Open AccessThe edge wave superposition method (2‐D scalar problem)
Author(s) -
KlemMusatov K. D.,
Aizenberg A. M.
Publication year - 1989
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1989.tb01693.x
Subject(s) - superposition principle , scalar (mathematics) , geology , mathematical analysis , geophysics , mathematics , geometry
Summary A method of computation of high‐frequency asymptotic scalar wavefields in 2‐D inhomogeneous media is suggested. It is based on the fact that the wave equation has two linearly independent high‐frequency asymptotic fundamental solutions. The first one coincides with zero‐order ray theory solution, the second is the edge wave. Unlike the Gaussian beam method, based on superposition of the first fundamental solutions, the presented method exploits the existence of the second fundamental solution. The wavefield is expressed by the superposition of edge waves, scattering from each point of an arbitrary contour where the initial data are known. A multicontour superposition technique allows consideration of diffractions, caused by unsmooth interfaces. The computing algorithm is expressed in matrix product form which is very convenient for wave modelling.