Body wave radiation patterns from force applied within a half space

1966 ◽  
Vol 56 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Half Space ◽  
Body Wave ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Numerical Results ◽  
Wave Radiation ◽  
Far Field ◽  
Radiation Patterns ◽  
Sh Waves ◽  
Vertical Displacements

abstract Expressions are derived for the horizontal and vertical displacements at an arbitrary depth within a homogeneous, isotropic, elastic half space when plane harmonic P, SV or SH waves are incident at any given angle. On the basis of the reciprocity theorem, these expressions represent also the far-field polar radiation patterns of P, SV and SH waves due to horizontal and vertical forces applied at a point within the half space. Numerical results for a few selected values of depth are shown for a solid half space.

Note on the use of reciprocity theorem for obtaining radiation patterns

1965 ◽  
Vol 55 (2) ◽  
pp. 277-281 ◽  
Author(s):  
Indra N. Gupta
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Half Space ◽  
Reciprocity Theorem ◽  
Far Field ◽  
Radiation Patterns ◽  
Vertical Displacements ◽  
Field Radiation ◽  
P And Sv Waves

Abstract Expressions for the horizontal and vertical displacements at the surface of an elastic half space when plane harmonic P or SV waves are incident at any given angle are already known. On the basis of the reciprocity theorem, these expressions are used to obtain “far-field” radiation patterns of P and SV waves due to horizontal and vertical forces applied at the free surface.

Body wave radiation patterns from elementary sources within a half space

1967 ◽  
Vol 57 (4) ◽  
pp. 657-674
Author(s):  
I. N. Gupta
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Body Wave ◽  
Point Sources ◽  
The Body ◽  
Wave Radiation ◽  
Seismic Sources ◽  
Vertical Force ◽  
Radiation Patterns ◽  
Double Couple

abstract The known expressions for the polar radiation patterns due to a horizontal or a vertical force, applied at a point within a uniform half space, are used to obtain the body wave radiation patterns from several other elementary seismic sources. Polar radiation patterns from seven elementary line sources, i.e., horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation, center of ratation, and double couple without moment, are first derived. Similar point sources in the three-dimensional space are also considered and the corresponding polar as well as azimuthal radiation patterns are obtained for P, SV, and SH waves. The results obtained include the effect of finite depth of the source below the free surface. Some of the results of Burridge et al for double-couple type seismic sources near a free surface are reproduced in a simple manner. For the elementary point sources considered here, the azimuthal radiation patterns for a uniform half-space are found to be identical with those for an infinite homogeneous medium. However the polar radiation patterns appear to be profoundly affected by the proximity of the free surface.

Standing waves in a layered half space

1966 ◽  
Vol 56 (5) ◽  
pp. 1153-1161 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Half Space ◽  
Body Wave ◽  
Standing Waves ◽  
Elastic Half Space ◽  
Layered System ◽  
Wave Type ◽  
Sh Waves ◽  
Earthquake Motion ◽  
Vertically Propagating ◽  
Layered Half Space

Abstract In a homogeneous elastic half space, plane harmonic waves give rise to standing waves only when on reflection there is no conversion from one wave-type to another. The existence of standing waves in a horizontally-layered half space is established for vertically propagating plane harmonic P, SV or SH waves. Expressions are derived for the particle displacements at the free surface and at any given depth. The layered system acts as a complicated filter suppressing certain periods while amplifying others. The results obtained may be helpful in an understanding of the ‘ground factor’, ambient seismic body-wave noise, and the vibration problem of a structure due to earthquake motion.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

1966 ◽  
Vol 56 (4) ◽  
pp. 925-936 ◽  
Author(s):  
I. N. Gupta
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Reciprocity Theorem ◽  
Point Sources ◽  
Dimensional Case ◽  
Wave Radiation ◽  
Radiation Patterns ◽  
Homogeneous Half Space ◽  
Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

Subsurface and Surface Cracking Due to Hertzian Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 347-351 ◽  
Author(s):  
L. M. Keer ◽  
M. D. Bryant ◽  
G. K. Haritos
Keyword(s):  
Crack Propagation ◽  
Half Space ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Vertical Crack ◽  
Subsurface Crack ◽  
Surface Cracking ◽  
Crack Geometry

Numerical results are presented for a cracked elastic half-space surface-loaded by Hertzian contact stresses. A horizontal subsurface crack and a surface breaking vertical crack are contained within the half-space. An attempt to correlate crack geometry to fracture is made and possible mechanisms for crack propagation are introduced.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

Sign in / Sign up

Export Citation Format

Share Document