Green's function for an infinite pre-stressed elastic medium

1976 ◽  
Vol 31 (2) ◽  
pp. 183-194
Author(s):  
E. Boschi ◽  
E. Di Curzio
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function

ON VOLTERRA'S DISLOCATIONS IN A SEMI-INFINITE ELASTIC MEDIUM

1958 ◽  
Vol 36 (2) ◽  
pp. 192-205 ◽  
Author(s):  
J. A. Steketee
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Displacement Field ◽  
General Problem ◽  
Function Method ◽  
Green’S Functions ◽  
Boundary Surface ◽  
Green’S Function Method ◽  
Plane Parallel

In this paper a Green's function method is developed to deal with the problem of a Volterra dislocation in a semi-infinite elastic medium in such a way that the boundary surface of the medium remains free from stresses. (A Volterra dislocation is here defined as a surface across which the displacement components show a discontinuity of the type Δu = U + Ω ×r, where U and Ω are constant vectors.) It is found that the general problem requires the construction of six sets of Green's functions. The method for the construction is outlined and applied to one of the six sets, which is of the type of two double forces with moments in a plane parallel with the boundary. The displacement field thus generated is computed. Several of the results obtained are believed to be of geophysical interest, but a more detailed discussion of these applications is postponed to a further communication which is being prepared.

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

Green’s function for the scattered field near the surface of a dissipative elastic medium.

2010 ◽  
Vol 127 (3) ◽  
pp. 2012-2012 ◽  
Author(s):  
Evgenia A. Zabolotskaya ◽  
Yurii A. Ilinskii ◽  
Mark F. Hamilton
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Scattered Field

Green's function for a two–dimensional exponentially graded elastic medium

2004 ◽  
Vol 460 (2046) ◽  
pp. 1689-1706 ◽  
Author(s):  
Youn-Sha Chan ◽  
L. J. Gray ◽  
T. Kaplan ◽  
Glaucio H. Paulino
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Two Dimensional ◽  
Exponentially Graded

The Elastodynamic Green’s Function for a Torsional Ring Source

1998 ◽  
Vol 65 (3) ◽  
pp. 566-568 ◽  
Author(s):  
Yichi Lu
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Legendre Function ◽  
Logarithmic Singularity ◽  
Hankel Transform ◽  
Linear Elastic ◽  
Half Degree ◽  
Homogeneous Linear ◽  
Ring Source

The elastodynamic Green’s fimction for a torsional ring source in a homogeneous, linear elastic medium is derived using the Fourier-Hankel transform. The Green’s function is found to possess the same logarithmic singularity as the Legendre function of half-degree of the second kind.

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