Open Access3‐D linearized scattering of surface waves and a formalism for surface wave holography
Author(s) -
Snieder Roel
Publication year - 1986
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1986.tb04372.x
Subject(s) - surface wave , formalism (music) , scattering , holography , surface (topology) , optics , physics , geology , geometry , mathematics , art , musical , visual arts
Summary. Scattering of surface waves by lateral heterogeneities is analysed in the Born approximation. It is assumed that the background medium is either laterally homogeneous, or smoothly varying in the horizontal direction. A dyadic representation of the Green's function simplifies the theory tremendously. Several examples of the theory are presented. The scattering and mode conversion coefficients are shown for scattering of surface waves by the root of an Alpine‐like crustal structure. Furthermore a ‘great circle theorem’in a plane geometry is derived. A new proof of Snell's law is given for surface wave scattering by a quarter‐space. It is shown how a stationary phase approximation can be used to simplify the Fourier synthesis of the scattered wave in the time domain. Finally a procedure is suggested to do ‘surface wave holography'.