A simple method to calculate Green's functions for elastic layered media

1981 ◽  
Vol 71 (4) ◽  
pp. 959-971
Author(s):  
Michel Bouchon
Keyword(s):  
Point Source ◽  
Green's Functions ◽  
Layered Medium ◽  
Time Window ◽  
Green’S Functions ◽  
Great Accuracy ◽  
Two Dimensional ◽  
Double Integral ◽  
Simple Method ◽  
Infinite Set

abstract Green's functions for an elastic layered medium can be expressed as a double integral over frequency and horizontal wavenumber. We show that, for any time window, the wavenumber integral can be exactly represented by a discrete summation. This discretization is achieved by adding to the particular point source an infinite set of specified circular sources centered around the point source and distributed at equal radial interval. Choice of this interval is dependent on the length of time desired for the point source response and determines the discretized set of horizontal wavenumbers which contribute to the solution. Comparisons of the results obtained with those derived using the two-dimensional discretization method (Bouchon, 1979) are presented. They show the great accuracy of the two methods.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional

THREE‐DIMENSIONAL INDUCED POLARIZATION AND ELECTROMAGNETIC MODELING

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Induced Polarization ◽  
The Body ◽  
Scale Model ◽  
Two Dimensional ◽  
Electromagnetic Modeling ◽  
The Earth

The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response varies significantly with conductivity contrast; the peak response occurs at higher contrasts for two‐dimensional bodies than for bodies of limited length. Very conductive bodies can produce negative IP response due to EM induction. An electrically polarizable body produces a small magnetic field, so that it is possible to measure IP with a sensitive magnetometer. Calculations show that horizontal loop EM response is enhanced when the background resistivity in the earth is reduced, thus confirming scale model results.

2.5D AND 3D GREEN'S FUNCTIONS FOR ACOUSTIC WEDGES: IMAGE SOURCE TECHNIQUE VERSUS A NORMAL MODE APPROACH

2013 ◽  
Vol 21 (01) ◽  
pp. 1250025 ◽  
Author(s):  
A. TADEU ◽  
E. G. A. COSTA ◽  
J. ANTÓNIO ◽  
P. AMADO-MENDES
Keyword(s):  
Wave Propagation ◽  
Normal Mode ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Element Formulation ◽  
Two Dimensional ◽  
Image Source ◽  
Point Pressure ◽  
Fluid Channel

2.5D and 3D Green's functions are implemented to simulate wave propagation in the vicinity of two-dimensional wedges. All Green's functions are defined by the image-source technique, which does not account directly for the acoustic penetration of the wedge surfaces. The performance of these Green's functions is compared with solutions based on a normal mode model, which are found not to converge easily for receivers whose distance to the apex is similar to the distance from the source to the apex. The applicability of the image source Green's functions is then demonstrated by means of computational examples for three-dimensional wave propagation. For this purpose, a boundary element formulation in the frequency domain is developed to simulate the wave field produced by a 3D point pressure source inside a two-dimensional fluid channel. The propagating domain may couple different dipping wedges and flat horizontal layers. The full discretization of the boundary surfaces of the channel is avoided since 2.5D Green's functions are used. The BEM is used to couple the different subdomains, discretizing only the vertical interfaces between them.

scholarly journals (FIELD) SYMMETRIZATION SELECTION RULES

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1216-1218
Author(s):  
PHILIP R. PAGE
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Rule Violation ◽  
Selection Rules ◽  
Large N ◽  
Ozi Rule ◽  
Infinite Set

QCD and QED exhibit an infinite set of three-point Green's functions that contain only OZI rule violating contributions, and (for QCD) are subleading in the large N c expansion. We prove that the QCD amplitude for a neutral hybrid 1-+ exotic current to create ηπ0 only comes from OZI rule violation contributions under certain conditions, and is subleading in N c .

Green’s Functions for a Point Load and Dislocation in an Annular Region

1991 ◽  
Vol 58 (4) ◽  
pp. 954-959 ◽  
Author(s):  
R. E. Worden ◽  
L. M. Keer
Keyword(s):  
Analytic Continuation ◽  
Rigid Inclusion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Point Load ◽  
Annular Region ◽  
Two Dimensional

This paper contains an analysis of a two-dimensional annular region whose inner boundary is that of either a hole or a perfectly bonded, rigid inclusion. Fast-converging Green’s functions for a point load or a dislocation on the annulus are determined using analytic continuation across the boundaries of the annulus.

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