scholarly journals PROPAGATION OF EXPLOSIVE SOUND IN A LIQUID LAYER OVERLYING A SEMI‐INFINITE ELASTIC SOLID

Geophysics ◽  
1950 ◽  
Vol 15 (3) ◽  
pp. 426-446 ◽  
Author(s):  
Frank Press ◽  
Maurice Ewing
Keyword(s):  
Phase Velocity ◽  
Pressure Distribution ◽  
Group Velocity ◽  
Normal Mode ◽  
Liquid Layer ◽  
Elastic Solid ◽  
Mode Propagation ◽  
Vertical Pressure ◽  
Velocity Amplitude ◽  
Incoming Signal

The Pekeris theory of normal mode propagation of explosion sound in two liquid layers is extended to include the case of a solid bottom. Curves giving phase velocity, group velocity, amplitude, vertical pressure distribution as a function of frequency are presented. The relative merits of geophones and hydrophones for underwater seismology and the best depth for each type of instrument are discussed in the light of the theory. The characteristics of an incoming signal are described.

Dispersive properties of a fluid layer overlying a semi-infinite elastic solid*

1954 ◽  
Vol 44 (3) ◽  
pp. 493-512
Author(s):  
Ivan Tolstoy
Keyword(s):  
Elastic Body ◽  
Group Velocity ◽  
Normal Mode ◽  
Fundamental Mode ◽  
Fluid Layer ◽  
Elastic Solid ◽  
Numerical Results ◽  
Stoneley Wave ◽  
Wave Velocities ◽  
Minimum Group

Abstract The dispersive properties of waves propagating in a system consisting of a fluid layer overlying a semi-infinite elastic body are investigated by means of new formulas for the group velocity. The distribution of stationary values of the group velocity is examined in the light of these formulas and of numerical results. Also it is shown that the minimum group velocity of the fundamental mode may belong either to the normal-mode branch or to the Stoneley-wave branch, depending on the contrast in wave velocities between the two media.

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.

Field Performance and Analysis of 3-m-Diameter Induced Trench Culvert under a 19.4-m Soil Cover

2008 ◽  
Vol 2045 (1) ◽  
pp. 68-76 ◽  
Author(s):  
Bethanie A. Parker ◽  
Rodney P. McAffee ◽  
Arun J. Valsangkar
Keyword(s):  
Pressure Distribution ◽  
Earth Pressure ◽  
Field Performance ◽  
Overburden Pressure ◽  
Vertical Pressure ◽  
Earth Pressures ◽  
Design Loads ◽  
Horizontal Pressure ◽  
Two Stages

An induced trench installation was instrumented to monitor earth pressures and settlements during construction. Some of the unique features of this case study are as follows: (a) both contact and earth pressure cells were used; (b) part of the culvert is under a new embankment and part was installed in a wide trench within an existing embankment; (c) a large stockpile was temporarily placed over the induced trench; and (d) the compressible material was placed in two stages. The maximum vertical pressure measured in the field at the crown of the culvert was 0.24 times the overburden pressure. The maximum horizontal pressure measured on the side of the culvert at the springline was 0.45 times the overburden pressure. The column of soil directly above the compressible zone settled approximately 40% more than did the adjacent fill. The field results at the crown and springline compared reasonably with those observed with numerical modeling. However, the overall pressure distribution on the pipe was expected to be nonuniform, the average vertical pressure calculated by using numerical analysis on top of the culvert over its full width was 0.61 times the overburden pressure, and the average horizontal pressure calculated on the side of the culvert over its full height was 0.44 times the overburden pressure. When the full pressure distribution on the pipe is considered, the recommended design loads from the Marston–Spangler theory slightly underpredict the maximum loads, and the vertical loads control the design.

Wheat Loads and Vertical Pressure Distribution in a Full-scale Bin Part I — Filling

1994 ◽  
Vol 37 (5) ◽  
pp. 1613-1619 ◽  
Author(s):  
C. V. Schwab ◽  
I. J. Ross ◽  
G. M. White ◽  
D. G. Colliver
Keyword(s):  
Pressure Distribution ◽  
Full Scale ◽  
Vertical Pressure

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>

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