scholarly journals A SEISMIC WAVE GUIDE PHENOMENON

Geophysics ◽  
1951 ◽  
Vol 16 (4) ◽  
pp. 594-612 ◽  
Author(s):  
K. E. Burg ◽  
Maurice Ewing ◽  
Frank Press ◽  
E. J. Stulken
Keyword(s):  
Phase Velocity ◽  
Shallow Water ◽  
Group Velocity ◽  
Seismic Wave ◽  
Normal Modes ◽  
Seismic Energy ◽  
Wave Guide ◽  
Energy Propagation ◽  
Effective Wave ◽  
Favorable Conditions

On one particular prospect in shallow water repetitive patterns appeared on short spread seismograms in such prevalence as to jeopardize identification of desired reflections. It is demonstrated that under favorable conditions, less restrictive than thought necessary heretofore, a layer of water comprises an effective wave guide for seismic energy propagation. Reinforcement fronts formed by multiple reflection of sound in water can develop into a set of waves completely overshadowing other seismic arrivals. With but minor modifications conventional wave guide theory applies. Examples from the prospect are presented to illustrate various reinforcement patterns. Observed frequency characteristics, group velocity, and phase velocity magnitudes are investigated for normal modes of propagation.

scholarly journals Analyzing sound speed fluctuations in shallow water from group-velocity versus phase-velocity data representation

2013 ◽  
Vol 133 (4) ◽  
pp. 1945-1952 ◽  
Author(s):  
Philippe Roux ◽  
W. A. Kuperman ◽  
Bruce D. Cornuelle ◽  
Florian Aulanier ◽  
W. S. Hodgkiss ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Shallow Water ◽  
Group Velocity ◽  
Sound Speed ◽  
Data Representation ◽  
Velocity Versus ◽  
Velocity Data ◽  
Versus Phase ◽  
Speed Fluctuations

Supercritical Group Velocity for Dissipative Waves in Shallow Water

2012 ◽  
Author(s):  
Tae-Hwa Jung ◽  
Changhoon Lee
Keyword(s):  
Energy Dissipation ◽  
Phase Velocity ◽  
Shallow Water ◽  
Group Velocity ◽  
Water Depth ◽  
Numerical Experiments ◽  
Angular Frequency ◽  
Wave Number ◽  
Geometric Optics ◽  
Complex Valued

The group velocity for waves with energy dissipation in shallow water was investigated. In the Eulerian viewpoint, the geometric optics approach was used to get, at the first order, complex-valued wave numbers from given real-valued angular frequency, water depth, and damping coefficient. The phase velocity was obtained as the ratio of angular frequency to realvalued wave number. Then, at the second order, we obtained the energy transport equation which gives the group velocity. We also used the Lagrangian geometric optics approach which gives complex-valued angular frequencies from real-valued wave number, water depth, and damping coefficient. A noticeable thing was found that the group velocity is always greater than the phase velocity (i.e., supercritical group velocity) in the presence of energy dissipation which is opposite to the conventional theory for non-dissipative waves. The theory was proved through numerical experiments for dissipative bichromatic waves which propagate on a horizontal bed. Both the wave length and wave energy decrease for waves with energy dissipation. As a result, wave transformation such as shoaling, refraction, and diffraction are all affected by the energy dissipation. This implies that the shoaling, refraction, and diffraction coefficients for dissipative waves are different from the corresponding coefficients for non-dissipative waves. The theory was proved through numerical experiments for dissipative monochromatic waves which propagate normally or obliquely on a planar slope.

Research on Elastic Scattered Wave of Submerged Elastic Plate

2013 ◽  
Vol 303-306 ◽  
pp. 2779-2783
Author(s):  
Wen Jian Chen ◽  
Hui Sun ◽  
Tie Lin Sun
Keyword(s):  
Elastic Scattering ◽  
Phase Velocity ◽  
Group Velocity ◽  
Elastic Plate ◽  
Lamb Wave ◽  
Arrival Time ◽  
Group Velocity Dispersion ◽  
Scattered Wave ◽  
Energy Propagation ◽  
Scattering Wave

It is proved by theory and experiment that the arrival time of elastic scattering wave is determined by group velocity of Lamb wave in plate and the speed of elastic scattering wave in water. The frequency dispersion equation of Lamb wave is derived for submerged elastic plate, and the phase velocity and group velocity dispersion curves are obtained by numerical calculation method. It is found that the phase velocity is greater or less than the group velocity at different frequency-thickness products. The energy propagation speed of wave is group velocity, so the arrival time of elastic scattering wave is determined by group velocity of Lamb wave in plate and the speed of sound in water. Experimental results show that elastic scattering wave is ahead of or behind the edge wave in echoes of elastic steel plate. The experiment results confirm validity of the theoretical analysis results.

Attenuation of the Lg phase and the determination of mb in the southeastern United States

1979 ◽  
Vol 69 (1) ◽  
pp. 45-63
Author(s):  
G. A. Bollinger
Keyword(s):  
United States ◽  
Phase Velocity ◽  
Group Velocity ◽  
Southeastern United States ◽  
Source Area ◽  
Wave Guide ◽  
Propagation Path ◽  
Lateral Heterogeneity ◽  
Related Effect

abstract A study of the Lg radiation from 17 southeastern U.S. earthquakes shows the attenuation of that phase to be at a 0.07°−1 rate for epicentral distances of 100 to 700 km. At longer distances, it is also at that rate for some of the earthquakes, but for five of the events it was at a somewhat greater (0.10°−1) rate. These different Lg attenuation rates are clearly a distance-related effect, but they are not caused by differences in source area, propagation path, radiation pattern, wave period, or group velocity. A possible explanation for the different attenuation rates is a shift from a normal-mode form of propagation to a leaking-mode form, brought about by slight phase-velocity variations in the crustal wave guide and/or in the underlying layer. Also, the influence of lateral heterogeneity and variations in the thickness of the crustal wave guide offer alternative explanations. Nuttli's (1973) mb (Lg) formulas, determined for central U.S. events, were found to be appropriate for use on southeastern U.S. shocks if their application is restricted to epicentral distances less than 2,000 km. This distance-restriction result agrees with that determined for the northeastern U.S. earthquakes by Street (1976).

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

The relationship between group velocity and phase velocity for finite, discrete observations

1977 ◽  
Vol 67 (5) ◽  
pp. 1249-1258
Author(s):  
Douglas C. Nyman ◽  
Harsh K. Gupta ◽  
Mark Landisman
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
The Other ◽  
Frequency Range ◽  
Finite Frequency ◽  
Discrete Observations ◽  
Practical Situation ◽  
Order Polynomial ◽  
Observational Errors ◽  
The Relationship

abstract The well-known relationship between group velocity and phase velocity, 1/u = d/dω (ω/c), is adapted to the practical situation of discrete observations over a finite frequency range. The transformation of one quantity into the other is achieved in two steps: a low-order polynomial accounts for the dominant trends; the derivative/integral of the residual is evaluated by Fourier analysis. For observations of both group velocity and phase velocity, the requirement that they be mutually consistent can reduce observational errors. The method is also applicable to observations of eigenfrequency and group velocity as functions of normal-mode angular order.

Attenuation of dispersed wave trains

1962 ◽  
Vol 52 (1) ◽  
pp. 109-112
Author(s):  
James N. Brune
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Seismic Waves ◽  
Free Oscillations ◽  
Wave Trains

Abstract It is shown that groups of seismic waves are attenuated by the factor exp −exp⁡−πXQUT where X is the distance, U the group velocity, T the period and Q−1 is a measure of the damping of free oscillations. Accordingly, observations of Q given by Ewing and Press (1954 a, b) and Sato (1958) are revised by the ratio of the phase velocity to the group velocity.

scholarly journals Sensitivities of surface wave velocities to the medium parameters in a radially anisotropic spherical Earth and inversion strategies

2015 ◽  
Vol 58 (5) ◽  
Author(s):  
Sankar N. Bhattacharya
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Love Waves ◽  
P Wave ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Wave Velocities ◽  
Spherical Earth

<p>Sensitivity kernels or partial derivatives of phase velocity (<em>c</em>) and group velocity (<em>U</em>) with respect to medium parameters are useful to interpret a given set of observed surface wave velocity data. In addition to phase velocities, group velocities are also being observed to find the radial anisotropy of the crust and mantle. However, sensitivities of group velocity for a radially anisotropic Earth have rarely been studied. Here we show sensitivities of group velocity along with those of phase velocity to the medium parameters <em>V<sub>SV</sub>, V<sub>SH </sub>, V<sub>PV</sub>, V<sub>PH , </sub></em><em>h</em><em> </em>and density in a radially anisotropic spherical Earth. The peak sensitivities for <em>U</em> are generally twice of those for <em>c</em>; thus <em>U</em> is more efficient than <em>c</em> to explore anisotropic nature of the medium. Love waves mainly depends on <em>V<sub>SH</sub></em> while Rayleigh waves is nearly independent of <em>V<sub>SH</sub></em> . The sensitivities show that there are trade-offs among these parameters during inversion and there is a need to reduce the number of parameters to be evaluated independently. It is suggested to use a nonlinear inversion jointly for Rayleigh and Love waves; in such a nonlinear inversion best solutions are obtained among the model parameters within prescribed limits for each parameter. We first choose <em>V<sub>SH</sub></em>, <em>V<sub>SV </sub></em>and <em>V<sub>PH</sub></em> within their corresponding limits; <em>V<sub>PV</sub></em> and <em>h</em> can be evaluated from empirical relations among the parameters. The density has small effect on surface wave velocities and it can be considered from other studies or from empirical relation of density to average P-wave velocity.</p>

Separation of acoustic normal modes in shallow water

2021 ◽  
Vol 149 (4) ◽  
pp. A66-A67
Author(s):  
Sergei Sergeev ◽  
Konstantin Dmitriev ◽  
Andrey Shurup
Keyword(s):  
Shallow Water ◽  
Normal Modes
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