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

Group speed versus phase speed analysis of sound speed fluctuations in a shallow water ocean

2012 ◽  
Vol 131 (4) ◽  
pp. 3450-3450 ◽  
Author(s):  
W. A. Kuperman ◽  
Bruce D. Cornuelle ◽  
W. S. Hodgkiss ◽  
Philippe Roux
Keyword(s):  
Shallow Water ◽  
Sound Speed ◽  
Phase Speed ◽  
Versus Phase ◽  
Group Speed ◽  
Speed Fluctuations

SIMULATION OF UNDERWATER ACOUSTICAL FIELD FLUCTUATIONS IN SHALLOW SEA WITH RANDOM INHOMOGENEITIES OF SOUND SPEED: DEPTH-DEPENDENT ENVIRONMENT

2014 ◽  
Vol 22 (01) ◽  
pp. 1440002 ◽  
Author(s):  
OLEG E. GULIN ◽  
IGOR O. YAROSHCHUK
Keyword(s):  
Shallow Water ◽  
Sound Speed ◽  
Scientific Literature ◽  
Water Layer ◽  
Statistical Simulation ◽  
Frequency Range ◽  
Shallow Sea ◽  
Field Fluctuations ◽  
Pekeris Waveguide ◽  
Speed Fluctuations

Statistical problems encountered in the study of the influence of random inhomogeneities in layered shallow water on the propagation of sound signal is considered. The study is carried out by the example of two-layer models of the sea — a stochastic Pekeris waveguide and a waveguide with a regular refraction in the water layer, which describes the presence of the thermocline. The results were obtained by statistical simulation without approximations and assumptions. In the middle frequency range for actual parameters of sound speed fluctuations in shallow sea with a loss penetrable bottom, the specific features of acoustic field statistical moments behavior have been discovered. They did not get adequate attention in the scientific literature.

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.

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.

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.

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