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Application of generalised finite differences method to reflection and transmission problems in seismic SH waves propagation
Author(s) -
Ureña Miguel,
Benito Juan José,
Ureña Francisco,
Salete Eduardo,
Gavete Luis
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4268
Subject(s) - mathematics , reflection (computer programming) , uniqueness , finite difference scheme , plane wave , transmission (telecommunications) , finite difference , stability (learning theory) , dispersion (optics) , mathematical analysis , seismic wave , scheme (mathematics) , matrix (chemical analysis) , wave propagation , finite difference method , plane (geometry) , geometry , computer science , physics , geophysics , optics , telecommunications , programming language , materials science , machine learning , composite material
A matrix formulation of the generalised finite difference method is introduced. A necessary and sufficient condition for the uniqueness of the solution is demonstrated, and important practical consequences are obtained. A generalised finite differences scheme for SH wave is obtained, the stability of the scheme is analysed and the formula for the velocity of the wave due to the scheme is obtained in order to deal with the numerical dispersion. The method is applied to seismic waves propagation problems, specifically to the problem of reflection and transmission of plane waves in heterogeneous media. A heterogeneous approach without nodes at the interface is chosen to solve the problem in heterogeneous media. Copyright © 2017 John Wiley & Sons, Ltd.