THE GROUP VELOCITY OF PLANE SURFACE WAVES

1960 ◽  
Vol 38 (6) ◽  
pp. 779-786 ◽  
Author(s):  
A. G. Mungall ◽  
D. Morris
Keyword(s):  
Surface Wave ◽  
Group Velocity ◽  
Plane Surface ◽  
Wave Mode ◽  
Theoretical Treatment ◽  
First Order ◽  
Mode Effects ◽  
Surface Wave Propagation ◽  
Group Velocities ◽  
Good Agreement

The velocity of transmission of a modulated microwave signal over a dielectric-covered plane conductor has been measured over a range of dielectric thicknesses for which the first order TM surface wave mode is known to propagate. An exact theoretical treatment of plane surface wave group velocity for both TM and TE surface wave modes of any order has been developed and calculations carried out for the first two orders. The experimentally determined signal velocities are in good agreement with the group velocities calculated for the first order TM mode. Effects of possible surface wave propagation on the accuracy of microwave distance-measuring methods are discussed.

Peculiarities of surface-wave propagation across central Eurasia

1992 ◽  
Vol 82 (6) ◽  
pp. 2464-2493
Author(s):  
Anatoli Levshin ◽  
Ludmila Ratnikova ◽  
Jon Berger
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Polarization Analysis ◽  
Period Range ◽  
Wave Refraction ◽  
Phase Velocities ◽  
Central Eurasia ◽  
Surface Wave Propagation ◽  
Group And Phase Velocities ◽  
Group Velocities

Abstract The recent installation of six broadband digital IRIS/IDA seismic stations in the USSR has provided new opportunities for studying surface-wave propagation across Eurasia. Group velocities of fundamental Rayleigh and Love modes between epicenters and these stations were determined for 35 events that occurred since April 1989 to the middle of July 1990 near Eurasia. Differential phase velocities were found for the same arrivals along paths between several pairs of stations. Group and phase velocities were obtained in the period range from 15 to 300 sec. Frequency-time polarization analysis was used for studying polarization properties of surface waves. In some cases, significant anomalies in the particle motion for periods up to 100 sec were observed. They are attributed to surface-wave refraction and scattering due to lateral inhomogeneities at the boundaries and inside the Eurasia continent.

Analysis and simulation for broadening first‐order sea clutter spectrum in high frequency hybrid sky‐surface wave propagation mode

2015 ◽  
Vol 9 (6) ◽  
pp. 609-621 ◽  
Author(s):  
Li Ya‐jun ◽  
Wei Yin‐sheng ◽  
Zhu Yong‐peng ◽  
Guo Ru‐jiang ◽  
Wang Zhuo‐qun ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
High Frequency ◽  
Propagation Mode ◽  
Sea Clutter ◽  
First Order ◽  
Surface Wave Propagation

Weak elastic anisotropy by perturbation theory

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. D45-D58 ◽  
Author(s):  
Vigen Ohanian ◽  
Thomas M. Snyder ◽  
José M. Carcione
Keyword(s):  
Perturbation Theory ◽  
Group Velocity ◽  
Elastic Anisotropy ◽  
Anisotropic Media ◽  
Orthorhombic Symmetry ◽  
Wave Group ◽  
Wave Polarization ◽  
First Order ◽  
Christoffel Equation ◽  
Group Velocities

We demonstrate the advantages of adopting a wave-vector-based coordinate system (WCS) for the application of perturbation theory to derive and display approximate expressions for qP- and qS-wave polarization vectors, phase velocities, and group velocities in general weakly anisotropic media. The advantages stem from two important properties of the Christoffel equation when expressed in the WCS: (1) Each element of the Christoffel matrix is identical to a specific stiffness component in the WCS, and (2) the Christoffel matrix of an isotropic medium is diagonal in the WCS. Using these properties, one can easily identify the small components of the Christoffel matrix in the WCS for a weakly anisotropic medium. Approximate solutions to the Christoffel equation are then obtained by straightforward algebraic manipulations, which make our perturbation theory solution considerably simpler than previously published methods. We compare and contrast our solutions with those discussed by other workers. Numerical comparisons between the exact, first-order, and zero-order qS-wave polarization vectors illustrate the accuracy of our approximate formulas. The form of the WCS phase-velocity expressions facilitates the derivation of closed-form, first-order expressions for qP- and qS-wave group-velocity vectors, providing explicit formulas for the direction of propagation of seismic energy in general weakly anisotropic media. Numerical evaluation of our group-velocity expressions demonstrates their accuracy. We discuss problems with the approximate qS-wave group velocities and polarizations in neighboring directions of singularities. Standard methods are used to transform our solutions from the WCS to the acquisition coordinates, as illustrated by application to orthorhombic symmetry.

Wavelet Analysis of Laser-Generated Surface Waves in a Layered Structure With Unbond Regions

1999 ◽  
Vol 66 (2) ◽  
pp. 507-513 ◽  
Author(s):  
T.-T. Wu ◽  
Y.-Y. Chen
Keyword(s):  
Wavelet Transform ◽  
Surface Wave ◽  
Surface Waves ◽  
Group Velocity ◽  
Layered Structure ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Copper Aluminum ◽  
Experimental Dispersion ◽  
Good Agreement

This paper presents the results on the utilization of a wavelet transform to study the dispersion of laser-generated surface waves in an epoxy-bonded copper-aluminum layered specimen with and without unbond areas. Laser ultrasonic experiments based on the point-source/point-receiver (PS/PR) technique were undertaken to measure surface wave signals in a layered specimen. The wavelet transform with a Morlet wavelet function was adopted to analyze the group velocity dispersion of the surface wave signals. A novel hybrid formula for group velocity dispersion is proposed for measurements across unbond regions. Results and data obtained are in good agreement with calculated and experimental dispersion curves. The general behavior of the group velocity dispersion for different measurement, configurations can be utilized to differentiate the unbond regions in a layered structure.

Extraction of phase and group velocities from ambient surface noise in a patch-array configuration

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. KS231-KS240 ◽  
Author(s):  
Malgorzata Chmiel ◽  
Philippe Roux ◽  
Thomas Bardainne
Keyword(s):  
Surface Wave ◽  
Group Velocity ◽  
Seismic Analysis ◽  
Vertical Component ◽  
Noise Sources ◽  
Array Design ◽  
Near Surface ◽  
Phase And Group Velocities ◽  
Group Velocities ◽  
Surface Noise

We have investigated the use of ambient-noise data to extract phase and group velocities from surface-noise sources in a microseismic monitoring context. The data were continuously recorded on 44 patch arrays with an interpatch distance on the order of 1 km. Typically, a patch-array design consists of a few tens of patches, each containing 48 strings of 12 single-vertical-component geophones densely distributed within the patch area. The specificity of the patch-array design allows seismic analysis at two different scales. Within each patch, highly coherent signals at small distances provide phase information at high frequency (up to 10 Hz), from which surface-wave phase velocities can be extracted. Between the pairs of patches, surface-wave group-velocity maps can be built using correctly identified and localized surface-noise sources. The technique can be generalized to every patch pair using different noise sources identified at the surface. We note that the incoherent but localized noise sources accelerate the convergence of the noise-correlation functions. This opens the route to passive seismic monitoring of the near surface from repetitive inversion of phase- and group-velocity maps.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

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