Elasticity and internal friction in a long column of granite*

1938 ◽  
Vol 28 (4) ◽  
pp. 243-254 ◽  
Author(s):  
Francis Birch ◽  
Dennison Bancroft
Keyword(s):  
Internal Friction ◽  
Elastic Waves ◽  
Seismic Waves ◽  
Frequency Range ◽  
Resonant Vibrations ◽  
Forced Resonant Vibrations

Abstract The forced resonant vibrations of a long column of Quincy granite have been studied with the object of discovering the effect of frequency upon the velocities of elastic waves. Longitudinal, flexural, and torsional modes were used, covering the frequency range 140-4500 cycles per second. For these frequencies the velocities were independent of frequency to within 1 per cent or less. The internal friction was also roughly independent of frequency, with Q = 150. The damping of seismic waves is considered with reference to these results.

SEISMIC DECOUPLING FOR EXPLOSIONS IN SPHERICAL UNDERGROUND CAVITIES

Geophysics ◽  
1961 ◽  
Vol 26 (6) ◽  
pp. 772-799 ◽  
Author(s):  
William M. Adams ◽  
DeWitt C. Allen
Keyword(s):  
Spherical Cavity ◽  
Seismic Waves ◽  
Free Field ◽  
Salt Mine ◽  
Cavity Pressure ◽  
Frequency Range ◽  
Overburden Pressure ◽  
Underground Cavities ◽  
Order Of Magnitude ◽  
Surface Measurements

A series of paired explosions in a salt mine near Winnfield, Louisiana, has been conducted to test a theory by A. L. Latter concerning seismic decoupling by underground cavities. The theory predicted a decoupling of 130. Free‐field and surface measurements from an explosion in either a 6‐ft‐ or a 15‐ft‐radius spherical cavity were compared with similar measurements from a completely tamped explosion of equal size. Shot sizes were from 20 pounds to a ton. Surface measurements were made out to 100 km and covered the frequency range from 0.05 to 100 cps. The experiment confirmed that decoupling does occur. For explosions that produce an average cavity pressure up to one‐fifth and possibly more of the lithostatic overburden pressure, seismic waves were decoupled by more than 100, i.e., two orders of magnitude. Even for explosions producing an average cavity pressure of six times the lithostatic overburden pressure, the seismic waves were decoupled by 20—more than a full order of magnitude. Minimum decoupling factors as a function of frequency are presented.

Diffraction of elastic waves from object in layer with slightly corrugated surface

2017 ◽  
Vol 23 (9) ◽  
pp. 1249-1262 ◽  
Author(s):  
Khaled M Elmorabie ◽  
Rania R Yahya
Keyword(s):  
Elastic Waves ◽  
Perturbation Technique ◽  
Scattering Problem ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Harmonic Load ◽  
Frequency Range ◽  
Corrugated Surfaces ◽  
Geometrical Shapes ◽  
Diffraction Of Elastic Waves

This work is concerned with the influence of corrugated surfaces on waves diffracted from an object in an elastic layer. A boundary value problem is formulated to simulate an anti-plane problem for a harmonic load acting on the upper surface of the layer. By using the boundary integral equation method and the perturbation technique, the considered problem is reduced to a pair of integral equations. By constructing the Green’s function, the scattering problem in a one-mode frequency range is solved. To check the validity of the proposed technique, several numerical examples for different geometrical shapes of the corrugated bottom are presented.

Apparent attenuation of shear waves propagating through a randomly stratified anisotropic medium

2016 ◽  
Vol 16 (04) ◽  
pp. 1650009
Author(s):  
Josselin Garnier ◽  
Knut Sølna
Keyword(s):  
Elastic Waves ◽  
Seismic Waves ◽  
Stochastic Partial Differential Equation ◽  
Heterogeneous Media ◽  
Seismic Attenuation ◽  
The Earth ◽  
Separation Of Scales ◽  
Coherent Pulse ◽  
Apparent Attenuation ◽  
Media Experience

Waves propagating through heterogeneous media experience scattering that can convert a coherent pulse into small incoherent fluctuations. This may appear as attenuation for the transmitted front pulse. The classic O’Doherty–Anstey theory describes such a transformation for scalar waves in finely layered media. Recent observations for seismic waves in the earth suggest that this theory can explain a significant component of seismic attenuation. An important question to answer is then how the O’Doherty–Anstey theory generalizes to seismic waves when several wave modes, possibly with the same velocity, interact. An important aspect of the O’Doherty–Anstey theory is the statistical stability property, which means that the transmitted front pulse is actually deterministic and depends only on the statistics of the medium but not on the particular medium realization when the medium is modeled as a random process. It is shown in this paper that this property generalizes in the case of elastic waves in a nontrivial way: the energy of the transmitted front pulse, but not the pulse shape itself, is statistically stable. This result is based on a separation of scales technique and a diffusion-approximation theorem that characterize the transmitted front pulse as the solution of a stochastic partial differential equation driven by two Brownian motions.

STUDIES ON SEISMIC WAVES: III. PROPAGATION OF ELASTIC WAVES IN THE NEIGHBORHOOD OF A FREE BOUNDARY

Geophysics ◽  
1947 ◽  
Vol 12 (1) ◽  
pp. 57-71 ◽  
Author(s):  
C. Y. Fu
Keyword(s):  
Surface Waves ◽  
Elastic Waves ◽  
Seismic Waves ◽  
Classical Method ◽  
Epicentral Distance ◽  
Harmonic Waves ◽  
Inhomogeneous Waves ◽  
Different Types ◽  
Propagation Of Elastic Waves ◽  
The Waves

Continuous and spherical harmonic waves are generated at an internal point of the medium. By use of the classical method of Sommerfeld, the different modes of propagation near a free surface after the arrival of the waves are examined. From the approximate evaluations of the integrals, it is found that in addition to the ordinary types of body and surface waves, there are also inhomogeneous waves and surface waves which are not of the Rayleigh type. The amplitude factors of these latter waves vary inversely as the square instead of as the square root of the epicentral distance. Altogether, there are not less than five different types of waves and they are obtained from integrations in the neighborhood of the singularities of the integrals.

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