
TY  - JOUR
A1  - Tygel, M. 
A1  - Hubral, P. 
T1  - Transient representation of the Somerfeld?Weyl integral with application to the point source response from a planar acoustic interface
JF  - Exploration Geophysics
JO  - Explor. Geophys.
Y1  - 1984
VL  - 15
IS  - 3
SP  - 190
EP  - 190
KW  - 
UR  - https://doi.org/10.1071/EG984190A 
N2  - Point source responses from a planar acoustic and/or elastic layer boundary (as well as from a stack of planar parallel layers) are generally obtained by using as a starting point the Somerfeld?Weyl integral, which can be viewed as decomposing a time-harmonic spherical source into time-harmonic homogeneous and inhomogeneous plane waves. This paper gives a powerful extension of this integral by providing a direct decomposition of an arbitrary transient spherical source into homogeneous and inhomogeneous transient plane waves. To demonstrate with an example the usefulness of this new point source integral representation, a transient solution is formulated for the reflected/transmitted response from a planar acoustic reflector. The result is obtained in the form of a relatively simple integral and essentially corresponds to the solution obtained by Bortfeld (1962). It, however, is arrived at in a physically more transparent way by strictly superimposing the reflected/transrnitted transient waves leaving the interface in response to the incident transient homogeneous and inhomogeneous plane waves coming from the centre of the point source. 
ER  -

