Far–field asymptotics of the Green's tensor for a transversely isotropic solid

2000 ◽  
Vol 456 (1995) ◽  
pp. 571-591 ◽  
Author(s):  
Dmitri Gridin
Keyword(s):  
Transversely Isotropic ◽  
Far Field ◽  
Isotropic Solid ◽  
Green's Tensor ◽  
Green’S Tensor

THE ALTERNATIVE KIRCHHOFF APPROXIMATION IN ELASTODYNAMICS WITH APPLICATIONS IN ULTRASONIC NONDESTRUCTIVE TESTING

2020 ◽  
pp. 1-17 ◽  
Author(s):  
L. J. FRADKIN ◽  
A. K. DJAKOU ◽  
C. PRIOR ◽  
M. DARMON ◽  
S. CHATILLON ◽  
...  
Keyword(s):  
Nondestructive Testing ◽  
Scattered Field ◽  
Far Field ◽  
Infinite Plane ◽  
Ultrasonic Nondestructive Testing ◽  
Total Field ◽  
Kirchhoff Approximation ◽  
Head Waves ◽  
Green's Tensor ◽  
Green’S Tensor

The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing.

The alternative Kirchhoff approximation in elastodynamics with applications in ultrasonic nondestructive testing

2021 ◽  
Vol 62 ◽  
pp. 406-422
Author(s):  
Larissa Fradkin ◽  
Audrey Kamta Djakou ◽  
Chris Prior ◽  
Michel Darmon ◽  
Sylvain Chatillon ◽  
...  
Keyword(s):  
Nondestructive Testing ◽  
Scattered Field ◽  
Far Field ◽  
Infinite Plane ◽  
Ultrasonic Nondestructive Testing ◽  
Total Field ◽  
Kirchhoff Approximation ◽  
Head Waves ◽  
Green's Tensor ◽  
Green’S Tensor

The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing. doi:10.1017/S1446181120000036

SEISMIC RECIPROCITY

Geophysics ◽  
1959 ◽  
Vol 24 (4) ◽  
pp. 681-691 ◽  
Author(s):  
Leon Knopoff ◽  
Anthony F. Gangi
Keyword(s):  
Scalar Product ◽  
Point Sources ◽  
Simple Experiment ◽  
Reciprocity Relations ◽  
Green's Tensor ◽  
Vector Case ◽  
Green’S Tensor

The reciprocity relationship describing the relations among the fields resulting from the interchange of point sources and receivers may be extended to the seismic case. Seismic reciprocity can be described either in terms of the scalar product of the vectors representing the excitation of the source and the field at the receiver, or in terms of a Green’s tensor describing these two quantities. Theoretical reciprocity relations give no information concerning reciprocity in the cases for which the scalar product vanishes. A simple experiment in the vector case demonstrates that reciprocity is not obtained when the scalar product of the two vectors vanishes.

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