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.

Comparison of seismic waves generated by different types of source

1963 ◽  
Vol 53 (5) ◽  
pp. 965-978 ◽  
Author(s):  
David E. Willis
Keyword(s):  
Seismic Waves ◽  
Nuclear Explosion ◽  
Test Site ◽  
Frequency Content ◽  
Nevada Test Site ◽  
Different Types ◽  
The Waves ◽  
Source Duration ◽  
Lower Frequencies

Abstract A comparison of the seismic waves generated by a nuclear explosion and an earthquake is discussed. The epicenter of the earthquake was located within the Nevada Test Site. Both events were recorded at the same station with the same type of equipment. The earthquake waves contained slightly lower frequency than the waves generated by the nuclear shot. The early P phases of the shot had larger amplitudes while the phases after Pg for the earthquake were larger. Seismic waves from collapses were generally found to be composed of lower frequencies than the waves from the original shot. Aftershocks of the Hebgen Lake earthquake were found to generate seismic waves whose frequency content was related to the magnitude of the aftershock. Spectral differences in quarry shot recordings that correlate with source duration times are also discussed.

EFFECTS OF A LIQUID CORE ON THE PROPAGATION OF SEISMIC WAVES

1959 ◽  
Vol 37 (2) ◽  
pp. 109-128 ◽  
Author(s):  
George Duwalo ◽  
J. A. Jacobs
Keyword(s):  
Seismic Waves ◽  
Wave Length ◽  
Liquid Core ◽  
Elastic Solid ◽  
Compressible Liquid ◽  
Diffracted Waves ◽  
Viscous Compressible Liquid ◽  
Method Of Residues ◽  
Propagation Of Elastic Waves ◽  
The Waves

Effects of a spherical cavity in an infinite, homogeneous, isotropic elastic solid, containing non-viscous compressible liquid, on the propagation of elastic waves are investigated mathematically. The waves emitted by a simple harmonic point source in the solid are of the types known as SH and P in seismology. The discussion is restricted to the case ka » 1 (ka = 2 π cavity radius/wave length). Series solutions are transformed into contour integrals by Watson's method. Evaluation of these by the method of residues results in expressions describing the P and S components of the diffracted waves.

scholarly journals Propagation of elastic waves

1966 ◽  
Vol 6 (1) ◽  
pp. 55-64 ◽  
Author(s):  
G. J. Cooper ◽  
J. W. Craggs
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Plane Strain ◽  
Elastic Waves ◽  
Hyperbolic Type ◽  
Elastic Solids ◽  
Stress Strain ◽  
Partial Differential ◽  
Propagation Of Elastic Waves ◽  
The Waves

AbstractThe behaviour of waves in elastic solids with linear stress strain curves is expressed, for plane strain, by a pair of simultaneous partial differential equations of hyperbolic type. Detailed behaviour of the waves is examined by solving these equations numerically.

Seismic waves in a wedge

1975 ◽  
Vol 65 (6) ◽  
pp. 1697-1719
Author(s):  
Z. Alterman ◽  
R. Nathaniel
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Particle Motion ◽  
Seismic Waves ◽  
Wedge Angle ◽  
Compressional Wave ◽  
Elastic Wedge ◽  
Compressional Wave Velocity ◽  
Quarter Plane ◽  
The Waves

abstract The equations for elastic-wave propagation caused by an explosive point source are solved, by a finite difference scheme, for the case of an elastic wedge, with free boundary. Varying the wedge angle shows that the amplitude of the motion, at the corner, increases as the wedge angle is decreased. The results indicate that for wedges with angles varying from 0° to 180°, the amplitude decreases with decreasing β/α (shear- to compressional-wave velocity). The corner of the wedge generates surface waves and the elliptical particle motion in the waves is analyzed. The particle motion is elliptic and the major axes of the ellipses are inclined at half the wedge angle to the free surface. The surface wave travels to the corner from where it is “transmitted” and reflected. Surface waves are shifted by 180° - θ after transmission. For the case of a quarter plane, we get the same result as Alterman and Loewenthal (1970).

SEISMIC WAVES FROM A HORIZONTAL FORCE

Geophysics ◽  
1956 ◽  
Vol 21 (3) ◽  
pp. 715-723 ◽  
Author(s):  
J. E. White ◽  
S. N. Heaps ◽  
P. L. Lawrence
Keyword(s):  
Surface Waves ◽  
Shear Wave ◽  
Qualitative Agreement ◽  
Seismic Waves ◽  
Shear Waves ◽  
Earth Surface ◽  
Horizontal Force ◽  
The Earth ◽  
Fundamental Research ◽  
The Waves

As part of a program of fundamental research on seismic waves, a generator was built for applying a transient horizontal force at the surface of the ground and the resulting seismic waves were observed in some detail. The force is applied when a mass swinging through an arc strikes a target anchored to the earth. Surface geophones along a line in the direction of the force register vertically polarized shear waves refracted back up to the surface, whereas geophones on a line perpendicular to the force register horizontally polarized shear waves. The speeds of the two types of shear waves are often different, indicating anisotropy. Geophones buried below the target show a down‐going shear wave. Variation of amplitude with angle, and other features, are in qualitative agreement with the results given by Rayleigh and others for the waves due to a force at a point in an infinite solid. Love waves and other surface waves were observed, which of course would not be expected from an nterior force.

scholarly journals Propagation of Elastic Waves in Prestressed Media

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Inder Singh ◽  
Dinesh Kumar Madan ◽  
Manish Gupta
Keyword(s):  
Elastic Waves ◽  
Plane Waves ◽  
Dynamical Equations ◽  
P Waves ◽  
General Solutions ◽  
External Forces ◽  
Propagation Of Elastic Waves

3D solutions of the dynamical equations in the presence of external forces are derived for a homogeneous, prestressed medium. 2D plane waves solutions are obtained from general solutions and show that there exist two types of plane waves, namely, quasi-P waves and quasi-SV waves. Expressions for slowness surfaces and apparent velocities for these waves are derived analytically as well as numerically and represented graphically.

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