applied for analysis of the radio waves propagation effects along a prolonged path including the atmosphere and two parts of the ionosphere. Model explains significant amplitude and phase variations at the altitudes 30–90 km of the RO ray perigee as connected with influence of the inclined ionospheric layers. An innovative eikonal acceleration technique is described and applied for the identification of the inclined ionospheric layers contributions and their location. Possibility to separate the influence of layered structures from contributions of irregularities and turbulence is analyzed.

Wave tilt of radio waves propagating over a layered ground

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1647-1652 ◽  
Author(s):  
James R. Wait ◽  
Khalid A. Nabulsi
Keyword(s):  
Frequency Dependence ◽  
Half Space ◽  
Electrical Characteristic ◽  
Radio Waves ◽  
Complex Wave ◽  
Height Dependence ◽  
Layered Ground ◽  
Wave Tilt ◽  
Layered Half Space

We call attention here to the limitation of the “Q approximation” in characterizing the complex wave tilt W over a layered half‐space. Using an improved formulation the frequency dependence of W is shown to be a discriminator of the electrical characteristic of the subsurface. The height dependence of the observer is also illustrated.

scholarly journals Spectral Equations for the Modular Oscillator

2018 ◽  
Vol 30 (07) ◽  
pp. 1840009 ◽  
Author(s):  
Rinat M. Kashaev ◽  
Sergey M. Sergeev
Keyword(s):  
Spectral Problem ◽  
Topological Strings ◽  
Numerical Calculations ◽  
Planck’S Constant ◽  
Analytical Results ◽  
Planck's Constant ◽  
Special Case ◽  
Calabi Yau Manifolds

Motivated by applications for non-perturbative topological strings in toric Calabi–Yau manifolds, we discuss the spectral problem for a pair of commuting modular conjugate (in the sense of Faddeev) Harper type operators, corresponding to a special case of the quantized mirror curve of local [Formula: see text] and complex values of Planck’s constant. We illustrate our analytical results by numerical calculations. In memory of Ludwig Faddeev

Dielectric Response of Structured Multilayered Polyvinylidene Fluoride Films

2013 ◽  
Vol 721 ◽  
pp. 121-124
Author(s):  
Long Jiang ◽  
Qiong Fu ◽  
Wei Ping Li
Keyword(s):  
Dielectric Constant ◽  
Theoretical Model ◽  
Dielectric Property ◽  
Spin Coating ◽  
Dielectric Response ◽  
Polyvinylidene Fluoride ◽  
High Energy ◽  
Multilayer Films ◽  
Material Structure ◽  
Number Of Layers

To make clear the effect of thickness and layer number on the dielectric property of poly (vinylidenedi fluoride) (PVDF), the different multilayer films were prepared by spin coating. The relation between them has been explained by both experimental results and theoretical model. It is found the dielectric constant of multilayer increase linearly with the number of layers but decrease with the thickness. It is helpful to optimize the material structure and size parameters of polymer films for high energy capacitors.

scholarly journals Energy characteristics of the uav-based georadar for searching a water layer in aroid areas.

2021 ◽  
Author(s):  
A.I. Baskakov ◽  
◽  
Bukhtsooj Odsuren ◽  
A.A. Komarov ◽  
Galbaatar Tuvdendorj ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Water Content ◽  
Unmanned Aerial Vehicle ◽  
Water Layer ◽  
Soil Types ◽  
Radio Waves ◽  
Energy Characteristics ◽  
Specific Attenuation ◽  
Aerial Vehicle ◽  
Desert Regions

In this paper we consider the calculation of the potential of a georadar on board an unmanned aerial vehicle designed to search for groundwater in arid and desert regions of Mongolia. The soil types prevailing in the regions under study were taken as soils as a medium for the propagation of radio waves. A feature of soils in arid and deserted regions is that they have almost the same dielectric constant, with only a slight difference in specific attenuation due to low water content. Soils with possible typical models of changes in the dielectric constant of the soil along the depth are considered.

THE REFLECTION OF WAVES IN A GENERALIZED EPSTEIN PROFILE

1965 ◽  
Vol 43 (5) ◽  
pp. 921-934 ◽  
Author(s):  
R. Burman ◽  
R. N. Gould
Keyword(s):  
Refractive Index ◽  
Wave Equation ◽  
Reflection Coefficient ◽  
Approximate Formula ◽  
Reflection And Transmission Coefficients ◽  
Stratified Medium ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Special Case ◽  
Reflection Of Waves

Epstein (1930) and Rawer (1939) studied the reflection of waves in a stratified medium by transforming the hypergeometric equation into the wave equation. A particular case of the Epstein profile is a symmetrical layer. Considerable attention has been given in the literature to this case as well as to symmetrical layers with certain other profiles of the refractive index. In the present paper a generalized Epstein profile is considered and the reflection and transmission coefficients are obtained. The special case in which the refractive index tends to the same constant value on either side of a layer is then discussed. The symmetrical Epstein profile is a special case of this layer which, in general, is asymmetrical. Particular attention is given to a layer differing only slightly from the symmetrical Epstein layer, a simple approximate formula for the reflection coefficient being derived.

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