Surface slope tolerances: the transition from geometric raytracing to scalar wave theory

2021 ◽  
Author(s):  
John R. Rogers
Keyword(s):  
Wave Theory ◽  
Scalar Wave ◽  
Surface Slope

scholarly journals Interpretation of Radio Echoes from Storglaciären, Northern Sweden

1986 ◽  
Vol 32 (110) ◽  
pp. 39-49 ◽  
Author(s):  
M. E. R. Walford ◽  
M. I. Kennett ◽  
P. Holmlund
Keyword(s):  
Wave Theory ◽  
Scalar Wave ◽  
Northern Sweden ◽  
Long Term Changes

AbstractStorglaciären (lat. 67.5° N., long. 17.5° E.) is a sub-polar glacier which has been the object of detailed study for many years. It responds in a sensitive way to annual and long-term changes in climate but it does not surge. Conditions at the bed and the distribution of englacial water are of considerable interest. In this paper we discuss an attempt to learn something about these matters by radio-echo soundings at metric and decametric wavelengths. We analyse radio-echo records mainly using a scalar-wave theory of the diffraction of pulses. The pulse shapes of echoes are useful because they help us to recognize the types of target and processes responsible for the echoes. We then use simple statistical measurements of radio echoes to provide estimates of certain average properties of the targets. We estimate, for example, the roughness of the glacier bed and the distribution and orientations of scatterers within the ice.

scholarly journals Interpretation of Radio Echoes from Storglaciären, Northern Sweden

1986 ◽  
Vol 32 (110) ◽  
pp. 39-49 ◽  
Author(s):  
M. E. R. Walford ◽  
M. I. Kennett ◽  
P. Holmlund
Keyword(s):  
Wave Theory ◽  
Scalar Wave ◽  
Northern Sweden ◽  
Long Term Changes

AbstractStorglaciären (lat. 67.5°N., long. 17.5°E.) is a sub-polar glacier which has been the object of detailed study for many years. It responds in a sensitive way to annual and long-term changes in climate but it does not surge. Conditions at the bed and the distribution of englacial water are of considerable interest. In this paper we discuss an attempt to learn something about these matters by radio-echo soundings at metric and decametric wavelengths. We analyse radio-echo records mainly using a scalar-wave theory of the diffraction of pulses. The pulse shapes of echoes are useful because they help us to recognize the types of target and processes responsible for the echoes. We then use simple statistical measurements of radio echoes to provide estimates of certain average properties of the targets. We estimate, for example, the roughness of the glacier bed and the distribution and orientations of scatterers within the ice.

scholarly journals Microwave synthesis of Bessel, Bessel–Gauss, and Gaussian beams: a fully vectorial electromagnetic approach

2021 ◽  
pp. 1-8
Author(s):  
Walter Fuscaldo ◽  
Alessio Benedetti ◽  
Davide Comite ◽  
Paolo Burghignoli ◽  
Paolo Baccarelli ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Electromagnetic Fields ◽  
Millimeter Wave ◽  
Microwave Synthesis ◽  
Wave Theory ◽  
Gaussian Beams ◽  
Scalar Wave ◽  
Leaky Waves ◽  
Millimeter Wave Range ◽  
Wave Range

Abstract Bessel, Bessel-Gauss, and Gaussian beams have widely been investigated in optics in the paraxial approximation, under the frame of a scalar wave theory. Such approximations can hardly be applied in the microwave/millimeter-wave range, where the vectorial nature of the electromagnetic fields cannot be neglected, and experimental realizations for some of these beams appeared only recently. In this work, we discuss the generation of Bessel, Bessel-Gauss, and Gaussian beams through a fully vectorial electromagnetic approach. The field derivation of all these beams is first illustrated and numerical evaluations are then reported to compare their different propagation and diffractive behaviors. Finally, an innovative approach for realizing such solutions with planar microwave devices exploiting leaky waves is demonstrated through accurate numerical simulations.

The Nature of Mining-Induced Horizontal Displacement of Surface on the Example of Several Coal Mines

2014 ◽  
Vol 59 (4) ◽  
pp. 971-986 ◽  
Author(s):  
Krzysztof Tajduś
Keyword(s):  
Underground Mining ◽  
Mining Industry ◽  
Horizontal Displacement ◽  
Surface Slope ◽  
Proportionality Coefficient ◽  
Model Studies ◽  
Displacement Vectors ◽  
Mining Conditions ◽  
Design Projects ◽  
Academy Of Sciences

Abstract The paper presents the analysis of the phenomenon of horizontal displacement of surface induced by underground mining exploitation. In the initial part, the basic theories describing horizontal displacement are discussed, followed by three illustrative examples of underground exploitation in varied mining conditions. It is argued that center of gravity (COG) method presented in the paper, hypothesis of Awierszyn and model studies carried out in Strata Mechanics Research Institute of the Polish Academy of Sciences indicate the proportionality between vectors of horizontal displacement and the vector of surface slope. The differences practically relate to the value of proportionality coefficient B, whose estimated values in currently realized design projects for mining industry range between 0.23r to 0.42r for deep exploitations, whereas in the present article the values of 0.33r and 0.47r were obtained for two instances of shallow exploitation. Furthermore, observations on changes of horizontal displacement vectors with face advancement indicated the possibility of existence of COG zones above the mined-out field, which proved the conclusions of hitherto carried out research studies (Tajduś 2013).

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